Bibliographic references
Ledkov A. S., Belov A. A., Tchannikov I. A. Comparison of laser ablation and ion beam efficiency for contactless space debris deorbiting from a quasicircular orbit. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/4c7/bhkledep2uueki1aitn3xa4ju68lnrjy/01_Ledkov_Belov_Tchanikov_.pdf The article deals with the problem of space debris removal from the nearEarth orbits. The motion of mechanical system, consisting of a spacecraft and an object of space debris sphere, is under study. Active spacecraft is a material point, while space debris is of a spherical shape moves moves on a circular orbit. In the first case, the contactless transportation of space debris is being realized by the laser, and in the second case, an electrojet engine jet is used. It is assumed that in the process of the ion transportation, the entire ion beam hits the surface of the sphere, and a simplified autosimilar model of plasma propagation is used to describe the far region of the electrojet engine plume. In the case transportation by laser, the laser beam control system ensures a point selection on the sphere, for which the normal is directed along the local horizon. The purpose of the study consists in comparing these transportation methods effectiveness in terms of the fuel rate of the active spacecraft. For this purpose, mathematical model of the mechanical system is being developed, and numerical simulation of the descent is performed. The numerical modeling results revealed that the laser ablation method appeared more effective compared to the ion transportation. It is associated with the fact that the force generated by the laser ablation effect appears greater than that generated by the ion beam. Besides, the engine generating the ion beam creates thrust, which should be compensated by the oppositely directed engine. It is supposed in the development of this work to account for the effect of aerodynamic drag forces acting of the active spacecraft and a space debris object, as well as studying special motion of the system and developing control law for the active spacecraft to sustain the required position out of the orbit plane. 
Averyanov I. O. Cargo with dampers parachute vertical landing dynamics research. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/2ee/askcpt2ik8fkwfqzp9yz470ukasoil1p/02_Averyanov_.pdf There are a lot of researches related to parachute landing dynamics and almost all of them consider the system of parachutecargo (SPC) that works on its flight regimes, before it contacts the landing area. There are a few researches that consider the task of SPC landing, where a pneumatic actuator is used instead of the cargo. Nevertheless these researches are focused on the behavior of canopy. In case of cargo with dampers landing researches dropped cargo regime is considered. This is a commonly used practice to consider this regime on design phase of a cargo damper system. This article considers a parachute landing process for the cargo with dampers on the phase of its contact with the landing area. The aim of this research is to compare these two regimes of landing — with and without parachute influence to the landing process — to define the load cases for damper system (air fiber dampers are considered). This work considers only a vertical parachute landing process. Mathematical model (MM) of the parachute landing process consists of differential equations of motion for two separate objects — the cargo and the canopy. The canopy is symmetrical. Air dampers are attached to the cargo. Both objects are considered as absolutely rigid. Straps are modeled as a function of distance between the corresponding points on the cargo and on the canopy. Parachute straps are elastic. Euler’s ratios are used to transform the angular velocities to the angles. Here the two tasks are considered: 1 — the drop case is presented to show that MM gives reliable results for the considered structure of the cargo and the system of air dampers; 2 — parachute landing. Comparison of the calculation results and experimental data shows their good correlation. Analysis shows that the parachute system has an essential influence on landing process dynamics of the cargo with dampers. This influence has to be taken into account in the case of damper’s design phase, analysis of cargo drop tests. It recommends to use this MM for statistical mathematical modelling of the parachute landing process in the task of reliability index evaluating. 
Popov I. P. A fragment of the dynamics of an aerodrome tractor with massive towed objects. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/51c/4vm3inp8f26kj59vc8w8xmsjamkh6zuq/03_Popov.pdf It is noted that the most difficult stage in the operation of an airfield tractor with massive towed objects is the starting mode. This is due to the need to overcome the static friction force, which significantly exceeds the motion friction force. As a solution to this problem, we can consider the use of the initial kinetic energy of the tractor, which can develop when using limited elastically deformable traction coupling devices. To optimize the mathematical model, the following assumptions are made: traction force F on the hook of the tractor is a constant value; the inertial masses of the tractor and towed objects are the same and equal m. To evaluate the effectiveness of the use of elastically deformable traction coupling devices, the obtained results are compared with similar results corresponding to an absolutely rigid traction coupling device. The use of elastically deformable traction coupling devices makes it possible to accumulate the initial kinetic energy of an airfield tractor, which makes it possible to overcome the static friction force and ensure the starting of heavy towed objects. Comparison of the kinematic and dynamic parameters of the tractor with towed objects for options with absolutely rigid and resiliently deformable traction coupling devices shows that the efficiency of using the latter increases with an increase in the number of towed objects. Elastically deformable towing devices can cause oscillations of the tractortowed objects system. To prevent them, the towing devices must be hard blocked at the moment they reach the greatest deformation. 
Bogachev V. A., Petrov Y. A., Bernikov A. S., Sergeev D. V. Investigation of the influence of various factors on the descent of the planetoid along the ladders of the lander. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/f1c/cimkmw28x135q473enpv42u5yclupxi1/04_Bogachev_Petrov_Bernikov_Sergeev.pdf To ensure a reliable exit of the vehicle along the ladders to the surface of the planets and their satellites, it is necessary to account for the effect of a large number of various factors, such as:
The undercarriage of the planetoid, as a rule, consists of six or eight driving wheels and an elastic suspension. An electromechanical drive is installed in the hub of each wheel, ensuring thereby high crosscountry ability and high reliability. One of the main problems consists in the reliable exit ensuring along the ladders to the surface of the planet (satellite). For this purpose, experimental selection of materials being installed on ladders that ensure a reliable grip without slipping with the wheels of the planetoid is necessary. To confirm the lunar rover guaranteed exit, The model allowed reproducing angular position of the landing unit supports, ladders and slope. A decision was taken on what shock absorbers should be «shotoff» to reduce clearance and thereby align the position of the vehicle on the landing surface. After that, the ladders, along which the lunar rover successfully moved to the Moon surface the were opened. Thus, when designing a landing unit for a spacecraft with a planet rover, it is necessary to envisage pyrotechnics in the design of shock absorbers that can be employed to improve the planet rover exiting conditions along the ramps. Shock absorbers with pyro nodes may also be employed in case of the groundintake device and other mechanisms presence onboard the vehicle. Tests on the material selection and the determination of the coefficient of adhesion were conducted with the technological wheel of the planetoid and fragments of ladders, on the working surface of which different materials were placed. With this purpose, testing programs and methods were developed, and a test bench, which ensured computed loadings and temperatures, was fabricated. To analyze the planetoid descent along the ladders on the loose soil, the ladder was tested at its interaction with loose soil. During the tests, the ladder and rested on the soilanalogue placed in a container. The top layer of the soil represented a loose finely dispersed soil, which is being characterized by low adhesion and rather high internal friction with low loadbearing capacity and high compressibility. If the vehicle lands on rock outcrops or there is a hard surface, such as a stone, under the end of the ladder, then the ladder lateral movement will be much greater than this in the case of a loose soil. With the landing stage roll and heavy loads on one side, the movement of the ladder ends may be significant and the vehicle might leave the track, which will lead to an accident. As the result of the analysis of the planet rover exit along the ladders, the gaps between the wheel of the planetoid chassis and the structural elements of the landing unit were determined for the case of the landing platform roll in a plane perpendicular to the installation of the ladders at an angle of 20°. The tolerances for the installation of ladders on the platform, backlash in the nodes of rotation of the ladder links, as well as the rigidity characteristics of the ladder (power beam and railing) were accounted for herewith. The article presents the results of the fullscale experimental studies of the various factors impact on the of a planet rover exit on the surface of planets and their satellites. As the result of the tests, the coupling coefficients were determined at different temperatures and loads between the fragments of the ladder layout made of various materials and the wheel. The article considers typical characteristics of the touchdown surface, such as slope, the soil bearing capacity and the presence of stones, and proposes the ladder working surface materials ensuring calculated coefficients of adhesion to the planet rover wheel. The technique for conducting tests on determining the coefficient of adhesion of the planet rover wheel is presented. Recommendations with regard to the structural design of the landing gear shock absorbers and the ladders fixing in the working position have been elaborated. 
Kriven G. I. Evaluation of damping properties of composites. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/268/ta2k4svcb21qf77mpke2tm6v0xr5kq5q/05_Kriven.pdf The article studies fibrous composites, particularly, analyzes their effective damping properties, natural frequencies and loss coefficients. Both effective dissipative and wave properties are being defined by the presence of a viscoelastic layer laid between the elastic fiber of high rigidity and a less rigid matrix. Analytical evaluations employing linear visoelastic analogy method are being presented. The author revealed that the three phases method was more preferable than the Race method for determining parameters with high accuracy. Whiskerized systems, grown on the fiber surface and submerged into the viscoelastic layer, were proposed for use to enhance dissipative properties and retain mechanical ones. The author conducted studies on oscillations damping of the stratified composite hinged beam. The viscoelastic interlayer is being inserted into the composite beam to enhance its damping properties. Resonant frequency and modal losses coefficient of the beam are being evaluated by the BernoulliEuler beam model and Timoshenko model. It is noted that in case of transversely oriented fibers both models, i.e. the BernoulliEuler beam model and Timoshenko model, account for the shear deformations. 
Kolodezhnov V. N., Veretennikov A. S. The translational motion of a cylinder along its axis in a space filled with a nonlinear viscoplastic fluid. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/93b/qz4kt7bso7x5i3970d5ihdf4mrurqny9/06_KolodezhnovVeretennikov.pdf The article studies fibrous composites, particularly, analyzes their effective damping properties, natural frequencies and loss coefficients. Both effective dissipative and wave properties are being defined by the presence of a viscoelastic layer laid between the elastic fiber of high rigidity and a less rigid matrix. Analytical evaluations employing linear visoelastic analogy method are being presented. The author revealed that the three phases method was more preferable than the Race method for determining parameters with high accuracy. Whiskerized systems, grown on the fiber surface and submerged into the viscoelastic layer, were proposed for use to enhance dissipative properties and retain mechanical ones. The author conducted studies on oscillations damping of the stratified composite hinged beam. The viscoelastic interlayer is being inserted into the composite beam to enhance its damping properties. Resonant frequency and modal losses coefficient of the beam are being evaluated by the BernoulliEuler beam model and Timoshenko model. It is noted that in case of transversely oriented fibers both models, i.e. the BernoulliEuler beam model and Timoshenko model, account for the shear deformations. 
Alexandrov L. G., Konstantinov S. B., Markov A. V., Platov I. V. About the method of confirming the operability of the phase separator of an intank capillary device. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/f8a/yzklywtdx3e75lhgg908h7wr5jcb32mp/07_Aleksandrov_Konstantinov_Markov_Platov.pdf For propulsion systems of space craft multiple burns engine, the condition for normal operation is the supply of liquid propellant components to the consumable lines without disturbing the continuity of the flow. The article discusses the method of conducting control tests of the phase separator of the capillarytype intank device at the stage of full readiness of the fuel tank. One of the most important stages in the creation of fuel tanks is their ground experimental testing, carried out under conditions close to operating conditions. The main purpose of such tests is to confirm the compliance of the technical characteristics of the tank with the required values specified in the technical specification for its development. As a criterion for assessing the quality of the phase separator, the efficiency coefficient was chosen, which is the ratio of the capillary holding capacity of the mesh field of the phase separator material to the hydraulic resistance of the phase separator to the flow of liquid passing through it and containing gas inclusions. The methodology given in the article for determining the operability of a capillary phase separation device at the stage of control tests of a finished fuel tank makes it possible to guarantee the required performance indicators of an intank capillary device at the stage of factory ground tests, which improves the quality of finished products. The result of this work is a decision on the compliance of the tested prototype tank with the specified requirements and the possibility of its fullscale operation as part of the propulsion system of the spacecraft. 
Rotermel A. R., Sevchenko V. I., Lizan V. M. Modernization of the working part of the wind tunnel for tensometric measurements of aerodynamic forces in supersonic flow. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/5f2/5gi2e83n0zrsnhftgk4zpoa02jn81lnr/08_Rotermel_SHevchenko_Lizan.pdf The article considers the result of the modernization of strain gauges installed in the working part of the supersonic wind tunnel (AT) ST3, which allows to increase the range of experimental studies on the angle of attack of the model under study from 0 to 20 degrees. Numerical studies of the flow of the model in the working part of the pipe have been carried out in order to verify that the model is located inside the rhombus of an undisturbed flow. The supersonic AT ST3 is widely used to create gas flows of specified parameters for the experimental study of the flow around models of aircraft elements in the range of Mach numbers from 1.5 to 4.2. To increase the range of experimental possibilities, the authors proposed to increase the range of angles of attack of the model under study, taking into account its finding inside the rhombus of a uniform part of the flow. The supersonic AT ST3 makes it possible to determine the aerodynamic forces acting on the model under study at angles of attack in the range from — 10° to +10°, which limits the field of study. The range of angles of attack is determined by the boundary of the rhombus of the uniform part of the flow in the working part of the pipe. To ensure the adequacy of the simulation, the conditions of adhesion and isothermicity were used on the surface of the body and the walls of the working part of the pipe. According to the values of pressure (p_{0}=14 kgf /cm^{2}) and temperature (T_{0}=283K) of the gas in the receiver, the flow parameters in the working part of the pipe were calculated (M_{∞}=4.2; p_{∞}=6467 Pa; T_{∞}=61.8 K; a_{∞}=8 m/s), and also determined the arrangement of the rhombus of the uniform part of the flow. For the calculations, the NavierStokes equations were used, which are closed by the turbulence equations kω SST. The calculation scheme is shown in Figure 5. A sphere with a radius of R = 20 mm was chosen as the model. Modeling was carried out using a structured prismatic finite element grid of 1032 thousand elements (26 elements accounted for the thickness of the boundary layer (parameter y+=0.3)). Modernization of the fastening system of strain gauges located in the path of the supersonic AT ST3, taking into account the requirements of permissible «cluttering» of the working part of the pipe, will allow experimental studies to determine the aerodynamic forces acting on the model at angles of attack up to 20°, which is of interest when conducting studies of the aerodynamic spectrum. 
Khafaga A. S., Ilyin A. G. Improving and processing of weak digital pulse signals using a narrowband noise structure. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/a6c/4ry3k56ko7chtg6gmdvh3nc4oaxoh1eb/09_KHafadzha.Ilin.pdf The article considers the result of the modernization of strain gauges installed in the working part of the supersonic wind tunnel (AT) ST3, which allows to increase the range of experimental studies on the angle of attack of the model under study from 0 to 20 degrees. Numerical studies of the flow of the model in the working part of the pipe have been carried out in order to verify that the model is located inside the rhombus of an undisturbed flow. The supersonic AT ST3 is widely used to create gas flows of specified parameters for the experimental study of the flow around models of aircraft elements in the range of Mach numbers from 1.5 to 4.2. To increase the range of experimental possibilities, the authors proposed to increase the range of angles of attack of the model under study, taking into account its finding inside the rhombus of a uniform part of the flow. The supersonic AT ST3 makes it possible to determine the aerodynamic forces acting on the model under study at angles of attack in the range from — 10° to +10°, which limits the field of study. The range of angles of attack is determined by the boundary of the rhombus of the uniform part of the flow in the working part of the pipe. To ensure the adequacy of the simulation, the conditions of adhesion and isothermicity were used on the surface of the body and the walls of the working part of the pipe. According to the values of pressure (p_{0}=14 kgf /cm^{2}) and temperature (T_{0}=283K) of the gas in the receiver, the flow parameters in the working part of the pipe were calculated (M_{∞}=4.2; p_{∞}=6467 Pa; T_{∞}=61.8 K; a_{∞}=8 m/s), and also determined the arrangement of the rhombus of the uniform part of the flow. For the calculations, the NavierStokes equations were used, which are closed by the turbulence equations kω SST. The calculation scheme is shown in Figure 5. A sphere with a radius of R = 20 mm was chosen as the model. Modeling was carried out using a structured prismatic finite element grid of 1032 thousand elements (26 elements accounted for the thickness of the boundary layer (parameter y+=0.3)). Modernization of the fastening system of strain gauges located in the path of the supersonic AT ST3, taking into account the requirements of permissible «cluttering» of the working part of the pipe, will allow experimental studies to determine the aerodynamic forces acting on the model at angles of attack up to 20°, which is of interest when conducting studies of the aerodynamic spectrum. 
Brodsky M. S., Zvonarev V. V., Khubbiev R. V., Sherstuk A. V. Computer model of the satellite communication and data relay system radio channel during multiposition signal transmission. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/58e/2d88k3qr30rmpd5l4s7zb8wh9uxeypmp/10_Brodskiy_Zvonarev_KHubbiev_SHerstyuk.pdf The paper proposes mathematical model of radio channel of the communication and data relay satellite system (CDRSS) in case of multiposition signal transmission by several spatially separated radioelectronic equipments. Based on the proposed mathematical model, computer model has been developed for estimating the noise immunity of signal reception under given technical limitations. The computer model under consideration makes it possible to calculate with high accuracy the values of the energy characteristics of radioelectronic equipments, such as the average radiated power of the equipments; transmitting (receiving) antenna gain; effective isotropically radiated power; ratio of signal bit energy to noise power spectral density; the ratio of the total signal power to the noise power at the input of the receiving device, at which the required noise immunity of the CDRSS facilities is ensured. A quantitative measure of radioelectronic equipments noise immunity is the probability of a bit error. To calculate the probability of a bit error, an algorithm for estimating the noise immunity of signal reception has been developed, which, unlike the existing ones, allows calculating the probability of a bit error for radioelectronic equipments spaceseparated emitting pairwise correlated signals in the direction of the receiving antenna of the satellite CDRSS. The proposed algorithm allows you to calculate:
The article gives an example of calculating bit error probability during multiposition signal transmission in the direction of the receiving antenna of satellite CDRSS, oriented towards the orbital electronic equipments. The simulation results testify to the correctness of the approach and make it possible to carry out systematic studies of the dependence of the energy characteristics of the receiving equipments of the CDRSS on the number of lowpower transmitting equipments emitting pairwise correlated signals. The proposed computer model can be used:

Dmitriev A. O. Proposal to provide power supply to a network of clusters of small spacecraft with a tandem spacecraft. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/609/30bgr7548lcdo6nnnm6fyvj0u2abylyx/11_Dmitriev.pdf This article proposes the construction of a tandem of spacecraft consisting of an autonomous satellite with a large area of solar phototransformers and an autonomous satellite for transmitting the received energy to small spacecraft using laser radiation. This tandem is connected by a contactless magnetic resonance method of energy transfer. To provide the cluster with energy, it is planned to develop a modular, i.e. not mechanically integrated into a single whole, satellite complex — a tandem with a contactless power transmission line. The tandem should consist of spacecraft moving in close orbits interacting with each other via wireless communication and energy transmission lines. The main task of this tandem is to supply energy to a cluster of small spacecraft performing target tasks. Then conceptually such a complex will have the following structure:
Although at first glance the integral execution of the photodetectoremitter system suggests itself, in practice this is a nontrivial task. Such a largesized design, which will experience serious temperature changes and at the same time have high requirements for targeting the receivers of the cluster spacecraft, will require a complex stabilization and guidance system. The advantage of fragmentary tandem construction is the absence of such serious requirements and the ability to increase the coverage angle with laser or microwave radiation for cluster satellites. It is also possible to use several satellite emitters for greater coverage of consumers from a cluster of small spacecraft. 
Abramov A. A., Yakush N. A. Development of USRP verification methodology for highprecision radio system research. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/aac/3d9ldtbvenaokhr846o11cxl62cwq5dk/12_Abramov_YAkush.pdf Currently, in telecommunications, there are problems of inefficient use of spectrum [3], the inability to flexibly control hardware devices, which have led to an increasing interest in softwarecontrolled radio (SDR), which has proven itself as a reliable system for thorough analysis of radio frequency signals with the possibility of flexible control and modification [4]. One of the prominent representatives of SDR is the highprecision and inexpensive USRP 2901 model from the 29xx series from National Instruments, capable of solving the problems of prototyping radio systems, radio reconnaissance, direction finding, creating local positioning systems, developing coherent multichannel transceiver systems and solving other important problems in the aerospace sphere. This work is devoted to the development and testing of the method of verification of USRP 29xx series devices for highprecision experimental studies for solving problems of a wide range in the field of information communications using the Omega radio complex. The subject of the study is the evaluation of the effectiveness of using SDR on the NI platform. To obtain the data closest to the true ones, to exclude the maximum number of different types of errors, the work analyzed in detail the plan and stages of experiments, in particular, the planning of experiments at the tactical level, the description of which is indicated in the publications [18, 19]. The calculation of the required sample ensures the required probability and reliability of the results [20]. However, there is no information in the technical documentation for USRP devices that they can be used for highprecision research. After planning the experiments, a method for verifying devices was developed, which included specific 6 stages of experiments that evaluate physical values that characterize the accuracy and quality of USRP equipment. The following results were obtained as a result of testing this method:

Vakulchik O. V. Cybersecurity of the functioning of the information management system with the SQL Server. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/b8e/eyle9t5xrx9yvtm0p2fbnlgki3ggxos1/13_Vakulchik.pdf This article regards the issue of cybersecurity of the information management system of the aerospace system (IMS). Database is the basic IMS component. The SQL server was employed as the database system. Monitoring execution is necessary for the Database information processes performance and security support. The article describes the development of the remote monitoring effective method. This method solves two basic problems, namely information transmission security in the open environment, and effective assessment of the information environment state. Analysis revealed that effective remote monitoring ensuring requires tool selection. The selected tool should wield enhanced security and employ SQL language for the Database performance evaluation. The tool tackled with in this article ensures information encoding in the open transmission environment. It acts as an administrative panel as well. After the tool selection, the SQL language objects analysis was performed. Selection criteria of the necessary objects are as follows: the provided information completeness, request preparation complexity, and the internal functionality enhancing capability. Analysis revealed that storable system procedures are the most informative. The next stage of development consisted in the stored procedures selection according to the «integral informativity» criterion. The sp_whoisactive stored procedure is of specially great capabilities. However, it has been found that these procedures were redundant. That is why optimized requests for the remote monitoring effectiveness improving were developed. The optimized requests reduce the status information volume, ensuring security, and provide herewith the remote monitoring completeness. 
Burenko E. A. Substantiation of the effectiveness of the use of signals with orthogonal frequency division multiplexing in aviation radio systems of information transmission. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/189/35lz12x2zqfp3n4u4kkcyv3aev5m1ojf/14_Burenko.pdf Aviation complexes of communication facilities are subject to stringent requirements in terms of weight and size indicators and energy consumption. Along with this, to ensure highspeed data transmission between a ground control station (GCS) and an unmanned aerial vehicle (UAV) over long distances (up to 300 km), it is required to provide high energy in the radio channel. This paper discusses the main negative factors of aviation radio channels that reduce the efficiency of the radio system of information transmission, which can be eliminated as a result of the use of signalcode structures based on the use of signals with orthogonal frequency division multiplexing (OFDM). Such negative factors include the presence of fading of the radio signal at the input of the receiver of the radio system and the possible impact on the operation of the radio system of interference. Discusses the main characteristics and advantages of signals with OFDM over classical singlefrequency signals (for example, with binary phase shift keying — BPSK) are considered, as well as basic engineering and technical calculations are presented confirming the validity of the use of these signalcode structures in aviation radio systems for information transmission, as one of solutions for combating fading caused by multipath signal propagation, and as a result, with intersymbol interference (ISI), which manifests itself in the superposition of rereflected signals on the direct (main) signal. Discusses the methods for ensuring the noise immunity and secrecy of a radio system with OFDM based on the use of broadband pseudonoise signals (PNS) together with OFDM signals are considered. For example, Msequences or Gold’s sequences, which are widely used in radio systems for various purposes, can be used as PNS. To combat narrowband interference, signal jamming protection can be used, which is reduced to a significant increase in the band occupied by the OFDM signal. Band increases as a result of superposition of the PNS signal with base B ≫ 1 on each subcarrier of the OFDM. The simplest method for reducing the interference power in the receiving part is the narrowband interference decorrelation method, which reduces the interference power to the base B times as a result of multiplying the interference signal with the reference PNS in the demodulator PNS. As a result of multiplication, the interference is converted into a signal with a uniform power spectral density in the interference band, similar to the effect of white noise. 
Kazantsev A. M., Knysh M. V., Makarov M. K. Selection of the rational composition of the radio information sensor group of a spatially distributed monitoring system. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/d8e/cybhjlh8zvo40ejkhh9f5hv1pjuz47le/15_Kazantsev_Knysh_Makarov.pdf In many application domains, group control problems arise under counteracting conditions. Examples are interaction processes of systems with conflicting and sometimes antagonistic target functions, such as a spatially distributed monitoring system (SDMS) and mobile airborne objects (MAO) penetrating into the system’s area of responsibility. However, in practice the resource of the SDMS, which determines the space review capabilities, can be limited, including due to low efficiency of groundbased radio information sensors (RIS) in detecting moving air objects at low altitudes. The specified problem can be solved by inclusion into the SDMS of mobile airborne RIS and joint application of airborne and groundbased RIS under unified control. Thus one of the most important tasks is the fullest realization of information possibilities of all RIS for the purpose of the maximum coverage of their working zones of airspace. The solution of this problem is possible at the expense of estimation of composition and forecasting of ways of actions and tactics of application of MAO with the purpose of definition of rational structure of heterogeneous grouping of RIS of SDMS. In the article a new methodical approach to the choice of rational composition of heterogeneous grouping of RIS of SDMS is proposed. In a basis of the offered decision methods of the theory of dynamic graphs and methods of vector discrete optimization are put. Features of formation of variants of structure of grouping of RIS are considered. An algorithm is offered, allowing on the basis of the minimum set of attributes of the adversary to choose a rational composition of heterogeneous grouping of RIS in accordance with the hierarchy of links «attributes of the of the opposing side’s activity — stages of preparation for use of MAO — variants of use of MAO». 
Glushkov A. N., Moiseev S. N., Ispulov A. A., Filippov A. V., Nikolaev S. V. Method for assessing the accuracy of the alignment of onboard radar systems of aircraft. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/aca/qvzzw6vlrvv41xoc2smws8u11jvpj0ao/16_Glushkov_Moiseev_Ispulov_idr.pdf The presented article proposes a method for the errors operational evaluation in the alignment of radar and optoelectronic stations applied in navigation and weaponaiming aircraft complexes. Its actuality is associated with the fact that the alignment accuracy of the location systems determines potential effectiveness of the aviation complexes, since the alignment errors cause the need to increase the location systems fields of vision and, as the result, lead to the aircraft in the potential efficiency decrease. These errors minimization will allow narrowing their fields of vision, while preserving radars search capabilities, and enhancing detecting capability and spatial resolution of optoelectronic systems by the integral background illumination reduction. As the result, both detection range and the probability of objects recognizing will be enhanced. The currently developed methods for the alignment errors evaluating do not allow performing operational correction of the of directional patterns relative position of the onboard location systems of navigation and weaponaiming complexes in real operating conditions, which requires new evaluation methods development. Natural requirements for these methods are the possibility of obtaining evaluations in real time or close to it, as well as the possibility of employing these evaluations for correcting relative location of the radars fields of view. Evaluation methods developed as of today do not meet these requirements, which stresses the relevance of the problem being solved. The problem of errors evaluation in the alignment of the onboard location systems is set and solved as a filtration problem, since in general case the object of the study is nonstationary. The authors developed an algorithm for mathematical formalization of the alignment errors behavior during the flight of an aircraft, allowing performing correction of the directional diagrams position of location systems in real time based on the values of their evaluation. Model experiments were conducted to confirm correctness of the developed solutions. 
Aslanova A. B. Optimization of the uav multisegment hovering mode in a heterogeneous flight zone. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/971/4dbrwhrmp9gjvak8dycke32ordwbsv1w/17_Aslanova.pdf The presented article proposes a method for the errors operational evaluation in the alignment of radar and optoelectronic stations applied in navigation and weaponaiming aircraft complexes. Its actuality is associated with the fact that the alignment accuracy of the location systems determines potential effectiveness of the aviation complexes, since the alignment errors cause the need to increase the location systems fields of vision and, as the result, lead to the aircraft in the potential efficiency decrease. These errors minimization will allow narrowing their fields of vision, while preserving radars search capabilities, and enhancing detecting capability and spatial resolution of optoelectronic systems by the integral background illumination reduction. As the result, both detection range and the probability of objects recognizing will be enhanced. The currently developed methods for the alignment errors evaluating do not allow performing operational correction of the of directional patterns relative position of the onboard location systems of navigation and weaponaiming complexes in real operating conditions, which requires new evaluation methods development. Natural requirements for these methods are the possibility of obtaining evaluations in real time or close to it, as well as the possibility of employing these evaluations for correcting relative location of the radars fields of view. Evaluation methods developed as of today do not meet these requirements, which stresses the relevance of the problem being solved. The problem of errors evaluation in the alignment of the onboard location systems is set and solved as a filtration problem, since in general case the object of the study is nonstationary. The authors developed an algorithm for mathematical formalization of the alignment errors behavior during the flight of an aircraft, allowing performing correction of the directional diagrams position of location systems in real time based on the values of their evaluation. Model experiments were conducted to confirm correctness of the developed solutions. 
Gorbunov S. A., Nenashev V. A., Mazhitov M. V., Khadur A. A. Algorithm for estimating the coordinates of the state of the helicopter in the onboard radar station. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/968/eaol24mcpszrzegg5d6m55toonga6kia/18_Gorbunov_Nenashev_Mazhitov_KHadur.pdf Functions and application areas extension of helicopters determines the demand and relevance of the new algorithms developing for the state coordinates estimating in the airbased pulseDoppler radar station, ensuring stable surveillance, which in its turn will positively reflect on the flight safety. Helicopter is a complex object under observation in terms of radar. Analysis of the existing algorithms for the state coordinates estimating revealed insufficient efficiency in a helicopter detecting and tracking at various kind of flying. Thus, there is an objective need to develop new estimation algorithms that account for the helicopter flight characteristics and ensure its stable observation. The authors propose employing mathematical apparatus on the optimal linear filtering theory as an approach to optimal algorithms obtaining for the helicopter state coordinates estimation. The purpose of the study consists in synthesizing an algorithm optimal by the root mean square error minimum for coordinates estimation of the helicopter absolute and relative motion in the onboard radar station at various kinds of its flight, including the hovering mode, based on the mathematical apparatus on the optimal linear filtering theory. As the result, the article presents the analysis of effectiveness of the said synthesized algorithm application. The specificity consists in two components application, namely estimation of Doppler frequency, stipulated by signal reflection from the fuselage, and Doppler frequency stipulated by the signal reflection from the rotating helicopter blades. The results of the study may be employed while the existing radar stations upgrading, or developing prospective ones based on the pulseDoppler principle of signals processing. 
Vernigora L. V., Kasmerchuk P. V., Sysoev V. K. Analysis of groundbased optical means of observing laser beacons on board nearEarth spacecraft. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/d97/m5ht0m80ouorsof4ca4dmj8lz9x8kimn/19_Vernigora_Kazmerchuk_Sysoev.pdf A critical issue in the spacecraft navigation consists in precise determination of the spacecraft position in space. The spacecraft navigation parameters measuring in the nearEarth space may be realized employing both onboard and groundbased measurement facilities, which include radiotechnical and optical systems. In the loworbit region with orbits altitude less than 5000 km radar measurement means are being employed as a rule. At the altitudes above 5000 km, a spacecraft is out of the radar stations visibility zone. In case absence of the onboard radiotechnical means as a part of the spacecraft, ensuring current navigation parameters measuring, photometrical surveillance becomes the only susceptible possibility for the spacecraft monitoring and its technical state evaluation. Optical measuring instruments are capable of ensuring higher accuracy than with the radio band application. However, optical means of observation have a number of disadvantages, which significantly limit their capabilities. Such disadvantages are as follows: their dependence on the time of day, illumination of the spacecraft, and weather conditions. Besides, a smallsized spacecraft has utterly low visible brightness, which aggravates their observation by optical means. These shortcomings can be partially overcome by installing optical laser beacons onboard the nearEarth spacecraft, which will allow ensuring operational monitoring of their condition (both orbital and rotation parameters, including the case of communication deficiency with them) by the groundbased optical means Groundbased optical observation stations of the Space Monitoring System perform monitoring of all objects located in the nearEarth space to maintain a catalog of orbital parameters for subsequent prediction of their position. Obtaining long photometric series for the tasks of the Space Monitoring System is possible, but only by suspending the main tasks execution. Besides its own standard optical groundbased observation facilities, the Space Monitoring System extensively employs of the observations results obtained at optical observation stations of scientific organizations, particularly, the Pulkovo Cooperation of Optical Observers (PulCON), the Russian Academy of Sciences (INASAN, SibIZMIR), the Roscosmos Research Institute and university observatories. All these optical observation stations are equipped with modern telescopes and photodetectors that will allow for confident registration of radiation from laser beacons installed onboard the nearEarth spacecraft, thereby increasing the reliability of the nearEarth spacecraft positioning regardless of their size and orbit type. 
Javadov N. H., Agayev F. G., Huseynov H. A., Zulfugarli P. R. Issues of assessing the feasibility of tasks assigned to unmanned aerial vehicles. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/210/knje6w7b4y80y00lruneq69zqnant39h/20_Dzhavadov_Agaev_Guseynov_Zulfugarly.pdf The article deals with the feasibility assessing of the tasks assigned to unmanned aerial vehicles (UAV), and presents a method for the quality assessment of the military purpose UAV. As the result of the said assessment, the resulting inference with account for the unmanned engineering requirements and preferences is being formed. Criteria, which include indicators such as conformity, capability, operational security, sustainability and readiness for solving the tasks assigned to the UAV are known as well. In this regard, it is especially important to address the issues of the used sensors capabilities matching to solve the tasks assigned to the UAV. This task is usually being solved by modeling. Besides, the descriptive structure of a special metric is employed as well to develop a criterion for the UAV tasks feasibility assessing. For example, the issue of the of UAV tasks feasibility while searching for some objects depending on the terrain real landscape should be solved by creating a special methodology for the terrain visualization assessing depending on the state of the surface relief under study. Solving the issue of tasks feasibility is closely associated with the issue of a rational compromise achieving between the UAV total load, various sensors and the UAV mission feasibility. The article studied the issue on the tasks feasibility assigned to the UAV by solving the problem of developing the new criterion of executing functions of objects detection on the surface of the soughtfor site by the UAV. Based on the wellknown empirical criterion of the said task feasibility, a new indicator has been formed as a logarithm of the ratio of the task fulfillment and nonfulfillment probabilities. Based on the proposed indicator, the invariant linking this indicator with the number of work cycles, which ensure the corresponding probabilities of the task fulfillment, has been formed. 
Maletin A. N., Glushchenko A. A., Mishina O. A. Investigation of the capabilities of modern space facilities for monitoring objects in nearEarth space . Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/b63/4cub5wida789zh9pmogd0pw177fc0c2a/21_Maletin_Glushchenko_Mishina.pdf The researches of near and far outer space is relevant in scientific and practical terms. For science, it is the study of the Solar system (including asteroids, comets, distant Galaxies). From a practical point of view, this is the control of space objects and the monitoring of the contamination of nearearth space with space debris. The world’s leading space powers continue to work on the creation of space facilities designed to solve the problems of testing technologies for remote inspection, autonomous rendezvous with specified objects, maintenance, repair, reconfiguration, modernization, refueling, changing orbit parameters, monitoring «space debris» and other necessary operations. This approach can be used to extend the service life of serviced spacecraft. Based on the tactical and technical characteristics known from open sources, the article presents the results of the analysis of the current state and prospects for the development of foreign automatic spacecraft of a new generation developed on the basis of unified space platforms. The introduction of advanced technologies has made it possible to significantly reduce the mass and size characteristics of spacecraft and the consumption of all types of resources, which has reduced the cost of developing, manufacturing and launching small spacecraft. New miniaturization technologies make it possible to create small spacecraft capable of performing tasks that 20 years ago were available only to largeclass spacecraft. The mass of such devices does not exceed 100150 kg, the overall characteristics may be less than 1 m^{3}. At the same time, the period of active existence can reach 57 years, the reserve of the characteristic speed is more than 400 m/s, the positioning accuracy is no more than 1050 m, and the orientation accuracy is 1015 angular s. The optical—electronic means of spacecraft have high resolution, allowing to observe geostationary spacecraft from low Earth orbit. Theoretical and experimental studies have been brought to the stage of creating real groupings of small spacecraft that demonstrate very high capabilities for solving problems of monitoring nearEarth space. First of all, this indicates a high level of theoretical and applied scientific research in this direction and the prospects for the miniaturization of space technology. In addition, this fact explains the priority of these studies, both for the state and for private companies developing modern space systems and complexes. 
Travin A. A., Kalashnikov E. A., Bakradze L. G. Improvement of diagnostics of machine mechanisms using nondestructive testing methods. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/068/bek6nsduu39vrjetil9j0nmrc5trylts/23_Travin_Kalashnikov_Bakradze.pdf The article tackles the problems of analyzing the industrial machine operation by more correct selection of place for the vibration acceleration control , as well as specially developed methods for spectra processing, The material being proposed describes the solved issue on the sensor positioning for correct vibration measurement and analysis, The article presents the spectrum, which analysis allowed detecting the signals with frequencies close to each other within the limits of the spectrum analyzer resolution capability. Besides spectrum identification of the direct Fourier transform of the separate links vibration, the common amplitude of its series of oscillations in time applying inverse Fourier transform was employed for each link analysis To improve diagnostics, the vibration curves during the process were compared with the course of alloy crystallization while industrial experiments on a machine. To obtain extra data and further improvement of the diagnostics method under consideration, the temperature indicators of the temperature fields were gathered employing the FLIR brand infrared imaging equipment. The obtained data may be significant while the machine significant components state assessing. It is assumed as well that the infrared imaging equipment allows more accurate determining of the sensors location places for vibrations measuring. The operation of individual machine units is described, as well as general dependence plotting of the total vibration amplitude, its isolation to a large extent and, thus, identification of the work of both mold and rollers, and comparison of the obtained results with the measured spectra. The article considers the possibilities of computer programs for obtaining general curves of the mold unbalance motion and after further Fourier transform obtaining an excitation spectrum and a response spectrum. The work describes theoretically the metal melt motion, allowing obtaining a parabolic type differential equation. The equation was solved for the case of a pulsed vibration impact on the melt. 
Lazeev A. S., Litovka Y. V. The algorithm of transformation of polygonal models to simplify the calculation of galvanic processes. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/696/9ern1kdeofh6cvsu7b8kzoxii3sent7a/24_Lazeev_Litovka.pdf Electrochemical coatings provide special properties of the surface of the parts. In the aircraft industry, electroplating coatings are widely used to protect against corrosion and increase the wear resistance of steel and aluminum parts. Efficient specification of the shape of a part in automated control systems for galvanic processes can be organized by exporting drawings for subsequent software processing where complex mathematical calculations associated with surfaces are not required. To solve problems that require complex calculations, various polygonal meshes are divided into simpler shapes. An algorithm for calculating the electric field in a galvanic electrolyte is presented, and the need for a mathematical description of the cathode surface to set the boundary conditions is shown. The paper considers the issues of creating algorithms for converting threedimensional polygonal models into voxel format to reduce computational complexity, which is estimated by indicators: the time of the algorithm and the amount of memory occupied. The algorithm for converting a polygonal model into a voxel model has the form:
When comparing the most productive «naive» algorithm, which has complexity O(n(1/h)^{3}) with the algorithm developed in this article, which has complexity O((log n)∙(1/h)^{3}), an increase in efficiency up to four hundred thousand times. The resulting geometric mathematical model reduces the search time for optimal parameters of the galvanic cell, especially when using modern effective optimization methods. 
Molotkov A. A., Tretiyakova O. N. Application of machine vision in laser technologies. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/542/cr54u58xf7udombk779x0iuf5eo04zqt/25_Molotkov_Tretyakova.pdf The article deals with the problem of applying machine vision methods for practical implementation in the production of modern laser technologies, in particular, selective laser melting technologies. The authors describe the software platform of machine vision created and implemented in production. Examples of the solved problems of machine vision and scientific visualization in the framework of the industrial implementation of new laser technologies are presented. The results of the executed work allowed creating a specialized machine vision platform with possibilities of functions expansion in future that empowers simplifying solution of a wide range of machine vision tasks for the of laser technologies implementation. The problems of object recognition occurring in the process of laser technologies developing were considered. One of the problems of the object recognition in industry has been solved, namely the problem of finding a sheet in the working field of the machinetool. The authors developed and implemented an algorithm for the object contours determining from the previously found angles, which was employed to solve the problem of finding and analyzing the quality of holes while perforation, as well as finding geometry of the fused layer in the process of selective laser melting. The developed software platform for machine vision allows processes recording in isolated environments, the objects boundaries determining in an image, analyzing and processing visual data, forming and presenting a pattern of heat distribution in a threedimensional object. It empowered combining the calculated data on the product geometry and the data, obtained by video data analyzing from visual observation tools, with the data on the heat distribution, obtained as the result of numerical experiment in accordance with the implemented mathematical model of the selective laser melting process under study. The proposed approach allows automating the production control process and simplifying analysis and identification of critical areas for technologists, as well as the technological parameters selection for the process of selective laser melting. The created machine vision software platform has been tested and implemented in the software solutions employed in a number of hightech industrial productions. 
Vatutin M. A., Klyuchnikov A. I. A technique for increasing the stability of the nonlinear link with a delay for the selfoscillating accelerometer. Trudy MAI, 2022, no 127, http://mai.ru//upload/iblock/e7e/0t53bs4yusjmvvmru9k3olnybn41ab42/22_Vatutin_Klyuchnikov.pdf The article presents the results of applying a scientificmethodological and circuit—engineering approach to the stability improving of acceleration measurements made by serial pendulum accelerometers, primarily micromechanical ones, as well as the results of studies on the stability increasing of the nonlinear link with lagging for the autooscillatory accelerometer. For the nonlinear link operation stability studying, its digital implementation was selected, allowing utterly high operation stability ensuring of the digital part namely. Besides the digital part, an analog comparator is employed in the nonlinear link, which ensures the several orders of magnitude worse operation stability than this of the quartz oscillator. The results of the comparator response time meansquare deviation are presented for the case of its operation in the normal configuration and for the case of application of the amplifier being recommended. The authors show that the additional amplifier implementation reduces the meansquare deviation value of the comparator response time. The study was being conducted by the comparator switching process modeling. Recommendations on the additional amplifier circuitry are given. The article presents specifics of electronic components allowing eliminating comparator in principal, as radio electronic component, form the circuit. The obtained results may be applied to the stability increasing of the accelerometer conversion coefficient and, as the result, determining more accurately parameters of the spacecraft orbit autonomously under conditions of disturbance factors of the outer space. 
Popov I. P. Monoreactive harmonic oscillator. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/90f/ln9lqg8yjeudn6suvgzp114p0yjk0sxr/01_Popov.pdf In classical oscillators, free sinusoidal oscillations are accompanied by an exchange of energy between its elements, which have the opposite nature of reactivity. In a spring pendulum, the potential energy of an elastic element is transformed into the kinetic energy of an inert element and vice versa. These elements have opposite character of reactivity. In an electric oscillatory circuit, the energy of the magnetic field of the coil is transformed into the energy of the electric field of the capacitor and vice versa. These elements also have the opposite character of reactivity. Oscillators are known in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element or the potential energy of an elastic element into the energy of the magnetic field of the coil or the energy of the electric field of the capacitor and vice versa. The synthesis of a monoreactive harmonic oscillator is based on three premises. First. The oscillator consists of two weights of the same weight. Second. Loads make sinusoidal movements. Third. The total energy of the oscillator does not change with time. In a monoreactive (mm) harmonic oscillator, inert elements can perform free sinusoidal oscillations, which are accompanied by the transformation of the kinetic energy of an inert бthe first inert element is zero. In this case, the energy of the second element has a maximum value. At the next moment of time, the first element acquires acceleration due to the kinetic energy of the second element, the speed of which begins to decrease. 
Safonov A. I. On periodic motions of a hamiltonian system with two degrees of freedom in the vicinity of a multiple resonance of the third order. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/cca/xgst10tkbjwg0v6qthn69gszhiekyax3/02_Safonov.pdf In this paper, we study the motion of a nonautonomous 2πperiodic in time Hamiltonian system with two degrees of freedom in a neighborhood of a trivial equilibrium that is stable in the linear approximation. It is assumed that the system contains a small parameter ε, and for ε = 0 the Hamiltonian of the system does not depend on time. Let the values of the parameters be close to the resonance values corresponding to the double (fundamental and combination) resonance of the third order. Then, the trivial equilibrium of the complete system is unstable. It is assumed that there is a resonant detuning in one of the frequencies of the linear oscillations of the system. The goal of the paper is to solve the question of the existence, number and stability (in the linear approximation) of periodic motions of the system in a small neighborhood of the origin. Using a number of canonical transformations, the Hamiltonian functions are reduced to the forms that are characteristic for each resonance case. Model systems corresponding to autonomous systems are studied. The parameter space of the problem is divided into regions, and in each region the question of the existence and number of resonance equilibrium positions of the model systems is solved. The results are compared with ones in the case of exact resonance. Using the Sylvester criterion, the sufficient conditions for the stability of the equilibrium positions are verified, and the equilibrium positions satisfying them are found. The characteristic equation of the linearized system of equations of perturbed motion is analyzed, and the necessary conditions for stability of the equilibrium positions are obtained in the form of the system of inequalities The equilibrium positions are found, for which one of these conditions is satisfied; the remaining equilibrium positions are unstable (in the complete model systems) A complete analysis of the necessary conditions for stability has not been carried out due to cumbersomeness. Using the Poincare small parameter method, the periodic motions generated by the considered equilibrium positions are constructed in the complete nonautonomous systems. They are analytic in ε and 12πperiodic in t. The conclusions are drawn about their stability (in the linear approximation) or instability. 
Avdyushkin A. N. On parametric resonance near the libration point L1 of a planar restricted photogravitational threebody problem. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/11f/iwgpqzr98pggy1xj6gr55gzcplgl93xk/03_Avdyushkin.pdf A planar elliptic restricted photogravitational threebody problem is considered, i.e. it is investigated the motion of a lowmass body under the influence of both gravitational forces and light pressure forces acting from two massive bodies that move along known Keplerian orbits. It is assumed that the all three bodies move in the same plane. There is a particular solution in this problem describing the motion, which the lowmass body is located on the segment between the attracting centers at the socalled collinear libration point L_{1}. In this paper, we study the problem of the collinear libration point L_{1} stability in the case of small eccentricity of the massive bodies’ orbits. The system of perturbed motion equations is written in Hamiltonian form. It is established that in this system there are possible both basic and combinational parametric resonances leading to instability L_{1}. The normal form of the Hamiltonian quadratic part of the perturbed motion equations is obtained in explicit form by the method of a small parameter. This made it possible to reduce the linear stability problem L_{1} to the equivalent stability problem of a linear autonomous system with a normalized Hamiltonian. The explicit expressions defining the boundaries of the parametric resonance regions were found on the basis of this autonomous system and it was obtained the stability conditions L_{1} in the linear approximation. Previously, the regions of stability and instability were obtained numerically in [12]. Carried out in that work the numerical analysis results are in good agreement with the results obtained analytically for small values of eccentricity in this article. 
Martirosov M. I., Khomchenko A. V. Computational and experimental study of the behavior of a flat reinforced carbon fiber panel on impact. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/79b/kt66qs88lka6rx9cjet5l5v4kayrusvy/04_Martirosov_KHomchenko_1..pdf Among the structural materials currently used in aviation technology (OT), polymer structural materials (PCM), for example, carbon fiber plastics, which have certain advantages over traditional metal materials for structural purposes, have become widespread. Among such advantages are relatively low density, high specific strength and rigidity, high wear resistance, fatigue resistance, low coefficient of thermal expansion, resistance to chemical aggressive media, damping ability. Speaking about the disadvantages of PCM, it should be noted that during the production and operation of structural elements made of such materials, defects of various types may occur, which have a serious impact on the residual strength. The level of safety of an AT created on the basis of new materials and new technologies should not be lower than the level of safety of an existing AT made of traditional structural materials (and according to traditional technologies). It is important to note that the purpose of developing new PCM is to combine various components to create materials with new specified characteristics that differ from the characteristics of the original components. In the works [1][4], the behavior of structural elements made of PCM in the presence of multiple defects such as bundles of arbitrary shape, size and location under the action of nonstationary loads of various nature was previously considered. The paper presents a numerical and experimental study of the behavior of a fourstringer flat panel made of a polymer composite material under lowspeed impact. Validation of the numerical experiment based on the results of field tests was carried out. The validation results showed that the maximum stratification area as a result of the impact differs by no more than 11%. 
Yu Z. ., Temnov A. N. Equivalent mechanical model of liquid linear sloshing under microgravity. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/7d6/hmeacnm5rtbnl4lhlt1pmbuvwv6y31y1/05_YUyCHzhaokay_Temnov.pdf A numerical approach to develop the equivalent mechanical models representing liquid sloshing is established and the effects of surface tension are taken into account which are predominant in lowgravity environment. An appropriate model is a pendulum that has a mass which represents the liquid fraction that participates in the fundamental model of the sloshing. Furthermore, the pendulum must be attached to the tank through a torsional spring which represents the stiffening effect of surface tension. A formulation is derived from the linearization of the motion equations of the liquid near its initial equilibrium position considering pressure jump on the free surface and freeend boundary condition at the threephase contact line. The continuous problem domain is discretized by the finite element method and its discretization gives a classical generalized eigenvalue problem, whose solutions are natural frequencies and mode shapes. Expressions for the parameters of the mechanical model are obtained by the principle of dynamic similarity. Several examples illustrate the influence of Bond number and fill levels on the behavior of liquid in toroidal tanks. Comparing numerical results with the experimental measurements obtained under ground conditions, it is found that the nondimensional eigenvalue and slosh masses increases as Bond number increases, but the spring moment and length of pendulum decreases. The results obtained in this paper can be used in the coupling dynamic analysis of the spacecraft with propellant tanks. 
Kutysh I. I. New methods for constructing uniformly convergent trigonometric Fourier series. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/177/vm9x9626jhtabrunqa68u63u8iff73m5/06_Kutysh.pdf New results of studies of convergence of trigonometric Fourier series (TFS) with Fourier coefficients constructed by various methods are presented. Using the concept of the square of the relative norm, the possibility of an analytical representation of a given TFS function is analyzed in detail and it is established that the cause of the divergence of the TFS with a sufficient increase in its degree is the occurrence of the Gibbs effect. It is shown that when assessing the convergence of the TFS to its function as an independent change of the relative norm, instead of the current value of the degree of the series k, it is reasonable to use the current value of the generalized variable Θ=kπ/n, which allows us to obtain more general results. Moreover, it is sufficient to control only the value of Θ, which determines the amount of calculations. Recommendations are given for the construction of such Fourier coefficients that ensure uniform convergence of the TFS to its functions f(x) and the correct finding of their first derivatives free of the Gibbs effect. Uniformly convergent TFSs constructed according to the proposed method are compared with the known Filon and Lanczos series. In contrast to the Lanczos method, it is proposed to use variables σmultipliers depending on the new variable ζ, which affects the rate of convergence of the series to its function f(x) and the accuracy of determining the first derivatives of the series without the occurrence of the Gibbs effect. The results on the construction of uniformly convergent TFSs relate to any maximumnormalized periodic function f(x) in the interval [π, π] satisfying Dirichlet conditions. Moreover, if the function f(x) has zeros at the ends of a given interval, then it is advisable to build a shortened TFS with decomposition only in terms of sinuses, hence a simpler TFS. The proposed uniformly converging TFSs can find application in solving various problems of gas dynamics and heat and mass transfer described by partial differential equations. 
Averyanov I. O., Zinin A. V. The use of RodriguesHamilton parameters in mathematical model of cargo landing system with dampers in tasks of its overturn. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/228/51fvojiwvv2o2ws7uwovwbmyvg4c2btg/07_Averyanov_Zinin.pdf In the previous article [1] we described the mathematical model of dynamic landing process for cargo dropped systems with dampers (System) that we developed for statistical modelling of the process. That dynamic model consisted of spatial equations of forces and moments equilibrium, kinematic Euler’s equations and contained contact boundaries from rigid plane to dampers and to cargo. The method of forth integration was used to solve the equations and the idea was that such modeling of landing process had allowed us to detect all the failures well known for such Systems. One of the possible System failure that may occur during landing is its overturn. In this case we have a deal with large angles that may lead to problems with kinematic Euler’s equations. Researching of sources shows that the problem of System overturn usually considers separately with analytical approaches, while the method we used implies continuity of the solution from the beginning of the process to its end. To avoid such problems in this article we consider the use of RodriguesHamilton parameters (or quaternion) instead of kinematic Euler’s equations to solve the dynamic task of complex System moving. We use the fourth order of RungeKutta method to realize the algorithm of RodriguesHamilton parameters. To convert the quaternion to spatial angles Krilov’s equations are used. To demonstrate accuracy and stability of the developed algorithm the task of complex rigid body spatial free motion is considered. Comparison of these results with the solution that comes from commonly used CAE shows us their similarity. After that, we also consider the task of System landing with its overturn. These results are considered from qualitative analysis point of view. Thus, the use of algorithm we realized with RodriguesHamilton parameters instead of kinematic Euler’s equation in the mathematical model of System landing process allows us to avoid «special points» and to generalize the solution to the tasks of large spatial angles, including System overturn. 
Lebedev E. L., Repin A. O. Method of acoustic emission control of the contact interaction of rolling bearing elements when evaluating the correctness of the resource assembly of ball bearing supports as a tribological system of power gyroscopes rotors. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/70f/thuaux5awqva6opwqe4e6hi0pdvoj5vi/08_Lebedev_Repin.pdf The autonomous functioning of the power gyroscopic complexes of small spacecraft does not allow maintenance during its operation. One of the most loaded elements of the power gyroscope are rolling bearings. Since the functioning of rolling bearings depends on the correctness of their assembly and the presence of lubrication, in order to ensure the autonomous functioning of the rotors of power gyroscopic systems, the technology of resource lubrication and resource assembly of the bearing assembly is used in their manufacture, which implies onetime lubrication and assembly (without the possibility of adjustment) for the entire life of the device. The article presents the results of research on the use of a method for quality control of assembly of ball bearing bearings of power gyroscopic complexes operating in vacuum space by estimating the size of the bearing clearance by the parameters of acoustic emission signals. The definition of the limiting state of the bearing supports of the rotors of power gyroscopic systems is given, by which it is necessary to understand the state when the friction losses of the bearing (taking into account the progressive heat release) will exceed the difference between the maximum torque generated by the electric motor of the rotor of the power gyroscope and the torque necessary to ensure the required angular velocity of the rotor flywheel, taking into account its moment of inertia. It is proved that the main criterion for the correctness of the resource assembly of a ball bearing assembly is to ensure the correct contact interaction of its elements as a tribological system. At the same time, the main controlled parameters are the force that the bearing perceives after the rotor assembly, as well as the parameters of elastic deformation in the ball—ring bearing system. A model of natural frequencies of elements of bearing supports of power gyroscopic systems has been developed taking into account their stressstrain state. The dependence of the frequency of natural oscillations of the bearing ball on the force acting on the bearing after its assembly is proved. This dependence is of a powerlaw nature and can be used in the development of a new method of quality control of the resource assembly of bearing supports of power gyroscopes. 
Goncharov P. S., Kopeyka A. L., Babin A. M. Method for experimental modeling of the effect of plasma radiation from an electric rocket engine on solar cells. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/0d5/c7i7uijczoof0uu43faapi835tari1on/09_Goncharov_Kopeyka_Babin.pdf The article presents a technique for experimental modeling of the impact of plasma radiation from an electric rocket engine on solar cells. The used laboratoryexperimental base and the procedure for conducting tests are described. Relationships for calculating the coefficients of degradation of the electrical characteristics of solar cells are given. The essence of the approach of experimental modeling of the effect of plasma radiation from an electric rocket engine on solar cells is to measure: the temperature field of a solar cell, the characteristics of the plasma flow, the electrical characteristics of solar cells before and after exposure to the plasma radiation of an electric rocket engine, and to calculate the degradation coefficients of solar cells. It is advisable to use the obtained values of the degradation coefficients in the design of spacecraft solar arrays. The presented technique makes it possible to determine the coefficients of degradation of the electrical characteristics of solar cells when exposed to plasma radiation from an electric rocket engine, as well as to carry out studies: — on the influence of the effect of plasma radiation from an electric rocket engine on the electrical characteristics of solar cells, depending on the parameters and modes of operation of an electric rocket engine; — on issues of increasing the energy efficiency of an electric rocket engine by using the energy of plasma radiation by returning it to the onboard network using photoelectric or thermal converters. The multiplicative degradation coefficient determined in the course of tests allows one to perform an estimated calculation of the power generated by a solar cell after exposure to plasma radiation from an electric rocket engine. 
Sha M. ., Sun Y. . Experimental study of damage to the structure of composite materials of highspeed aircraft from raindrop impact erosion. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/0a6/xvvfnj11z4r1bvl1ae0f065pljltojkl/10_SHA_idr2_.pdf Bodies moving at very high speeds through a rainfield can experience severe damage caused by the impingement of raindrops on their surfaces. This effect is usually referred to as"rain erosion". Rain erosion has been a concern of the aviation industries for many decades, and rain erosion resistance is one extremely important parameter of the interaction of materials with the flight environment. In this paper, a single waterjet impact test platform was established based on the firststage light gas gun in order to conduct the rain erosion tests on materials. Its principle was that the gas gun launches a metallic projectile to impact the water storage chamber sealed by the rubber piston, and then the liquid was driven from the small nozzle to form a highspeed waterjet. The apparatus could generate stable waterjets with speeds of 200−600 m/s, diameters of 4−7 mm and a smooth circulararc head, which simulated a waterdrop with the same diameter. A series of single waterjet impact tests were carried out on a symmetrically crossply carbonfiberreinforced composite (CFRP) laminate under different waterjet velocities and diameters. The results show that the typical damage modes of CFRP laminates impacted by single waterjets are as follows. The impacted surface is depressed, and the surface damage consists of resin removal, matrix cracking, minor fiber fracture and fiber exposure around the rim of a central undamaged region. The internal damage range gradually expands from the impact surface to the bottom ply, mainly composed of intralaminar matrix cracking with a pyramid shape and interlaminar delamination with a diamond shape. Both the surface and internal damage are more extensive in the longitudinal than the transversal direction, thus presenting typical. 
Sedel'nikov A. V., Orlov D. I., Serdakova V. V., Nikolaeva A. S. Investigation of disturbances from a temperature shock of a solar battery panel when simulating the rotational motion of a small spacecraft around the center of mass. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/02f/z2ilh6xiyd5zu4r4qgl23vv3lqf1w54w/11_Sedelnikov_Orlov_Serdakova_Nikolaeva.pdf The main goal of the work is to evaluate the effect of the solar battery panel temperature deformations when a small spacecraft leaves the Earth’s shadow on the parameters of its rotational motion. The problem lies in the transformation of a small spacecraft after the end of its active existence into space debris, which significantly complicates the successful implementation of new space projects due to the threat of collision. Currently, many methods have been developed for cleaning up space debris. One way involves towing space debris using tether systems. At the same time, the connection between the tug and space debris is not sufficiently reliable so the cable can separate from space debris under the influence of various disturbances. One of such disturbances may be a temperature shock of the solar panel when the space debris is a small spacecraft with large elastic structural elements. The greater the mass fraction of the elastic element in the total mass of a small spacecraft, the more significant the effect of the temperature shock on the dynamics of its rotational motion. An analysis of research by scientists from around the world shows that the temperature shock can disrupt favorable conditions for the implementation of gravitysensitive technological processes, causing temperature fluctuations in large elastic elements, which lead to unacceptably high microaccelerations. During experiments on the International Space Station with promising solar panels of the ROSA type, temperature fluctuations were so intense that they did not allow the panels to be rolled up at the end of the experiment. In this case, the question of the controllability of a small spacecraft equipped with such solar panels already arises. The article deals with issues related to the influence of angular acceleration from the temperature shock and a disturbing factor on the functioning of the spacecraft. The influence of angular acceleration from the temperature shock is estimated on the basis of numerical modeling and construction of the deflection field of the plate median surface as a result of the temperature shock in the ANSYS software. For the small «Starlink» spacecraft, the values of the angular acceleration from the temperature shock and the deflection field of the plate middle surface as a result of the temperature shock were obtained. As a result of the research, the dependence of the angular acceleration on the temperature shock of the small «Starlink» spacecraft was obtained and the maximum value of the disturbing moment was estimated. When transporting such a small spacecraft using tether systems after the end of its active life, this disturbance must be taken into account in order to avoid the contact loss between the tether and space debris as a result of temperature shock. The results obtained can be used to analyze the possibilities of transporting space debris using tether systems. 
Polyakov P. O., Shesterkin P. S. Numerical modeling of damping coatings. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/88e/4zv7zp14kg6ia1ga21aterm6ne8pxc2q/12_Polyakov_SHesterkin.pdf In various industrial sectors, damping materials are used that are suitable in their properties for specific working conditions. The use of damping tapes is one of the existing ways to improve the damping properties of materials. At the moment, for modern thinwalled structures, there is a need to develop more advanced calculation models, for which the actual operating conditions of structures should be sufficiently fully reflected, taking into account the mechanical properties of the material from which its elements are made. The damping properties of the materials from which they are made, as well as the amplitudes of their oscillations, have a significant impact on the dynamic tension of the elements of thinwalled structures. Improving damping properties is one of the methods to increase the service life of structural elements subject to cyclic loading during operation. To damp vibrations in different frequency ranges that occur under external influence, as well as on the weight characteristics of the system, the choice of optimal types of damping coatings depends. This article explores the effect of 3M brand damping tape on the dynamic characteristics of a cantilever beam and the simulation of this process. and modeling of this process. The results of numerical simulation of free vibrations of an aluminum beamplate without damping layers and with damping tapes glued to the front surfaces (threelayer beams) are presented. For numerical simulation of models of plates of all investigated sizes with a damping tape, simulation of the oscillatory process was applied similarly to physical testing. A finite element model of a plate with a grid is constructed. The dynamic characteristics of threelayer beams are determined. The dependence of the change in the damping coefficient on the amplitude for samples with and without damping tapes for different amplitudes is established, the amplitudefrequency characteristic, the logarithmic damping decrement, the damping coefficient and the natural frequency of the samples without a damping layer and with its participation are obtained. Numerical modeling was carried out in order to compare the experimental results of the dynamic characteristics of a cantilever beam without and with a damping layer. 
Dinyaeva N. S., Kravtsov S. B., Krumlyakov S. O., Benkalyuk G. A. Numerical modeling of damping coatings. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/ba6/nu24tkqnm105g3colnic618q7opi8597/13_Dinyaeva_Kravtsov_Krumlyakov_Benkalyuk.pdf The paper considers the development of a special device  a stand for filling flat heat pipes with a liquid coolant, as well as a method for filling them, based on controlled flow under the influence of gravity of the coolant in the internal space of heat pipes (HPs). The coolant (coolant) used for pouring into heat pipes is pretreated — dissolved gases are removed from it. The degassing of the coolant is carried out in order to minimize the process of oxidation of the internal metal parts of the case and the evaporative capillaryporous structure (ECS) of the HP. In order to increase the efficiency of the process of filling experimental batches of heat pipes, reduce material and time costs, a special device is proposed  a filling stand that combines all technological operations that were carried out separately into a single technological cycle. Degassing is carried out by ultrasonic (US) cavitation in a special container installed in an ultrasonic bath, which is an integral part of the filling stand. The implementation of this development allows you to get a useful result, which consists in:  saving labor costs by reducing the number of technological operations and design features of the installation;  increasing the reliability of HP sealing associated with the possibility of visual control over the entire technological cycle of refueling;  an increase in the depth of coolant degassing, which in turn affects the extension of the service life of filled HP;  reducing the probability of failure of the radar by increasing the reliability of the cooling system PPM AFAR;  possibility of production in a short time of pilot batches of HP for further research. 
Bakhtin A. A., Volkov A. S., Solodkov A. V., Eletskikh E. V. A research of influence of clipping on OFDM system performance. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/2c1/4yq47or17v8yujrawgtu15mzoq7uhbak/14_Bakhtin_Volkovidr..pdf 
Khazov A. S., Ortikov M. Y., Gusev S. N. A method for estimating the resolution of a space radar with a synthesized antenna aperture, taking into account the compensation of atmospheric distortions. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/999/r6jpuwd8d0ximcslkobantfjbf6sunuq/15_KHazov_Ortikov_Gusev.pdf The article proposes the methodical approach allowing to solve a problem of improvement of quality of the radar images received by space synthetic aperture radar radars from the antenna synthesized by an aperture due to accounting of atmospheric distortions. The purpose of work is improvement of approaches to formation of radar images. Object of research are methods of estimation of resolution of the s space synthetic aperture radar which is used as the key information indicator and characterizes detail and quality of radar images. The result of the work is a the technique of estimation of resolution of the space synthetic aperture radar taking into account compensation of atmospheric distortions. The proposed technique is based on the use of compensation of atmospheric distortions from positions of geometrical optics. The offered technique of estimation of resolution of the space synthetic aperture radar allows to determine the amendment to inclined range taking into account the joint impact of distortions of the troposphere and an ionosphere at a stage of formation of basic function by an azimuth in synthesis algorithms of radar images. Accounting of a refraction of electromagnetic waves and correction of inclined range are realized with use of index of refraction of the environment and a method of approach of geometrical optics at distribution of radio waves in the nonuniform environment. For use of this approach it is necessary to define a condition of the atmosphere with use of models of the troposphere and an ionosphere in a zone of the review of the synthetic aperture radar taking into account real geophysical conditions. Results of imitating modeling confirm a possibility of use of the proposed technique for estimation and accounting of the errors brought by the atmosphere of Earth in measurements of radar parameters by means of methods of calculation of trajectories of radio waves at the set index of refraction of the environment. The developed technique allows to carry out compensation of impact of atmospheric distortions and to increase quality of the received radar image. The proposed methodical approach can be used for performing synthesis of radar images, for elimination of errors of measurement of coordinates of objects and for improvement of values of resolution and contrast of radar images. 
Detkov A. N. Optimal discrete filtering of samples of a continuous random process against the background of correlated Markov noise. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/b83/1liglpqbky63lwkamtol39nadftu4cxy/16_Detkov.pdf In modern onboard informationmeasuring systems (IMS) of UAV, algorithms for optimal or quasioptimal processing of random processes are practically implemented using digital signal processing tools. Therefore, these algorithms must be synthesized in a discrete form in the form of recurrent relations that are convenient for such an implementation. However, in most cases, the mathematical models of the processes evaluated and observed in the IMS have a continuous form of recording, which is due to the physical nature of the phenomena occurring with the signals. In this regard, the problem of synthesizing optimal algorithms for discrete filtering of counts of continuous random processes arises. At the same time, the modern element base makes it possible to use a high sampling rate in onboard IMS, which leads to autocorrelation of measurement readings. Therefore, in the statistical synthesis of filters, it is necessary to take into account the correlation of measurement noise, which significantly affects the generated filtering estimates. In this paper, proposes a new discrete Kalman filter (KF) based on a statistically equivalent discrete representation of continuous state and observation vector models to solve the problem of optimal linear filtering of samples of a continuous vector Markov random process, taking into account the known statistical characteristics of additive vector Markov correlated noise. The problem of filtering a statespace linear model with colored measurement noise and precise noise covariance matrices is converted to a problem of estimating a statespace linear model with white Gaussian measurement noise and precise noise covariance matrices using the measurement difference method and without state vector augmentation. The structure of analogtodigital conversion and discrete KF is presented. The main feature of this algorithm is the accumulation (integration) of continuous observation on the time intervals between adjacent samples of the estimated state vector. To illustrate the potential characteristics of the accuracy and noise immunity of the synthesized algorithm, a simple example of filtering a continuous Gaussian Markov random process against the background of Markov random noise is considered. From the graphs presented, one can quantify how much analog and discrete algorithms for optimal filtering of a continuous random process depend on the ratio of the width of the spectral density of the measurement noise to the width of the spectral density of the random process and the signaltonoise ratio. The presented discrete filtering algorithm allows us to quantify the deterioration of the potential characteristics of accuracy and noise immunity in the case of optimal estimation of continuous random processes due to the coloration of measurement and sampling noise. The use of the method of difference measurements does not increase the computational costs in the discrete KF, since the dimension of the state vector remains unchanged, as in the case of filtering continuous random processes against the background of white Gaussian noise. At the same time, the analog part of the analogtodigital converter is significantly simplified in comparison with similar algorithms, since a onecycle delay is implemented in a discrete KF after the ADC. It should also be noted that there is no operation of analog differentiation inherent in classical algorithms for filtering continuous random processes in continuous time using the method of difference measurements. 
Ibragimov D. N., Berendakova A. V. Method of constructing and estimating asymptotic controllability sets of twodimensional linear discrete systems with limited control. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/a08/rzvzamv7qtr3u4e42gt65hwebiv3kfco/17_Ibragimov_Berendakova.pdf 
Pavlov A. N., Umarov A. B., Kulakov A. Y., Gordeev A. V. The problem of planning the reconfiguration of the motion control system of a small space vehicle for remote Earth sensing under the conditions of the unknown cyclogram of its functioning. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/e8c/mw4512qg8hre20jk0bp4dbaa2v9kb90t/18_Pavlov_Umarov_Kulakov_Gordeev..pdf Of particular importance at the present time in the development and operation of small spacecraft are the issues of ensuring the required degree of autonomy and survivability, as well as increasing the efficiency of the small spacecraft in various environmental conditions. The relevance of solving these problems for small observation spacecraft is caused, on the one hand, by the peculiarities of the orbit on which this type of spacecraft operates, and on the other hand, by the lack of the possibility of timely control in the event of emergency situations on board the small spacecraft. To ensure the autonomy and survivability of a small spacecraft, it is necessary that it be in working condition for a maximum time or quickly restore its working capacity. That is, it is necessary to be able to change (rebuild) the structure (structures) of the small spacecraft in various environmental conditions in order to maintain the required level of performance. In practice, when solving problems of ensuring reliability, survivability, disaster tolerance and fault tolerance of complex technical systems within the framework of the currently developed theory of structural dynamics control, such a variant of managing the structures of a complex technical object as reconfiguration has become widespread. This article proposes a method for solving the problem of planning the reconfiguration of a complex technical object based on structural and functional reconfiguration under the conditions of an unknown cyclogram of the activation of the complex technical object operating modes. A computational experiment was carried out on the example of a small spacecraft for remote sensing of the Earth «Aist2D». 
Sokolova Y. V., Leun E. V., Primakov P. V., Samoylov S. Y. Approach to planning the load of processors of critical multiprocessor systems. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/722/1kut1ylzf58sb0v3t0pj701j6v0gzbag/19_Sokolova_Leun_Primakov_Samoylov.pdf One of the priority areas in economically developed countries is the security of critically important, especially complexly organized systems. Examples of such systems are a variety of robotic production; nuclear power plant control systems; onboard computing systems; groups of unmanned aerial, land and water robots; global navigation satellite system (GLONASS); large software systems of high importance and many other systems. The main problem of building computing systems at all times remains the task of ensuring their longterm functioning. This task has three components: reliability, availability and serviceability. Of particular relevance is the use of computer systems for managing critical objects operating in real time. The main difference between realtime operating systems and any other operating systems is the guarantees for the start or end time of processes that are provided by realtime systems. In the event of a failure, such systems are subject to high requirements for operability, nonfailure operation, safety, security, etc. Obviously, the most important thing is to minimize the time and hardware costs required for the response of a multiprocessor system to an emergency situation. One of the options for solving this issue may be planning the load of processors in multiprocessor systems. In this case, you can avoid simultaneous loading of several processors by one task (program, subroutine, algorithm, file, etc.) and, at the same time, schedule the queue of incoming tasks in such a way that they are served simultaneously. This allows you to reduce unplanned downtime and at the same time increase its availability along with increased speed. The article is devoted to multiprocessor systems. The issue of compiling a plan for loading processors in them is touched upon. It is supposed to use the socalled realtime systems. 
Mokhov A. I., Kislinskiy V. G., Alekseychuk A. S. Session based recommender system with multistage candidate sampling. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/55e/mx3ysdlfuf1gavj0uz9twvxootsu7sy0/20_Mokhov_Kislinskiy_Alekseychuk.pdf Understanding users’ preferences is a challenging task especially with a huge amount of items. Modern recommender systems are keen to solve this task by applying stateoftheart methods of candidate sampling and simple heuristics in couple with Machine Learning ranking algorithms. This paper presents an algorithm of candidate sampling from three different sources followed by a ranking algorithm. These two stages form a sessionbased recommender system that is capable of building a user’s probable preferences based on its current session. For candidate sampling, we use a language model (Word2Vec) and sparse vectors for item representations, and the most popular items from a dataset. Each stage is divided into multiple substages making it really simple to add new candidate sources or remove existing ones. The same technique can be easily applied to ranking algorithms — one can remove a ranking algorithm or add the new one in order to blend model predictions maximizing Precision or Recall metrics as well. We also show the importance of ranking algorithms in recommender systems by measuring Learning to Rank (L2R) specific metrics on test data. There are several ranking algorithms in this paper. All of them belong to the pairwise algorithms subclass. Such algorithms as LambdaRank, YetiRank, and StochasticRank are used in comparison to nonranked recommendations. We use CatBoost implementation of gradient boosting and PyTorch to build a neural ranking net. As a result of the experiment, we get a ready endtoend recommender system pipeline with flexible modules that are easy to add/remove and show the benefits of ranking models with recommendations on real data. 
Deniskina G. Y. CAD/CAM/CAE system for manufacturing structures from fibrous composite materials using 3Dprinting. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/ac0/z47y5yu2d7ccd5khue9l5hgza212irq0/21_Deniskina.pdf The problem of development and implementation of a CAD/CAM/CAE system for manufacturing structures from fibrous composite materials using 3D printing is considered. The general configuration of the system and the assignment of its functional modules are described. The advantages of the mathematical support and software developed for the system for creating digital twins, which allow generating control programs and conducting virtual modeling of a 3D printing process to be used in the manufacture of products of complex geometric shapes, as well as developing rational schemes for the reinforcement of printed composite structures and finding optimal printing modes, are shown. CAD/CAE system is focused on modeling, visualization of the placement of fibers in the printing area, finding the optimal printing scheme based on the requirements conditioned by the product operating conditions. In this connection, it must meet the following requirements:
The main principles of development of a CAD/CAM/CAE system for manufacturing functional structures from fibrous composite materials using 3D printing are considered. The task of modeling and visualization of the 3D printing process is formulated. The main specifications of the developed CAD/CAM/CAE system associated with the possibility to set the structure of a facility with its subsequent adjustment and smoothing. triangulation of the print area and modeling of placement of fibers using analytical functions during the printing process are determined. Mathematical tools for solving equations characterizing mechanical properties of composite materials based on wavelet analysis methods, as well as for calculating the optimal directions for placing fibers of composite materials are described. 
Budaev G. A., Danilov D. A., Konotop O. I. Numerical calculation of the flap Tgearbox kinematic error. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/baf/463g1tjq7i0jxg96z14k7edyl0klv4dk/22_Budaev_Danilov_Konotop.pdf This article is devoted to research of the kinematic error in the units of servo systems with mechanical transmissions. The flap Тgearbox of the high lift transmission was considered as the object of the study. Numerical simulation methods were used to determine the kinematic accuracy of the research object. Geometric dimensioning and tolerances of gearbox components were assigned, a 3D CAD model was built with the worstcase combination of tolerance fields, material characteristics were assigned, forces, constraints and boundary conditions were specified, and the results were evaluated. There are many methods of solving this issue. Analytical methods and methods using 3D modeling allow to determine the kinematic error in the early stages of the design, but they are not automatized. Experimental methods of calculation have the greatest accuracy, but are not possible in the early stages of project development. The numerical simulation method is devoid of the disadvantages of analytical methods. The basic equation of dynamics for the investigated system was formulated and solved using the HHT integrator based on the αmethod. The interface between the surfaces of the rigid bodies was defined by contact force. In the first case of the calculation, the gearbox housing was fixed in space, the other bodies were constrained to move in a plane perpendicular to the plane of rotation of the shafts. In the second case, only the outer rings of the bearings and their sleeves were constrained to move in the plane, because they were fixed in the axial direction in the real construction. Because of the shaft axis displacement possibility in angular directions and the possibility of axial displacement, the kinematic error increased significantly. At the early stage of development, the value of gearbox kinematic accuracy was determined. The obtained value complies with the requirements for the accuracy of the high lift transmission. The specified geometric dimensioning and tolerances are not very precise or too rough and can be applied to other single stage bevel gearboxes used in high lift transmissions. 
Golyakov A. D., Richnyak A. M., Fominov I. V. Investigation of the accuracy parameters of a spacecraft with an adaptive autonomous navigation system. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/3fe/935k4mhor7x3pzvn9t63v4n535le34b8/23_Golyakov_Richnyak_Fominov.pdf The paper presents the results of solving the scientific problem of synthesizing an adaptive autonomous navigation system of a spacecraft and presents the results of a study of the accuracy of determining the navigation parameters of a spacecraft under the influence of disturbing factors that can be continuous, periodic and shortterm. Their manifestation is difficult to predict. The impact of disturbing factors on the onboard equipment can lead to both a gradual and a sharp decrease in the effectiveness of spacecraft target tasks due to the deterioration of technical characteristics of optical elements of star sensors, external optical elements of navigation devices, temperatureregulating coatings and electronic equipment of the autonomous navigation system, which, in turn, can cause a metrological failure of onboard measuring instrument devices. To estimate measurement errors of navigation parameters of the spacecraft, an algorithm for the operation of an autonomous navigation system has been adopted, where the zenith distances of two navigation stars and the altitude of the spacecraft above the Earth’s surface are used as primary navigation information. Simulation results are presented for the case when measurements of onboard measuring instruments contain random errors distributed exponentially. It has been shown that the disturbing factors of the outer space lead to an increase in characteristics of random errors of onboard measuring instruments and, as a consequence, to an increase in spacecraft navigation errors. The study has been carried out by modeling the process of solving the navigation problem, taking into account the impact of disturbing factors navigation parameter onboard measuring instruments. The basis for obtaining numerical estimates of the accuracy of the spacecraft autonomous navigation system is the simulation of the process of solving the navigation problem using computer technology. To process the results of navigation measurements containing unavoidable random errors, a nonrecurrent weighted least squares method has been used in the work. The obtained results can be used to counteract disturbing factors of the outer space that reduce the accuracy of the spacecraft navigation and to justify adaptive and reconfigurable systems that allow autonomously to determine the parameters of the spacecraft orbit in the conditions of disturbing factors of the outer space. 
Minakov E. P., Aleksandrov M. A., Verbin A. V. Algorithms for estimating the number of lunar asteroid detection tools with a vertical orientation of the sight axes. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/c9d/2sgdzbn46zxl16720r0y1hwbzxj271mm/24_Minakov_Aleksandrov_Verbin.pdf Due to the peculiarities of the orbital movement of asteroids approaching the Earth, a significant proportion of them either in principle cannot be detected using existing monitoring tools located on the surface of the Earth, or detection can occur too late. The lack of influence of the atmosphere on optical observation means leads to the advantages of the location of asteroid detection means in space. In this article, a study is carried out on one of the possible ways of their stationary location — uniform distribution with regard to visibility zones on the surface of the moon. An algorithm is proposed, which allows on the basis of initial data on the angle of solution and the maximum range of detection of dangerous space objects by lunar means. The zone of near and longrange explosive detection, as well as the zone of continuous multiple detection of asteroids, their description and illustrations are given. Computational experiments were carried out using the developed algorithm for estimating the number of means for detecting asteroids when placing on the entire surface of the Moon or its part, dependencies of the angular distance between the standing points and the angular dimensions of the visibility zones of the means for detecting asteroids on the maximum range of detecting asteroids were obtained. In addition, an algorithm was developed and the number of means for detecting asteroids with vertical orientation of the sighting axes was estimated with the exception of a part of the Lunar Surface for their placement, due to the closure of the outer space region by the Earth («dead zone» of asteroid detection means), when placed on the entire surface of the Moon or its part, the dependence of the angular distance between the standing points and the angular dimensions of the visibility zones of the asteroid detection means on the maximum detection range of asteroids is also obtained. The presented algorithms for estimating the angular distance between the points of standing on the surface of the Moon of the same type of asteroid detection means with vertical orientation of the sighting axes and their number for forming the asteroid detection line allow obtaining correct results and can be used for further research to determine the parameters of the asteroid detection line zones, reduce the number of asteroid detection means and estimate the probability of asteroid detection. 
Javadov N. H., Aslanova A. B. Optimization of the use of hybrid multirotor drones for atmospheric research in vertical takeoff mode. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/6cb/h3xk91v993gk9fcy34krxzoa86u8p8tc/25_Dzhavadov_Aslanova.pdf With the advent of drones, it became possible to use unmanned aerial devices to study the pollution of the atmosphere with aerosol, various gases and water vapors. For these purposes, the method of radiometric probes operating in vertical lift mode is still widely used. At the same time, the successful performance of this function with the help of UAVs depends on a number of factors, one of which is the limited time of their flight. For example, the typical flight time of multirotor batterypowered drones is 2050 minutes. One of the ways to solve this problem is the use of a hybrid hydrogen fuel cell (FCHS) system containing a fuel cell and an electric battery The question of using a drone equipped with a hydrogen cell of a hybrid power supply system and electric batteries to study the vertical profile of the atmosphere has been investigated. The problem of finding the optimal dependences of the energy of the power supply system and the power consumption on the altitude is solved, at which, taking into account the limitation on the average height of the power consumption, the flight time can be minimized. This minimization of flight time is explained by the need to eliminate the influence of changes in the atmosphere on the overall result of the study of the structure of the atmosphere. Taking into account the obtained solution, as well as the known dependence of the drone’s power consumption on mass, acceleration of free fall, air density and the area of the propeller disk, a formula for calculating the mass in the optimal mode is obtained. It is shown that in the optimal mode, the condition of mass constancy is provided if the energy of the power supply system increases exponentially. In the absence of such growth, the discharge mode of spent batteries is recommended for the implementation of the described optimal flight mode. 
Huseynov H. A., Zulfugarli P. R., Abdurrakhmanova I. H. On the accuracy of direct georeferentiation of uavs in areas with different climatic conditions. Trudy MAI, 2022, no 126, http://mai.ru//upload/iblock/928/lvx4hwvybqzghhxlqznffxihp8m1a3or/26_Guseynov_Zulfugarmy_Abdurrakhmanova.pdf The tasks of carrying out measurements with relatively high temporal and spatial resolution using UAVs can be successfully performed when carrying out accurate georeferentiation of their position, i.e. linking photogrammetric devices to any coordinate system. There are indirect and direct georeferentiation. With indirect georeferencing, the real coordinates of ground control points (GCP) are taken into account and they are compared with the measurement results of these points in the images. With direct georeferentiation, the direct use of known objects in the image is carried out. An unambiguous determination of the optimal density of GCP placement in RTK GPS systems does not seem to be justified, since the total influence of both technical factors and meteorological factors (water vapor, pressure, temperature) is taken into account. This article suggests a way to account for the influence of such a common factor. The definition of such a generalized factor and the assumption that the magnitude of this factor is not constant in space allows us to formulate and solve the optimization problem of calculating the optimal dependence of the GCP placement density on the specified generalized indicator. The accuracy of direct georeferencing of UAVs in zones with different climatic conditions is analyzed. The optimization problem of finding such indicators of georeferentiation of measuring instruments in x and y as the density of GCP placement (control points) and the pedestal of exponential dependence of the error of georeferentiation on the number of established control points is formulated and solved. It is shown that if we assume the presence of an analytical dependence of the number of control points along the flight path on the value of the specified pedestal, then the minimum of the average integral value of the relative error of referencing is achieved with the presence of an inverse logarithmic dependence of the number of control points on the height of the abovemarked pedestal. 
Barkova M. E. On the issue of constructing a spacecraft route for the disposal of space debris and a space debris object. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/14b/uo7qxe3nwx6fw5h08b3cb0jejne1k5bn/01.Barkova_.pdf The article is a continuation of research published in issue No. 110 of the Proceedings of the MAI and AIP Conference Proceedings 2318, 020009 (2021). The research is devoted to the rendezvous of a space debris disposal spacecraft (hereinafter SDC — space debris collector) with a space debris object for the purpose of capture and processing into fuel. The main problem of the article is a graphical evaluation of the study performed earlier. The purpose of this work is a graphical assessment of the approach of the SCM and the selected space debris object by constructing their paths. The relevance of this work is to increase the number of space debris objects that can damage spacecraft in a collision. According to space debris data provided by the European Space Agency, the number of debris objects is as follows: — 36,500 space debris objects larger than 10 cm; — 1 million space debris objects ranging in size from more than 1 cm to 10 cm; — 130 million space debris objects ranging in size from more than 1 mm to 1 cm. The author concludes that the amount of space debris decreases slowly and only during periods when its formation is small and there is no particularly strong fragmentation. The probability of a spacecraft colliding with space debris increases at orbital altitudes of 800 — 950 km. In satellite orbit, you can see that the disturbing forces and additional masses from the collected space debris had little effect only in small periods. 
Popov I. P. Mechanical analogue of cyclotron motion. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/751/bczyfsulpprrz4om3o3zrukuawd0rs69/02.Popov.pdf The purpose of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device, which is appropriate to call a stabilized rotator. The topic of speed stabilization is relevant. From the key circumstance that determines the possibility of generalizing cyclotron motion to mechanics, which consists in the fact that the Lagrangian of an electron is twice as large as its kinetic energy, which, as applied to a stabilized rotator, should be interpreted as the equality of kinetic and potential energies, it follows that the composition of a stabilized rotator should include elements , which are able to store both of these types of energy, namely, the load and the spring. The natural frequency of rotation of a stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the moment of momentum) and remarkably coincides with the natural frequency of oscillations of a pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this capacity it may have strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and are determined by the extreme simplicity of the design. 
Bairamov F. D., Bairamov B. F. Optimal stabilization of operation of liquidpropellant rocket engine. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/4a1/agf6cxd3ukjs4r5jr5l6bxt32yvgnepk/03.Bayramov_Bayramov.pdf The Lyapunov function method is applied to solve the problem on optimal stabilization of the steadystate mode of operation of the twocomponent liquidpropellant rocket engine with turbodriven pump assembly by regulating the pressures in the oxidizer and fuel tanks with considering wave processes in the flow lines. Liquidpropellant rocket engine is a complex mechanical system containing two distributed links and finitedimensional links located at both endpoints of the distributed links. The linearized equations of dynamics of separate links are drawn up. After an exception of some variables from these equations system of dynamic equations of liquidpropellant rocket engine in general have been obtained. To solve the problem on stabilization, first, the Lyapunov function method is used to determine the set of controls (laws for regulating the pressures in tanks) ensuring asymptotic stability of liquidpropellant rocket engine operation. Then, the optimal control is determined on this set by the Lagrange function method from the condition for minimum of the norm at each moment of time. Based on specific equations, the Lyapunov function is constructed as the sum of integral and ordinary quadratic forms, the signdefiniteness of which is checked by the Sylvester criterion. The developed control laws can be implemented quite simply and accurately in practice. It is not possible to ensure the asymptotic stability of liquidpropellant rocket engine operation without regulating the pressures in the tanks. The liquidpropellant rocket engine belongs to the class of systems with distributed and lumped parameters, described by linear equations in partial and ordinary derivatives. Some equations of dynamics of liquidpropellant rocket engine do not contain time derivatives. The methodology of synthesis of optimal controls with the smallest value of the norm at each moment of time in systems with distributed and lumped parameters, some equations of which do not contain time derivatives, has been developed. The need for such control arises, for example, when determining the boost pressure in the hydraulic tanks of the hydraulic system; when determining the boost pressure of the fuel tank, which ensures stable operation of the heating furnace. The developed methodology can also be used to study stability of such systems. For example, when studying the stability of operation of a rotarytype wind turbine with a vertical axis of rotation together with a pump. The shaft that transmits the torque of the wind turbine to the pump has a considerable length, so the problem is solved, taking into account the elasticity of this shaft. 
Algazin S. D., Solovyov G. H. Formulation of the flutter problem of a plate of variable thickness of arbitrary shape in the plan. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/c88/g12z62t682bxenxpy3i4dl4u73cx07nk/04.Algazin_Solovyev.pdf By the method of mathematical modeling the flutter of orthotropic plate of rectangular shape in plan at different angles of attacking stream is investigated. For numerical modeling of unstable oscillations of a plate the effective numerical algorithm without saturation which allows on a rare grid to receive admissible accuracy in the approached decision is offered. The type of eigenform depending on the angle of direction of the attacking flow velocity vector is studied numerically. The resulting quadratic eigenvalue problem can be reduced to a double sized standard linear eigenvalue problem. The term «panel flutter» refers to the flutter of a thin plate, shell, or membrane when typically, one of the surfaces is exposed to airflow and the other to still air. The panel then experiences elastic, inertial and aerodynamic forces, which can lead to dynamic instability of the structure. The paper shows that the resulting quadratic problem for eigenvalues can be reduced to a standard linear problem for eigenvalues of twice the size. Questions related to the existence, uniqueness and regularity of the solution are not considered in the work. We refer the interested reader to the work. The first recorded occurrence of flutter for circular cylindrical projectiles appears to have been on a German V2 rocket. The study of the stability of the oscillations of a thin plate of arbitrary thickness in the plan, which in the plane , occupies the region with the boundary and is blown by the gas flow, leads to a nonselfadjoint spectral problem for the amplitude value of the deflections , , which is obtained by generalizing the results of Kiyko I. A. and Ilyushin A. A. 
Levitskiy D. Y., Fedotenkov G. V. Nonstationary stressstrain state of the Timoshenko plate. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/4b1/spe038nazvto8x0iz3kyyr8gk74mxo22/05.Levitskiy_Fedotenkov.pdf Rapidly developing technical progress poses new, more complex and interesting tasks for engineers. This did not bypass the area of problems of the mechanics of a deformable solid body, and specifically the theory of plates. Plates and shells are extremely widely used in the construction of a wide variety of engineering structures. At present, nonstationary problems in the theory of plates remain poorly studied. In this work, vibrations of the Timoshenko plate under the action of nonstationary pressure are studied. investigated. The plate is assumed to be infinitely extended. To describe the movement of the plate, the wellknown equations of the S.P. Timoshenko. The solution method is based on the principle of superposition, according to which the normal displacements of the plate are a convolution of a given pressure with an influence function in spatial coordinates and time. The influence function for a plate is its formal displacements under the influence of a special type of pressure, namely, a unit concentrated force applied instantaneously in time. Mathematically, such a distribution is given by the product of the Dirac delta functions. A spatial problem is considered in a Cartesian rectangular coordinate system. In this case, expansions in double trigonometric Fourier series and the integral Laplace transform in time are used to construct the influence function. The original coefficients of the expansion series are determined analytically using the second expansion theorem for the Laplace transform. Using the principle of superposition and the constructed original of the influence function, the solution of the problem of nonstationary oscillations of a rectangular Timoshenko plate, as well as displacement at a point under the influence of a distributed load, is obtained. The paper investigates the response of the hinged Timoshenko plate to the impact of various nonstationary loads. For the solution, a numerical algorithm was developed and implemented on a computer. Examples of calculation of the deformed state of the plate are given. 
Snazin A. A., Shevchenko A. V., Panfilov E. B. Investigation of the finite element mesh local adaptation in the problem of supersonic flow near body. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/34b/7rnanrnb4bpiwbkeo083hcjlcr65kabr/06.Snazin_SHevchnko_Panfilov.pdf The traveling at supersonic speed generates a detached bow shock wave ahead of it. Downstream of that, the flow attains large increases of pressure and temperature, which are responsible for the high drag and aerodynamic heating. High drag values increase fuel usage and reduce the ratio of payload to total takeoff weight [1]. The paper considers supersonic flow at Mach number M=4.2. The condition of adhesion and isothermicity with a temperature T = 300 K is established on the streamlined surface of the object of study. The flow is considered axisymmetric with respect to the OX axis. The simulation was carried out in a twodimensional formulation on a structured prismatic grid containing 506 thousand elements, 65 elements account for the boundary layer. The ratio of the diameter of the main cylinder to the length of the needle is L/D = 1.4. During the calculation, the mesh cells are adapted in the zones of flow inhomogeneities. The number of adapted cells is 835 thousand, the number of unadapted cells of the original grid is 234 thousand. A homogeneous grid with the size of the cells corresponding to the adapted cells would contain about 2687 thousand cells. Thus, local adaptation allowed to reduce the amount of calculations by 2,5 times. As a result of the calculations carried out, the difference in the distribution of the pressure coefficient on the surface of the model and in the position of the head shock wave between the adapted and nonadapted grid is clearly traced. Comparison of the results of visualization of flow inhomogeneities in supersonic body flow obtained experimentally on a wind tunnel and numerical modeling. The results of numerical simulation are in good agreement with experimental data. The calculations presented in the article showed that the use of local grid adaptation in the areas of gasdynamic inhomogeneities allowed not only to reduce the cost of computing, but also to achieve a good agreement of numerical results with the results obtained experimentally on a supersonic wind tunnel. 
Sposobin A. V. Calculation of the large particle interaction with a supersonic shock layer using the meshless algorithm. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/d6b/zye028mxubua028087hkwg6amcbwlm6n/07.Sposobin.pdf The presented work deals with the numerical modeling of the twophase flows, namely, the computation of a blunt body supersonic flowaround by a viscous gas flow with an admixture of a small amount of large particles, which, after reflection from the surface, go outward the shock layer, being moved by the inertia towards the incoming flow. Testbench and numerical experiments reveal that the motion of high inertia particles changes the structure of the gas flow in the shock layer, and impact jets herewith directed to the body being formed cause the gas pressure increase near the surface areas and a multiple growth of the convective heat flow. A computational model of the blunt body supersonic viscous flowaround with an admixture of large solid particles was developed in threedimensional space. The system of nonstationary NavierStokes equations in conservative variables is being numerically solved by the meshless method, which employs the cloud of points in space of computational nodes for the gas flow parameters representation. The spatial partial derivatives of gasdynamic values and functions, containing them, are being approximated by the least square method on the set of nodes distributed in the area of computation. Nonviscous flows computing is being performed by the AUSMPW+ method in conjunction with the third order MUSCLreconstruction, while viscous flows are being computed by the secondorder scheme. Each particle, as well as a barrier streamlined by a flow, is being surrounded by a cloud of computational nodes belonging to its domain and moving together with the particle in space. The computational nodes position is being adapted to the body shape and allows resolving the flow in the boundary layer with enough accuracy to determine the convective heat flow from the gas surface. The gas state computing at the nodes associated with the particles is being performed by solving the NavierStokes system of equations in a moving coordinate system attached to the moving particle. A model of evolution of a single cloud of computational nodes is built. The nodes that fall into the domains overlapping zone are being temporarily excluded from the calculation, and external nodes of one domain become neighbors of the nodes of another domain to compute both viscous and convective fluxes between nodes with account for transformation of the gas state vectors between moving coordinate systems. Integration of the gasdynamic system of equations in both basic and local systems of coordinates is being performed by the explicit RungeKutta method. The proposed model was verified by comparing the gas flowaround of the stationary and moving particles while maintaining relative velocity of the incoming flow. The software implementation of the presented algorithms based on the OpenCL parallel heterogeneous computing technology with the possibility of simultaneous usage of several GPUs for the calculation of the same task was performed. The authors performed computations of the particles movement in the shock layer near the sphere surface flown around by the supersonic airflow with the Mach number of M = 6. The particle was being launched along the sphere axis of symmetry, as well as at an angle to it. Appearance of local zones of higher pressure and multiply strengthened heat flow on the sphere surface is being observed. Gasdynamic interaction of a pair of particles in the shock layer, which started one after the other with a time interval between them, was simulated. Having fallen into the supersonic wake region of the first particle, the second particle, moving under the action of aerodynamic drag force, moves away to a significantly smaller distance from the sphere surface than the first one. The built computational model and the software, developed on its basis, provide wide opportunities for the numerical study of the gasdynamic interaction of large particles with the shock layer. 
Belyaev B. V., Lebedev A. S. Methodology for predicting the residual resource during depressurization of aircraft. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/1c0/p0bce3c41ymjevqgczgszdvprurdibr0/08.Belyaev_Lebedev.pdf When determining the flight safety of aircraft, one of the urgent tasks is to diagnose a possible violation of the tightness of compartments during operation. Mechanical damage to sealed compartments of aircraft can occur due to fatigue, wear, thermal load, creep of the material, shock load, elastic deformation, surface fatigue, radiation damage, erosion wear and other causes. Leakproofness tests during the preparation of aircraft for operation are not always able to determine microcracks or other design defects that lead to a violation of the tightness of the device during flight. The article is devoted to the topical topic of diagnostics of the process of functioning of sealed compartments of aircraft with through microcracks. In the article, expressions are obtained that allow us to describe the patterns of changes in the leakage of the working medium through through cracks, depending on their changing geometry. An algorithm has been developed for constructing patterns of changes in the leakage of the working medium from sealed compartments in the presence of developing through cracks in their shells. Typical patterns of changes in the leakage of the working medium over time through through cracks are given. The results of calculating the time of depressurization of the compartment are presented, depending on the length of the through crack, the degree of its opening, as well as the free volume of the sealed compartment. The results presented in the article make it possible to more correctly diagnose failures of aircraft in flight operation. In addition, the results obtained make it possible to solve the inverse problem for instrument and habitable compartments of spacecraft. Namely, having the data of telemetric information about the parameters of the gas state (pressure and temperature) inside the compartment and the change of these parameters over time, it becomes possible to diagnose the characteristics of micron densities in the conditions of orbital flight. This, in turn, makes it possible to estimate the time reserve for localization of leaks or to make a decision for an emergency landing of a manned spacecraft. The proposed technique for diagnosing the tightness of aircraft during flight operation can be used to justify the requirements for sensors and pressure detectors in the hermetic compartments of aircraft and for the parameters of the system of reserve gas reserves. In case of emergency leaks during flight operation, it is possible, using the proposed methodology, to determine the remaining time reserve for eliminating the consequences of an accident, ensuring the safety of crew members or emergency landing on the Ground. 
Kolodezhnov V. N., Veretennikov A. S. Flow in a cylindrical channel of a nonlinear viscoplastic fluid. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/cfa/z1uhft0ycoxk4204pnmqipaj7y32zbs3/09.KolodezhnovVeretennikov.pdf A combined rheological model has been proposed for viscoplastic working media that exhibit a nonmonotonic dependence of viscosity on shear rate. This model assumes three typical behaviors in three adjacent ranges of shear rate variation. In the first range, the dependence of the shear stress on the shear rate is described by a linear function and characterized by a constant viscosity value. In the second and third shear rate ranges, this dependence is approximated by nonlinear functions describing dilatant and pseudoplastic behavior. On the basis of such a model, the solution to the steady flow of fluid in a cylindrical channel has been obtained. It is shown that three different flow patterns can be implemented depending on the level of pressure drop along the channel length. For each of the schemes inside the channel, characteristic zones of flow should be identified. In the case of the most complex third flow pattern inside the channel, four zones with different mechanical behavior of the fluid should be distinguished. In such a situation, the zone of plastic flow is formed in the central part of the channel in the vicinity of its foreandaft axis of symmetry. The next zone is characterized by shear flow with a constant viscosity value. Two more zones of nonlinearviscous flow, in which the fluid exhibits dilatant and pseudoplastic behavior, are formed in the vicinity of the channel wall. Expressions for determining the boundaries of flow zones, and expressions for calculating the liquid velocity profile and the dependence of the volume flow on the pressure drop were obtained. The influence of the main parameters of the system under consideration on the velocity distribution characteristics and the dependence of the volumetric flow rate on the pressure drop over the channel length has been analyzed. 
Sha M. ., Sun Y. . Theoretical study of hydrogen degradation processes of drop impact erosion of structural materials. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/682/j23ga4ftjmqsxz68hfphds438cygvck6/10.SHa_Sun.pdf The unique physical and chemical properties of hydrogen and its practically unlimited resources on our planet in the composition of water make it possible to rely on hydrogen energy systems in the development of energy [1,2]. Industrial products, components and assemblies, structural elements, as a rule, operate in aggressive hydrogencontaining media (corrosive, erosive). Rain erosion damage, caused by repeated droplet impact on wind turbine blades, is a major cause for concern, even more so at offshore locations with larger blades and higher tip speeds. Hydrogen, penetrating into the metal of the product and being absorbed in it, changes the chemical composition, structure, and also redistributes the fields of internal stresses. These processes, generalized by the term «degradatio», prepare and stimulate the development of microdiscontinuities of various scales. At the moment, despite intensive research, hydrogen degradation is still an unsolved problem of metal physics, theoretical and practical materials science. It is known that the maximum destructive effect of hydrogen is observed when hydrogen has maximum diffusion mobility and activity, that is, at the stage of unsteady diffusion. Moreover, as the author notes, destruction under the influence of diffusionmobile hydrogen is little predictable and most dangerous due to the high diffusion mobility of hydrogen and the ability to redistribute under the influence of various physical fields, and there is also uncertainty about the magnitude of the critical concentration of hydrogen in the destruction zone. Since during the electrification of the working fluid, the surface of the working blades is exposed to electrophysical phenomena, conditions appear for increasing the absorption of hydrogen by metal, including in a diffusionmobile form. These conclusions about the significant impact on the damage to the blades of the flood are consistent with the conclusions. Based on the above qualitative assessments of the process of the impact of a stream of wet steam with charged droplets on the blade material, it is obvious that the magnitude of the negative effect on electrical processes depends mainly on the magnitude of the ion current in the space of the flow part. 
Averyanov I. O., Wasilchenko A. G. Mathematical model of air damper with permeable fabric shell. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/103/09hl5fvu1bttv2fmlws4mo021zgts9s4/11.Averyanov_Vasilchenko.pdf 
Gerasimchuk V. V., Zhiryakov A. V., Kuznetsov D. A., Telepnev P. P. Computational and experimental method of accounting for the dewatering system in the analysis of natural frequencies and waveforms. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/a73/kpp9q51boxm8n9o5moucciw5sbgurdr5/12_Gerasimchuk_ZHiryakov_Kuznetsov_Telepnev_.pdf The article is devoted to the issue of ensuring the adequacy of the developed finite element models of oscillators to real samples of the spacecraft. In the computational and experimental method, the correction of KE models of dynamic systems minimizes the difference in values between the target characteristics of the real design and the computational model. The main stages of the method are:
The computational and experimental method of accounting for the dewatering system in the analysis of natural frequencies and waveforms allows us to obtain an adjusted model fully suitable for further development of spacecraft control algorithms on a system (dynamic circuit) as close as possible to the real one. Using the example of two oscillators — a solar panel wing and a rod for carrying out scientific equipment — the article demonstrates practical and theoretical techniques for correcting finite element models using experimental research data. Based on the results of the fullscale determination of the natural frequencies and vibration patterns of the structure, the correction of finite element models developed using the Femap with NX Nastran package was carried out, and the adequacy assessment (verification of the correspondence of the model to the real system) of the dynamic circuit of the spacecraft, taking into account the influence of the dewatering system. The achieved difference between the target characteristics of the real design and the calculated model was less than 9%. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Antonova V. A., Gaifutdinov E. A. Comparative analysis of the time delay of telecommunication equipment STP and SDN. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/3bd/1fyq1qnba8pl814vo1crek4xrpo2h13v/13.Buzhin_Antonova_Mironovidr.pdf The article considers the architecture of softwaredefined networks, their principle of operation, as well as the protocols for the interaction of the controller with network devices. The main components of traditional networks are investigated, including a comparative analysis of the time delays of telecommunications equipment of traditional and softwaredefined networks. There are 4 types of delay in modern data transmission networks: packet processing delay, packet delay in the queue, packet transmission delay along the line, propagation delay. The operation of the spanning tree algorithm is considered, its main advantages and disadvantages are highlighted. A comparative analysis of traditional and softwaredefined communication networks is carried out, the features of building corporate networks based on the SDN concept are considered. A network model was built in the Mininet emulator, in which an analytical assessment of the time delays of the SDN telecommunications equipment was carried out. As a result of the experiment and comparison of the obtained data, two different approaches to the network response to topology changes can be evaluated. The experiment showed that the traditional approach to building networks is vulnerable to changing the network topology, which introduces certain network delays and is the reason for the decrease in network performance. 
Kamensky K. V. Trajectory instabilities and onboard navigation system characteristics influence on synthetic aperture radar image quality. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/8e1/hjg00xqpps8pi629jb4p5wc2eg53hxz2/14.Kamenskiy.pdf The goal of this work is to determine requirements imposed on onboard navigation system for the radar that is to be placed on a small unmanned aerial vehicle and to work in stripmap sidelooking synthetic aperture mode with linear frequency modulated continuous wave. To achieve this goal the methodology is proposed to investigate trajectory instabilities effects on radar image in continuous wave synthetic aperture radar. The same methodology can be used to obtain the estimates of onboard navigation system characteristics impact on radar image quality. These characteristics are: measurement accuracy of radar antenna system phase center coordinates and data sampling frequency. The proposed methodology is based upon the use of backprojection method to process a track signal obtained through direct simulation in the condition that there is only one point reflector on the illuminated scene. Quality of the amplitude radar image obtained this way can be estimated by objective criteria: main lobe width and side lobes relative level in the point reflector’s response. The results of the proposed methodology implementation are estimates used to choose the onboard navigation system for a specific radar. In this paper the cases were investigated where trajectory instabilities are absent, represent a constant value, a linear function, or a nonlinear function (sinusoid). It is concluded that onboard navigation system data sampling frequency should be not less than track signal sampling frequency in slow time, and acceptable accuracy of coordinate measurement depends on expected intensity of trajectory instabilities. The practical value of the conducted work is in that the proposed methodology allowed to provide rationale for requirements imposed on the onboard navigation system characteristics. 
Moroz A. V., Sahno I. V., Sherstuk A. V. Technology of image transmission in an ultrasonic communication line. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/fab/73e416gyjo0n4j1ywv54xp9hziy5yhok/15.Moroz_Sakhno_SHerstyuk_.pdf The paper presents a description of a largescale physical modeling of a data transmission channel in the ultrasonic range through a medium, designed to solve the problems of evaluating testing of groundbased tests of an endtoend radar path of a spacecraft with a synthesized aperture antenna and groundbased equipment for digital processing and formation of radar images. As a subject of research, digital information packages are considered, formed from a color or monochrome image, sequentially transmitted through a distribution medium. The main elements of an ultrasonic data transmission system are similar to those used in radio data transmission channels. The need to solve this problem is due to the shortcomings of mathematical modeling in the form of introduced restrictions and assumptions. Thus, the aim of the work is to develop algorithms, software modules for transmitting raster (amplitude, analog) images and clarifying the research methodology on an ultrasonic data transmission system, as an integral part of the laboratory layout of the endtoend radar path of a spacecraft with a synthesized antenna aperture. The proposed largescale physical modeling is based on the principle of linebyline formed from a raster image of digital information packets that are sequentially transmitted in the ultrasonic range. After receiving and digital processing by a software receiver, the information is restored in the form of an image matrix. The result of the work is a developed laboratory setup in the form of an ultrasonic data transmission system, which makes it possible to obtain an assessment of the quality of transmitted information packets with bitmap images. The technique for studying the noise immunity of a digital ultrasonic data transmission line has been refined. Algorithms for digital signal processing and software for the ultrasonic data transmission system have been improved. The technical characteristics of the layout are experimentally determined and the limits of its change are specified. The values of the signaltonoise ratio are determined, at which there are no failures during the transmission of a raster image with a size of about bits. It is shown that the implemented model of the ultrasonic data transmission system can be used for image transmission when modeling the endtoend information path of earth remote sensing systems. The visibility of the simulation results makes it possible to use the ultrasonic data transmission system in the educational process when studying the principles of construction and operation of data transmission systems and methods of programmatic signal reception and processing. The next stage of the work will be the transfer of acoustic holograms obtained at the location acoustic complex, which will make it possible to form a hardwaresoftware stand for modeling the radar channel of a spacecraft with a synthesized antenna aperture. 
Anan’ev A. V., Ivannikov K. S., Filatov S. V. Construction basic principles of communication systems based on unmanned aerial vehicles. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/63f/hxji6eed7ydh7ubkph3k1ez2u6zkeaxg/16.Ananev_Ivannikov_Filatov.pdf The research object in the article is air communication element: a communication system based on unmanned aerial vehicles, the relevance of which is justified in the previous works of the authors. However, despite the variety of related studies conducted, there are a fundamental questions number, without answering which it is impossible to understand the essence of creating a communication system based on unmanned aerial vehicles and determine its final purpose. So, on the one hand, unmanned aerial vehicles are an extremely important resource, in practice, which will always be in short supply. Therefore, talking about a fullfledged independent communication system based on unmanned aerial vehicles is very doubtful. On the other hand, there are very striking examples of the practical use of unmanned aerial vehicles as communications repeaters. It is only clear that the main condition for creating a communication system based on unmanned aerial vehicles is its organic inclusion in the overall communication system. Given the above, the subject of research article are the principles of creating a communication system based on unmanned aerial vehicles. Accordingly, the article purpose is to develop them based on a generalization of the existing backlog on known and promising technical and organizational and technical solutions in the field of communications. In the interests of developing the principles, first of all, the general scientific method was used, which consists in systematizing the existing knowledge, as well as the universal method — the method of analysis. The result of the work is a generalized list of principles for building a communication system based on unmanned aerial vehicles. A number of principles are formed in the development of the previously existing ones. At the same time, new principles are proposed: reasonable selfsufficiency, current interaction and evolutionary creation, etc. The developed principles can be used as the basis for practical work on building a communication system based on unmanned aerial vehicles and are the starting point for the formation of its technical appearance. 
Teplikova V. I., Sentsov A. A., Nenashev V. A., Polyakov V. B. Analysis of the direction pattern of a flat multielement active phased array. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/b13/6yssvwufljgle9gprotp4ow09tge3lla/17.Teplikova_Sentsov_Nenashev_Polyakov.pdf The article presents a study of a technique for correcting distortions in the radiation pattern parameters caused by the mutual effect of radiators, on the example of a rectangular active phased antenna array with the following number of radiators: 64 in the azimuthal plane, and 8 in the elevation plane. The authors considered the dependence of the main characteristics of the directional diagram on the beam deflection while electron scanning and the change in the strength of the electromagnetic field during the cosinesquare amplitude distribution forming on the pedestal. The nature of the dependencies is determined and a technique is proposed for controlling the distortions of the characteristics occurring while the beam deflection. This technique realization will allow correcting the directional pattern, having distortions due to the changes in mutual effect of radiators, obtaining the required characteristics of active phased antenna array, and implement operation modes, which require keeping the antenna array parameters unchanged. The following initial data is necessary when developing an algorithm: the number of rays, minimum scanning step, and the beam setting accuracy. As long as the result of this algorithm realization represents a data array, it is necessary to pay special attention account for the minimum memory size required for the initial data storage for the algorithm. This technique realization allows correcting parameters of the directional pattern, which contains distortions due to changes in the mutual effect of radiators, to obtain the required the APAA characteristics. Its application allows employing the radar operating modes, which require keeping the antenna array parameters unchanged. 
Kasmerchuk P. V., Vernigora L. V. Practical use of EPM and DE ephemeris. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/c31/sgr84qcp39jpvgdmppcoc57tuva7w1sd/18.Kazmerchuk_Vernigora.pdf The design of interplanetary space missions is impossible without knowledge of the position of solar system objects and their dynamics. To determine the position and speed of an astronomical object at a specific point in time (on a specific date), special tables called ephemeris are used. Modern ephemerides are built on the basis of integrating rather complex equations of motion that take into account the gravitation of many bodies in the solar system, including large asteroids and transNeptunian objects, relativistic effects, perturbations from the dynamic compression of the Sun, mutual perturbations of the planets, the Sun and the Moon, etc. When building dynamic models ephemeris, data from radar observations of planets, laser observations of the Moon, data on the parameters of the movement of spacecraft during their approach to large planets, the results of interferometry with very long bases, etc. are used. To date, one of the most accurate are the Ephemeris of Planets and Moon (EPM) ephemerides developed by the Institute of Applied Astronomy of the Russian Academy of Sciences (IPA) and the Development Ephemeris (DE) ephemeris of the NASA Jet Propulsion Laboratory (JPL). Various variants of the DE series ephemeris appeared in the 60s of the XX century, the EPM ephemeris began to be created in 1974. The coordinate system used in a particular version of the ephemeris must be specified in the documentation. In most versions, the coordinates are as close as possible to the International Celestial Reference System (ICRS — International Celestial Reference System). The origin is the barycenter of the solar system. The X axis is directed to the vernal equinox at the J2000 epoch, the Z axis is perpendicular to the plane of the Earth’s equator, the Y axis completes the system to the right. The resulting coordinate system is independent of the Earth’s rotation. Units of measurement of coordinates are kilometers, measurements of time are days of barycentric coordinate time (TDB). The Julian day is used. Algorithms for converting a calendar date to a Julian day and vice versa can be found in. There are quite a few tools that allow you to calculate the ephemeris data of astronomical objects, for example, online ephemeris services, as well as offline libraries. However, if the task is to use ephemeris in your own software, in which for some reason the use of thirdparty libraries is impossible or there are high performance requirements for subroutines working with ephemeris, which require specific code optimizations, you can use the text representation of ephemeris in the DE format available for free download from the IPA and NASA servers. 
Kulvits A. V., Zhitnikov T. A., Mikheev O. Y. Theoretical aspects of the formation of a cluster of small spacecraft. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/4db/4fprvi4vbcxn2npkhhlifkhmk6fait7h/19.Kulvits_ZHitnikov_Mikheev.pdf The article discusses the theoretical aspects of the substantiation of the ballistic structure of the cluster of small satellites. For the ballistic justification of the small satellites cluster, it is necessary to solve several interrelated tasks. First, it is necessary to justify the parameters of the orbits, the functioning of which would allow the cluster to successfully solve the target task. Secondly, after launching the small satellites into orbit, it is necessary to provide the required configuration in space, which is determined by the ballistic structure. Thirdly, due to the influence of disturbing factors acting on the small satellites while moving in orbits, the configuration will collapse over time. Therefore, the stable relative position of the small satellites in the cluster can be provided by the justification of the ballistic structure in orbits of the same radius and inclination. For the three small satellites as part of the formation implementing the tasks of radio monitoring by the differencerangefinder method (DRM), acceptable performance indicators are achieved when the small satellites form an equilateral triangle during operation, since in this case the accuracy indicators of the DRM are optimal, while the onboard equipment also imposes restrictions on the formation in the form of minimum and maximum relative distances between satellites. Over time, the triangle formed by three small satellites deforms, while the indicators of solving the target problem decrease. Thus, the task is reduced to determining the set of parameters of the orbits of the small satellites cluster with a restriction on the relative position, which will ensure the maximum time functioning of three small satellites in the cluster of the required configuration. The proposed approach to solving this problem is based on the decomposition of the problem of finding optimal parameters into two special cases, which make it possible to determine the range of acceptable variants of ballistic structures of the small satellites cluster and thereby significantly reduce the area of possible iteration when solving the optimization problem. The analysis of the parameters of the small satellites orbits and the ballistic structures of the cluster makes it possible to ensure a stable relative position of the small satellites in space with the required periodicity. The results of solving the multiparametric problem of searching for a ballistic structure can be used at the stages of ballistic design of satellite systems consisting of clusters of small satellites. 
Tanygin M. O., Chesnokova A. A., Ahmad A. A. Increasing the speed of determining the source of messages by limiting the set of processed data blocks. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/226/qyha1r6v1el3foe2oazlrmcndfvm4jx7/20.Tanygin_chesnokova_Akhmad_Ali_Ayed3.pdf The purpose of the study consists in developing a mathematical model, which allows evaluating the computational complexity of the original method of i the messages source identifying, which is based on forming the groups of messages and checking the condition of belonging to the target source for the entire group. An increase in reliability and decrease in computational complexity in the method under study is being achieved by assuming that the sequence of messages from the source to the receiver is maintained. This allows cutting down the number of messages involved in the group forming, and, accordingly, reduces the number of options for such groups’ formation. To study the computational complexity of the algorithm for the groups of messages forming, the number of elementary operations for comparing hashes of such messages was studied, i.e. of the basic operation determining membership of a particular message to the structured set being formed. The length of the message hash, the number of interacting subjects of the distributed system, a number of messages in the group, as well as the parameter limiting the set of messages being analyzed, were the parameters of the model. The process of messages receipt to the receiver was represented as a linear dynamic process characterized in each discrete time instant by the probabilities of a certain number of messages receipt from the target source and all other sources of the distributed system. The results obtained with this model allow asserting that the condition of warranty of the messages sequence, received by the device, does not change complexity of the message source detection. It stays linearly dependent on the length of the group of messages and a number of devices interacting in the framework of the system of devices. At the same time, in absolute numbers, the number of comparison operations is reduced by two orders of magnitude compared to the group forming method, which does not employ the stationary property of information flows between the distributed system components. 
Kuznetsova S. V. Features of crossplatform mobile applications development using Xamarin. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/436/0dfe43gy61r854kufmslgxrdw3uoecc8/21.Kuznetsova.pdf Today, the development of mobile applications is one of the most actively developing sectors of the IT industry. In this regard, there are many projects for the development of applications on mobile platforms. Digital transformation in the aviation industry covers the production of aircraft, as well as passenger and cargo transportation. As for transportation, the work of airlines, airports, interaction with passengers, customers of cargo transportation, the functioning of a unified air traffic management system deserves special attention. One of the technological trends actively developing today in terms of digitalization of the aviation industry is the development of mobile applications for aviation, including aircraft construction, air transportation and airport services. Mobile applications provide significantly faster access to data and are an effective means of interaction regardless of the user’s location. For example, they provide quick access to technical information and direct data entry, optimizing engineering and production processes. The classic version of mobile application development is native development, in which a separate application is developed for each operating system (OS), which is quite expensive and time—consuming. An alternative is a crossplatform technology, the main purpose of which is to provide developers with a tool for parallel creation of applications for multiple operating systems at the same time. This will allow them to write a single source code for several mobile platforms, but the result of each individual build will be separate executable files. Obviously, crossplatform development is needed to optimize the cost and speed of development, as well as application support. At the same time, the output result is no less qualitative than with native development. Currently, there are the following most popular crossplatform frameworks: Xamarin, React Native, Flutter, and NativeScript. They are very different and not in all situations will be equally useful (or even necessary in principle). The article discusses the technology of developing crossplatform mobile applications Xamarin: the principles of developing crossplatform mobile applications using it are outlined, the main features provided to developers within this approach, its advantages and disadvantages are presented. A range of issues related to the design, implementation and testing of mobile applications is considered: the use of the MVVM architectural pattern, the XAML markup language to describe the user interface, a possible development environment. A methodology for creating crossplatform mobile applications on the Xamarin platform is presented, containing a brief, consistent and comprehensive description of all stages of development. 
Brekhov O. M., Ratnikov M. O. Comparative analysis of test systems for FPGAS and their environment. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/a9a/nug42u2tyrb3tk9yc4ktrfbqp9p8j2sc/22.Brekhov_O_M_Ratnikov_M_O_.pdf This work is devoted to the study and analysis of currently used FPGA test systems and their system environment, developed by both domestic and foreign researchers. More than 30 test systems based on the use of: builtin selftest structures (BIST), specially designed systems and systems that partially or completely use the target firmware are considered. The systems in question were used to solve various tasks: FPGA input control, testing of internal interconnection resources, testing of individual cells and embedded IP cores, testing of the FPGA system environment (external connections of FPGAs and the power subsystem), analysis of electrical, dynamic and functional characteristics in various conditions, search for single failures and failures. The systems used in the study of microcircuits for resistance to laser exposure, the flow of charged particles (including studies within the Alice CERN project and studies conducted by both FPGA suppliers and thirdparty researchers to compare the characteristics of various FPGAs), the accumulated dose of radiation, elevated temperature and changes in supply voltage are considered. The systems and methods that are used to debug the FPGAbased system are also considered. Also in the list of test systems considered there are systems used as a demonstrator of the application of methods for analyzing energy consumption, dynamic characteristics, reliability and fault tolerance, as well as testing and developing systems based on FPGAs. The result of the work is a classification of the considered systems, an analysis of the advantages and disadvantages of the considered systems and proposals for the further development of FPGA test systems and their system environment. 
Dorozhko I. V., Gorokhov G. M., Kirillov I. A. Methodological approach to the development of a decision support system for the operator of an automated process control system based on dynamic bayesian networks. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/4e6/kivgzugjmtbohqhoy98i27361ehtnyst/23.Dorozhko_Gorokhov_Kirillov.pdf The article describes a scientific and methodological approach that can be used in the development of intelligent decision support systems for operators of automated process control systems. The proposed approach is based on the mathematical apparatus of dynamic Bayesian networks, as well as the basic concepts and relations of the theory of reliability and technical diagnostics of systems. The initial data are information about the algorithm of the system functioning and the course of the technological process, information about the reliability (structural and logical circuits, failure rates of elements) of technological equipment, as well as diagnostic models linking the types of technical conditions and diagnostic signs. It is proposed to use temporal connections (temporal logicalprobabilistic dependencies) in a dynamic Bayesian network to simulate changes in the technical states of elements of technological equipment and describe the dynamics of the technological process. A posteriori conclusion allows combining heterogeneous initial information and incoming new data to obtain a comprehensive assessment of the progress of the technological process and the condition of technological equipment in order for the operator to make an informed decision on the continuation or suspension of the technological process, search for the causes of abnormal situations and the choice of proactive measures. The implementation of this approach is given on the example of a decision support system for an operator of an automated control system for technological equipment of a booster refueling system, the peculiarity of which, when analyzing reliability, is the need to take into account elements with three incompatible states — operable, failure of the «break» type and failure of the «closure» type, affecting the course of the technological process in different ways. The variants of using the developed decision support system for the current control of the technological process, forecasting and retrospective analysis in the search for the causes of abnormal situations are shown. 
Minakov E. P., Privalov A. E., Bugaichenko P. Y. A model for evaluating the control efficiency of multisatellite orbital systems. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/7d8/he7vorb7rzgoqvmvz7h7j076hzgqik20/24_Minakov_Privalov_Bugaychenko.pdf The article is devoted to solving the important problem of evaluating the control efficiency of multisatellite orbital systems. The article introduces definitions of an orbital system (OS), a multisatellite OS (MS), and an control system of OS. The relevance of the problem of evaluating the control efficiency of MS by stochastic modeling is substantiated. Based on the principle of A.N.Kolmogorov, the MS control efficiency indicator has been identified and its mathematical model has been developed. The mathematical formulation of the problem of evaluating the control efficiency of MS, which consists in determining the efficiency coefficient of management, expressing the degree of achieving optimal efficiency at the current values of the controlled parameters, is realised. A model for evaluating the efficiency of MS management in the form of a continuous Markov chain has been developed. With the application of the developed model, the evaluation of the control efficiency of a perspective MS of remote sensing the Earth based on the Berkut spacecrafts, which is being developed within the framework of the Sphere program, has been carried out. The dependences of the control efficiency on the quality indicators of the control system for solving various remote sensing tasks has been obtained. The developed model can be used at the stage of development of methods, techniques and algorithms of MS control for their elaboration, verification, calibration, optimization, evaluation of the impact of their quality indicators on the control efficiency of MS, and also for justification of requirements for them and confirmation of compliance with the declared requirements. 
Ezrokhi Y. A., Kizeev I. S. Assignment of the compressor performances at mathematical modelling of the aviation gas turbine engine. Trudy MAI, 2022, no 125, http://mai.ru//upload/iblock/f56/m2wzx8tatiig7lg24lrqagfipjtcyxtp/25_Ezrokhi_Kizeev.pdf Efficiency of aviation engine mathematical model (EMM) application at various stages of the engine creation substantially depends on accuracy and «physical» descriptions of working procedure in airgas channels of the engine and its units. As now the course of creation of the aviation gas turbine engine (GTE) and the aircraft works can depend on reliability of the engine parameters and performances estimation, increase of EMM accuracy is rather important problem. One of the most significant components of the gas turbine engine mathematical model accuracy is accuracy of the basic engine units’ performances; in particular, elements of the compression group (fans and compressors). In article features of the assignment of compressor performance with air extraction from its airgas channel in gas turbine engine mathematical model are considered. It is shown that the distributed air extraction can lead to appreciable compressor performances exfoliation, especially to its part located behind a place of extraction; it is necessary to consider at the aviation gas turbine engine parameters computation. For this purpose the relative extracted air flow, and also part of the compressor work from enter to an air extraction place are defined. These parameters allow calculating the physical air flow, enthalpy and temperature of extracted air. As show results of the numerous experimentcalculated researches, now widely used simplified technique of air compressor extracted air enthalpy definition can lead to considerable errors in GTE parameters calculation. The main reason of wrong calculation aviation GTE parameters is discrepancy of methodical approaches to independent estimated and/or experimental definition of units’ performance to how this performance is used in engine mathematical model. That correctly to use the performance of engine units (for example, compressor cascades) in integrated engine mathematical model, it is necessary to know, how they were characterization and that is understood as value of this or that experimentally received parameters have been received. Techniques of the compressors’ cascades tests results handling for its characterization, calculation of the air extractions’ parameters, and also the turbine power for a drive of the considered compressors’ cascade in core and gas turbine engine system are presented. 
Fedorova L. A., Sofin A. P., Gorshkov L. K., Uhanov I. G. Assessment of stability of the root link of the manipulator under the action of axial load on it. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/7a3/4bs8qib1ov9fs92av9z4joae95txdhh3/Fedorova_Sofin_Gorshkov_Ukhanov.pdf The development of space manipulation systems is directly related with obvious expansion of the possible range of work and operations that can be carried out in difficult and dangerous conditions with technical orbital objects and equipment installed on them. By now, the main construction option used has developed — a hingetype manipulation system of different degrees of complexity. Modern manipulators must be carried out with condition of maintaining stability of elements. Taking into account the priority of influence of the root link on stability of the manipulator as a whole, it is proposed to investigate the equilibrium positions of the rod for stability at a range of deviations π < φ < π. Criterion of stability of equilibrium position for systems with holonomic and stationary constraints located in conservative force field is determined by LagrangeDirichlet theorem: According to the theorem equilibrium positions of a conservative system in which its potential energy has minimum are stable. The results of the study of stability by taking into account angle of inclination of the link are determined by the dependence between the angle of inclination φ and the dimensionless force λ. The formation of the real appearance of a service multilink manipulator for use in space conditions should be carried out on the basis of taking into account functional tasks and the available database on specifics of creation and use of existing devices. The studies carried out to date indicate that, along with geometric interpretation, which provides an assessment of the initial structure and approximate dimensions of the manipulator elements, it is necessary to analyze the operational loads that determine stability of circuit elements. Obviously, the actual dimensions of the manipulators will be determined by motion parameters (for example, angle of rotation) of hinge elements. The calculations performed show that to a large extent the condition and, consequently, the operability of the root link are determined by the axial load. The proposed studies allow us to assess the danger of such a load and give recommendations on the design of the manipulator, taking into account the properties of the elastic hinge and the size of the links. This will prevent monotonous departure from the considered equilibrium positions or fluctuations increasing in scope over time. 
Popov I. P. Absolute reference systems in relative motion. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/7bf/p2acxmxiux109rnlikl2q31ocy0rxqh9/Popov.pdf It was noted that the problem of reference system selection at relative motion of the objects of commensurable mass is of particular relevance while interplanetary flights at a considerable distance from the planets. For the same inert objects moving relative to each other, different coordinate systems give completely different total kinetic energies of objects. In this sense, it impossible to recognize them as equivalent. It is obvious that none of these coordinate systems can be considered as absolute. Only the system which selection completely eliminates arbitrariness, can be considered as the absolute system of cordinates. This requirement is met by a system in which the total kinetic energy of objects is minimal. The absolute coordinate system coincides with the center of mass of the objects and with the epicenter of their hypothetical repulsion from the state (hypothetical as well) of mutual immobility. After a hypothetical repulsion, the velocities of objects relative to the center of mass acquire the same values as in the absolute coordinate system. Along with a wide variety of reference systems at the mutual motion of unaccelerated objects, including those associated with these objects (these reference systems can be considered relative), there is one absolute reference system associated with the center of mass of the objects under consideration. The considered repulsions of objects are calculated and may have nothing to do with reality. The number of objects while the absolute coordinate system definition is not limited by anything. It may be both two objects and a star system. 
Smirnov A. S., Smolnikov B. A. Construction and analysis of rational modes of rigid body motion control. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/891/0w6l7f708e7jyqeir0ngbcrj7qf4ntzd/Smirnov_Smolnikov_1_.pdf The paper considers the motion of a rigid body under the action of a control moment, formation of which is carried out in various ways and meets the specific control goals. The main properties of the collinear control and its modified version are discussed, which lead to an increase or decrease in both kinetic energy and kinetic momentum, and as a result they allow overclocking or braking of a rigid body. Orthogonal control is also considered, which does not violate the constancy of kinetic energy and kinetic momentum and leads to a reorientation of the rigid body in space. In addition, combined control options are constructed, which have the features of both collinear and orthogonal controls in their structure. First control option allows dissipating or accumulating kinetic energy at a constant kinetic moment, and the second option, on the contrary, leads to a decrease or increase in the kinetic moment at a constant kinetic energy. Such controls can be interpreted as rational, since they are efficient, have a fairly simple structure, and are convenient for practical implementation. Moreover, physical analogies are given for the constructed control options, which make it possible to correlate their action with inertia forces, dissipative forces of external and internal friction, as well as gyroscopic forces. Based on various methods, exact analytical solutions are constructed for the mentioned modes, and these solutions describe the process of controlled motion of a rigid body and demonstrate its properties. The results obtained in the work are not only of fundamental theoretical significance, but can also be used in solving applied problems of rigid body dynamics. 
Barkova M. E. Safety system for shredding space debris in orbital conditions. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/fd9/h52sunesstwb2l2qeclqx56h8jfeked9/Barkova.pdf The space debris shredding safety system is a fundamental system in the processing of space debris into fuel directly in orbit. This study is devoted to the possibility of testing the technology for processing metallized debris on Earth, as well as the development of the concept of a safety system for shredding space debris. In the wreckage of the stages of rockets, propellant vapors remain, which, if crushed, can provoke an explosion. The main problem of the article is the development of the concept of a safety system for shredding space debris directly in orbit. The purpose of this work is to consider ground tests of the technology for processing metallized space debris into fuel. The relevance of this work lies in the concept of a safety system for shredding space debris directly in orbit. The most important source of nonfragmentation debris was more than 2,460 firings of solid rocket motors, which released aluminum oxide (Al_{2}O_{3}) in the form of micrometer dust and slag particles ranging in size from mm to cm. The main cause of inorbit explosions is due to residual fuel that remains in tanks or fuel lines, or other leftover energy sources that remain on board after a rocket or satellite stage has been dropped into Earth orbit. These fragmentation events are thought to have generated a population of objects larger than 1 cm, numbering on the order of 900,000. The sporadic flux from natural meteoroids can only dominate the flux from humanmade objects near sizes of 0.11 mm. 
Rabinsky L. N., Babaitsev A. V., Shesterkin P. S. Investigation of the effect of rolled products in layers of aluminumfiberglass on static and dynamic properties. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/649/qt9lltv4iqllm5qkaoqf888ljvr6hksb/Rabinskiy_Babaytsev_SHesterkin.pdf The composite materials is a new invention of the material combination which can be used in the aircraft industry. The main purpose of the invention is to have the lightweight structure and anticorrosion effect with better strength. This type of materials is hybrid because of the combination of the metal and fiberglass. The new characteristic of this hybrid material is a combination of each advantage of aluminum, steel and fiberglass. Based on previous studies, the manufacturing of aluminumfiberglass based material must follow the concept of interlaminar for the better bonding. This work is devoted to the study of the effect of rolled products in aluminum layers of aluminaglassreinforced plastic. In particular, the study of static and dynamic properties along and across rolled products was carried out. Aluminum alloys are the most common materials used in the aviation and space industry. These alloys have a relatively high specific strength and a lower density than steels. Consistent optimization of the design of aircraft elements in terms of reducing their weight and the simultaneous fulfillment of specified strength requirements has led to the emergence of metalpolymer composite materials. These materials have a number of advantages over aluminum alloys: lighter weight, higher specific strength, crack resistance. Aluminum fiberglass plastics developed in Russia in the Russianlanguage literature are called SIAL. Over the past few years, a large number of works have been devoted to the study of materials of this type including in relation to the modeling of large parts of aircraft structural elements. This material consists of alternating layers of aluminum alloys and fiberglass reinforced epoxy. A composite of this type is a promising, improved material with improved specific strength, damage resistance, impact resistance, and fatigue strength. Formed from several layers of aluminum alloy sheet and layers of glassfiberreinforced glassfiberreinforcedpolymer (GFRP), aluminoglassreinforced plastic behaves like an elasticplastic material primarily due to the presence of layers of aluminum alloys, and its complex failure mechanisms are determined by its composite structure. 
Medvedskiy A. L., Martirosov M. I., Khomchenko A. V. Fracture and deformation mechanics of polymer composites in the presence of multiple bundles of arbitrary shape under the action of dynamic loads. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/6d1/lp8302o9v3o8x9rcvvzouil7c31hzkwe/Medvedskiy_Martirosov_KHomchenko.pdf Currently, elements of structures made of polymer composite materials (PCM) are becoming increasingly important, which have a number of advantages: high specific stiffness and strength, low specific gravity, high wear resistance and fatigue resistance, as well as the ability to create unique mechanical properties depending on the requirements for the finished product, etc. With the above advantages, PCM products also have disadvantages, which include their sensitivity to damage. To prove that the strength characteristics of PCM structures meet the certification requirements, it is necessary to carry out computational, theoretical and experimental work according to methods that allow us to show that the designed structural elements from PCM fully meet the requirements. Such elements can be largesized aggregates (wing and tail panels, center section panels, forkill, wing spars, stabilizer and keel), or they can be quite compact (fairings, fairing, nacelles, structural elements of mechanization). Traditional structural metal materials, due to their stable characteristics, the duration of the period of preservation of mechanical and technological properties, provide the specified strength characteristics of the aviation structure. The level of safety provided by the PCM construction should not be lower than the level of safety provided by the metal construction. In the work, studies were carried out to assess the impact of internal defects (damages) of the type of bundles of various sizes and locations in layered elements of structures made of polymer composite materials (PCM): a cylindrical reinforced shell, a reinforced cylindrical panel, a rectangular reinforced plate. A technique is proposed for modeling structural elements made of PCM with defects of the type of bundles under the action of dynamic loads of various nature. 
Kanashin I. V., Grigorieva F. L., Khromov A. I., Grigorieva Y. Y. Tension of a strip made of a compressible material with a continuous velocity field under plane deformation. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/18d/s3tz0emh7e72ov7l7pqgvtmt3gkjsls5/KanashinGrigoreva_KHromov_Grigorev.pdf The subject of the study of the presented article consists in determining conditions of the moment of a crack nucleation at the stretching of the plane sample from the compressible material under conditions of the plane deformation. The purpose of this study is studying the process of stretching a flat sample made from compressible material with a continuous displacement velocities field under the plain strain conditions. The material compressibility associated with the mass conservation law, which is formulated in the form of the equation of continuity, leads to a density change while loading process, in accordance with which the logarithm of the material derivative of density in time is being added to the system of equations defining the displacement velocity field. This system is being converted to a system of inhomogeneous wave equations. The following methods were applied while this research conducting. They are: — Analytical method for the velocity and deformations field determining; — Averaging method for obtaining the mean value of the auxiliary function on the sphere; — Method of descent for transition from the sphere surface integration to the circle integration. In the course of the studies, an intermediate result, namely the general solution of the system of wave equations for the velocities field determining, was obtained. The results of the study can be applied while mathematical models developing of the behavior of real structures’ elements in the problems of modern mechanical engineering and construction, as well as in assessing their strength. 
Cherkasova M. V. Approaches to modeling the process of erosion products deposition on the gas discharge chamber walls of an ion engine. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/621/2anviynd8e3qg7kdxqt5b1p52x37ogx4/CHerkasova_.pdf Currently, many tasks of space exploration use ion engines, including highfrequency ion thrusters. At the same time, special attention is paid to the terms of active engine operation. In the design of a ion thruster, the ion beam is extracted from the discharge plasma and accelerated using an electrode system operating on the principle of electrostatic lenses. The accelerating electrode of such system is subject to erosion due to bombardment with exchange ions. Electrode damage results in engine performance change for two reasons. Changing the electrode configuration worsens the characteristics of the ion beam and also the sprayed electrode material penetrates the discharge chamber and settles on its walls, changing the discharge characteristics. Extensive theoretical and experimental studies have been devoted to the erosion of the accelerating electrode itself, while the problem of deposition of sprayed material on the walls of the gas discharge chamber has not been practically investigated. This paper proposes a physical and mathematical model for depositing sputtered atoms of accelerating electrode material on the walls of a gas discharge chamber of a highfrequency ion engine. Twodimensional model of spatial sputtering of accelerating electrode surface by exchange ions and interaction of sputtered material atoms with primary beam ions is considered. Possible ranges of emission angles of sprayed atoms penetrating inside the discharge chamber through the holes of the emission electrode are estimated. Based on the created model, calculation of the accelerating electrode erosion of the twoelectrode ionoptical system with the accelerating electrode from molybdenum was carried out. In the first approximation, the penetration of sprayed molybdenum atoms into the plasma of the discharge chamber was simulated. An estimate of the distribution of polluting atoms over the conditional model surface was obtained. Quantitative estimates of surface contamination rate have been made. The developed physical and mathematical model of processes will allow in the future to create an engineering methodology for calculating the dynamics of deposition of sprayed material on the walls of the gas discharge chamber of a highfrequency ion engine. The use of such a technique will reduce the time of life tests and better predict the change in engine performance for long service life. 
Pismarov A. V., Kirpichev V. A., Sazanov V. P. Prediction of the resistance of tired threaded parts. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/e26/hacmtmx5r6c4yc68vvg5nmaxayg563f6/Pismarov.pdf A method for threaded parts surface hardening is being widely employed to the fatigue strength increase. Maximal result of its application is being achieved under conditions stresses concentration with regard for the fact that destruction occurs as a rule in the places of prismatic shape violation. Thus, establishing a qualitative and quantitative relationship between static stresses and fatigue resistance of threaded parts is highly uptodate task. A large group of parts in assemblies and structures has stress concentrators in the form of threads. Threaded joints are highly loaded elements, which operation defines the strength and reliability of the structure as a whole. The strength of threaded parts operating under conditions of an asymmetric cycle, which average stresses are stipulated by the tightening force, depends mainly on the tensile working stresses, as well as on the strengthening treatment. In this regard, development of the technique for determining the endurance limit of the threaded part by the known residual stress diagrams as well as average stresses of the cycle using the linear elastic fracture mechanics provisions presents interest. Based on the foregoing, the object of the study in this work is highcycle fatigue, and the subject of study is threaded parts with residual stresses. The purpose of the study consists in developing a technique for predicting the fatigue resistance of the threaded parts by developing a technique for assessing the relationship between the stress intensity factor (SIF) and highcycle fatigue characteristics. Using the graphs of the distribution of residual stresses in the cavities of threaded parts as the initial data, the nature of the SIF dependence on maximum stresses of the cycle of a hardened threaded part was determined in the work. The graph can be presented in the form of the three sections. The first section corresponds to the state when the crack edges are completely pressed against each other, that is, the fatigue crack does not open, despite the presence of cycle tensile stresses. The second section corresponds to the state when the crack opens from the inside, while the sides of the crack remain closed. The third section represents a straight line running parallel to the similar dependence of the nonhardened thread and corresponds to the scheme when the crack is fully opened. The starting point of the third section of the graph corresponds to the maximum stress. It was found from the calculations that the criterion for the most optimal technological mode of thread manufacturing with creation herewith of a compressive residual stresses field is the stress of the transition point of the second section into the straight third section. Starting from this point, the fatigue crack opens completely. The proposed technique for predicting the fatigue resistance of threaded parts from the standpoint of linear fracture mechanics allows predicting maximum amplitude of the cycle. 
Sanchugov V. I., Rekadze P. D. Calculation of hydrodynamic characteristics for bench systems. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/110/mxbsonv107ekqebze9rqklc2qofvu4bn/Sanchugov_Rekadze.pdf The problem of article is the developing the V.P. Shorin’s load variation method for solving the problem of determining the own dynamic characteristics of a hydraulic pump as a vibrations source of the working medium. The method consists in calculating the pumps dynamic characteristics (considered by models of equivalent oscillation sources) while changing the bench systems behind the pump, registering pressure pulsations and converting into the own pump characteristics by V.P. Shorin’s models of equivalent oscillation sources. In known works, dynamic models of bench systems, as a rule, are idealized, either do not take into account all the elements of bench systems, or implement a limited set of bench systems (such as «acoustically open end», «acoustically closed end», etc.). While calculating the dynamic characteristics of bench systems, we propose to use information about the design and geometric dimensions of the systems flow part. The article summarizes the main aspects of calculating the bench systems dynamic characteristics, their hydrodynamic schemes describing the influence of both cavities, throttles and main lines, and connecting fittings, adapters and the units’ internal channels are presented. The work aims to create special bench systems with known dynamic characteristics in order to solve the problem of determining the own dynamic characteristics of a hydraulic pump. The developed models of bench systems with a throttle, a cavity, a «short» and an extended pipeline at the pump outlet, when used in the load variation method, will make it possible to calculate the pulsating state of the working medium behind the hydraulic pump both in the hydraulic systems of machine tools and in the fuel systems of a gas turbine engine at the early stages of design. The results of the work can be important for engineers and designers of hydraulic systems, because they contain specific formulas and recommendations on how to use them. 
Petrov I. I., Serdyuk D. O., Skopincev P. D. Fundamental solutions for orthotropic cylindrical shell. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/20d/9t07edagrw956lezo6s6vlub8ocv2amy/Petrov_Serdyuk_Skopintsev.pdf
A circular cylindrical shell of constant thickness is considered, the side surface of which is affected by nonstationary load. The shell material has symmetry with respect to the median surface, is linearly elastic, orthotropic. The motion is described in a cylindrical coordinate system associated with the axis of the cylindrical shell. The mathematical model of the object under consideration is described using the Kirchhoff — Love hypotheses. Fundamental solutions (Green’s functions, influence functions) are constructed for a cylindrical shell of great length, as well as a cylindrical shell pivotally supported at the ends. The Green function for an orthotropic shell is a solution to the problem of the effect of an instantaneous concentrated load on the shell, modeled by the Dirac delta function. To find the influence function in the case of an unlimited cylindrical shell, expansions into exponential Fourier series in angular coordinate, the integral Laplace transform in time and the integral Fourier transform in longitudinal coordinate are used. The inverse integral Laplace transform is being performed analytically, and the original integral Fourier transform is being found using numerical methods for integrating rapidly oscillating functions. In the case of a limited cylindrical shell, expansion into double trigonometric Fourier series in the angular and longitudinal coordinates is applied, as well as the integral Laplace transform in time. The inverse integral Laplace transform in this case is performed analytically. Verification of fundamental solutions has been carried out. Examples of calculations are given. The results are presented in the form of graphs. A new numericalanalytical fundamental solution of the dynamic problem of elasticity theory for an orthotropic elastic thin unlimited cylindrical shell is obtained, as well as an analytical fundamental solution in the case of a limited KirchhoffLove shell. The convergence of the solution is established. To demonstrate the realism of the constructed functions, examples of calculations for one variant of the symmetry of an elastic medium are presented. The nature of the movement of nonstationary perturbations allowed us to evaluate solutions. Fundamental solutions open up opportunities for solving new contact and inverse problems of load identification, allow performing applied research on calculating the stress and strain levels of orthotropic shells. 
Averyanov I. O., Zinin A. V. Mathematical model of nondeformed cargo landing system with dampers to rigid plane landing process. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/792/o4ty3r1sfwdlnck924u5ntltlj43g82m/Averyanov_Zinin_otredaktirovano2.pdf To calculate dependability measures for developed dropped cargo landing systems with dampers we usually use statistics from similar models and mathematical statistical modelling of landing process. In this article we describe the mathematical model of dynamics landing process for cargo dropped systems with dampers we developed for its further using in statistical modelling. This mathematical model considers all the phases of dynamic landing process — from the phase when air dampers start resisting to the phase of system stopping — and is able to indicate typical failures like excessive acceleration and system overturn. It should also be appropriate from time cost point of view. Analysis of sources shows that existing models are not appropriate for the considered task: almost all of them consider only the dampers resisting phase; in case of finiteelement models solutions it is not appropriate according to the time cost. A rigid body with dampers dropped to the rigid landing area (plane) is consided. The body is freely located in 3D space in the beginning of the process as well as the plane. We use dynamic equations of forces and moments equilibrium in 3D space with reactions from dampers and the plane. The body and the plane interaction realizes with contact algorithm. To solve the equations numerical simulation with finitedifference schemes is used. There are two tasks presented to demonstrate how the developed model works. The first task considers the translational motion of the dropped body with dampers. The second one — complex body movement. As the considered equation system is closed the algorithm we developed has benefits related to the existing solutions from the point of view of time cost. Thus, the dynamic landing model we developed is appropriate for statistical modelling tasks. 
Zvonarev V. V., Vitaly V. ., Popov A. S. Method of calculating influence of frequency scanning interference on reliability of signal reception with QPSK modulation. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/863/5cdajbcvj38lkdijvfs9m8e4u97o9tz3/Zvonarev_Karabelnikov_Popov.pdf To accurately assess the channel resource and determine the maximum signal attenuation in a complex electromagnetic environment, the article describes a technique that allows calculating the probabilistictemporal characteristics of a radio channel with high accuracy and reliable forecasting. As the main characteristics of a radio channel in a complex electromagnetic environment, the article considers the probabilities of bit and character errors affecting the reliability of signal reception. The article presents a mathematically correct method for calculating the probabilities of symbolic and bit errors of coherent optimal characterbycharacter reception of a radio signal with QPSK modulation in the presence of interference with linear frequency modulation inside the symbol. The basis of the technique is the representation of a fourdimensional probability measure of the vector of output voltages of the correlation channels of the receiving device in the space of the eigenvectors of the covariance matrix of this vector. The results of the article are necessary to calculate the influence of interference in a connected radio channel, when finding the probabilities of symbolic and bit errors. The calculation method is integrated into the energy calculation algorithm of the transmission channel in the presence of interference with LFM modulation. The developed technique of the influence of frequencyscanning interference on the reliability of receiving a signal with QPSK modulation makes it possible to accurately determine the probability of symbolic and bit errors at given values of the level and deviation of the interference frequency. The results obtained show that the curves of the average probabilities of symbolic and bit errors have a threshold character. The presence of interference with linear frequency modulation significantly degrades the quality of the communication channel, completely disrupting the reception of information at the values of the interference level when the interference level exceeds the signal level. The extension of the graphs to the region of zero signal value at zero and nonzero interference value shows that the average probability of a symbolic error is 0.75. In the same case, the probability of a bit error is 0.5. It is determined that the phaseaveraged interference probabilities of correct reception, and, consequently, errors in receiving signal positions in the presence of interference with LFM modulation, are the same, which allows the calculation of the transmission channel to be limited to using as an average the probability of receiving one signal position. 
Letfullin I. R. Standards and technologies of shortrange wireless communication networks. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/e20/k7hcoan2khtfobr217xg5elxky4nnuti/.Letfullin.pdf The article discusses the main technologies and standards for wireless data transmission, provides an overview and comparative analysis of shortrange wireless technologies («last 100 meters» technology), and also discloses some technical characteristics. The advantages and disadvantages are shown. For the analysis of nearradius technologies, a method for comparing parameters was chosen based on information from domestic and foreign literature, scientific articles and publications. The analysis contributes to the selection of the most optimal wireless data transmission standard for organizing an efficient nearrange network aimed at solving the main problem of Internet of Things devices — ensuring the secure connection of a large number of devices with limited power deployed over a wide area and meeting the performance criteria of the Internet of Things. Currently, shortrange wireless communication is based mainly on Bluetooth, UWB, ZigBee and WiFi standards, which are based on IEEE 802.15.1, 802.15.3, 802.15.4 and 802.11a/b/g/ah standards, respectively. The specified IEEE standards define physical (PHY) and MAC levels for wireless communication in a range of about 10100 meters. Based on the review, it can be concluded that 802.11ah is the most promising nextgeneration WiFi technology for largescale applications of the Internet of Things with low power consumption, which combines support for high data transfer rates over long distances, low power consumption, low latency, and thanks to builtin mechanisms such as RAW, TWT and TIM, significantly reduces collisions when accessing the channel, and also provides the required QoS. It is also important to note that wireless technologies are changing rapidly following the needs of the Internet of Things market and it is recommended to monitor updates to existing standards and technologies, as well as the emergence of new shortrange technologies. The requirements for power consumption of devices, data transmission security, high network fault tolerance, the ability of devices to withstand radio interference and ease of connection remain unchanged. 
Ageev F. I., Voznuk V. V. A method for calculating the probability of a bit error of optimal characterbycharacter coherent reception of binary opposite phasemanipulated signals in the presence of narrowband noise interference in the radio communication channel. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/40e/uktc6x80t55850i0yso6e838nbmd1uiu/Ageev_Voznyuk.pdf The article is solving the problem of the bit error probability computing of the optimal characterbycharacter coherent reception of the opposite phasemanipulated signals (BPSK signals) at the presence of the inadvertent narrowband noise interference. The article considers the Gaussian noise interference with uniform spectrum limited by the frequency band and arbitrary power, entering the pass band of the BPSK signals receiver. Application of the receiver based on either correlator or matched filter tuned to the signal being considered under conditions of the intrinsic noise of the receiver presence only is being understood to in the article as the optimal receiving of the opposite phasemanipulated signals (BPSK signals). Analytical expressions were derived and a technique for computing the bit error probability of the optimal characterbycharacter coherent receiving of BPSK signals with the presence of both intrinsic receiver noises and narrow band noise interference. The wellknown expressions, being used for the probability estimation of the bit errors of the optimal characterbycharacter coherent reception of the BPSK signals against the background of the white Gaussian noise, form the basis of the obtained relationships. Based on the obtained results, the basic inferences were formulated ,and asymptotic probability estimations of the bit error of the optimal coherent BPSK signals reception at the presence of both intrinsic noise of the receiver and narrow band noise interference for the uttermost narrow band and wide band Gaussian interference were obtained. The article demonstrates the presence of the narrow bane noise interference, which spectrum overlaps the BPSK signal spectrum leads to the noise immunity degradation of the information radiotransmission channel, and the degree of the noise immunity degradation herewith depends drastically on both power, spectrum width and this interference place of location in the BPSK signal spectrum. 
Moiseev S. N. Simulation of the difference error in target tracking by airborne radar and optoelectronic stations. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/542/68y8ihdz0goh6o1sg9vk91cbxh2gb3oe/Moiseev.pdf The article deals with the task of modeling differential errors of target tracking by the onboard radar and optoelectronic stations of navigation and weaponaiming complexes of aircraft in the interests of studying their accuracy characteristics. The presented work employs simulation model, developed for obtaining statistical estimation of the onboard highprecision target tracking systems based on employing wellknown noise characteristics of reference measuring means and tracking channels of target tracking systems under study. The article demonstrates that the misalignment between the aircraft radar and optoelectronic stations leads to the shift occurrence in the differential error of the target tracking. The law of the shift in the differential error changing of the target tracking is similar to the misalignment error changing. This may be used for the error value evaluation and its program minimization. 
Ermakov P. G., Gogolev A. A. Software complex of algorithms for autonomous determination of the angular orientation parameters of unmanned aerial vehicles. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/8e4/m2ou886yi44mbk9zfj2l6ht3yrva8mqu/Ermakov_Gogolev.pdf The article «Software complex of algorithms for autonomous determination of the angular orientation parameters of unmanned aerial vehicles» by P.G.Ermakov and A.A.Gogolev compares three approaches used for an Attitude and Heading Reference System (AHRS), namely Mahony, Madgwick and Complementary filters. For attitude determination on UAV’s board widely used a magnetic and inertial measurement unit (MIMU). MIMU consists of a 3axis MEMS gyroscope, accelerometer and magnetometer. The accelerometer measures the acceleration of a UAV, the gyrosocope measures the angular rate of a moving object, and the magnetometer measures the Earth’s magnetic field. So, Mahony uses a proportional and integral controller to correct the gyroscope bias, Madgwick uses the gradientdescent algorithm. Both approaches use a quaternion representation, which a fourdimensional complex number representing the orientation of an object. A Complementary filter is proposed that combines accelerometer output for low frequency attitude estimation with integrated gyroscope output for high frequency estimation. Madgwick obtains better heading orientation than Mahony and Complementary AHRS approach in respect of the root mean square error (RMSE) of the Euler angles when compared to the motion capture system. 
Abadeev E. M., Piskunova O. I., Tretyakov A. V. Method for adaptive control of the longitudinal movement of a smallsized aircraft with a signal limitation of the integral component. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/041/vqd3i0tk4qm48j5j9t7rjep9t0rkbb80/Abadeev_Piskunova_Tretyakov_.pdf The article conducts the studies of characteristics of the promising control and longitudinal motion stabilization system of a dynamic object, such as a smallsized aircraft (SSA), based on the technique of the adaptive signal formation [1, 2]. The study of the control method being considered was conducted by the mathematical modeling method of an isolated pitch channel with implementation of the proposed SSA control laws at rather characteristic external impacts on it. Simulation was being performed under conditions of changes by the given “slow motions” law [3] of the flight parameters such as altitude and velocity. Comparison of the control processes of the SSA with the system being proposed and control processes with the conventional proportionaldifferential control technique [4] adapted to the given situation in [5, 6, 7] was performed to evaluate the effectiveness of the newly introduced control specifics. The relevance of the presented work consists in the fact that the velocity increase being achieved by the proposed technique, overshoot degree reduction and, correspondingly, increasing the control signals processing accuracy may contribute to the SSA maneuvering and controllability characteristics improvement. 
Rozin P. E., Simonov A. V., Gordienko E. S., Zaiko Y. K. Inflight calibration of the "DEKART" CubeSat magnetometer. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/bc7/7ct3mr329kornes9rtctrhb80mu8iod6/Rozin_Simonov_Gordienko_Zayko.pdf As part of the ADCS of CubeSat LEO satellites magnetic control systems have become the most widespread. The magnetic control system, as a rule, magnetorquers that create control momentum and magnetometers. Magnetometers are used in this system to determine the direction and magnitude of the Earth’s magnetic field intensity vector. To reduce the cost of creating a CubeSat spacecraft, it is common practice to use household digital magnetometers. These devices are characterized by low accuracy due to the lack of calibration of the zero offset and mutual orthogonality of the measurement axes of the device. Thus, the task of developing an algorithm and software implementing it for calibration of magnetometers become very important. The algorithm considered in the paper is based on the processing of measurements of a 3axis magnetometer on Earth, after their transmission from the spacecraft. The processing consists in searching by the method of configurations minimum of the functional, as a result of which the values of the calibration parameters are determined. The value of the functional is determined as a result of numerical simulation of the spacecraft flight and determination of the calculated value of the Earth’s magnetic induction vector, followed by comparison with the transformed measured induction vector of the Earth’s field. The practical application of the algorithm is considered on the example of the «DEKART» spacecraft launched as part of the UniverSat program on September 28, 2020 at 14:20 (Moscow time) from the Plesetsk cosmodrome. «DEKART» CubeSat spacecraft was developed and assembled at the D.V. Skobeltsyn Research Institute of Nuclear Physics of Moscow State University. 
Piyakov A. V., Sukhachev K. I., Dorofeev A. S., Bandyaev V. A. Electrodynamic accelerator control system with calculation of motion parameters in real time. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/9ad/yg2kbnfmkslqdheyw1xkc2sbii001pcz/Piyakov_Sukhachev_Dorofeev_Bandyaev.pdf The work relates to the field of accelerator technology and is devoted to improving the control system of an electrodynamic linear accelerator of dusty charged particles. The existing accelerator is used to simulate the factors of the space environment and makes it possible to study the effect of highspeed micronsized particles on the elements of the surface of the spacecraft under conditions close to real. However, this accelerator has a complex control system that requires the operator to control a large number of parameters in real time and to constantly adjust during the experiment. The need to measure physical quantities and calculate particle parameters, as well as manual control, increase the error in the formation of accelerating pulses in the dynamic section, which leads to inefficient particle acceleration or the loss of most of them. The article proposes a new method for controlling a dynamic accelerator, the basis of which is a method for determining the parameters of a particle, which makes it possible to refuse any measurements other than timeofflight, made in an improved measuring section. The structure of the measurement section is presented in the article, while it is clear that minor changes are required in the already existing design of the accelerator. A control system has been developed that allows, according to data from timeofflight sensors, to automatically control the dynamic section of the accelerator with high accuracy. This is achieved, among other things, by refusing to use memory banks with precalculated voltage switching times on the drift tubes. In the new control system, the calculation of the particle position and its instantaneous velocity occurs in real time, since the calculation of the particle's specific charge is no longer required. Knowing the position of the particle in the path allows timely switching of the voltage on the drift tubes while the particle is inside them. The proposed method for determining the particle parameters and the control system have a calculation error associated with the discreteness of the measured time intervals. An analysis of the error and its influence on the acceleration process was carried out, from which it is clear that the system allows particles to be accelerated in a wide range of specific charges, and the maximum deviation of the particle coordinate when switching the voltage on the drift tubes does not cause it to leave the fieldless space of the drift tube. In addition, the system has a margin of accuracy, since the simulation was carried out for the existing accelerator design and an increase in the frequency of timeofflight sensors and a computer is not required, although this is possible if necessary. Thus, the proposed method for controlling a dynamic accelerator makes it possible to automate the process of conducting experiments and increase the efficiency of particle acceleration in an extended range of charges, masses, and initial velocities, and also makes it possible to increase the number of accelerating sections, thereby increasing the equivalent accelerating voltage of the system. 
Storozhev S. A. Multiagent control of the combustion chamber oxidizer using neurofuzzy technology in the MISO system. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/4d7/lejs1w26418zguk2kh72kabbvlds29dt/Storozhev_.pdf The an aircraft gas turbine engine (GTE) of aircraft from the point of view of control theory is a complex nonlinear object, the frame mathematical description of which is known a priori, has one input and several outputs. When operating a gas turbine engine, continuous monitoring of parameters is required (gas temperature behind the combustion chamber, rotor speed of the lowpressure compressor (free turbine), rotor speed of the highpressure turbocharger (gas generator). The selective controller controls these parameters, realizing control in different modes of operation of the gas turbine engine. Further The development of GTE control can be associated with the use of neurofuzzy control of the oxidizer flow into the GTE combustion chamber. Purpose: improving the control of the combustion process in the combustion chamber of the gas turbine engine. Methods: a new approach to designing an adaptive state controller based on neurofuzzy technology using triangular terms with equal bases equal to the interval 0–1, whose vertices are shifted according to the arithmetic mean of the path traveled by the input variables, is proposed. Determination of the degree of membership is performed by singletons, synchronously shifting depending on the change in input parameters using proportions. On the basis of the proposed approach to designing an adaptive state controller with an oxidizer flow, the relationship between the input parameters of the combustion chamber and the development of the control control with maximum speed is estimated using the area ratio method or the weighted average method. The idea of the experiment, using the designed state controller, is to estimate the temperature change behind the combustion chamber, which should not leave the specified zone. Results: the developed adaptive state controller is characterized by the best values of the probability of nonfailure operation during the experiment. Practical relevance: the research results can be used in the control of the combustion chamber. This can significantly reduce the uncertainty in the operation of the combustion chamber, ensuring a minimum release of harmful substances and guaranteed thrust of the aircraft. 
Sudarenko D. A., Kakadei M. S., Yazykov A. A. Compare of technology ADO.NET and SQLite for the development of LTCC structuralparametric description database. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/e9c/s6h55ylys5u9u9a9icv31vy3mhl309ju/Sudarenko_Kakadey_YAzykov_1.pdf The technology of lowtemperature cofired ceramics (LTCC) is considered. This technology provides an inexpensive solution in the mass production of electronic devices in the field of telecommunications, medicine, automotive technology, military equipment, aerospace and other industries. In the process of implementing LTCC technology, difficulties were identified associated with the influence of a large number of parameters depending on the components used, the time of use and configuration of equipment at each stage of production on the quality of products. The parameters of technological operations (TO) are highlighted, grouping is made according to the characteristics of parameters: resource, process, result, control and management. In real life, there is no system that would collect all of the above parameters together, compare them and give recommendations for improving quality. In this paper, a method for creating, describing and modeling parameters in the form of information support based on a structural parametric description (SPO) according to regulatory documentation is proposed to improve the quality of production of microwave components. Based on this classification, workplace models are built, and the data is aggregated into the MS Access database management System (DBMS). Since Access has a number of disadvantages and is not, in fact, a fullfledged database, technologies were considered as a DBMS ADO.NET from Microsoft (the Sharp C language framework) and the Qt SQLite framework (in C++). ADO.NET manages both internal data (created in computer memory and used inside the application), and external, located outside the application — for example, in a database or text files. The Qt framework contains a universal interface for working with various databases. Databases in the Qt view are drivers for the QtSql module. By default, when installing the framework, the SQLite database is available, for the rest of the databases, installation and assembly of drivers for Qt is required. A comparative analysis of these databases has been carried out, on the basis of which it can be assumed that the SQLite DBMS is suitable for prototyping at the initial stage and crossplatform applications, and the DBMS ADO.NET it is more complex, but more promising in terms of commercial use. 
Zaitseva N. I., Pogarskaia T. A. Development of software complex for analysis and optimization of the aircraft assembly process. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/962/ytwck77k30zwwj82amn8trt6z6tbfz4f/Zaytseva_Pogarskaya_.pdf The presented work is devoted to describing the multiprocessor software complex ASRP (Assembly Simulation of Riveting Process), being developed as part of a joint project of Peter the Great St. Petersburg Polytechnic University and the AIRBUS SAS. This complex is meant for simulating and optimizing the aircraft assembly process, with account for the fact that aircraft building places rather strict requirements to the parts assembly quality due to high operational loads. The authors propose employing in the complex mathematical modeling and numerical optimization methods, which allow predicting and optimizing the quality of the parts joints prior to implementation of the technologies for the assembly line being developed. In the aircraft building industry, one and the same assembly technology is being employed while series assembly for all aircraft of the same type being assembled. Accordingly, while modeling the assembly process it is necessary to account for random assembly deviations, such as deviations of parts from the rated shape or errors in positioning. The ASRP suggests accounting for these deviations through modelling the random initial gap between parts. To optimize assembly processes, it is necessary creation and analysis of various options of the fixing elements positioning is required. A fundamentally new approach has been developed for the ASRP to optimize the temporary fastener patterns, based on the preliminary assessment of the stressstrain state of the assembled structure. When modeling assembly processes considering assembly variations and the fastener patterns optimizing, the necessity to solving many similar problems with hundreds of different initial data arises. For this reason, the ASRP suggests employing parallel computations for analyzing and optimizing the assembly processes. This presented article describes the structure of the ASRP software package, the developed methods for the assembly process modeling, methods for the initial gap modeling, as well as methods for optimizing the fastener elements placing. The efficiency of the proposed optimization methods and parallelization algorithms is being studied on a practical example associated with the analysis of the assembling process of the tail section of Airbus A350. 
Dementiev A. N., Klyuev D. S., Novikov A. N., Mezhnov A. S., Peterskova Y. A., Zakharova E. V., Dementiev L. A. Development of a method for spacetime processing of broadband signals in an adaptive antenna array. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/f3f/uwu5mc43139pr3nsdkt5unv05z0zi3w1/Dementev_Mezhnov_.pdf Numerous scientific articles and monographs are devoted to the theory of spacetime signal processing in antenna arrays. This type of processing is possible only in directional antennas, namely in adaptive antenna arrays, since they have a multichannel structure and allow you to identify the direction of signal arrival due to the accumulation of phase delay. Adaptive antenna arrays make it possible to form «nulls» of the radiation pattern in the direction of the interference signal by adjusting the vector of weight coefficients in the processing channels. The level of development of science interprets that these channels operate at the same frequency, that is, they are harmonic, which does not allow solving the problem of processing broadband signals. In this regard, a number of nuances arise that require more detailed theoretical and practical studies. At present, the issues of processing broadband signals in adaptive antenna arrays have not been studied both theoretically and practically. There is no clear understanding of the methods for selecting and calculating the vector of weighting coefficients in the frequency band. Also, the issue of receiving signals and suppressing interference, the sources of which are in motion, was not considered. These issues are relevant, since the development of modern technologies dictates the need to expand the spectrum of the transmitted signal, which makes it possible to increase the volume of transmitted information, ensure electromagnetic compatibility in conditions of saturation of the frequency range, and also increase the resolution. The article developed a method that allows spatiotemporal processing of broadband signals with the suppression of interference of various spectra, the sources of which are in motion. This method is based on the gradient descent method, which makes it possible to form «nulls» of the antenna array radiation pattern in real time and provide the required signal/(interference+noise) ratio at the output of the antenna array, which in turn provides the required bit error probability for transmission systems. Data and accuracy of determining the parameters of the object of observation and location for radar and radio navigation systems. 
Morozov A. Y. Interpolation approach in problems of modeling dynamic systems with ellipsoid parameter estimations. Trudy MAI, 2022, no 124, http://mai.ru//upload/iblock/8e0/qi4o7kibgsdfjunhq8gsnwnv5ix3i6qe/Morozov_2.pdf 
Korovaytseva E. A. Comparative study of soft shells of canonical meridian forms static deforming at inflation. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/4ca/rn613z3ggadjg0jjtaq0p1gimt3ddt0e/Korovaytseva.pdf The presented work compares behavior of the soft shells of revolution with various canonical shapes of meridian (semisphere, cylinder, torus, cone) from the nonHookian material at large deformations under the impact of the pressure uniformly distributed along the meridian. The shells’ sizes are being selected from the condition of the geometric sizes equity in the in terms of nondeformed shells surfaces areas.
The shells deforming is being described by the unified system of equations, applicable for any meridian construction form considered at arbitrary displacements and strains. Boundary conditions are being considered equal as well. Resulting relations of the nonlinear problem, being considered physically and geometrically, are formulated in the vectormatrix form. The problem is solved using parameter differentiation method algorithm. The initial nonlinear equation system herewith is being differentiated with respect to solution continuation parameter, which leads to interconnected quasilinear boundary and nonlinear initial problems forming. These problems are solved in steps using iteration method.
A number of features of the considered problem solution is established. In particular, for the hemispherical shell, the solution can be considered verifiable only until reaching some minimal value of pressure in supercritical area. However, from the calculations viewpoint, this problem solution possesses the highest iteration convergence rate. An ability of bearing the smallest magnitude of pressure among all the considered variants of shell meridian is characteristic for the conical shell.
For subcritical area, increasing of meridian and decreasing of circumferential strains is characteristic while approaching the fixed boundary of the shell, and for cylindrical shell, it is more intensive. Meridian and circumferential stresses in cylindrical shell exceed the ones in the spherical shell on the largest part of the meridian. In the toroid shell, stresses as well as strains remain minimal.
In supercritical area, the meridian strains in cylindrical and spherical shells decrease while the fixed boundary approaching. Strains in cylindrical shell become the smallest ones, and meridian strains in the toroid shell are the largest. Similar behavior is being observed for the stresses distribution along the meridian. 
Zhukov N. A., Kiselev I. A. Investigation of the influence of cutting tool flank face contact forces on the dynamics of end milling. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/9c6/8z7txawkyh3zisf1exp16q3uc0ofy2dw/ZHukov_Kiselyev.pdf In the modern machinery 5 axis end milling operations are widely used in the production of thinwalled workpieces with complex 3D surface geometry [13]. Such processes are always accompanied by vibrations of different elements of the technological system (e.g., workpiece, tool): free, forced, parametric vibrations may arise, as well as selfoscillations. One of the most undesirable vibration types are regenerative selfoscillations, which may cause dynamic instability of the steadystate cutting process: these vibrations arise due to the fact, that each tooth of the mill is cutting the surface, formed by a previous tooth, so the time delay effect is introduced [46]. At the early investigations of cutting dynamics it was observed, that vibrations amplitudes of the technological system’s elements decreased while machining with low spindle speeds [7,8]. This effect was called “process damping” and its presence was explained by contact interaction between the flank face of the tool and the machined surface [9]. The intensity of process damping is the higher, the lower is the ration of the mill’s teeth pass frequency to the vibrations frequency [10].
Modern timedomain models of 5 axis end milling processes lack process damping accountment [1719], so numerically simulated machining dynamics at low spindle speeds (comparatively to the arising vibrations frequencies) are not correct, which is extremely actual for machining of thinwalled workpieces from nickel and titan alloys. In this work a new timedomain numerical model of end milling dynamics of flexible workpieces is presented. This model allows to consider complex 3D contact forces between the workpiece and both rake and flank faces of the cutting tool during end milling dynamics simulation. Model’s structure and its main blocks are described. The developed model was used to perform numerical experiment on the influence of contact forces, arising on the flank face of the cutting tool, on the dynamics of the flexible workpiece end milling. Obtained numerical results qualitatively match well known experimental data from literature. 
Seregin S. V., Dobryshkin A. Y., Sysoev E. O., Zhuravleva E. V. The influence of the reinforcement of carbon thinwalled open cylindrical shells on free vibrations. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/8f2/mdt6axfjpljfr0gl07bmu97wrzq6jryy/Seregin_Dobryshkin_Sysoev_ZHuravleva.pdf Thinwalled cylindrical shells found wide application in various industries. The development of technology puts forward more and more serious requirements for the strength and stability of structures along with their low weight and cost. Such requirements are being applied to aeronautical engineering and unmanned aerial vehicles. The optimal solution in many cases consists in applying thinwalled shells made of carbon materials with high strength properties. The shell structures are being exposed to temperature and wind loads, variable atmospheric pressure during the aircraft flight and many other dynamic impacts. Thus, the structural materials of the shells should be lightweight and durable. Recently, carbon materials, which are an order of magnitude lighter and stronger that metal, are being applied more often. Under operating conditions, shells are being exposed to high dynamic stresses that may lead to adverse effects. However, the problem of the multilayer carbon shells dynamics is not fully understood up to now. Thus, for example, the known theoretical studies in a number of cases, have significant discrepancies in the values of the lowest frequencies of the vibration spectrum of reinforced shells with numerical calculations performed by the finite element method. This fact requires an experimental study on the behavior of low frequencies. The article provides an experimental study of the effect of multilayer reinforcement of thinwalled carbon fiber open cylindrical shells on their free vibrations. Experimental samples were created on the KomsomolskonAmur State University basis for the experimental study of the effect of multilayer reinforcement of carbon thinwalled open cylindrical shells on their free vibrations. Models of shells with singlelayer reinforcement were made of 2/2 12K1000600carbon fabric. Twolayer reinforcement was created from a layer of 2/2 12K1000200carbon fabric and a layer of 2/2 12K1000400 fabric. A threelayer reinforcement was created from three layers of 2/2 12K1000200carbon fabric. The experimental data was compared with the analytical solution. The experiments revealed an increase in the vibration frequencies of carbon thinwalled open cylindrical shells with an increase in the number of layers of carbon fabric reinforcement in relation to the values of frequencies obtained analytically. 
Zotov A. A. An analytical form for presenting a filler for threelayer systems, consisting of staggered coneshaped elements. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/978/wf11jryt4t45f7j6k7nz9n1cjwqzbs0j/Zotov.pdf This paper considers the problem of analytical determination for the stiffness characteristics due to the use of a filler in the form of a regular coneshaped (or pyramidal) cell’s system arranged in a checkerboard pattern for threelayer plates
At the moment, the most widespread are honeycomb, corrugated or folded fillers. The main filler’s advantages are low weight and high rigidity. However, there are circumstances that prevent their wider use. The closed volume formed by the core’s cells e promotes the accumulation of condensate, at the same time preventing its removal. On the other hand, there are technological difficulties associated with the provision and control of a reliable connection between a filler and bearing layers (especially on curved surfaces), thereby increasing the product cost. The structure of the cellular filler considered in the article largely allows to solve the above problems.
Due to the complexity and laboriousness of solving strength and stability problems for systems of variable stiffness, analytical solutions for a wide class of such structures are practically absent or hardly applicable in solving problems related to the design of products.
The article proposes a method for analytical filler’s representation in the form of a regular discrete coneshaped cell’s system, with the aim of further determining the geometric properties.
Based on the analysis of the filler’s shape under study, contemplation its shape as a surface described by the trigonometric Fourier series was proposed. However, upon further analysis of the problem, it was possible to reduce the function describing the filler’s geometry to a simpler form. The final version of the shape function was a set of coefficient, cosine and sine. Filler’s representation in the form of a similar function allows one to determine the variable bending stiffness of a threelayer package when solving the problems of bending of plates with variable stiffness.
Representation of the shape of the considered filler in this form with high accuracy conveys the true geometry of the product and allows to analytically describe the geometric stiffness characteristics of the structure (areas, moments of inertia and static section moments) included in the differential equations of bending and buckling of a variable stiffness plate. 
Popov I. P. Artificial moment of inertia. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/da3/69snoq1inw7nm5l888f8fwcqxxd0uzlg/Popov.pdf The article demonstrates that creation of the “artificial mass”, which associates with neither volume, nor the density of the material, encased in the inertial object, is based on the requirement to the Newton’s second law satisfaction. As far as the equivalence principle of inertial and gravitational mass is not extended to the artificial mass, a device with the artificial mass may be incommensurably lighter than its mechanical analog with the same moment of inertia. This quality makes this device particularly attractive for application in aviation and astronautics, including light flywheels. The purpose of the study consists in analytical synthesizing of the artificial moment of inertia and identifying parameters determining it.
The existence of analogies between physical quantities of different physical nature does not automatically lead to the possibility of obtaining the corresponding functional dependencies. For this, technical means ensuring dimensionalities concordance of the dual quantities are necessary in the first place. If an artificial flywheel is being placed in a “black box”, it will be impossible to determine by any experiments whether an artificial or “natural” flywheel is inside it.
The main advantages of the artificial flywheel over a “natural” one are its incomparably lower weight and the possibility of electrically controlling the moment of inertia over a wide range by changing the magnetic field (excitation) and capacitance, which creates a good prospect for its application in automatic control systems. 
Mikhailova E. Y., Fedotenkov G. V. Transient deformation of the halfspacemembrane system. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/ac4/0hdgg2br81cvopf9emfldm77n46m4rlj/Mikhaylova_Fedotenkov.pdf 
Egorov I. A. Taking into account the features of the flow around the arcshaped wings at the design stage. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/ff6/7r6tmb3fsmepylqywhcaisuqpif07f9x/Egorov.pdf Currently, arcshaped wings are widely used for smallsized missiles. Therefore, techniques are needed to determine the aerodynamic characteristics of such wings, primarily the lift coefficient.
1.The peculiarity of the arcshaped wing flow is reduced to three aspects
Reduction of local angles of attack
2. Reduction of the «useful» component of the local lifting force of the panel
3.The convergence of the wing panels, and the amplification of the mutual influence of the panels.
Consideration of all these aspects is possible when using the discrete vortex method.
The wing is divided into panels with a given pitch in span and chord. In each panel there is a Πshaped vortex.
When determining the geometric parameters that determine the position of the wing point relative to the vortex, it is necessary to take into account the curvature of the wing.
Two schemes of arcshaped wings are considered: with an opening angle of 90° and with an opening angle of 135°.
The scheme with an opening angle of 90° is taken as the basis for consideration.
The transition to a scheme with an arbitrary opening angle is reduced to a simple recalculation of coordinates.
The calculation is performed in the following sequence:
1.The coordinates of the wing points in space are calculated.
2.The parameters of discrete vortices in space are determined.
3.A matrix of coefficients of the system of equations is formed.
4.The angles of attack are determined taking into account the spatial orientation of the wing element
5.The circulation values and the value of the wing lift coefficient are determined.
The calculation results for a rectangular wing are presented.
The wing is divided into 24 panels.
Mach number M = 0.8, angle of attack α = 1º.
The conclusion:
1.The discrete vortex method is very convenient for constructing an arcshaped wing calculation model.
2.Acceptable calculation accuracy can be obtained already with a large grid.
3.The greatest influence on the accuracy of the calculation has an increase in the density of the grid along the span
4.To obtain acceptable accuracy, the curvature of the arched wing must be taken into account at all stages of the calculation
5.An arched wing with an opening angle of 135° has bearing characteristics close to those of a flat wing 
Kornev S. V., Pimenov I. A. Numerical investigation of velocity field behind the wing by different vertical position horizontal tail. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/45e/dm8eqemt8fz48w8wj4ytkdl4mhhhuxlv/Kornev_Pimenov.pdf The flow field of two lifting surfaces modeling wing and horizontal tail is investigated in this article. Aerodynamic characteristics and simulation of lifting surfaces’s flow pattern were calculated in the angles of attack were varied from 0 to 25 when the horizontal tail had have diverse positions in height: upper, initial and lower. As can be seen, if the horizontal tail has the lower location, it will be more efficient because the horizontal tail is located outside from vortex wake’s area behind the wing in high the angles of attack.
The main objective of this research is aerodynamic design’s optimization consisting in the choosing of horizontal tail position in height in order to reduce control system requirements and improving its reliability by reducing moment’s characteristics nonlinearity. Aerodynamic computation of lifting surfaces which geometry are the same surfaces of prototype MIGAT was calculated for determination an efficient horizontal tale’s position in height. Fluid flow and gas calculation with turbulence was done on base numerical solution total system of hydrodynamics’s partial differential equationscontinuty equation, NavierStokes equations, energy equation which were modified with Reynolds’s averaging procedure. The flow field around two lifting surfaces was computed in the software package Ansys Fluent. Visual simulation’ s analysis of velocity distribution has shown that the horizontal tail which has low and high position is located outside of wing’s vortex wave area in higher angles of attack. However, if an angle of attack increases, the horizontal tail which has higher location will be situated in wing’s vortex wave, that the lower horizontal tail. In this case, it will lead to pitch moment’s characteristics degradation. To sum up, when the horizontal tail has the lower location, it is more efficient because in this case, this variant has favorable characteristics of pitch moment, in spite of, lifting properties’s neverthless minor reducing compared with more high position of the horizontal tail. 
Khatuntseva O. N. Generalized analytical solution of the plane Poiseuille problem for the turbulent regime of incompressible fluid flow. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/70e/0abmov69pyir58wrny2iinpkgulattsb/KHatuntseva_.pdf The possibility of describing both laminar and turbulent modes of fluid flow based on the same equations has been investigated. It is proposed to consider the NavierStokes equations (NSE) in a phase space expanded by the introduction of an additional stochastic variable. As a result, an additional term appears in the expression for the total time derivative, characterized by the production of entropy due to the excitation of stochastic perturbations.
For laminar flow modes, entropy production takes zero value, the additional term disappears, and the transition to the NSE in their standard form is carried out, while the corresponding solutions describe only laminar flow modes.
The inclusion of an additional term, characterized by entropy production (which is always nonnegative), into the equations allows us to take into account the time irreversibility of physical processes in cases where this production is nonzero.
It is shown that the occurrence and maintenance of nondeterministic – stochastic processes – in a liquid is possible in those systems, where incompatible boundary condition occurs. In this case, the existence of one smooth solution becomes impossible, and we can only talk about the presence of two or more nonintersecting or nonsmoothly intersecting asymptotes of the solution. The region located between these asymptotes (or in the vicinity of the point of “discontinuity” of derivatives) is an uncertainty domain that generates a stochastic process.
As generalized solutions to problems with two asymptotes of the solution, functions were considered that are the sum of two terms, each of which is the product of two functions: one of which determines one of the asymptotes of the solution, and the second determines the degree of influence of this asymptote on the overall solution at each point of the studied domain.
The “laminar” and generalized “turbulent” solutions of the plane Poiseuille problem are found in this formulation. The comparison of the found solution with experimental data of the wallmounted universal velocity profile is given for different values of the Reynolds number. 
Gavrilova A. Y., Kulizade M. E., Cherkasova M. V. Plasmomechanical interpretation of excited inert gas atoms states. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/c7e/8nuxof666u2cjjgdcy3eqa2swhyonq3t/Gavrilova_Kuli_zade_CHerkasova.pdf A plasmamechanical approach to the problems of gas kinetics has been developed to improve passive optical diagnostic methods. The article considers the solution of quasistationary system of equations of radiationcollision model of inert gases lowtemperature plasma depending on priority of electronic and photoprocesses. The system of linear differential equations of kinetics is being reduced to a matrix form with a nonzero right part, which is being interpreted as an influence factor, for which a relaxation matrix is being introduced. The obtained matrix equation is being solved by iterative methods for the selected final configuration of the inert gas atom levels (argon, xenon, krypton) using various models of influence factors.
If electronic processes are considered as an influence factor, then the calculated dependencies of electron concentration on the total number of nuclei correspond to the state of local thermodynamic equilibrium. Graphically, this dependence on a logarithmic scale is represented by straight lines. The populations of excited levels correspond to the Boltzmann distribution.
If photoprocesses are being regarded as an influence factor, then, a deviation from the rectilinear dependence of the electron concentration on the total number of nuclei is being observed in the area of low and high electron concentrations. However, the populations of excited levels still correspond to the Boltzmann distribution.
The dissociative recombination processes addition to the “influence factor” in the case of twotemperature plasma, when the electron temperature is much higher than the temperature of heavy particles, fundamentally changes the character of the diagrams. The article presents diagrams of the metastable states of heavy inert gases, which include a nontraditional hysteresis region. Without accounting for the dissociative recombination, the curves of the metastable state diagram degenerate into a typical dependence.
The metaequilibrium states diagram is useful for estimates in plasma spectroscopy, as well as for optical diagnostics of plasma flows. 
Gidaspov V. Y., Duong M. D. The effect of the properties of a real gas on solution of riemann problem in detonating gas. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/0b0/0fqod12fjlrd89o6u5izagvj1aus491f/Gidaspov_Zyong.pdf The article considers a selfsimilar Riemann problem on the border between multicomponent gases which properties are being described by a virial thermal equation of state with a singlefluid mixing model. A physicalandmathematical model, computational algorithms and numerical simulation results are presented. The computational model is implemented for the three cases, namely, the first one is “frozen”, i.e. physicochemical processes in gases do not originate, and the components concentrations do not change. The second one is “equilibrium”, which means that concentrations of chemical components satisfy the chemical equilibrium conditions. The third is a combined one, i.e. the of components concentrations to the left and right of the gap can be eother “frozen” or “equilibrium”. The solution of Riemann problem always includes a discontinuity separating the initial gas mixtures and, depending on the initial parameters, a fan of rarefaction waves or a shock wave propagating to the left and right of the discontinuity. In the case of an explosive mixture, a recompressed detonation wave or a ChapmanJouget detonation wave with a fan of rarefaction waves docked to it can propagate through it, while it is assumed that the composition of the combustion products is equilibrium.
A computational algorithm has been developed for solving the corresponding system of differentialalgebraic equations expressing the laws of conservation of mass, momentum and energy for the cases of continuous flows (fan of rarefaction waves) and discontinuous flows (shock and detonation waves), supplemented by thermal and caloric equations of state and, if necessary, thermodynamic equilibrium conditions.
Computational and theoretical studies of the decay of the gap at the boundary: argon – methaneair combustible mixture and helium – hydrogenair combustible mixture have been performed. The initial data ranges at which the results of calculations using the thermal equation of state of real and perfect gases differ significantly are determined. 
Privalov A. E. Unified software platform for develop of multiagent models of orbital spacecrafts constellation. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/24f/vj7ov1pokfmbq39vfyar57eivzt4h8bg/Privalov.pdf The article proposes a unified software platform designated for multiagent models developing of orbital spacecraft constellation with various target purpose. Mathematical model of the software platform was developed at a high abstraction level, ensuring a generalized description of orbital spacecraft constellation operation, regardless its target purpose and life cycle stage. Besides, the basic systems of coordinates, employed in the spacecraft ballistics, as well as function of transition between them were defined in the space of the model functioning. These specifics allow considering this mathematical model as a basis for the multiagent models of the orbital spacecraft constellations of various target purposes. The objectoriented model based on the mathematical model in the form classes diagram, ensuring the platform program realization, was developed in the UML language
The software platform has realized in the Python programming language in the form of two packages, containing a set of classes and methods for developing multiagent models of orbital spacecraft constellation with certain target purpose. Besides the program platform, such model should include the following modules: user classes library, which are the platform subsidiary classes, reflecting the target purpose of the spacecraft constellation; the experiment control subsystem, and information analysis and display subsystem.
The unified software platform may be implemented as a core for the multiagent models developing of orbital spacecraft constellations with various target purposes. A high abstraction level allows creating models with various degrees of detail, corresponding to the life cycle stage of the orbital spacecraft constellation, keeping herewith the unity of the model, methods and algorithms. 
Ezrokhi Y. A., Kalenskii S. M. The mathematical modelling methods for inflight definition of the degradation of the gas turbine engine components performance . Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/87d/1ek2olbzpycac8e97lnm5wlzbrqfo1hc/Ezrokhi_Kalenskiy.pdf During the operation of the aviation gas turbine engine (GTE) its component technical state worsens continuously. It leads to degradation of the GTE main parameters, first of all, the engine trust and the specific fuel consumption.
Therefore the problem of the diagnostics of the gas turbine engine and its components during their operation is very actually, and its decision makes it possible to define authentically enough "critical" degree of deterioration of GTE components when their repair or replacement is necessary.
This problem is especially claimed, if there is a possibility to carry out engine components diagnostics not only during special separate ground tests, but inflight operation in engine system.
The offered diagnostics way is based on an assumption that influence of efficiency change δη_{i} of each taken separately turbojet components on its trust are independent among themselves and has linear character.
In this case it is possible to present the relative change of the engine trust δR as the sum of products of relative deviations δη_{i} on the influence parameter В_{i} of the engine components efficiency on the trust change.
The numerical indicators of deterioration of separate engine components efficiency received according to a presented method can be used for the analysis of the reasons of engine trust loss during its operation and for to work out losses indemnification methods.
Also these methods can be used for definition of the engine components state necessary at transition to modern strategy of management by a GTE resource  operation according to a state.
The example of definition of the change of engine components efficiency for a two shaft turbofan engine with the typical level of parameters corresponding to 4 generation is considered. 
Morozov A. Y. Adaptive interpolation algorithm for solving problems of celestial mechanics with interval uncertainties. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/6b2/jof4ff2n3imnkjifm3xbsi8nqwqdy10o/Morozov.pdf The presented work performs the application of the previously developed adaptive interpolation algorithm to the problem of XF11 asteroid motion simulation with regard for the interval uncertainties in the asteroid position and velocity. The XF11asteroid motion around the Sun is being considered without accounting for the effect of the other planets. The original problem is formulated as a Cauchy problem for a system of ordinary differential equations (ODE) with interval initial conditions.
The essence of the adaptive interpolation algorithm consists in plotting for each time point piecewise polynomial function that interpolates the dependence of the solution to the problem on the point values of the interval parameters. An adaptive grid is being created over the region of the parameter uncertainty. Each node of the grid corresponds to the original problem solution with the parameters values determined by the node position in space. The grid adaptation is being performed depending on the interpolation error. In the places where the error is large, new nodes are being added, and in the places where the error is small, the grid is being rarefied.
The article presents the description of various existing methods and corresponding software libraries, such as AWA, COZYVI, RiOT, verifyode, for solving this class of problems. Employing the adaptive interpolation algorithm, the obtained interval system of ODEs is numerically integrated and compared with known results from the standpoint of the interval estimates accuracy and computational costs. Application of the fundamentally different approach to solving interval problems, allowed the adaptive interpolation algorithm obtaining solution boundaries with controlled accuracy. The algorithm is not subjected to the wrapping effect, and runs orders of magnitude faster than its analogs. 
Kondratieva L. A. Analytical approximation of inertial manifolds for the satellite motion model. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/5ce/8x6p1ue8sjj9iwlqpw7q11hd2l1odi7t/Kondrateva.pdf 
Zheleznyakov A. O., Sidorchuk V. P., Podrezov S. N. Simulation model of the system of maintenance and repair of electronic equipment. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/422/li8cthdqmaaou007siznige8w41m2i39/ZHeleznyakov_Sidorchuk_Podrezov_.pdf Simulation modeling is one of the most effective tools for studying complex systems today. Imitation is a kind of means of reproducing phenomena, just as a model is an abstract description of a system, object, phenomenon or process. That is, modeling is such an abstract form of reflection of reality, in which certain properties of the proposed objects are represented in the form of an image, a diagram, a plan, or a complex of equations, algorithms and programs. The use of simulation modeling in many fields of activity has a number of undeniable advantages. Firstly, it is an experimental method of cognition, which is a simple and visual tool for analysis. It helps to find optimal solutions to problems and gives a clear idea of complex systems. The advantages of this method are: simplicity, visibility, cheapness (compared to the experiment with recreating a real model), speed and convenience. The article provides a brief analysis of existing simulation models of complex systems in various environments. Due to the increased technical complexity of onboard equipment installed on aircraft, there is a problem in highquality and timely maintenance and repair, therefore, when organizing these types of activities, it is necessary to take into account a large number of factors that can affect the timing and quality of work. To solve these problems, on the basis of generalized statistical information about failures, the AnyLogic system has developed a simulation model of the process of organizing, functioning and repairing blocks with all the external and internal conditions affecting it, which allows making a rational decision about choosing a repair site, assessing the workload of specialists when performing various types of work, as well as forming requirements for the rational composition and quantity of spare parts of aircraft products required for operational restoration of operability. 
Dementiev A. N., Klyuev D. S., Novikov A. N., Mezhnov A. S., Peterskova Y. A., Zakharova E. V., Dementiev L. A. Мodel of the process of assessing the electromagnetic compatibility of the onboard equipment of the aircraft. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/693/38ik7upo5a6b6jq5o2gj6kpykyd6wnrp/Mezhnov_idr..pdf As of now, the problem solution on spacerocket technology (SRT) application is impossible without radioelectronic means (REM) employing. This fact leads to the radiofrequency space oversaturation with electromagnetic radiation in the whole frequency range. The main causes, requiring effectiveness enhancing of the frequency spectrum employing and providing the REM joint operation under conditions of restricted spacetime and frequency resources are:
 Expansion of the scope of the REM application for the SRT;
 Increase in their power and number;
 Sensitivity growth of radio receiving equipment;
 Impact of the great number of jamming sources on the REM
Problems of assessing electromagnetic environment (EME), and determining various electromagnetic compatibility (EMC) characteristics occur while the RST REM operation. Thus, the search for new ways of ensuring the REM joint functioning with the specified quality under conditions of limited frequency, time and territorial resources is uptodate.
The EMC tasks consist in the following:
– establishing regularities for the optimal application of the radio frequency fields being created for information transmitting and/or receiving or extracting;
 establishing regularities of undesirable interaction of simultaneously functioning REM;
 identifying the ways and developing criteria and methods for the radio frequency space maximum application efficiency and capacity, including operationaltechnical characteristics of the REM, affecting the REM EMC;
 synthesizing the REM with the specified characteristics of the radio frequency spectrum (RFS) application, i.e. the characteristics, which include accounting for both outofband and stray radiation, and side reception channels.
With the scores of the onboard equipment with various characteristics and widely ramified onboard cable network (OCN) on the SRO, solution of the above said tasks relative to their interaction is of utter importance while the SRO development and manufacturing.
This will allow:
 analyzing the EME onboard the RST objects;
 evaluating the EME level with account for the frequency and spatial separation of the onboard equipment and OCN;
 determining the ways to EMC ensuring of the OE and OCN under specific operating conditions;
 simulating the processes of the electronic equipment functioning under complex EME.
This set of techniques and algorithms novelty consists in solving partial problems with the subsequent comparison of the obtained total values of the electric field strength at the specified points of the RST object, and the voltage induced on the OCN cables with the specified requirements, according to the developed techniques. 
Azarov A. v., Karavaev M. N., Rozhkov S. S., Slavyansky A. O., Smolka K. A. Synthesis of the aircraftbased phase direction finder. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/71a/vr3gb24k025qhyhonjf69h07l3meixxe/Azarov_Karavaev_Rozhkov_Slavyanskiy_Smolka.pdf The aim of the work is to create a smallsized passive radar complex for placement on an unmanned aerial vehicle.
The principles of construction of a radio direction finder operating in the range from 1 to 18 GHz, limited on weight and size characteristics, are considered. A direction finder with a different number of antennas (from three to five) was simulated.
An antenna system is proposed that provides a high probability of obtaining an azimuth to a radio source with an accuracy of up to one degree in the viewing area up to 180 degrees with elements representing a combined spiral antenna consisting of printed, hemispherical and cylindrical spiral antennas using plates of radioabsorbing material. Laboratory models of antennas were created and measured. A comparative analysis of the characteristics of the mathematical model and the antenna layout created by 3D printing was carried out, according to the results of which it should be noted the high efficiency of the manufacturing method used due to the high repeatability of the results, low cost and high speed of sample production.
When placing a passive radar complex on a UAV, it is possible to determine not only the direction to the radiation source – its angular, but also geographical coordinates, and hence the range to the source of signal. The calculation of several bearings on the source of signal from different points of the UAV trajectory spaced in the plane allows us to solve the problem of locating it using the maximum likelihood method based on a set of measurements of bearings on the source and UAV motion parameters (angle measurements and altimeter information). 
Muratchaev S. S., Volkov A. S., Margaryan R. A., Bakhtin A. A. Development of an adaptive version of the OLSRV2 routing protocol in MANET networks. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/4b5/mhsf3ep1mawhwlu0102qfd1afh7sksht/Muratchaev_Volkov_Margaryan_Bakhtin_.pdf In this section, the results of simulation modeling of a MANET network based on the OLSR routing protocol were demonstrated. Two versions were taken: the standard OLSR routing protocol and the energy efficient OLSRv2 routing protocol, as well as the reactive AODV routing protocol. The developed algorithm for selecting routing protocols based on channel metrics was also implemented in the NS3 simulation environment. Simulation was carried out for various speed parameters, as well as for various network density parameters. When developing the algorithm for selecting routing protocols, the standard formats of broadcast data packets were changed to be integrated into the overall structure, since the algorithm involves switching between routing protocols based on the current network metric.
First of all, to test the operation of the energyefficient algorithm in the model, a comparison was made of the residual energy parameters in the network models. Thanks to the energyefficient algorithm, the developed network model with an energyefficient protocol saves more residual energy than a model with a standard routing protocol.
The simulation results are presented in the form of diagrams demonstrating the effectiveness of the modified protocol over the standard one in terms of network lifetime and packet delivery rate, as well as average delay. In a scenario with low node mobility, there is a 7% increase in the parameter compared to the standard routing protocol. When analyzing the results of simulation modeling, scenarios were identified in which the developed algorithm outperformed classical routing protocols in terms of average delay and data packet delivery rate. Also, a drawback was identified associated with a large number of added metrics, which leads to an increase in the number of generated service messages in the network. However, due to the stability of the protocol and its efficiency in various simulation scenarios, these shortcomings are compensated by parameters based on the residual energy in the nodes. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Antonova V. A. Analysis of hazardous events and vulnerabilities of 5G transport communication networks. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/098/w3e32b7y8qst7kblmol09ls3bo6w0cnk/Buzhinidr.pdf Being compared to the 3G and 4G, the 5G network offers significant increase in datatransmission rate, delay reduction and highreliability connection. These advantages will allow organizations to operate more effectively, as well as render services quicker, enhancing their quality. Data throughput of the fifthgeneration networks is higher, thus, connection of comparatively greater number of users and devices is possible.
The most serious safety hazards facing consumers and enterprises in the 5G networks are as follows:
1. Significantly larger surface of attack.
2. Severe aftermath caused by cyberattacks.
3. A potential for more aggressive spying.
4. Subscribers' activity monitoring attacks.
5. Dangerous DDoS attacks.
Let us consider the 5G/SDN/NFV possible vulnerabilities classification. Vulnerabilities occurring due to the insufficient organization of information technical protecting from the unauthorized access and technical channels of information leakage are beyond the scope of the system under consideration. In general, the SDN/NFV security ensuring issues are considered in [1, 2, 3, 4, 5, 6]. They are:
• Software vulnerabilities.
• Vulnerabilities caused by the presence of a softwarehardware bug in the 5G/SDN/NFV equipment [7].
• Vulnerabilities of network interaction protocols implementation and data transfer channels (IP, OpenFlow, etc.) [7].
• Vulnerabilities of the information security tools (the ones in the form of PNF, VNF), software and hardware.
Let us adduce a possible information security threats (IST) classification [7]:
• The IST by the information type being processed in the system:
– voice information;
– information processed by technical means of information processing;
• The IST by type of possible sources:
– an external intruder;
– an internal intruder;
– malware;
– a hardware bug (embedded or standalone) (not considered in this model).
• The IST by type of the information security property that is violated:
– information confidentiality (leakage, interception, capture, copying, theft, provisioning, distribution);
– information integrity (loss, theft, destruction, unauthorized changes);
– information availability (blocking);
– accountability of processes;
– repudiation of information or actions.
• The IST by the system type: since the 5G/SDN/NFV refers to the class of distributed 5G/ SDN/ NFV connected to the international information exchange network, threats specific to this type of system are considered.
• The IST by type of implementation:
– implemented through special impacts (of mechanical, chemical, acoustic, biological, radiation, thermal, electromagnetic nature) (not considered in this model);
– implemented through leakages from technical channels (not covered in this model);
– implemented through unauthorized access to the 5G/SDN/NFV;
• IST by type of the vulnerability utilized:
– related to the use of software vulnerabilities (hypervisors, virtual features);
– associated with application vulnerabilities;
– implemented through hardware bugs (not covered in this model);
– related to vulnerabilities in network protocols and communication channels (IP, Openflow);
– the ones the implementation of which is possible due to the vulnerabilities related to the gaps in the technical protection of information from unauthorized access (not covered in this model);
– implemented through vulnerabilities associated with the technical channels of information leakage (not considered in this model) [10];
– related to the vulnerabilities of information security tools;
– manmade threats.
• IST by type of the object being affected:
– information processed at the automated workstations of the system administrator and user;
– information processed in peripheral processing equipment (printers, plotters, remote monitors, video projectors, sound reproduction equipment, etc.) (not covered in this model);
– information transmitted through communications channels (while transmitted, while processed);
– information processed within the 5G/SDN/NFV virtual infrastructure and that includes storage;
– applications;
– software providing the 5G/SDN/NFV operation (SDN/NFV units, virtualization tools).
Considering the possible consequences of the IST implementation, we should focus on violating the key properties of information to ensure its security: confidentiality, integrity, availability, accountability, nonrepudiation. 
Podstrigaev A. S., Smolyakov A. V. Experimental investigation of the multisignal timefrequency parameters estimation accuracy in the digital receiver with subnyquist sampling. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/3f4/q5om5j3s7xi8eiv9vzfpd9bizaza9yp7/Podstrigaev_Smolyakov_.pdf The modern cognitive radio systems and the spectrum monitoring devices used in spectrum management have to perform wideband signal analysis. One of the ways to achieve a wide instantaneous analysis band is to use a multichannel subNyquist receiver. Such a device receives signals from the many Nyquist zones and analyzes their aliases in the first zone. By aggregating information from the several independent channels having different sampling frequencies, it can disambiguate frequency measurements. However, due to such a receiver’s extensive analysis band (up to several dozen gigahertz), time overlaps of the input pulses become inevitable and regular events. Therefore, investigating timefrequency parameters estimation accuracy in the subNyquist receiver processing multisignal input gains great importance. The particular interest arouses the case in which the input signals are in distant Nyquist zones.
To perform the described investigation, we developed and built a subNyquist receiver prototype. As a source of the input for the prototype, we used two microwave signal generators connected to the prototype through the microstrip power combiner during the experiment. The first generator formed a pulsed signal and swept its carrier frequency, and the second generated a continuous unmodulated signal with a fixed frequency. We chose the frequencies of these two signals, so they were several Nyquist zones far from each other, but their aliases in the first zone were close.
The experiment showed in the example of 1 microsecond wide pulses that the frequency estimation accuracy remains almost the same in the cases of onesignal and multisignal input. However, the pulse width estimation error grows significantly for the multisignal input due to the receiver mixingup signals having close aliased frequencies. At the same time, the effect disappears entirely if the signals’ aliases are 20 MHz or farther from each other.
Nevertheless, we consider the errors estimations and the receiver’s frequency resolution obtained using the prototype enough for the vast majority of the wideband analysis tasks. Moreover, further errors reduction is possible through a runtime changing of the sampling frequencies and the fast Fourier transform width, and through the SDR techniques. Such techniques may include postprocessing based on signal accumulation, softwaredefined processing methods, and tunable bandstop filters at the receiver input suppressing the powerful interfering signals.
It is also worth noticing that most of the described in the paper effects related to the processing of the multisignal input do not result from any inherent properties of the subNyquist receiver. One can equally observe the same effects in the receivers with narrowband signal processing. 
Belskiy A. B. Requirements for onboard opticalelectronic means of aerial reconnaissance of aircraft. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/cae/8n21z2sfubt2u2yteesv1w5ggx2wv3mm/Belskiy.pdf The need for roundtheclock, allweather and safe execution of combat and special missions by military aircraft, ensuring full situational awareness of the crew of the aircraft in the cockpit and the background situation under conditions of enemy information countermeasures impose increased requirements on airborne reconnaissance assets, namely on the functional characteristics of airborne monitoring, detection and recognition of targets, as well as determination of their coordinates and target designation
Airborne reconnaissance (monitoring) is carried out by special airborne technical means of reconnaissance of the aircraft, providing acquisition, registration, indication, processing and transfer of necessary data on objects and target environment.
Technical reconnaissance facilities include radar, radiotechnical, and optoelectronic systems operating in various spectral wavelength ranges, independently or together in various combinations.
Opticalelectronic systems are the most effective means for solving air reconnaissance tasks and obtaining information about the location and types of enemy objects due to their passive operation mode and high level of image resolution of targets (objects), including in complex backgroundtarget and operationaltactical environments.
The article discusses and analyzes the features of creating onboard optoelectronic systems to expand the capabilities of onboard optoelectronic systems for conducting aerial reconnaissance: building a system based on functionallyconstructive unified subsystems and modules; multichannel; using a hyperspectral channel for detecting, recognizing hidden, disguised objects; intellectualization of functioning; integration of individual subsystems and channels; automation of the processes of mutual alignment of channels, builtin monitoring and troubleshooting; automatic tracking of areal, point objects, with the allocation and further tracking of several targets; stabilization of the line of sight; interfacing with sensors for obtaining heterogeneous information; application of digital information processing methods; generation of output data from various sensors for processing and solving recognition problems; ensuring group interaction as part of the various control circuits. 
Sokolov D. Y. Application of artificial neural network for solving problems of forecasting the movement of ground objects. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/e62/2chl4obmsyjx7blm5q1yv2u74u2n1kr2/Sokolov.pdf The article deals with considering the artificial neural network application for solving the problems of the groundbased object motion predicting. It proposes a new approach to the neural network architecture elaboration and applying its training techniques as applied to the specifics of the problem of motion trajectory prediction in the space of parameters. Estimation of various training techniques is given, and optimal parameters of coefficients, employed in the neural network training algorithms are determined.
The task of the groundbased objects motion predicting is uptodate as applied to both combat helicopters actions, in the case of their aiming at a moving maneuvering target, and civil aviation, including unmanned aircraft, when it is necessary to track various ground objects.
Application of the known types of neural networks for solving the problem of the motion predicting of a ground object (as an image of the object trajectory en masse) does not account for the sequence of passing the trajectory points by the object, which is an important information for solving the problem of the object motion predicting. Additional data processing and mathematical transforms allow solving the problem of accounting for the information on the sequence of passing points. However, this increases the overall complexity of calculations and may level the effectiveness of NN application for solving the forecasting problem.
The article proposes a certain architecture for a neural network building, in which each neuron corresponds to a separate point or region of space where the movement of an object being performed. This architecture assumes elaboration of a recurrent neural network, which imposes certain specifics on the training process and subsequent application of the neural network. Thus, the training process of a recurrent neural network should be iterative until a certain minimum of the objective function is reached.
The article discusses various ways of a neural network training and determines the most suitable ones from the standpoint of minimizing the errors and duration of the training cycles.
This article considers the movement in two coordinates (on a plane). However, in the general case, the space of parameters, in which the movement occurs, may contain greater number of coordinates (hyperplane). Both training and application of predictive neural network for the motion prediction in the space of parameters with any number of coordinates will be realized by the technique similar to the one for the motion on the plane.
In the prospect, the proposed version of a neural network building may be applied to predict the movement of various objects, including the abstract ones in a multidimensional hyperspace of their parameters. 
Anan’ev A. V., Ivannikov K. S., Kazhanov A. P. Model of the aviation target destruction process based on nonstationary markov random processes. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/f4f/z0743giev0mdzpercrtj843mg2drzv3g/Ananev_Ivannikov_Kazhanov.pdf The analysis of existing approaches to the assessing effectiveness of the aviation destructive means application is carried out in the article. It was shown that during the assessing effectiveness required release determination can be carried out both without and with taking into account the means of enemy air defense, which is substantiated in general. At the same time, the attention is focused on the fact that in case of the probability approach employment in different calculations, the probability in models of aviation destructive means application is assumed to be constant in many sources. The current state of affairs is inconsistent, because as the air strikes are delivered, the error correction is done by the aviation complex crews on the one hand, and the opposing side increases the counteraction by air defense and electronic warfare application, or by withdrawal of the forces and equipment from the attack.
The application of a mathematical model based on nonstationary Markov random processes is proposed with the aim of efficient combat aviation application and taking into account the alterations in the defeat probability assessment. Considering the alteration probability in air strikes cycles in this case consists in its representation as a variable quantity depending on time, which is the main difference between the proposed model and known approaches.
In this article a new approach to the effectiveness assessment of the aviation destructive means application is proposed. That approach takes into consideration alternating the probability of different ground (sea) objects destruction during air strikes cycles. Based on calculations of the obtained differential equations employing numerical methods the comparative analysis of the results acquired by using the known techniques and the new approach proposed was carried out. The account of the alteration probability is carried out by introducing a time dependence of probability, which allows determining required release of aviation destructive means, according to the alternating from cycle to cycle combat application conditions. The proposed mathematical models of the aviation target destruction process based on nonstationary Markov random processes, have significant universality and can be extended to a wide range of tasks. 
Kurennykh A. E. Software development for the integration of decision support models. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/42e/12bnk8wzdh5ayu18pc4tn9znej0f7p9h/Kurennykh_.pdf The article deals with the issues of decision support and development of recommendations using computer modeling and methods for increasing the consistency of judgments, as well as issues of integration between information systems. The method for using sets of parameters and results of computer modelling in the process of multicriteria evaluation of alternatives is proposed and formalized. This paper regards a possible solution to the problem of usage of simulation models in the process of decisionmaking support carried out with enterprises information systems. The integration of simulation models and models of decision support is settheoretically formalized. Developed software form a separate module in the decision support system that makes it possible to rank alternatives submitted by simulation models. Designed architecture allows applying this approach for variable scientific and technical civil and military problems due to its universality.
In addition, in this paper the author formalized and developed mathematical and software to improve the consistency of judgments on the example of the method of paired comparisons, providing a sketch for an effective method to increase the consistency of judgments in a pairwise comparison matrix. Initially, there were identified criteria that are of great importance for experts who make judgments and then proposed a multicriteria optimization task and a way to solve it. Basically, the method is based on wellknown properties of matrixes containing paired comparisons marks, such as transitivity of judgments or consistency index for example. The use of both methods: integration of computer models and judgments consistency allows carrying out multicriteria analysis effectively with high precision. 
Knyazev A. S., Antonenko A. S., Arbuzov E. D., Chebotaryov A. D. The use of a multifunctional aircraft indicator simulator in the educational process of the university. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/6f3/z1kymam3ikxw7m5zfjwwxnp1vfst5hl3/Knyazev_idr..pdf The experience of education program mastering by the students of aviation universities reveals that constant contact, physical or visual, with aviation engineering is necessary for apprehending the operation principles of the aircraft aggregates and systems. In some cases, training becomes extremely difficult or ineffective until the aggregates and systems being described are shown in operation, in progress. The educational material presentation employing posters or slides with diagrams, graphs and static images does not allow the students to form an understanding and perception of the material being presented to the full.
The cockpits of modern aircraft are equipped with multifunctional indicators (MFI), through which the crew interacts with the onboard complex. Working with the MFI prior to the flight allows making a flight route, enter the targets coordinates, landmarks, and radio beacons. Application of the MFI in flight allows the crew to solve the tasks of piloting, navigation and combat employment, providing the necessary information for this. In this regard, it is necessary to pay more attention to learning how to work with multifunctional indicators when mastering modern types of aircraft.
The best way to learn is training on real technical facilities. An alternative option consists in employing aviation simulators. However, they are rather expensive and require qualified maintenance. Besides, their placement requires a separate area in specially equipped premises with electric power and/or hydraulic power installations, as well as other necessary equipment.
The article considers the issue of obviousness and effectiveness increase of cadetpilots training by employing separate cockpit element simulator in the educational process, namely multifunctional indicator, which allows cadets to choose necessary practical skills for working with the onboard equipment complex.
To introduce the MFI simulator into the educational process, information frames of the central information system (CIS) of the DA42T aircraft were reproduced. The content of the developed CIS frames on the MFI simulator reproduces completely the indication in the DA42T aircraft, contributing to the training quality improving and developing practical skills for working with CIS through the MFI in a real object (DA42T aircraft). The obtained results of the work can be employed further to develop simulators of multifunctional indicators for other aircraft types. 
Lukin V. N., Chechikov Y. B., Sekretarev V. E., Dzyubenko A. L., Altukhova N. F. Problems of maintenance of software and hardware systems. Trudy MAI, 2022, no 123, http://mai.ru//upload/iblock/a30/gueh38grzh1o8n2tsqtooisgvo5ur104/Lukin_CHechikovDzyubenko_idr.pdf This article discusses the problems associated with the complexity of maintenance of hardware and software systems in conditions of lack of time, expansion of the complex and updating of the element base. The purpose of this work is to reduce the complexity of the development and maintenance of the software complex, increase the reliability of programming. The objective of the research is to substantiate the approach to the construction of software and hardware systems in the paradigm of objectoriented programming, as well as its application to the construction of systems of various levels of complexity. This article analyzes external and internal problems affecting the life cycle of hardware and software systems for various subject areas. An approach to solving problems is a technology based on an objectoriented paradigm that includes the concepts of interfaces, abstract base classes, vertical and fan inheritance, virtual functions, polymorphism. Objectoriented programming technologies ensure the simultaneous functioning of existing and newly appeared devices without rewriting the system. A variant of the RT adaptive OS for connecting onboard equipment is proposed, which significantly reduces the development time of serial and individual products and increases their reliability. An example of the possible application of the proposed methodology in the field of automation of laboratory research in medicine is given and it is shown how, with a wide variety of autoanalyzer fleet, common architectural solutions make it possible to develop a basic laboratory model with the possibility of detailing for each device. The novelty is the use of an objectoriented approach in the development of a realtime operating system (RTOS), which reduces the time and complexity of developing serial and individual products. 
Titov K. D. Principles for constructing an ultrawideband communication channel on an unmanned aerial vehicle of a lightweight helicopter type. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/435/u66pivqswou69ugib3fujz1hg8y7nooi/Titov_.pdf The article describes the relevance and state of development of an unmanned aerial vehicle of a lightweight helicopter type of the homeproduced “Grach” series. By reference to application specifics of the unmanned helicopter with a wide range radio reconnaissance station as a objective load application, the requirements imposed to the control and data transmission system place on it were formulated. The compliance of the installed system with the requirements is analyzed, and technical, economic and operational advantages of the communication systems based on ultrawideband signals are demonstrated. Based on the earlier studies, devoted to the issues of creating a lightweight helicopter type unmanned aerial vehicle, as well as generating, processing and studying ultrawideband signals, specifics and principles of a ultrawide band communication channel design, which determine technical appearance of control, data transmission and local radio navigation system being installed on the aerial vehicle were formulated. Technical characteristics of the control and data transmission system, associated with pulses generation and processing; the signals radiation, and noise immunity assessment of antennae systems; frequency range selection, signal width and type; the issues of the system placing on the flying vehicle, as well as assessing the possibility of local navigation system integration into the communication system were analyzed and proved. Inferences were drawn on the substantiated technical characteristics impact on the tactical characteristics such as communication range, flight time, takeoff mass etc. 
Maklashov V. A., Piganov M. N. Algorithm for determining the bias of coordinate estimates. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/0fd/lzv9o754ky4fvlaijmlsbdsjux06e6j3/Maklashov_Piganov..pdf The article deals with the methodology for determining the radio emission source location in the tasks of electronic reconnaissance. To determine the radio emission source location, the azimuth direction finding from the aircraft is employed. It is noted that the previously proposed model allows determining the source location, however, it requires the zones of uncertainty calculating. The article shows that the need to calculate the uncertainty zones is associated with the fact that the error ellipse, calculated during models operation, requires an unbiased estimate of the source coordinates. The unbiased estimation obtaining while triangulation is possible only in symmetrical geometries, when the triangle formed while position determining is close to the equilateral one. In all other cases an estimation bias (the mean coordinates estimation value deflection from its true one) is being observed. As far as it is necessary to have bounded area of the most probable location of the radio emission source, the problem of this area plotting comes into being. The authors developed an algorithm for determining the radio emission source coordinates estimation bias relative to their true values for the uncertainty zones computing while using triangulation method for its location detection. Modeling of the radio emission source location determining process was performed. It was suggested to employ the basic TargetLocation algorithm to obtain the output data. It realizes the triangulation method. With this, three steps should be performed. These are triangulation base size computing; determining angles of the triangle; computing the source relative distances from the bearing points; determining the target coordinates. Basic simulation stages were performed in MATLAB. The following procedures were executed herewith: computing correlation coefficient and mean square deviation of the target coordinates; computing semiaxes of errors ellipse and angles between the X axis and the main ellipse axis; correcting the errors ellipse sizes. Analysis of the simulation results was performed, which revealed that the method consisting in measurements sorting out and ellipse sizes correction by the bias value yields the uncertainty zone encompassing true position of the radio emission source. The authors established that the presented method allows increasing the location determining accuracy. The bias value largely depends on the tactical situation geometry. Thus, in practice, it is necessary to know either analytical dependence of this bias on the geometry and measurement errors, or possess the table of these values. To obtain the above said dependencies, a large series of experiments conducting is required. 
Bannikov A. V., Litovka Y. V. Computational and logical intelligent control system for a multicathode galvanic bath. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/743/bfe5yj2bdnhblt701n0v794zrxcdst2k/Bannikov_Litovka.pdf The most important electroplating quality indicator is the uniform distribution of the applied metal thickness the on the part surface. It is advisable to process smallsize parts conjointly, since largevolume electroplating baths are being used as usual in industrial conditions. Accordingly, it is unprofitable to process one part in one operation cycle of the electroplating bath. Given that the shapes of the parts being processes may differ and the number of parts may vary, this or that parts’ placing on the special suspending device may lead to various values of the total unevenness. Besides, the ineffectual placing may cause significant metal losses and excess electric energy consumption. Accordingly, the task of such multicathode system optimal control comes into being.
The article considers a computationaland logical intelligent system for controlling electroplating applying on the multiplicity of the partscathodes. The computationaland logical intelligent optimal control system solves the problem of searching for the optimal placing of several cathodes of various shapes and weights in an electroplating bath to obtain coatings with minimal unevenness.
To solve the set problem, the developed system employs the full search method, modified Gomori algorithm and the branches and boundaries method. The initial data for one of the three methods selecting is the number and shape of the parts to be electroplated. Afterwards, employing both database and knowledge base, the best method for the problem solving being defined, and the problem solution of optimal partscathodes placing on the suspension from the viewpoint of the unevenness criterion is being solved. At each stage, the technologist has the ability to control the process of the task solving and result correcting.
As the result of the optimal control system application in electroplating production, the total unevenness of the galvanic coating on the surface of many simultaneously processed parts decreases; the parts processing speed increases; the number of defects in the production process decreases, and the load on the electroplating line operator decreases. It is worth noting as well the electrical energy consumption reduction by the galvanic line when implementing a computationalandlogical intelligent system for optimal control of the galvanic coating applying process employing a variety of partscathode of various shapes and sizes. The proposed Gomori method modification increases the control system efficiency and reduces the amount of time required to calculate the optimal parts placing on the suspension. 
Sofin A. P., Fedorova L. A., Sudar Y. M. On the issue of the use of amorphous devices. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/154/aev9lucnb5z0xry3t7u73cl9dwemlmch/Sofin_Fedorova_Sudar.pdf Amoeboid movement application in robotic and transport devices is associated with partial repetition of movements existing in nature. Design of prospective devices with amoeboid thrusters will require the research based on the dynamic computations of the object. Mathematical model forming therewith depends directly on the device structure and established option of its movement. The main tasks needed to be solved while such kind of propulsor design are set. A cylindrical body rolling along a rough plane was selected as the object. The external forces applied to the cylinder are being reduced to the resultant vector, which, together with the point of contact, determines the plane of motion position. The device body contacts with the rough surface via the protruding pseudopods. Its orientation in space may be altered by the liquid volumes moving inside the rigid hull, which allows changing position of the point of contact with the surface and the resultant vector of external forces.
The device movement in one of the planes is being considered in the course of dynamic computation. With this, the limit values of the force under which contact of the cylindrical body rolling both without and with sliding is being exercised, are being determined. The other problem being solved is associated with determining characteristics of movement of mass center of the hull and its rotation relative to the axis passing through the center of mass center.
The numerical study results reveal the presence of characteristic sections of motion determined by the selected parameters of the problem. The performed computations accuracy corresponds to the model being used.
The complex of kinematic indicators should ensure the forming of requirements for the control laws for the device being developed. Devices with amoeboid propulsors may be considered as bodies with a movable internal mass.
In the prospect, amoeboid propulsors may prove to be more efficient means of motion and transportation compared to the conventional wheeled and rotary mechanisms. The extremely low impact on the environmental objects associated with low ground pressure and trifling atmospheric emission should be considered the most important advantage of the amoeboid aggregates application.
A detailed study of the implementation options for each method of movement points at the significant number of their variety, and they are fully dependent on the concrete conditions and functions being realized. Along with the typical ones, the presence of the variety of transitional and combined forms of movement should be accounted for. Modern literature analysis allows soundly consider that the next stage of the studies development related to the amoeboid devices creation seems to be application of a device with basic hull shape in the form of a sphere. 
Aslanov V. S., Neryadovskaya D. V. A tether system at the L1, L2 collinear libration points of the marsphobos system. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/e1e/t5dndsqn4g9uq84h2ia0uu7zexum4m7t/Aslanov_Neryadovskaya_.pdf The article considers one of the L_{1} or L_{2} collinear libration points application for a tether system deployment in the direction of Phobos in a plane circular restricted threebody problem in the MarsPhobos system. An orbital spacecraft by which one of the tether ends is being fixed is located in L_{1} or L_{2} collinear libration points and is being held in one of these unstable points by the low thrust of its engines. The equation of the tether system motion in the polar coordinates system was obtained for the tether of constant length, the equilibrium positions were found, and the dependence of the vibrations period on the tether length was determined. Comparison of approximate solution for the small angles of the tether deviation from the local vertical with the numerical one was performed. The article demonstrates that the system “fixed” either in both the L_{1} point and L_{2} has potential wells in cases when the tether is being directed towards the Phobos side. It was revealed that the dependencies of the vibrations period on the tether length for the L_{1} and L_{2} points were fundamentally different. Comparison for both L_{1} and L_{2} of approximate and numerical solutions revealed herewith that the vibrations amplitude remained constant in contrast to the frequency. The results of this study may be employed for the future space missions provision. Thus, for example, a space lift may be arranged in the MarsPhobos system, which tether will pass through the L_{1} or L_{2} libraion point. Besides, such lift may serve as an intermediate station for conducting studies associated with the space exploration around it, as well as a platform for the interplanetary flights. “Fixing” the tether system in the L_{1} or L_{2}collinear libration point of the MarsPhobos system will allow conducting remote studies of Phobos employing a vehicle with sensors, which will hover above its surface. 
Popov I. P. Types of mechanical power for harmonic vibrations. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/4df/8w3ohdn5iv14zz66644rgwn50tzjapbd/Popov.pdf The purpose of the study consists in detailing the types of mechanical power while harmonic oscillations. Due to the irreversibility of thermal energy, its derivative takes only positive values. With this, derivatives can be taken of both potential and kinetic energy. Harmonic oscillations herewith at which the derivatives (instantaneous powers) are necessarily signchanging functions, which fundamentally distinguishes them from thermal power, deliver the most interesting case. The inductance coil magnetic field energy is the kinetic energy analog in electrical engineering, the capacitor electric field is the potential energy analog, and thermal energy dissipated by the resistor is the mechanical energy analog. The article shows that at mechanical vibrations not only signpositive thermal power develops but the signvariable reactive powers as well, which characterize the potential and kinetic energies reversibility. The active power is understood as the average value of instantaneous power over half a period, and reactive power is its amplitude value. The total mechanical power, on the one hand, is being described by the Pythagorean formula, and on the other hand, it is equal to the product of the rms values of the harmonic quantities. A feature of the complex representation consists in the fact that while the total power calculating, one of the multiplied vectors should be conjugate. The concept of mechanical reactive, active and apparent powers is a generalization of the corresponding concepts from electrical engineering, which is a manifestation of electromechanical dualism. 
Egorov I. A. Consideration of plastic deformations in the design of wafertype compartments. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/8b3/yfxpui892xs1xgf3ygukuy8cgz5bb06j/Egorov.pdf 
Dobryshkin A. Y., Zhuravleva E. V., Sysoev E. O., Sysoev O. E. Vibrations of composite thinwalled cylindrical open shells. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/8e3/dp4sw01b4yumhu99w0exnqpeepjhaexw/Dobryshkin_ZHuravleva_Sysoev_Sysoev.pdf Structures with thinwalled open shells bear an optimal ratio of the internal volume to the area of the enclosing surface. Such shells application therewith has disadvantages, namely, they are very sensitive to the forced vibrations originating from the external forces, such as wind and snow loads, equipment operation, etc. The article shows the necessity to shell structures calculating on dynamic processes caused by the forced vibrations impact. A model for the circular vibration frequency computing of a thinwalled cylindrical composite open shell with hinged support was obtained. A numerical experiment was conducted to compare the results and determine the error between the obtained computational model and the proven computer aided calculation performed with the LiraCAD program. The effect of the number of longitudinal halfwaves on the circular vibration frequency of the composite open shell was determined. The numerical characteristics of the vibration frequency of thinwalled shells may as well change due to the extra inclusions on the shells, such as an orifice, reinforcing rib, an attached plate, etc. Experimental data testify that these changes are of nonproportional character, which does not correspond to the generally known results of theoretical studies. Thus, the structures analysis on the dynamic vibrations requires refined mathematical models development. The authors propose a new approach to the finitedimensional model creation – a form of solving the problems of vibrations of a shell, carrying a small attached mass. The mathematical model refinement led to better quantitative and qualitative results compared to the known analytical solutions. In their earlier works, the authors analytically and numerically showed that the frequency reducing effect does not depend only on the magnitude of the shape initial irregularities, as is commonly believed at present, but on the geometric and wave parameters of the shell as well. The proposed approach is generalized for the case of vibrations of shells of finite length.

Potanin D. V., Samokhin P. A., Zelenyi A. E., Yakovlev I. M., Samokhina E. A. Computer modelling of shock impacts influencing on flight consoles considering nonlinear properties of materials. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/290/61hrnb39zklf861qi2783gyijpnwzkng/Potanin_Samokhin_Zelenyyidr._.pdf The prediction of strength characteristics of flight elements at the initial stage of design is important for constructions subject in use to shock influences. This paper investigates dynamic loads and strength characteristics of flight control console at disclosure and latching of a console. These loads arise on the initial site of flight because of blow about an emphasis. Calculation is made in dynamic module finite element software based on the explicit method of integration of movement differential equations. Suggest calculation model considers friction between components. Friction is set between between plugs and an axis, between an emphasis and the console, and also between a stopper and the console. Elastoplastic properties of materials the most subject to deformation of assembly details are simulated with use of the diagram of plasticity. As a result of the simulation, the reaction forces between the most loaded parts of the assembly, the maximum flight console scope and fluctuations are defined. The period and amplitude of cross fluctuations of the console and longitudinal fluctuations of a compartment mean fluctuations. The stressstrain state of a console as a part of a flight compartment is investigated in the conditions of shortterm shock loading. Verification of calculation is carried out by means of comparison of modeling results with the values received at a natural experiment on disclosure of consoles by the pyrotechnic mechanism. The relative deformations of the emphasis and the compartment upon impact were measured by strain gauges. To register the rotation of the console, a video was taken. Good convergence of calculation results with a natural experiment is shown. Values received by a numerical method of calculation differ from results of an experiment less than for 8%. 
Khatuntseva O. N. Finding a generalized analytical solution to the plane Couetta problem for a turbulent flow regime. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/515/x9824fr64dhp66z7xu4ftnue4y8j0hkv/KHatuntseva_.pdf Despite the fact that random processes are ubiquitous, doubts remain as to how random they are, and whether this randomness is seeming, based only on the limitations of our knowledge.
If the uncertainty of the processes occurring at the quantum level is already largely beyond doubt, the stochasticity of macroprocesses, and turbulence in particular, is still a subject of scientific discussion, if only because they are described by deterministic equations.
The article shows that the NavierStokes equations used to describe hydrodynamic flows lose their deterministic properties when they are integrated by computational methods. This can explain the rather successful application of these equations in solving many practical hydrodynamic problems in the implementation of turbulent flow regimes. However, this approach to describing turbulent flows can be correlated rather with analog modeling of turbulence.
In order to describe both laminar and turbulent flow regimes in a controlled manner, the author proposes to consider the NavierStokes equations in the phase space expanded by introducing an additional variable characterizing the entropy production. For laminar flow regimes, the entropy production takes on a zero value, the additional term disappears, and the transition to the NavierStokes equations in their standard form is being realized.
The article considers the issues of the possibility of emergence and maintenance of nondeterministic, i.e. stochastic processes in a liquid due to the existence of incompatible between each other boundary conditions, as well as the ways of describing them relating to the turbulent flow. It is shown that the velocity profile of a turbulent flow can be described as a generalized solution of the problem, which is the sum of the two terms, each of which is the product of two functions: one of which determines one of the asymptotes of the solution, while the second one determines the degree of influence of this asymptote on the general solution in each point of the area of interest.
The plane Couette flow problem was solved by dint of this approach. Good agreement of the results with experimental data is demonstrated. 
Baklanov A. V. The effect of the annular diffuser design on pressure loss. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/1a1/djy9tid1arhxred15jf3x0zo0qvg5ily/Baklanov.pdf Despite the fact that random processes are ubiquitous, doubts remain as to how random they are, and whether this randomness is seeming, based only on the limitations of our knowledge.
If the uncertainty of the processes occurring at the quantum level is already largely beyond doubt, the stochasticity of macroprocesses, and turbulence in particular, is still a subject of scientific discussion, if only because they are described by deterministic equations.
The article shows that the NavierStokes equations used to describe hydrodynamic flows lose their deterministic properties when they are integrated by computational methods. This can explain the rather successful application of these equations in solving many practical hydrodynamic problems in the implementation of turbulent flow regimes. However, this approach to describing turbulent flows can be correlated rather with analog modeling of turbulence.
In order to describe both laminar and turbulent flow regimes in a controlled manner, the author proposes to consider the NavierStokes equations in the phase space expanded by introducing an additional variable characterizing the entropy production. For laminar flow regimes, the entropy production takes on a zero value, the additional term disappears, and the transition to the NavierStokes equations in their standard form is being realized.
The article considers the issues of the possibility of emergence and maintenance of nondeterministic, i.e. stochastic processes in a liquid due to the existence of incompatible between each other boundary conditions, as well as the ways of describing them relating to the turbulent flow. It is shown that the velocity profile of a turbulent flow can be described as a generalized solution of the problem, which is the sum of the two terms, each of which is the product of two functions: one of which determines one of the asymptotes of the solution, while the second one determines the degree of influence of this asymptote on the general solution in each point of the area of interest.
The plane Couette flow problem was solved by dint of this approach. Good agreement of the results with experimental data is demonstrated. 
Berezko M. E. Influence of the choice of boundary conditions on the results of the calculation of wall mounted flows. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/f66/63c0pndoe8matllj497iy9r9pb5129zo/Berezko.pdf 
Kozlov K. V., Volkov A. P., Starovoitov E. I., Popov E. V. A fullwave simulation of onboard earth surveillance radar electromagnetic fields for an emc ensuring. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/e2f/gko4gyvpga1bhn8mtoaxkzg240421lx4/Kozlov_Volkov_Starovoytov_Popov.pdf The use of onboard Earth surface surveying radar (including SAR) solves a number of tasks, which include the survey of the underlying surface, obtaining radar images of the terrain with a required resolution, detection of natural and artificial ground objects, operational mapping, etc. The installation of radar on board an aircraft is associated with the layout of various equipment in a confined space, taking into account the requirements of electromagnetic compatibility. Due to the fact that the strongest source of electromagnetic interference on board of aircraft is the radar, the assessment of its impact on the operation of the rest of the equipment is of paramount importance. The peculiarity of the UHFband under consideration is that the wavelengths are comparable with the lengths of external and internal cable lines, as well as with the dimensions of the electronic equipment blocks. The paper presents the methodology of numerical modeling of the distribution of the electromagnetic field in the near zone, created by onboard radar of the UHFband, designed for Earth surface surveying. For electrodynamic modeling of the electromagnetic field's distribution, the authors used a Finite Difference Time Domain Method. An assessment has been made of the electric field strength and current density induced on the electronic equipment block's housings located next to the active phased antenna array of the radar. These data can be used in works on electromagnetic compatibility of onboard electronic equipment. A description is presented of laboratory research schemes and the sequence of complex checks of equipment on the aircraft, associated major challenges. The authors separately considered problems arising during testing of satellite navigation equipment. 
Smolyakov A. V., Podstrigaev A. S. Experimental study of the noise figure of the digital receiver with undersampling up to 18 GHZ. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/467/m2gu603qp6xbewf7759qupkkyrjwlm0x/Smolyakov_Podstrigaev.pdf Due to the expansion of the frequency range and the number of emitting radioelectronic means in many scientific and technical fields, performing a wideband analysis of the signal environment becomes necessary. For this, one can use a multichannel undersampling digital receiver (USDR). Such a receiver estimates a signal carrier frequency by unfolding its spectrum in each channel from the first Nyquist zone to the subsequent zones. The unfolded spectrum components in each channel are then compared with each other. The goal is to find the frequency at which the components from all channels coincide. This frequency is assumed to be the true carrier frequency of the received signal and not its alias. In this work, we investigated the USDR prototype, which does not contain a lownoise amplifier (LNA) at its input. Therefore, the prototype’s noise figure (NF) is high and reaches 41 ... 52 dB. However, using an input LNA can significantly reduce the total NF of the device. At the same time, one should bear in mind that with an increase in the LNA’s gain above a certain value, the receiver’s dynamic range begins to rapidly narrow. The resulting frequency dependence of the NF in the 18 GHz band has significant nonuniformity (11 dB). Therefore, when creating wideband analyzers to reduce the sensitivity variation, it is advisable to use equalizers and amplifiers with compensating frequency dependences of the NF and gain. Using the USDR with characteristics similar to those obtained for the prototype, we can achieve a –125… –116 dBm sensitivity for the wideband analyzer. This sensitivity is high enough for the considered 18 GHz frequency band. 
Nikitin A. D., Ivliev A. S. Possible methods for controlling the output power of amplifier modules based on mtype devices. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/928/y9wcftv45nyuswiu6ch8b2kbdrbtiivw/Nikitin_Ivliev.pdf The article is devoted to the study of the operation of Mtype amplifiers in various output power control modes, to realize the possibility of multimode operation of transmitting modules of radar stations (RLS) on active phased array antenns using Mtype electrovacuum devices (EVD). The need for such studies arose with the increasing requirements for powerful transmitting modules. The results of studies of various methods for controlling the output power of the amplitron are presented. A fundamentally new way to control the output power of Mtype amplifiers is considered  control of the operating voltage with a change in the magnitude of the magnetic induction. As a result of the studies carried out on the possibility of operating Mtype amplifiers in the output power control mode, the following was revealed: when controlling the input signal, the range of output power variation is at least 1.0 dB;  when controlling the anode current, the range of output power variation is at least 5.0 dB;  when controlling the operating voltage, the range of output power variation is at least 5.2 dB. The results obtained can be of great practical importance in the construction of powerful transmitting amplifying modules for multimode radars with active phased array antennas and passive phased antennas array. It is shown that the use of a combined method of output power control, which combines the control of the input signal, anode current and control of the anode voltage, will allow changing the output power of the amplifier in the range of more than 11 dB. It was also shown that when controlling the input signal of the amplifier, it is possible to expand the operating frequency range of the amplifying module up to 1012%. 
Vorotyagin V. N. Method of structural and parametric configuration of the motion and navigation control system of a small space vehicle for remote earth sensing under different scenarios of destructive impacts. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/1ba/8kc119w0o7x7n1lwr48dx26iyywf2epn/Vorotyagin_.pdf Today, methods and technologies employing Earth remote probing data being developed by Roscosmos enterprises allow suggesting unique ways for ensuring safety, increasing efficiency of exploration and extraction of natural resources, introducing the latest practices into agriculture, preventing and eliminating consequences of emergencies, as well as protecting environment and controlling climate change. The issue of new space technology developing (a small spacecraft for the Earth remote probing in particular) is becoming most relevant.
To increase the degree of the design decisions validity while creating a small spacecraft, the article considers:
 Conceptually new approach to the development of a scientificandmethodological apparatus for multicriteria selection of the onboard control system structure and parameter on the example of a small spacecraft motion and navigation control system;
 Optimization of its limited resources to ensure proactive compensation of destructive external agency impacts
The article presents the developed structuralandlogical scheme for motion and navigation control system configuring of the Earth remote probing small spacecraft. The proposed approach allows putting into practice a multicriteria selection of effective configuration options for motion and navigation control system of a small spacecraft with account for various types of structural redundancy of the onboard equipment, and a wide range of element base. The conceptual and mathematical statements of the problem are given, and an algorithm for multicriteria synthesis of the motion and navigation control system appearance of a small spacecraft is developed.
The proposed technique will allow, even at the spacecraft design stage, significantly reducing the number of design errors by the decisionmaker, as well as improving the quality and efficiency of the created space systems application. 
Anan’ev A. V., Ivannikov K. S. A dynamic model for assessing the effectiveness of scenarios for conducting aerial reconnaissance by an integrated spatially distributed reconnaissance aviation complex. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/9b1/cx0ic0t1s23fs3l1ma1ysu3pqk3rmt86/AnanevIvannikov.pdf Aerial monitoring (reconnaissance) piloted complexes application in the interest of operational strategic decisionmaking is of great importance for the State security ensuring. However, such complexes employing is often performed in extreme conditions stipulated by climatic (severe meteorological) conditions, the destructive effects of manmade disasters, the danger of air defense means employing by unlawful armed formations, conditions of armed hostilities waging, etc.
In this regard, the article proposes an integrated spatially distributed reconnaissance aviation complex, which, unlike the known ones, includes unmanned aerial vehicles, controlled by the onboard operators situated directly on the manned aircraft for waging and controlling reconnaissance (by air monitoring).
Application procedure of such complex has been considered for the most difficult case, namely aerial reconnaissance waging under conditions of armed hostilities while the ground situation disclosure two stages. At the first stage, under condition of radio signals receiving possibility, such as radio distress signal, radio signals of the survey targets etc., passive radio and radiotechnical reconnaissance is being waged with the technical capabilities of the piloted aircraft onboard sensors. At the second stage, supplementary reconnaissance and reconnaissance of the objects of interest is being performed by the optoelectronic and other means positioned on the unmanned aerial vehicles.
When proposing modernization of the aerial reconnaissance (monitoring) and basing on the system approach, it is important to apprehend how the solution being proposed will affect the system of a higher rank, namely executive, or, in a particular case, striking. For this, a dynamic model of the reconnaissancestrike actions process was developed. It represents a state graph with time and probabilistic parameters indication. The article shows the equations system solution based on the states graph in the form states probabilities time dependences. The article demonstrates the solution of the system of equations, which are formed on the basis of the state graph in the form of time dependencies of the probability states.
The proposed model wields significant commonality and may be propagated on the wide spectrum. 
Blinov A. V., Razumov D. A. The procedure of formalization of strategies as an element of the methodology for taking into account uncertainty factors in forecasting the indicators of the implementation of space technology development programs. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/45e/ia5nkt364wc6ufsg3tbuvyizif8qy5gs/Blinov_Razumov.pdf In the process of space technology development programs realization, various factors affect the program activities and implementation indicators. Development of respective technique for the factors considering is required. The forecasts of programs realization are based on the variant basics.
The program realization strategies defining is the initial stage of the uncertainty factors considering while the program indicators forecasting. The realization strategies are being based on the goals and priorities of the State policy of the Russian Federation in the field of space activities.
The twolevel system of priorities is applied when defining strategies. The first level is strategic priorities based on the priorities of the State policy of the Russian Federation. The second level is the priority of the event within the strategic priority.
Program activities are being distributed among separate groups, affecting various properties of the program. When forming various options for strategies, a sequential search of the formed groups of program activities is used. The program activities priority is distributed by the Fishburn method according to the number of results achieved.
Possible strategy options are sequentially considered. Program activities are being ranked according to the degree of their impact on the contribution to various properties of the program.
The strategy under consideration will focus the allocated resources on the realization of a group of program activities aimed at achieving one of the properties of the program. The results changing of the program activities realization occurs due to the funding redistribution between the various groups activities. The funds of the lower priority groups of program activities are distributed in favor of the activities of the group with the highest priority.
Formation of groups’ priority of program activities aimed at achieving various tasks and properties is being performed. Further, the priority group's program activities are filled at the expense of the lower priority group, with account for the effect of the uncertainty factors. Funding redistribution of program activities according to the formed options of strategies takes place.
Sequential consideration of the the program realization options will allow selecting the most rational strategy. 
Ezrokhi Y. A., Kalenskii S. M. Identification of gte mathematical model by test data. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/d86/sq98t941zpzx33b0izjehxt42cb5u13m/Ezrokhi_Kalenskiy.pdf One of the important tools applied at all stages of the aviation gas turbine engine (GTE) life cycle is the mathematical modelling of GTE operation. Such the engine mathematical model (EMM) allows to calculation of its altitudevelocity and throttle performances to form the initial data for gas dynamic calculations and designing of GTE units, for control system design, for planning of various kinds of tests, carrying out of GTE diagnosis and also decisions of other problems arising during the GTE creation and operation.
Efficiency EMM at various stages of the engine creation depends on adequacy of the modelling to its real operation. In this connection increase of accuracy EММ is rather important problem on which decision the expediency and productivity of application EММ in the practice substantially depends.
The problem of ЕMM accuracy and adequacy increase can be resolved during some stages.
At the first stage the initial aprioristic EMM was analyzed by audit of basic equations, inequalities, logic conditions, and also approximating dependences about conformity to those physical processes for which they were got.
So, in particular, at this stage correctness of use in EMM the thermodynamic equations applied to enthalpy and temperature of a working medium and it thermo physical properties, approximating dependences for the unit performance (received in advance by means of independent tests or calculations) from the viewpoint of their interpolation and extrapolation from area of their preliminary settlementexperimental definition is checked.
Besides, correctness of the continuity equation on an engine flowing path (taking into account possible selections, leaks and supplies of a working medium), conservation of energy and an impulse, and also the laws of engine control (taking into account accuracy of regulation and limitations), defining fuel flow into the combustion chamber, position of the compressors guide vanes and jet nozzle door (if these elements are changed from a one mode to other) is checked.
Generally the method of EММ identification with the engine tests results is reduced to a finding of certain number of correction factors to conditionally constant EMM parameters (to units performance, the sections of a flowing path area values, values of selections and leaks of a working medium and another), capable of the least divergence of the settlement and experimental results. 
Zulfugarli P. R. New criteria for optimizing the functioning of imaging devices installed on highspeed unmanned aerial vehicles. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/4d4/4aw2fpsekg7azgdh7z25yhgh2r9b68lg/Zulfugarly.pdf Effective visual monitoring of the ground situation can be carried out using various imaging devices installed on the UAV. In this case, the spatial resolution can be up to 1 cm. The dominant direction here is the fulfillment of the criterion for overlapping images of each other, obtained at the rate of UAV movement. It is common knowledge. That in order to obtain a highquality orthomosaic image, adjacent terrain images obtained during the UAV flight should overlap 60% in the forward direction and 20% in the direction perpendicular to the direction of movement. At the same time, when the carrier is flying at supersonic speed and the requirements for the overlap of timesequential images are often not met. In such cases, qualitatively new criteria are required to optimize imaging systems. The resolution of photogrammetric images obtained from aircraft equipped with imaging devices is determined by such a metric as the Ground Sample Distance, or GSD for short, which is defined as the distance between two adjacent pixels.
With regard to highspeed flying objects equipped with imaging devices, the following optimization criteria have been proposed: (1) Design criterion α_1, (2) Functional optimization criterion α_2 The first criterion is put forward in order to achieve small design dimensions of the imaging unit for a given value of the number of pixels per unit image width and GSD = const. In turn, the second criterion is put forward from the conditions for achieving stealth devices for various detection systems. The solution of the formulated optimization problems showed that the criteria α_1 and α_2 are fulfilled with a square root dependence of the distance from the sensor to the ground object and the size of the sensor area on the focal length of the device, respectively. 
Aslanova A. B. Questions of optimization of the combined power supply of the UAV with the use of solar batteries and ground air transmission of energy by a laser beam. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/a3d/pw6wmm5yegu8ay85r5koh6buig0n3iyy/Aslanova.pdf To ensure the reliable operation of the UAV, a promising solution is the wireless transmission of energy through specialized ground base stations. At the same time, such power supply systems are expensive and dangerous for the population due to the high intensity of the laser beam and excessive electromagnetic radiation. A partial solution to this problem is the joint transmission of information and energy from a single base station. There is also another solution to the problem  the use of solar panels. However, the effectiveness of such a solution is still too low. In this case, the power supply of the UAV can be carried out according to the following simple rule (1) If there is a cloud, then the power supply is carried out through ground base stations by sending highintensity laser beams; (2) If there is no cloud, then solar power supply is used.
The case of a cloudy sky is considered in detail, when the UAV, by definition, flies at the level of the lower boundary of the cloud cover.
The problem of finding the optimal height of this boundary with a constant height of the upper boundary of the cloud layer is formulated and solved. The corresponding algorithm for the implementation of the proposed method has been compiled. The possibility of optimizing the construction of combined power supply systems for UAVs by minimizing the total energy losses along the paths of their propagation is considered. The case of a cloudy sky is considered in detail, when the UAV, by definition, flies at the level of the lower boundary of the cloud cover.
The problem of finding the optimal value of this height with a constant height of the upper boundary of the cloud layer is formulated and solved. The corresponding algorithm for the implementation of the proposed method has been compiled. 
Krasnov A. M., Tregubenkov S. Y., Rumyantsev A. V., Khismatov R. F., Shashkov S. N. Methodology for estimating the efficiency of opticalelectronic systems using an analytical model. Noise model of the «Oesoperator» system. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/91e/nw5cn6qcsnsqfw991umemi3j6syvpsfu/Krasnov_Tregubenkov_Rumyantsev_KHismatov_SHashkov.pdf Efficiency assessment is an integral part of optoelectronic systems (OES) development stages, testing and operation. The lack of a unified technique for optoelectronic systems effectiveness assessing leads to the fact that various assessment methods are employed to compare different systems, which results in obtaining contradictory results that do not provide objective data for making appropriate decisions at various stages of optoelectronic systems life cycle. One of the ways to this problem solving consists in an analytical model developing, which will represent the basis for creating the unified complex of means for intellectual support for optoelectronic systems design and maintenance at all stages of the lifecycle.
The purpose of the presented article consists in describing an analytical model for the optoelectronic systems effectiveness assessing, in a part concerning the noise model of the “OESoperator” system.
The following noise components of the “OESoperator” system are considered: the noise variance of the visual system of the OES operator, and the noise variance displayed on the OES display. The article presents the formula dependences of the noise variance components displayed on the OES display. These are the spectral density of the noise on the display, the temporal noise bandwidth and the spatial noise bandwidth. A model for computing the temperature difference equivalent to the noise was considered.
Further, the article presents the example of the initial data presentation in the analytical model for optoelectronic systems effectiveness assessing, and the results of the noise impact assessment on such OES efficiency indicators as detection range, recognition and identification of an object.
The considered noise model of the “OESoperator” system as an integral part of the analytical model for optoelectronic systems effectiveness assessing is a tool for an objective assessment of the of the optoelectronic systems sensitivity, which excludes the subjective opinion caused by the human factor.
It is advisable to employ this noise model of the “OESoperator” system in the development of tactical and technical requirements for optoelectronic systems, and optoelectronic systems themselves at the preliminary and technical design stages.
Computing temperature difference equivalent to the noise allows performing assessment:
 Of noise components impact on the values of detection range, recognition and identification of the object to the specified tacticalandtechnical requirements at the stage products testing;
 Of the OES radiation receiver sensitivity for this parameter compliance with the values indicated in the specified in operational documentation at the stages of mass production and operation.
Thus, the noise model of the “OESoperator” system implementation, which is an constituent part of a single software package for intelligent support of design and maintenance of optoelectronic systems at all stages of the life cycle, was considered. 
Apollonov D. V., Bibikova K. I., Shibaev M. V., Efimova I. E. Creation of algorithms for the automatic control system of the convertible unmanned aerial vehicle. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/2a9/t3crggob5i2g68ejziebw5gvwkaq506j/Apollonov_.idr.pdf Convertible unmanned aerial vehicle called a tiltrotor is considered. Tiltrotor can flight airplane mode and helicopter mode by changing the propulsion thrust vector by tilting the axes of rotation of the engines. The tiltrotor has the ability to make a vertical takeoff and land, it can also perform horizontal flight at highspeed cruise. It is difficult to develop tiltrotor control system due to the variable characteristics of the UAV during flight. This paper describes analysis of methods for selecting controller parameters of control system regulators. When analyzing fault tolerance ensuring controllability imposes requirements on the choice of control laws in the angular motion control loop and trajectory motion control loop. In addition to the widely used PD and PIDcontrollers and the linearquadratic controller, algorithms based on the concept of the invers dynamic problem and fuzzy logic are considered. Results of research on the creation of algorithms for the automatic control system of a convertible unmanned aerial vehicle are presented. All the described methods were analyzed to ensure the robustness of the automatic control system in order to ensure the necessary quality of control in cases where the control object differs from the calculated one. In case of failure of individual elements of the system the characteristics of control object change during operation, this problem is also considered in this paper. A comparative assessment of various methods for implementing control loops for UAV trajectory and angular motion using proportionalintegrodifferential, linearquadratic, nonlinear controllers and the method of the inverse dynamic problem is carried out to identify the advantages and disadvantages of all these methods. 
Panteleyev A. V., Belyakov I. A. Application of the bioinspired optimization methods in the solar sail optimal openloop control problem. Trudy MAI, 2022, no 122, http://mai.ru//upload/iblock/b25/qp6jyivcs7xugl1yo1623ppmrrtf4huw/Panteleev_Belyakov.pdf This article discusses application of bioinspired metaheuristic global optimization methods: Grey Wolf Optimizer (GWO) and Whale Optimization Algorithm (WOA) for the problem of optimal loopopen control. Optimal control needs to manipulate space probe with solar sail. These algorithms belong to the class of swarm optimization methods, which feature is possibility of data transfer between individuals. At the same time GWO and WOA were inspired by nature, therefore we may relate them to bioinspired category. The behavior of a nonlinear deterministic continuous model of a plant is described by a system of differential equations with given initial conditions and a nonfixed terminal time. It is assumed that only time information is available during control, i.e. the openloop control is used. Numerical solution is found in the form of saturation function, which guarantees fulfillment of parallelepiped control constraints. Function arguments are finding in the linear combination of given base functions. Since terminal moment is undefined, this article applies method of transformation to the fixed terminal time problem, which introduces new independent variable, related with time.
The task is to find optimal control law for realizing solar system mission flight from the Earth’s orbit to the Mercury’s orbit in the shortest possible time. Algorithm of two bioinspired metaheuristic optimization methods application and software were created for numerical solution solar sail openloop control problem. Software gives mathematical modelling with various parameters for a subsequent visualization. Comparison with known results was provided. Recommendations were provided for parameters choose to solve typical model optimization and applied solar sail control problem. 
Korovaytseva E. A. Formation of a family of trajectories of free spherical motion of a spacecraft as a rigid body, providing reorientation of its axis of dynamic symmetry to a given position. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/c5c/uqktey4ygvzjjfjta4cs4x8a41nsq9js/Korovaytseva.pdf The presented work studies opportunities of automatic segmentation method implementation for solving problems of axisymmetric static deforming of soft shells of revolution at large displacements and strains. Mathematical statement of the problem includes four quasilinear differential equations and nine nonlinear algebraic equations. Geometrical relations of thin shells nonlinear theory are employed herewith, and elastic potentials of various views are being engaged for nonlinear physical relations formulation. The opportunity of composite shell analysis is supposed, which corresponds to the statement of multipoint boundary problem. Algorithm of the parametric differentiation method is used for the problem solution. The initial relations of the nonlinear boundary problem are being differentiated herewith by the preselected parameter of the problem solving continuation. As the result, a system of interconnected quasilinear boundary and nonlinear initial problems is being formed. The result of the obtained system solving while studying shell deforming under conditions of large displacements and strains depends on simultaneous successful setting of a whole range of computational algorithm parameters. As far as the method of arbitrary search of parameters leads to irrational increasing the time of computer work with the program, the article suggests a reasonable setting of one of the algorithm parameters, namely, the number of segments into which the integration interval of quasilinear boundary value problem is divided. The said number of segments is being determined at the stage of preprocessing with the help of authored automatic segmentation method, which was successfully applied earlier when solving the linear boundary value problems. The article presents results of the three problems solutions on soft shell inflation by the pressure, uniformly distributed along meridian, using parameter differentiation method, one of the steps of which is the automatic segmentation method. Selection of inflation problem of a cylinder from MooneyRivlin material fixed at its ends by a roller is stipulated by the existence of this problem analytical solution. Three cases of arbitrary selection of a number of segments, into which the shell is divided, and a case of automatic segmentation are considered. The article shows that it is possible in the last case to obtain an optimal combination of solution accuracy and iteration processes convergence rate. The choice of a hemisphere inflation from neohookean material fixed along the equator by a roller problem is dictated not only by the existence of analytical solution of this problem, but also by the presence of singular coefficients in resolving equation system Jacobi matrix at the problem integration interval. The said feature leads to the fact that in a fairly large vicinity of the shell pole the condition, used as a criterion of shell division into segments, is violated in each point of the meridian. As the result, the number of segments determined by the automatic segmentation method appears to be quite large. However, the problem solution result turned out to be one of the best among the shell segmentation options considered from the viewpoint of both solution accuracy and iteration processes convergence rate. It is worth emphasizing that in both examples under consideration, one of the options of arbitrary setting of segments number lead to a principally unsatisfactory solution result. Thus, the automatic segmentation method application is necessary to obtain correct solution. The problem of inflation of a hinged hemisphere of neohookean material is selected as it does not have analytical solution. As the result of calculations, it was established that automatic segmentation leads to the lowest iteration processes convergence rate among all the shell meridian division considered options. Along with this, with insufficient number of segments the solution obtaining turned out to be impossible. The performed studies revealed that automatic segmentation method application was necessary for the computer groundless actions minimizing concerning the calculation algorithm parameters setting, as well as for the problem solution results accuracy and iteration processes convergence rate increasing. Along with this, when solving problems, which resolving equation system has singular coefficients at some point of integration interval, the said method application requires additional studies, and apparently, application of some auxiliary techniques. 
Alimov N. I., Gorbulin V. I., Sudar Y. M. Formation of a family of trajectories of free spherical motion of a spacecraft as a rigid body, providing reorientation of its axis of dynamic symmetry to a given position. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/94b/467uktl6xhmt9hs7lkuipcfsa2hqqh2g/Alimov_Gorbulin_Sudar.pdf Analytical relations for trajectories parameters determining of the free (by inertia) spherical movement a satellite as a solid, which ensures reorientation of its dynamic axis of symmetry to the specified position in the regular precession mode, were obtained. A canonical inertial coordinate system, in which angles of orientation of the associated coordinate system, i.e. Euler angles, change in time linearly, was introduced. A peculiarity, explanating the ambiguity of determining the initial value of the rotation angle, is indicated, and the option of the pointed ambiguity elimination is suggested. The article demonstrates that spherical movement trajectory of a solid, which ensures the dynamic axis of symmetry retargeting to the required position in the predetermined time is a basic problem while reorientation control selection in the pulsing statement and computing required increment, kinetic moment and kinetic energy in the points of impulses application. The solutions being obtained allow assessing rather accurately the retargeting process duration and required energy consuming, necessary for further analysis. Besides, these solutions are a good initial approximation for the continuous control tasks. The authors introduced the notion of control strategy for spherical (angular) satellite motion control at lengthy time intervals, consisting of sequence of controls of the two active sections and ensuring transition from one angular motion trajectory to another, which kinematic and dynamic parameters are being determined based of the spacecraft flight program. The article proposes realizing continuous angular motion control computing at each active section based on the utilizing the concept of inverse problems of dynamics and algorithms for solving the problem twopulse control of the satellite reorientation. 
Gyagyaeva A. G., Kondratov D. V., Mogilevich L. I. Derivation of the dynamic equation for a geometrically nonlinear plate interacting with a thin layer of a viscous incompressible fluid. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/00e/fcw36dxooljzykj4czghplud2rz8m5qs/KondratovGyagyaevaMogilevich_2.pdf At present, different methods for solving the problem of hydroelasticity are applied. They allow solving a set of problems in question be means of assumptions and limitations with a required precision and reliability. To make engineer decisions while examining hydroelasticity problems, specialized computer software is used. It allows simplifying the calculating process of hydroelasticity problems and demonstrating a graphical solution of the problems. Thinwall structures interact with viscous incompressible fluid, particularly plates and shell structures. They are used in machine industry, in instrument making industry, in aviation and space industry. Thus, one needs to build mathematical models and apply program systems to make decisions in designing machines and devices.The article consider the model of a mechanical system consisting of an absolutely rigid body (vibrator); an elastic rib, rectangular plate (stator) and viscous incompressible fluid. Using the Hamilton’s variation principle, the equation for the elastic geometrically nonlinear plate dynamics is derived. The mathematical model of the presented mechanical system consists of the incompressible fluid dynamics equations, the elastic geometrically nonlinear ribbed plate dynamic equations, the equation of motion for the absolutely rigid vibrator and the corresponding boundary conditions. The program for the analytical derivation of the dynamic equations for an elastic irregular nonlinear stator was developed. It takes into account the boundary conditions of a free support and the conditions of free fluid flow on the ends. The constructed mathematical model can be applied for the design of hydrodynamic supports. The mathematical model can be used in designing of hydrodynamic bearings that are operated in machine industry, in instrument making industry, in aviation and space industry. 
Grishanina T. V., Guseva E. E. Method for calculating elastic vibrations of a cyclically symmetric structure. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/2ee/u05dgr27cgt3b24oz9k7xx4neo8yxyuu/Grishanina_Guseva.pdf The article presents a new approach to the oscillation equations composing of elastic structures with cyclically symmetric structure. A cyclically symmetric elastic system is under consideration. At the k = 0, 1, 2, ..., N — 1 nodes of the system, located on a circle at equidistant points with angular coordinates of θ_{k}, the identic elastic rods of constant crosssection are being connected, working in tensioncompression, torsion and bendingshear in and out of the plane of the system. To compose the oscillations equations of the system, both displacement and rotation angles components, symmetrical with respect to the radial plane passing through the kth node, are being represented as cosine expansions in the circumferential direction, while skew symmetric ones are represented as sine expansions with wave numbers of n = 0, 1, 2, ..., N/2. Expressions of potential and kinetic energies for all elements of the system are being composed. With account for the cos nθ_{k} and sin nθ_{k} functions orthogonality conditions for different n on a system of equidistant points, the terms of these expressions for different n from the set of n = 0, 1, 2, ..., are being obtained uncoupled among themselves. As the result, the Lagrange equations in generalized coordinates for a cyclically symmetric system with 6N degrees of freedom disintegrate into separate groups of six equations for each number n being accounted for. Thus, the solution of the problem of a cyclically symmetric system oscillations of еру 6N order is being reduced to solving a number of problems for uncoupled subsystems of equations of the sixth order, representing separately harmonics n = 0, 1, 2, ..., ≤ N/2. 
Zotov A. A., Nagornov A. Y., Volkov A. V., Popov V. O. Analysis of the dynamic characteristics of threelayer shells with discrete filler. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/5a4/93wby3swgy21oh19g8ir24zrvrroyg92/Zotov_Nagornov_Volkov_Popov.pdf The problem is posed to study dynamic characteristics of a threelayer cylindrical shell with the discrete filler, which is a regular system of coneshaped (or pyramidal) cells arranged in a checkerboard pattern. Threelayer structures in various technical objects often have a honeycomb filler’s structure are widely used. Despite the obvious advantages of honeycomb filler (low weight, high rigidity), there are circumstances that prevent their wider use. The closed cellular structure prevents the removal of condensate entering the internal space. And the complexity of ensuring and controlling reliable connection of the aggregate with the bearing layers (especially on curved surfaces) increases their labor intensity and cost. The proposed discrete structure largely allows you to solve the above problems. The design features influence of the of this threelayer shells type on the stressstrain state and stability under static loading has been studied in sufficient detail earlier. A complete solidstate and FEmodel of the investigated shell has been constructed. A modal analysis of the cell design was carried out as a next step, and then, having selected the zones of interest, the frequency response of the structure was investigated in order to plot the frequency response and frequency response. The NASTRAN solver is used to calculate eigenmodes and frequencies, the analysis type is set to Normal Modes / Eigenvalue. The geometry of the model was built using PLATE elements. In threelayer structures, the dynamic characteristics can be changed by varying the thickness of the bearing layers or filler and, thus, to obtain the optimal weight, damping, and also radiotechnical parameters. To determine the frequency response, a harmonic Frequency / Harmonic Response analysis is performed. It allows you to evaluate the response of the structure with a sinusoidal action. To assess the considering filler structure feasibility a comparative analysis of the dynamic characteristics between smooth and threelayer shells of equal dimensions material, was carried out. Based on the obtained results, it can be concluded that with an thickness increase, and, accordingly, the filler rigidity, the natural frequency decreases, however, with an increase in the bearing layers thickness, an increase in the values of the natural frequencies is observed. Also noted that main vibrations emanating from gas turbine engines are in the range up to 5000 Hz, and the coneshaped structure is preferable for use in places subject to dynamic loads. 
Korolenko V. A., Soliaev J. O. Evaluation of stress concentration around microsized holes within simplified models of strain gradient elasticity. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/430/nsqxubq278k649xulkmvv5olwq53to5f/Korolenko_Solyaev.pdf This paper presents the results for the modeling of the deformed state and the level of stress concentration around the microsized holes. Analytical solutions are derived for the deformations of an infinite plate containing a cylindrical hole within several simplified oneparametric models of the strain gradient elasticity theory (SGET). Namely, we used the simplified strain gradient elasticity theory, the couple stress theory, the dilatation gradient elasticity theory and the fully symmetric GusevLurie theory, which all are the special cases of the general MindlinTupin SGET. Linear elastic isotropic behavior of the material is assumed. New variant of the PapkovichNeuber solution of SGET equations in terms of displacements is involved for analytical derivations. It is shown that this solution can be reduced to the standard Helmholtz decomposition for the gradient part of the displacement field and to the standard representation of its classical part. Based on the derived solutions we investigate the changes of the stress and strain state around the holes of different diameter. It is shown that the choice of a suitable variant of a simplified SGET model and identification of the length scale parameter for the certain materials can be performed based on the experimental data for the failure loads for the samples containing holes of different diameters (with a minimum size of ~100 µm). It is also shown that identification can be also carried out on the basis of direct methods of strain measurements around the smallsized holes, for example, by using digital image correlation methods, which requires the use of microscopy or, at least, macro photography techniques at the microscale level. 
Popov I. P. Umov integral vector, back impulse and other mechanical quantities. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/b7e/4huv1d5m7h2thei16jrjc6jmma9f9ham/Popov.pdf Due to the widespread application of advanced scienceintensive technologies in the space industry, these industries themselves are becoming a source of development not only of applied, but fundamental science as well. In this regard, Umov’s integral vector, backward impulse and other mechanical quantities in perspective may be of interest including the applied one. The said quantities are associated with the formal analogs of the Schrödinger equation (FAUSH). Formally, the Schrödinger equation (SH) induces the magnitude of mechanical motion of the zero order (in the sense that it is contained in the SH). It is noteworthy that the quantum mechanical design generates a macromechanical quantity. Obviously, other ACF can induce values of mechanical motion of other orders. The following theorem is proved: The following theorem is proved: the value of m_{e}v^{—1} in a hydrogenlike atom is quantized. The value of m_{e}v^{—1}, corresponding to the basic energy level is a fixed (unchanged) quantum. Almost all of the obtained results were a consequence of the quantum mechanical differential equations application, however, the results themselves are predominantly macromechanical. The mechanical motion quantities of various orders are being induced by formal analogs of the Schrödinger equation. These quantities include both known (mass, momentum, kinetic energy) and unknown (Umov’s integral vector for kinetic energy, backward momentum, etc.). In all FAUSHs, the orders of the partial derivatives differ by one. For quantities of motion with a positive degree of velocity, the order of the temporal derivatives is higher than that of the spatial ones. For mechanical quantities with a negative degree, the order of spatial derivatives is higher. 
Malinin G. V. Methods of calculation of ribbed plates for strength and stability. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/763/mz8xfo5df9laz51bdk94m3tjbmh0jk6u/Malinin_red_1_.pdf The desire to increase the reliability of structures forces engineers and designers not only to turn to new materials, in particular composite materials, but also to the introduction of additional reinforcing elements that do not significantly affect the change in the weight of the structure. As such effective means is the use of stiffeners, which have become widespread in engineering practice. The foundations of analytical methods of structural mechanics applied to the problems of calculating ribbed plates and shells were laid by Russian scientists S.P. Timoshenko, I.G. Bubnov, P.F. Papkovich, V.V. Novozhilov, A.I. Birger. Currently, many scientists are also engaged in the calculation of ribbed plates and shells for strength and stability. In this paper, two analytical methods for calculating ribbed plates supported by a cross system of stiffeners are proposed: a method for calculating strength in determining the stressstrain state and a method for calculating stability in determining the critical load. The calculation of the stressstrain state and stability of the structures under consideration is associated with significant mathematical difficulties that an engineer can currently overcome with the help of modern mathematical packages. In this paper, the technique of strength analysis of the stressstrain state of a ribbed plate is implemented in the Mathcad package, and the stability problem is successfully solved in the Maple package. The calculation of the strength and stability of ribbed plates reinforced with ribs placed crosswise or parallel to one of the sides of the plate is considered. The proposed computational mathematical model is based on the replacement of the original ribbed plate with an equivalent flat isotropic plate. The stiffness characteristics of the equivalent plate are calculated taking into account the contribution of the reinforcing elements of the ribbed plate. It is assumed that the thinwalled structure is supported by a sufficiently large number of ribs located at a sufficiently small distance fr om each other, which allows their «smearing» relative to the median surface of the plate.Control examples of calculation according to the proposed methods are given. The results of analytical calculations are in good agreement with the results of numerical analysis performed by the finite element method in the MSC.Nastran/Patran package.The proposed methods will allow the engineer at the stage of preliminary calculation and design of the structure to identify the features of its stressstrain state, such as stress concentration sites wh ere it is necessary to reduce the size of the finite element grid during the refinement calculation in industrial packages of finite element analysis. 
Sposobin A. V. Meshless algorithm for calculating supersonic viscous gas flows. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/bc8/45be264r39xqrkrkyz6cgpg2wfzg31gg/Sposobin.pdf Тhe article presents in detail the algorithm for the numerical solution of the NavierStokes equations [12] by the meshless method [8, 10]. The described method is used for numerical simulation of blunt bodies flowaround by supersonic viscous gas flow [1, 2]. Cartesiangridbased immersed boundary method presented in previously published works was successfully applied to simulate such flows in the twodimensional planar and an axisymmetric formulation [3]. Numerical studies of the gas thermal impact change on the streamlined surface while the highly inertial particle motion against the incoming flow along the symmetry axis were performed by dint of it [4, 5, 6]. Particles motion along various trajectories required gasdynamics problems solving in the 3D formulation, for which the Cartesiangrid based methods application required too much computer memory. When solving gasdynamics problems by the meshless method, a finite sets of nodes is being selected in the space. Approximation by the least square method is applied for spatial derivatives computing in computational nodes. The said approach is being used for convective and viscous fluxes computing. The convection fluxes are being computed by the AUSMPW+ method in conjunction with the MUSCL scheme and van Abada limiter. The system of equations time integration is being performed by the explicit RungeKutta method of the third order of accuracy. The flowaround surface is being represented by the model of isothermal wall with the specified temperature. Conditions of gas adhesion, as well as pressure gradient equality to zero, which modeling also employs the least square method, is realized on the said model. The meshless method gives the opportunity to compute the gas flow in the areas with complex geometry, it is simpler in realization herewith compared to the finite volumes method, since it does not require generation of the highquality computational grid. It allows setting anisotropic distribution of nodes in space, which is of vital importance for qualitative resolution of the boundary layer near the flowaround surface. Along with the 3D realization, adaptation of meshless method for computing flat and axisymmetric viscous gas flows was performed. The software implementation of the described method is realized in the C++ programming language and employs the OpenMP technology for computations parallelization. A computational experiment was performed on modeling the sphere flowaround by the supersonic airflow at the Mach number of M = 3 and Reynolds number of Re = 10^{5} was conducted for the said method verification. The spatial shadow patterns of the flow, pressure field and Mach number are presented. Comparison of gas parameters in the boundary layer, obtained by the meshless method with the computational results of continuous flow combined with the boundary layer equations is presented. Correspondence of the gas computational parameters on the flowaround surface to the reference data and approximateanalytical expressions is demonstrated. The heat flow value in the critical point coincides with the one calculated with the Fay and Riddell formula, and the heat flow distribution curve along the surface is close to the approximateanalytical one. The next stage in the development of the meshless method is planned to solve numerically the unsteady multiphase flows problem, in particular, to simulate the solid particles motion in the shock layer. 
Bernikov A. S., Petrov Y. A., Sergeev D. V., Shtokal A. O. Depreciation of automatic spacecraft when landing on planets and their satellites, taking into account the elasticity of the landing device design. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/243/qroj2f3ub0d5xpdcmon38e0of0snvsk5/Bernikov_Petrov_Sergeev_SHtokal_PRAVLEN_.pdf The spacecraft touchdown on the surface of planets and their satellites is one of the crucial flight stages. Since the planets surfaces are insufficiently studied, the kinematic parameters of the spacecraft movement may vary in a wide range. For the spacecraft shock absorbing while touchdown, landing devices are being used, which should ensure a touchdown with permissible overloads and a stable position of the craft on the surface. The landing gear consists of three or four supports, depending on the power scheme of the landing vehicle. The craft shock absorbing while landing is performed due to energy absorbers placed in the shock absorbers of the landing device. A rod, honeycomb, pipe and tape (flat rod) are being applied as singleuse energy absorbers, which absorb the energy of the craft while landing due to plastic deformation. The accounting for the landing device design elasticity will allow correctly determining the dynamic loads and stability area of the craft while landing, which is especially important when landing on comets or satellites with low gravity. When solving the problem of landing dynamics, the equations of motion of the landing gear supports are employed, with account for the elastic deformation of the structure. The regard for the elastic deformation energy accumulated in the elements of the landing gear and in the places where they are attached to the body will allow determining the dynamic loads on the apparatus and structural elements, as well as correctly determining the area of the apparatus stability to overturning. To determine the friction forces originating from the contact interaction of the heel of the landing device with the ground, experimental studies on the of friction coefficients measurement are being used. Tuff, basalt, foam concrete of different strength, sinter sand were being considered as analogous soils. AMG6 aluminum alloy, MA21magnesium alloy, and OT4titanium alloy were being considered as a material for the heel of the landing gear support. It follows from the experiments that for all combinations of rubbing metalground pairs, the friction process is oscillatory. When a spacecraft tpuchdown on bodies with low gravity, such as the Mars satellite Phobos, for which the acceleration of gravity is equal to df 0.005 m / s2, and even more so when landing on comets, for example ChuryumovGerasimenko, for which the acceleration of gravity is up to 80 thousand times less than on Earth, accounting for the elastic forces of the landing device design when solving the problem of landing dynamics is essential. On the «Rosetta» spacecraft, three landing gear supports contain clamping motors to ensure landing on a slope without tipping over, which is possible due to the energy of elastic deformation of the supports. When performing works related to soil drilling, the spacecraft must be securely fixed on the touchdown surface of satellites (comets). The clamping motors application here will be inefficient, since high axial forces are required while drilling, and the drilling time is rather long. In this case of touchdown, the spacecraft can be held on the surface with harpoons. 
Zagornyj S. V., Naumchik I. V., Dzitoev M. S., Mikhaylenko A. V. Exergetic analysis of elements of thermostating systems. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/67d/u2prg1cr23sinfevyewi5009k2y1d1t3/Zagornyy_Naumchik_Dzitoev_Mikhaylenko_RED_3..pdf The subject of the research is the regularities of changes in the thermodynamic parameters of thermostating systems of rocket and space complexes, depending on the composition of their equipment. The purpose of the work is to improve the thermostating systems of special RKK equipment to ensure the specified heat and cooling capacity, as well as temperature to ensure and maintain the accuracy and stability of their output parameters. The article presents the main results obtained during the study. The exergic analysis of thermostating systems for objects of rocket and space technology has been carried out. Research has been carried out on the possibility of using heat pump installations for thermostating objects of rocket and space complexes, which allows obtaining energy of a higher potential using lowpotential renewable energy from natural sources of heat or lowtemperature secondary resources. The expediency of including a vapor compression refrigeration machine into the thermostatting system based on a heat pump installation has been substantiated. Conditions are formulated under which the use of a heat pump will be more profitable than the use of a chemical heat source. A method of comparative analysis of a heat pump and a chemical heat source is presented, the results of which showed that direct heating consumes approximately twice as much fuel as heating using a heat pump. A schematic diagram of a universal allseason thermostating system based on a refrigeration and heating unit has been developed. The work performed is theoretical and experimental. The provisions outlined in the work are the result of the analysis and generalization of the research results of Russian and foreign scientists in the field of thermodynamics and heat transfer, the theory of heat engineering, the theory and practice of operating thermostating systems for rocket and space technology, as well as the results obtained in the course of research on the topic of research work of organizations industry and military scientific organizations of the Ministry of Defense of the Russian Federation. The main research results can be used both at the design stage in the formation of requirements for ensuring the specified heat and cooling capacity, temperature conditions and improving the level of thermodynamic efficiency of various objects of special equipment of rocket and space complexes, as well as to ensure the required values of the output indicators of the elements of thermostating systems at the stage exploitation. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Antonova V. A., Korchagina A. S., Kanishcheva M. G. Exergetic analysis of elements of thermostating systems. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/df2/v02k5afnxfy1u56dx1rlhhiag74asp7t/Buzhin_Antonova_Mironov_Antonovaidr.pdf AdaptiveMobile has identified a vulnerability in the of the Network Slicing mechanism implementation, which could disclose information about arbitrary network segments or cause a denial of service. The vulnerability was assigned the CVD20210047 number. Federal Service for Technology and Export Control (FSTEC of Russia) introduced vulnerability to the bank of threats and determined the level of danger as medium. One of the trends for this vulnerability elimination in the 6G networks is formulation of the classification principles and filtering of the 6G transport network traffic for effective application of the Network Slicing mechanism. The basic principles of collecting, filtering and traffic classification of the data transmission network are as follows:
The proposed principles and ways of solving the filtering and monitoring problem are aimed at eliminating the dangerous CVD20210047 vulnerability. 
Bakhtin A. A., Volkov A. S., Solodkov A. V., Sviridov I. A. A neural networkbased signal modulation recognition system implemented on a FPGA. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/f42/drhhk81jcbo65rxqa1bjdk2a5ehpp9mw/Bakhtin_Volkov_Solodkov_Sviridov.pdf In cognitive radio systems including softwaredefined radio, an important task is to recognize modulation type of received signals under various signaltonoise ratios in the communication channel. The detection of the modulation type in a received data packet can be used in ad hoc networks, as well as to provide dynamic spectrum access. To solve this problem, there are few common approaches, including the shape detection of the signal constellation, the study of the statistical characteristics of the signal, the use of deep neural networks and others. The use of deep convolutional neural networks leads to higher accuracy for large sets of different types of modulation. In addition, implementing the neural network on an FPGA allows not only changing the weights of the neural network, but also configuring the types and arrangement of layers without replacing the hardware component. The proposed system consists of hardware and software parts. The hardware part includes a Digilent Zedboard and an ADFMCOMMS3EBZ development board (based on an AD9361 configurable radio transceiver connected via an FMC connector). The software part of the system consists of the Petalinux distribution kit version 2019.1, the Linux industrial I/O driver, developed software for preprocessing the received signal and a trained neural network model. The developed software part performs the preprocessing of the signals and controls the configurable coprocessor located on the FPGA. The preprocessing consists in normalizing the received signal. Moreover, as the coprocessor does not support the softmax layer of the neural network, the necessary calculations are performed at the postprocessing stage. To train the neural network, a set of samples of radio signals with different types of modulation (dataset) was generated in the Matlab environment. The generated signal samples were transmitted at a 1 GHz carrier frequency over a low noise wireless channel. The carrier frequency was chosen arbitrarily as it does not affect the processing algorithm. Before transmitting the signal, the transceivers were manually calibrated in order to reduce the frequency desynchronization, however, during the transmission; the frequency deviation value was being changed arbitrarily. The received signals were preprocessed and divided into bursts of 1024 samples in the inphase and quadrature channels. Then AWGN with different power was added to the samples. Thus, samples with various SNR in range −5...15 dB with step 1 dB were formed in the dataset. The use of the DPU v3.2 coprocessor allows it to perform necessary computations for the neural network in the FPGA. We decided to use a compact neural network with a small number of Inception modules and fast connections. The most significant impact on errors in determining modulation at high SNR is the incorrect classification of the 8PSK and 16PSK modulations — instead of the first type, the second is often predicted and vice versa. At low SNR QAM modulations of different orders are erroneously classified as higher order QAMs due to the influence of noise. Despite this fact, the developed system shows an average accuracy of 90% of successful recognitions for SNR values above 12 dB and 70% and higher for SNR values exceeding 2 dB. The proposed system has great flexibility and a large possibilities for further improvement of performance. 
Smolyakov A. V., Podstrigaev A. S. Experimental study of the accuracy of determining the timefrequency parameters of a pulse in a digital receiver with undersampling under a singlesignal impact. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/b76/0m2sfvfy1kk5xr9ubdothk83z3p1o44d/Smolyakov_Podstrigaev.pdf One can use digital receivers based on undersampling (subNyquist receivers) to solve tasks of ESM, cognitive radio communication, electronic signals intelligence and passive radar. The main advantage of the subNyquist receiver for the user is software adapting the characteristics to the current tasks and the signalinterference environment. The efficiency of the subNyquist receiver largely depends on the accuracy of determining the timefrequency parameters of the received signals. Since we can consider any signal as a pulse during a longterm analysis of the signal situation, it is advisable to carry out the study for individual pulses with the accumulation of measurement statistics. We investigate the errors in determining the carrier frequency and pulse duration to estimate the accuracy of measurements on the device’s prototype. We obtained the results in the form of dependences on the carrier frequency and the duration of the received pulse. With a decrease in the pulse duration, the mathematical expectation and the standard deviation in determining the frequency increase. The average relative error in determining the pulse duration increases with decreasing pulse duration. The standard deviation of the error in determining the duration for long pulses is more significant than for short ones. The article describes in detail the reasons for these phenomena. The most critical errors, as expected, correspond to short pulses. Analyzing existing radio systems allows us to conclude that obtained errors are acceptable for wideband analysis tasks. An additional increase in the accuracy of determining the frequencytime parameters of the signal can be performed based on the approaches proposed in the paper. 
Vernigora L. V., Sysoev V. K., Kasmerchuk P. V., Dmitriev A. O. The concept of highprecision trajectory measurements using a coupled system of an onboard optical arc meterinterferometer and optical laser beacons. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/43f/ud8koie0g3lz6z3es4v0v1vp7och223a/Vernigora_Sysoev_Kazmerchuk_Dmitriev.pdf As far as the transition to a submillisecond accuracy level of optical angle measurements in space is inevitable in the near future, and the joint use of an onboard space optical arc meterinterferometer and optical laser beacons will significantly increase the accuracy of measuring spacecraft equipped with beacons. The small massandsize characteristics of beacons and their low energy consumption allow retrofitting the devices already prepared for launch with optical laser beacons, without going beyond the limits of the spacecraft design mass saving. A simplified version of the «OSIRIS» astrometric arc meterinterferometer of the microsecond accuracy level — the LIDA device for applied use is capable of achieving the accuracy of coordinates determining of the spacecraft equipped with optical laser beacons, almost four orders of magnitude higher than is currently achieved when nearEarth space monitoring. The LIDA arc meterinterferometer can be placed onboard a small spacecraft or be a passing load. GLONASS spacecraft observation by a space optical arc meterinterferometer of, provided they are equipped with optical laser beacons, will allow increasing coordinates accuracy determining of the spacecraft of this grouping to a centimeter level (or even better). Spatial position measuring of a spacecraft in the interplanetary space is extremely important for correcting the spacecraft trajectory during interplanetary missions. Until now, there are still no autonomous navigation systems of this level. In search of an acceptable solution to this problem, the Americans are even making attempts to develop navigation principles for measuring pulsed radio emission of pulsars. Angular positions measurements of the spacecraft with the onboard optical laser beacon by a space optical arc meterinterferometer will lead to the errors by the position in the tangential direction even at the distances of one million kilometers, not exceeding the size of the spacecraft. These capabilities are unlikely to be in demand in the decades to come for practical navigation. However, they may be of interest to fundamental science, for example, to clarify the gravitational constant magnitude and the scale of the Solar System. 
Ilyin A. G., Khafaga A. S. Study of the passage of a mixture of a radio pulse and narrowband noise through a phase detector. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/894/ynbvck1lovvtgrpv201of1120r42il7k/Ilin_KHafadzha.pdf The article considers the possibility of applying structural dissimilarities between the mixture of valid signal and noise, and simply noise to receive weak signals in digital information transmission systems. The presented work demonstrates that for structural differences application for the task of a radio pulse detecting against the background of noise and interference, it is necessary to employ nonlinear conversion. One of the technical solutions consists in a phase detector application. The article shows the possibility of the research results utilization for developing twochannel receiving units with enhanced noise immunity for digital signals transmission. The possibility of substantial noise immunity increase of the receiving unit by extra receiving channel application with phase detector is shown. This signal receiving technique may be successfully employed in the regions remote from the cities devoid of the developed internet communication structure. The areas of national economy, included in State programs, such as »Far East Hectare» and similar purposeoriented programs, financed by the local budgets of Russian Federation provinces and regions may be given as an example of the area of lowpower digital data transmission systems employing. State programs such as the Far Eastern hectare and similar targeted programmes financed from local budgets of regions and regions of the Russian Federation. 
Torishniy R. O. Application of the secondorder optimization methods to the stochastic programming problems with probability function. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/1c4/yaueu5su9rj9j4y76fbpf6htfw1ig8jz/Torishnyy.pdf The author considers the application of the secondorder optimization algorithms for stochastic optimization problems with the probability function as the objective or/and constraint function. The approximation of the probability function is based on the replacement of the Heaviside function with its smooth analog — the sigmoid function. It has been shown previously that such approximation and its first order derivatives with respect to the elements of the control vector converge to the exact ones. Moreover, the replacement of the probability function with its smooth approximation within the stochastic optimization problem leads to a good approximation of the optimal control vector and the optimal value of the target function. The smooth approximation of the derivatives allows us to use the firstorder optimization algorithms. Now the direct formulas for the second order derivatives of the approximated probability function with respect to the elements of the control vector are provided. The proof of convergence of the secondorder derivatives is not considered in this research. Possible applications of such approximations include the development of the new numerical algorithms for solving stochastic optimization problems, and new algorithms to determine the surface level of the probability function. Some numerical examples are considered in this article. For the cases of linear, quadratic, and logarithmic loss functions it was shown that the values of the smooth approximation of the probability function and their derivatives tend to exact values as the parameter in the sigmoid function tends to infinity. Also, an example of the constrained stochastic optimization problem with the logarithmic loss function and the probability function as the target was considered. The modification of Newton’s method is used to solve this problem to determine an optimal investment portfolio with three possible assets. 
Zaitsev D. O., Pavlov D. A., Nestechuk E. A. Methodology for monitoring the technical condition of onboard launch vehicle systems based on the processing of rapidly changing. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/e57/xo7oi36go6czb8vm92eq4zjdhdmkw9xh/Zaytsev_Pavlov_Nestechuk.pdf The article proposes a technique for monitoring the technical condition of onboard systems of spacerocket and technology based on the rapidly changing parameters processing on a time scale close to real. This technique novelty lies in the proposal of a new of quality indicators system, on which base the estimated characteristics of rapidly changing parameters are being selected for the technical condition monitoring of onboard systems of space rockets at the operational processing stage. The process of initial data preparation for the of diagnostic signs forming based on the rapidly changing parameters processing to analyze technical condition of the onboard systems of spacerocket technology at the operational stage is under consideration. The task of rapidly changing parameters processing on realtime scale is being set, and both restrictions and goal function are being described. The authors propose a quality indicators system, by which the decision is made on one or another alternative selection. The article presents classification of methods for optimization problems solving, as well as optimization methods, on which basis statistical search method for the set problem solution was selected. The system of indicators, which includes indicators of accuracy and efficiency of rapidly changing parameters’ characteristics processing option, as well as of the technical condition monitoring completeness indicator of onboard systems of space rockettechnology is disclosed. The article solves the problem of the rapidly changing parameters processing option selection the best by the efficiency indicators with account for accuracy limiting, as well as by the technical condition monitoring completeness indicator of onboard systems of space rockettechnology. A practical example of this technique application in the object domain is presented. Certain characteristics of rapidly changing parameters of the spacerocket technology from documentation, as well as the set of initial data for the set of alternatives forming were employed as a practical example. The developed technique includes a number of steps. At the first step, the initial data is being formed as a set of all alternatives. At the second step, a set of alternatives, reduced according to the accuracy indicator, is being formed from the one obtained at the previous step. At the third step, a set of alternatives, reduced according to the technical condition monitoring completeness indicator of onboard systems of space rockettechnology, is formed from the one obtained at the previous step. At the fourth step, the best set of characteristics is being formed in terms of completeness indicator, which can be processed on a realtime scale. At the fifth step, a set of diagnostic features from the characteristics of rapidly changing parameters is being combined with the existing set of diagnostic features. A new requirement for the telemetering program and for making changes to the instructions for evaluating the operation of onboard systems of space rockets is being formed at this step A set of 26250 alternatives is presented as an example. The number of alternatives was obtained as the number of combinations from the ten characteristics of rapidly changing parameters extracted from the documentation on telemetry information processing of the Soyuz2 launch vehicle, three methods of characteristics processing, five window functions, five options for window function size, five options for window function steps and seven options for processing nodes. This number is being considered for an example, since the Soyuz2 launch vehicle uses 369 characteristics and much more other variables. A complete set of variables consideration is impractical, since it will lead to the need for about two million alternatives considering. Inferences on the presented technique applicability in the object area to form diagnostic signs for the technical condition analyzing of onboard systems of rocket and space technology are drawn. The developed technique application is expedient for improving the algorithms for the technical condition analysis of onboard systems of spacerocket technology at the operational stage. 
Uryupin I. P. Methodology for monitoring the technical condition of onboard launch vehicle systems based on the processing of rapidly changing. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/962/lf03q0r7eyuykj95e4k6t4gjxouvmbae/Uryupin.pdf The purpose of the research consists in developing an optimization algorithm for continuous systems in the class of piecewise constant controls. In classical problems of optimal control of continuous systems, the admissible controls are, as a rule, bounded measurable ones (in applied problems, they are piecewise continuous). In some complex continuous systems, physical implementation of such admissible control seems impossible Then one can narrow down the set of admissible controls, for example, to the class of piecewise constant controls with a fixed number of switchings and search for a solution in this narrow class. It is clear, the suboptimal controls herewith will be obtained, which, however, with an unlimited increase in the number of switchings, will tend to the optimal one. Thus, the problem of minimizing the number of switchings becomes actual. To solve the set problem, a numericalanalytical algorithm has been developed based on the necessary conditions for optimality of switched systems. Boundary problems and formulas expressing the optimal values of piecewise constant control are obtained analytically, according to the necessary conditions. The resulting system of equations, as a rule, is transcendental and its solution is rather difficult. Thus, the author proposes to use the numerical minimization of the functional, followed by fulfillment verification of the necessary conditions to search for the optimal switching moments. The proposed algorithm is realized in MATLAB. The problem of a linear oscillator controlling with quadratic functional is being considered as an example. The optimal solution to this problem in the class of continuous controls was obtained using the maximum principle. In this work, the optimal solution to the problem in a narrower class of piecewise constant controls is being searched for. This solution is being found using necessary conditions for the switched systems optimality. It may be regarded as a solution close to optimal continuous control. Besides the problem of an optimal piecewise constant control synthesizing, the problem of finding the minimum number of switchings, at which the difference between the approximate solution and the exact one does not exceed a given error is also solved. The main result of the work is a numericalanalytical algorithm for minimizing the number of switchings of optimal piecewiseconstant controls for an approximate solution of the optimal control problem for continuous systems. 
Borzov D. B., Chernyshev A. A., Sizov A. S., Sokolova Y. V. Methodology and algorithm for constructing a computer network based on a wireless protocol. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/d4e/y3tf5su2n02lmjuhsu9wud7romax2xin/Borzov_CHernyshev_Sizov_Sokolova.pdf With the wireless protocols development, reconfigurable computing systems consisting of multiple processor modules keep on evolving. Systems based on wireless protocols are being considered as prospective for reconfigurable systems building. The purpose of this work consists in reducing the time consumptions contributing to a reconfigurable realtime system performance improvement. The research methods employed in this work are based on the set theory definitions, graphs, probability theory and mathematical statistics. Particularly, the graph theoretical approach to distribution supplemented with introduction of the system of the realtime reconfigurable computing system criteria, built on the wireless protocol, is taken as the technique basis. The research task consists in developing a technique for building a computing network based on the wireless protocol, ensuring data exchange between spatially separated processor modules, as well as an algorithm for building the computing network, which realizes the developed technique. This article presents the developed technique and algorithm for building a computer network based on a wireless protocol. The developed technique novelty consists in introduction of the distance factor for more accurate selection of the preferred processor module for the wireless network. The developed technique and algorithm of a realtime computing system built on a wireless protocol allows ensuring the optimal tasks distribution organizing in a reconfigurable computing system. It appears possible to develop software for distributing computational tasks to processor modules in order to reduce the time spent on data transmission within the system based on the presented algorithm. 
Nikulin V. S., Khizhnyakov Y. N., Storozhev S. A. Virtual adaptive vectormatrix meter of the oxidizer of the combustion chamber of a gas turbine engine. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/dd6/j5tnuka94h7nmqri0tqu1m3jl2et1cnc/Nikulin_KHizhnyakov_Storozhev.pdf Fuzzy logic methods have found wide application in control problems. However, when using the apparatus of fuzzy logic, it is necessary to sel ect models of fuzzy logical operations, being selected fr om empirical considerations. This complicates the algorithms construction for specific problems solving. Application of »classical» operations is justified only for solving simple problems and does not require a large number of rules. The purpose of the study consists in modernizing the vectormatrix approach applicable to the design of a neurofuzzy adaptive meter for the oxidizer of a gas turbine engine algorithm. The vector models application is being proposed, aimed at the ease of implementation, high speed and of the field application expansion. Practical significance consists in application of the vectormatrix approach of adaptive fuzzy control in the design of the combustion chamber coefficient meter of a gas turbine engine allows computational accuracy increasing, training time reduction, the scope of application expanding at the nondeterministic objects automation in the MISO system. Application of the matrix apparatus replaces the projections of the linguistic variable (termset) vector with the fuzzy vectors. The main operations on fuzzy vectors are given in the works of M.A. Martsenyuk, on which basis the design of a vector fuzzy oxidizer of the combustion chamber of a gas turbine engine is considered. Relevant is application of a singleton base for fuzzifier fuzzy vectors activation, as well as the fuzzy forward and backward vector implicators application for the turboprop scalar control forming. Vectormatrix representation of the initial information is convenient when programming the stateoftheart controllers of various objects. The disadvantage of this representation consists in the fact that it is not adaptable. Thus, the article proposes to supplement the vector part of the meter with Sugeno polynomials, which coefficients are being adjusted with the teacher by least squares method. 
Sviridov V. V. Methodology for assessing the quality of group interaction of robotic complexes in a variable phonotarget environment. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/299/yqwhe8u9hbianvovlarapmhrlslmfqq7/Sviridov.pdf The main priority of the Russian Federation in the field of military construction is the creation of a modern army, the basis of which are systems and complexes of weapons, military and special equipment, which include robotic complexes (RTK), providing an adequate response to the entire range of security threats, not only existing, but also likely in the future. Nowadays the nature of modern wars has significantly changed, which have become hightech, dynamic and remote, requiring fundamentally new approaches to both their conduct and militarytechnical support. Therefore, to modern robotic security complexes strict and, as a rule, contradictory requirements on providing such quality indicators as reliability, efficiency and completeness of problem solving, which is explained, first of all, by a priori uncertain dynamic environment in which the complexes operate. Maintaining these quality indicators of RTK group control at a given level is the most important factor in ensuring effective protection of critical facilities. With the increase of combat capabilities on the part of the enemy, the difficulty of controlling a group of RTK increases, it is no longer possible to maintain a given quality of their functioning manually. To solve this problem is possible only on the basis of automation of the process of RTK group control, i.e. development and creation of such adaptive system of group control of complexes, which under unpredictable influences of external conditions, based on analysis of own state of complexes changed values of parameters and/or structure of their interaction so that the preset quality of functioning of complexes for achieving common goal was kept. The purpose of this article is to develop a methodology for assessing the quality of group interaction of RTK when countering the enemy, based on the assessment of the contribution of each group complex to solving the overall target task. Group interaction of complexes is formed by adapting the group control system of RTK to terrain conditions, changing quantitative and qualitative characteristics of the enemy. The main problems facing the design of RTK is the complexity in the organization of their outgroup and ingroup interaction in a changing and nondeterministic environment, in the face of enemy opposition. One of the ways to solve these problems is to build a hybrid control strategy, i.e. integration of functional capabilities of centralized, collective, swarm and swarm control, in which, depending on changing and uncertain out and ingroup conditions, behavior of each complex is built on coordinated actions with neighboring complexes, which, in turn, depend on intentions of the complex itself in given conditions. In order to maintain a given quality of functioning of a group of complexes it is necessary to control the parameters, algorithms of their work and structure. At the same time control actions should be formed as a result of analysis of actual information received from means of reconnaissance RTK, internal controlled parameters of the complexes themselves. We have developed a methodology to assess the quality of RTK group control under conditions of changing background conditions, which represents a complex of models, the results of which together allow to achieve the set goal, namely: a model of detection of the enemy by RTK reconnaissance means based on the analysis of influence of terrain conditions and enemy characteristics, a model of counteraction of a RTK group based on equations of average dynamics, a model of assessment of probability of enemy defeat by RTK group under conditions of changing number of parties and chaos. The theoretical basis for the development of the presented methodology is the developed fundamental and applied research in the field of robotic control systems, viz:
The practical significance lies in the fact that the developed methodology of assessing the quality of group interaction of robotic complexes will allow to form the image of an adaptive system of group control of complexes, as well as to develop recommendations on the forms and methods of group application of RTK when solving problems of countering the enemy. 
Sudarenko D. A. Development of a database management system for a structural and parametric description of LTCC technology using Qt SQLite. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/68f/gu0pypk4cwrmktl4ck1vu8a898wu9p9d/Sudarenko_pravl_14.12.2021.pdf The low temperature cofired ceramic (LTCC) technology was selected as the technology under study. This technology has found wide application for the manufacture of RF and microwave microcircuits of low and medium degree of integration and can be applied in various industries such as telecommunications, medicine , automotive, military and space technology. Variable data of LTCC technology (sheet sizes, pastes naming, time, equipment setup, and others) are scattered throughout the documentation. The number of documents and procedures for production, control and management is quite large. The presented article proposes a method of structuralparametric description of the LTCC technology to improve the quality of the of microwave components production. Based on this method, a database based on MS Access was developed. The MS Access database has a number of disadvantages, since it is nonnetworked and does not allow making multiuser systems. These problems are being solved by the SQLite DBMS, which will be discussed in detail in this article. The process of a database creating in the SQLite DBMS for the microwave components production developed on the Qt framework is proposed. SQLite is a C ++ Qt framework library that implements a small, fast, selfcontained, highly reliable, fullfeatured SQL database engine. Databases are being partitioned into: 1) server databases, to which one can connect from different devices, and the data itself is stored on a specially dedicated server (MySQL, MS SQL, PostgreSQL); 2) standalone databases, to which SQLite belongs. SQLite implements a standalone (serverless) transactional SQL database engine with no installation, setup, or configuration required. Its code is an open source, and it is free to use for any purpose, commercial or personal. SQLite reads and writes directly to regular files on the disk. Thus, a complete database with multiple tables, indexes, triggers, and views is contained in a single file. The database file format is crossplatform, i.e. one can freely copy the database between 32bit and 64bit systems or between direct order and inverted order bites architectures. The Qt framework contains a universal interface for working with various databases. The databases in the Qt view are the drivers for the QtSql module. By default, when installing the framework, the SQLite database is available, for the rest of the databases, one need to install and build drivers for Qt. Qt provides an extensive database compatibility, with support for both open source and proprietary products. SQL support is integrated with Qt’s «modelview» architecture, simplifying GUI applications integration with databases The way of data aggregation in general form, as well as the relationship of tables in which the data is stored, and the way of data aggregation into aggregated indicators and portraits are presented. Assembly and connection of the other database libraries (PostgreSQL / MySQL / ETS) are adduced. A detailed process of a database creating in the SQLite DBMS for the microwave components production based on the LTCC SQLite Qt is shown. 
Deniskina G. Y. Method for finding approximate solutions of elasticity equations using spline wavelets. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/d0f/8oeej0kdterjpklseikgcyn6086r9slr/Deniskina.pdf In the technique being proposed the spline wavelets, built on the basis of an uneven subdivision scheme and a lifting scheme, are being employed for solving problems of the elasticity theory. The choice of such basic functions is justified by the fact that wavelets have a number of advantages compared to other basic functions. For example, the lifting scheme application allows composing wavelets with the given properties, such as smoothness, compactness of the carrier, symmetry, the required number of zero moments, vanishing at the boundary of the domain of functions corresponding to nonboundary mesh vertices. Lately, the wavelet analysis is attracting a lot of attention from the researchers, scientists and specialists in various disciplines. There are several reasons why wavelets are being successfully applied in signal processing, information compression, methods for finding approximate solutions of differential and integral equations [1, 2], computer geometry [35]. Such reasons include the following. Firstly, the high rate of wavelet coefficients decay. This allows obtaining rather accurate function approximations employing only a small number of summands in the expansion. Secondly, availability of fast cascade algorithms for finding coefficients of the function wavelet expansion. Thirdly, many commonly used wavelets (such as spline wavelets and Daubechies wavelets) have a compact carrier. In the proposed technique, a waveletsystem, consisted of smooth functions with the compact carrier, was built using the lifting scheme and a mask. Such wavelet systems may be employed for finding approximate solutions of partial differential equations and, as a consequence, they may be applied to solving problems of the elasticity theory. This application presupposes the use of the least squares method for finding approximate solutions of boundary value problems of mathematical physics [7]. 
Apollonov D. V., Bibikova K. I., Shibaev M. V., Gavrilova A. V. Сhoosing the architecture of the automatic control system of a convertible unmanned aerial vehicle – a tiltrotor. Trudy MAI, 2021, no 121, http://mai.ru//upload/iblock/07a/o63ooh2qxw9zfbr3hm5u7rzs6n9kt455/Apollonov_Bibikova_SHibaev_Gavrilova.pdf Unmanned Aerial Vehicles (UAVs) has been the research subject of several recent applications. This paper describes the flight dynamics simulation and automatic control system architecture development of the tiltrotor UAV. This tape of vehicle combines the highspeed cruise flight capabilities of a conventional airplane with the hovering capabilities of a helicopter by tilting their four rotors. The paper presents a mathematical model of convertible unmanned aerial vehicle (tiltrotor) and the architecture of a unified automatic control system for all flight modes of the tiltrotor. The authors propose a control system structure that uses a limited set of »toplevel» control parameters, including the total engines thrust and three moments acting on the UAV. The principle of forming the total thrust and moments by means of redundant set of »lower level» effectors, including engines orientation angles and each engine thrust, as well as aerodynamic control surfaces deflection, is determined. The possibility of using the proposed control principle is confirmed by the results of flight dynamics simulation of UAV executing a typical application scenario including vertical takeoff and landing modes, flight along a given route and transient acceleration and deceleration modes. The paper considers the issues of assessing the safety of UAV flight in the event of possible individual control failures, taking into account the existing redundancy. A criterion for assessing controllability in the form of the maximum guaranteed angular acceleration is proposed which allows comparing the consequences of failures of each control effector. The paper shows that in order to guarantee UAV controllability we need to impose requirements on the choice of controller operational algorithms, both in the UAV angular motion control loop and in trajectory motion control loop. 
Popov I. P. Combined rotations in technical systems. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/a15/0kjyvixxag99eul6bjio87zuyggtnx2k/Popov_.pdf The purpose of the research consists in generalizing the principle of a combination of movements to the circular movements. The relevance of the work is stipulated by the fact that in technical systems, including aviation and space technology, particularly, in aircraft transmissions, bearings, orbital systems, helicopter mechanisms and many others, combined rotational movements are widespread, and it is important to represent the nature of the total movement when designing. The author considers an xʹ0ʹyʹ coordinate system, which rotates in an x0y one without angular acceleration with the velocity of ɷ. The radius of rotation is ρ_{1}. Wherein 0x0ʹxʹ, 0y0ʹyʹ. The object a rotates in a xʹ0ʹyʹ coordinate system without angular acceleration at a speed ±ɷ. The radius of rotation is ρ_{2}. All standard characteristics of the ellipse were determined in relation to the case under consideration. The elliptical trajectory inclination is set. The article shows that in the case of the trajectory of the total motion is elliptical and the semiaxes are equal to (ρ_{1}+ρ_{2}) and ρ_{1}–ρ_{2}, the object performs circular motion in the coordinate system xʹ0ʹyʹ without angular acceleration with velocity –ɷ. Just as the result of the two nonaccelerated movements superposition is also an nonaccelerated movement, i.e. it is uniform and rectilinear movement, at rotations in the same direction the trajectory of the total movement represents a circumference. At circular motions with multiple speeds, the trajectory of the total motion represents spirals. The practical aspect of the study is being determined by the fact that the formulas obtained can be directly used in CAD when performing design work. 
Lurie S. A., Shramko K. K. On the correctness condition in boundary value problems of gradient elasticity theory. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/09e/3n4o7n6a1m04z3qmzplw6o8f76k78o0c/Lure_SHramko_.pdf The main subject of study in this article concerns the variational formulation of gradient models of elasticity and specific symmetry conditions in gradient theories of elasticity of a general form. Special attention is being paid to the symmetry conditions, which are a consequence of the fact that it is possible to change the order of differentiation in the components of the displacement gradient tensor in the potential energy density expression. First, the conditions of symmetry in the theory of elasticity and gradient elasticity are discussed, the features of the properties of symmetry in gradient models are noted in comparison with the classical theory of elasticity. Then the variational statements of gradient elasticity and the structure of the boundary conditions following from this statement are briefly discussed. Finally, the conditions for the formulation correctness of the of boundary value problems and their connection with the symmetry property of gradient elastic modules are established. This article presents the symmetry conditions analysis for components of the generalized elastic properties tensor of gradient models of elasticity. It is demonstrated that one of the conditions is related to the correctness of boundary value problems of gradient elasticity theories. It is established for the first time that physically and energetically insignificant components of the elastic modulus tensor may appear on the surface under boundary static conditions for stresses (with variations in displacements) and under boundary conditions on the contours of edges, which can lead to significant errors in solving applied problems. A procedure allowing always obtaining correct boundary conditions for arbitrary optioins of gradient elasticity theories is presented. 
Panfilov E. B. Mathematical model of the flow processes around a body with gasdynamic controls for the highspeed flow. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/05d/xvb04j2x1rkshep9g74nv5g7zo9ce3d2/Panfilov.pdf The objects interaction with a highspeed flow is accompanied by the occurrence of high dynamic and thermal loads. At the same time, it is necessary to ensure the reliability of functioning and the efficiency of movement control. One of the directions for improving the aircraft movement control efficiency is the development of gasdynamic movement controls, movement stabilization and reduction of temperature loads on surface areas. In this regard, it is necessary to correctly determine the thermal regimes of the most heatloaded areas of the aircraft surfaces. For this purpose, the study of thermogasdynamic processes near a conical surface with the presence of gas injection into a highspeed flow was carried out. A mathematical model of a highspeed flow around a body with the presence of gas injection into a highspeed flow is presented, which takes into account the processes of chemical kinetics that occur in air at high temperatures. The air was considered as a mixture of five components (O_{2}, N_{2}, O, N, NO). In the first approximation, for the model of chemical kinetics, the initial five reactions of the Park K. model are applied. With regard to motion in the upper layers of the atmosphere, these reactions describe the main features of the processes occurring in air at high temperatures. The rate constants of each forward and reverse reaction are determined using the generalized Arrhenius formula. Investigations of the processes were carried out in a highspeed flow (M_{∞} = 10) of a conical surface (θ = 10^{о}) with gas injection holes located along the generatrix at a distance x/l = 0.3, 0.6, 0.9 from the nose. Free stream parameters: P_{∞} = 79.8 Pa, Т_{∞} = 270.7 K, mass fraction γN_{2} = 0.767, γО_{2} = 0.233. The parameters of the injected jets Tj = 293 K, J = 4.95 is the coefficient of penetration of the gas jet into the highspeed flow [4,5]. The mathematical model was verified by comparing the results obtained in a numerical experiment with the data of [7] and [8]. A good correlation of the calculation results was obtained. Small differences in data may depend on the choice of the chemical kinetics model and, accordingly, the reaction rate constants. Verification of the results obtained using the mathematical model with the results obtained experimentally showed a good visual coincidence of the shockwave structure. Application of the model of chemical kinetics made it possible, in the first approximation, to obtain the thermodynamic parameters of the highspeed flow near the investigated body with the gasdynamic movement controls with sufficient accuracy. Comparison of the temperature data obtained in the course of the fullscale and numerical experiments showed a discrepancy of the order of 18—23%. he data obtained in the course of the research showed that the developed mathematical model gives sufficiently accurate results and allows them to be used in the study of processes occurring near a body in a highspeed stream with a gasdynamic movement controls. 
Duong M. D. Real gas, combustion and detonation, thermodynamic equilibrium, equilibrium detonation adiabat, mathematical modeling, power plants, methaneair combustible mixture, hydrocarbon fuel, extremum of thermodynamic functions. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/5cd/7j6amuo3megry3ze67o85469dl7cfrmn/ZyongMinDyk_.pdf The article presents physicomathematical models of equilibrium onedimensional detonation with account for the real gas state equation. An original computational algorithm is presented for plotting an equilibrium detonation adiabat employing a simplified real gas state virial equation. Specifics of the numerical simulation algorithm implementation employing the real gas state virial equation are analyzed. Singlefluid approximation, according to which the extra additive, associated with the existence of the intermolecular interaction, appears in the equations of the real gas thermodynamic functions for transition from the pure gas state equation to the combustion products as a model of mixture was employed. The results of comparing the problem solution on the equilibrium parameters computing of the stoichiometric methaneair mixture combustion products at the constant specific volume and internal energy with the known literature data are presented for the developed algorithms verification. The difference was less than 1%. The perfect gases model application at high initial pressure may lead to the pressure dissimilarity from the real gas model by more than 30%. A study of equilibrium adiabat characteristics detonation products of a stoichiometric mixture of methane and air for initial pressures up to 50 atm was conducted. In this case, the perfect gas model application leads to the pressure decrease behind the detonation front up to 13%. The ChapmanJouguet detonation velocity at the increased initial pressures may exceed the one calculated by the ideal model by more than 10%. The need to account for the properties of a real gas for detonating mixtures in the highpressures region was confirmed based on the analysis of the numerical modeling results.

Boikov A. A. Depressurization loads analysis method for flange connection of pipes with metal Zshape seal. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/953/ft0hd5k01zt4jteppat60ieliuujj51n/Boykov_.pdf The article considers coupling of the pipelines by the noncontacting flanges, which is being pressurized by installing a Zshaped metal seal into the connecting block. The issue of the coupling assessment necessity with a view to the seal edges breakaway from the flangesrsquo; surfaces is being put forward. This checkup should be performed prior to the tightness computing, since it may appear that the wedgelike seal edge breaks away from the seal surface under the impact of the internal pressure or axial external force, which leads to the impossibility of performing sealing functions by the assembly. Computational models applied by the author in the previous articles while obtaining expressions describing the pipelines flange coupling behavior with the Zshape metal seal at the stage of both loading by the internal pressure and axial force were used. Derivation of expressions for the depressurizing loads is being based on introduction of other initial data concerning values of the force factors acting on the parts of the coupling. The reverse problem is being solved. Previously, the contact load was being defined through the known internal pressure and external axial force. In the present case, it is necessary to find the internal pressure of the external axial force, which will be the possible depressurizing load, by the known contact load on the detached edge. In the case of both with the internal pressure and external axial force, two possible values of the pressure and depressurizing force will take place, namely in the case of the upper or lower edge detachment. Minimum of the two possible values is being selected as the depressurizing force. As the result, the possibility will arise to define which edge will be the first to detach. 
Prokudin O. A., Rabinsky L. N., Tran Q. T. Depressurization loads analysis method for flange connection of pipes with metal Zshape seal. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/aa6/sbkjn8xlxem5hoa1tnlk01si41a17imx/Prokudin_Rabinskiy_CHanKuetTkhang_.pdf The article presents the studies of mechanical characteristics of a new composite material. The beamshaped samples of rectangular crosssection from the laminar composite material were fabricated. The composite represents a pack of aluminumlithium and fiberglass plastic sheets of 0.3ndash;0.5 mm thickness. The effective elastic moduli of the composite pack obtained this way were determined by the experiment for quasistatic uniaxial tension. The basic dynamic tests were performed for cantilever beam samples made from the aluminumfiberglass composite laminate for the freely damped oscillations. The freely damped oscillations were being excited kinematically by applying some initial transversal translation to the freeend section of the beam or dynamically by applying some transversal concentrated shock load. The gainfrequency characteristics of the samples of various geometric dimensions were obtained, and the peaks on the gainfrequency curves corresponding to the resonant frequencies of first eigenmode oscillations were revealed. The effective elastic moduli of the composite material were computed employing the obtained results. The damping factors of the studied composites were determined using the measured peaks widths in the vicinities of the resonant frequencies. The appropriate statistical analysis of the obtained tests results was performed, scattering of the results, corresponding to the samples of different widths was revealed. The exact solution to the direct problem on oscillation of the cantilever composite beam of laminated structure with the assigned physical constants was obtained for the accuracy evaluation of the obtained results. A model of transversal oscillations of the beam was developed, accounting for the transversal shift deformation, but neglecting the crosssection crimping deformation. The longitudinal and transverse translations of a point along the line, connecting the symmetry centers of crosssections as well as the angles of rotation of crosssections around transverse horizontal axe, are accepted as the model main kinematic variables. Relations for the deformations are written, and equations for both kinetic energy and strain energy of an oscillating beam are obtained. The appropriate equations of motion as well as their natural boundary conditions were obtained by the Hamilton variation principle. The boundary value problem for harmonic transverse oscillations of the cantilever beam was stated, and the corresponding characteristic equation for the frequency was derived. This equation is transcendental, and is being solved numerically. The complex moduli approach was applied to account for the damping effects. The frequencies and damping decrements obtained after the numericalanalytical solution of the direct problem of the beam oscillation are in good correlation with the test data. 
Kyaw Y. K., Soliaev J. O. Topological optimization of reinforced panels loaded with concentrated forces. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/e93/a5ox8y9whd8ilqeadgqhek3ve6ovzvh7/CHzho_Solyaev_.pdf A method of topological optimization of geometry of reinforcing panels loaded with concentrated forces is proposed. The proposed method is based on the numerical solution of the deformation problem of a panel of variable thickness. The optimization parameter is the thickness of the panel defined by a fictitious density function. The objective minimized function is the total energy of deformation of the panel. As a result of solving the optimization problem, an arrangement of stiffening ribs is determined which provide, at their own minimum mass, a maximum increase in the stiffness of the structure. The advantages of the proposed method, as compared with the standard topological optimization approaches, are the reduced requirements to the computational resources and the possibility to obtain the geometry of the stiffening ribs, which can be manufactured, for example, by milling. The paper investigates the effectiveness of the approach used in comparison with variants of regular finning of panels. It is shown that for some loading variants mass efficiency of optimized structures can be more than 25 times higher in comparison with the best variants of regular finning. Application options for numerical calculations of both classical plate theory and revised theory taking into account the transversal shear are considered. It is established that in the considered optimization problems with the condition of minimization of total energy of deformations application of classical theory is more effective. 
Eliseev A. V., Kuznetsov N. K., Eliseev S. V. New approaches to the estimation of dynamic properties of vibrational structures: frequency functions and connectivity of movements. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/74a/8faj3f15zm546nolzfoxam2l83niasq8/Eliseev_Kuznetsov_Eliseev_.pdf The scientific and methodological foundations for solving dynamics problems of technological and transport objects, operating under high vibration loads, are being developed. The purpose of the study consists in developing methods for dynamic properties analyzing of technical means (machines, equipment, devices), which design schemes are being reflected in the form of mechanical vibratory systems with several degrees of freedom. The studies are based on application of analytical apparatus of system analysis and its applications to the problems of machines dynamics, equipment and instruments protection fr om the vibrational impacts, which constitutes the basis for operational safety and reliability provision of hardware components. The issues of extra bonds, being realized by the simplest mechanisms, impact on the dynamic properties of the systems were regarded. Specifics of mechanical vibrational systems were studied based on introducing the notions on frequency systems and their forms. Specifics of dynamic vibrations damping modes under single and joint (by two coordinates) effect of the two periodical disturbances were studied. The numerical modeling data is presented. Characteristic modes of natural vibrations can be distinguished in the dynamics of mechanical vibrational systems, being regarded as design schemes of technical objects of both transport and technological purpose. Vibrations occurring herewith reflect the system reaction on the harmonic type external disturbances, representing movement of elements with certain amplitudes vibrations ratios along various coordinates. These ratios are being formed based on the parameters values of the system elements at the introduction notion on frequency functions, associated with the detailed regard of potential and kinetic energies ratio, as well as natural vibrations frequencies function of the energy expressions structure. Particularly, extremal property of the potential and kinetic energies ratio of the system is associated with the natural vibrations frequencies values. Within the framework of the approach being developed, the effect of frequencies closingin of the dynamic vibrations damping to the one of the natural frequencies was considered. The possibility of the lim it mode of the mechanical system realization with two degrees of freedom in the form reduction to the system with one degree of freedom was demonstrated. 
Lokteva N. A., Serdyuk D. O., Skopincev P. D., Fedotenkov G. V. Unsteady deformation of anisotropic circular cylindrical shell. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/846/03kjxqy4l3a2wx6uc93m18ouk6g89zrj/Lokteva_Serdyuk_Skopintsev_Fedotenkov_.pdf The unsteady deformation of a thin, infinitely long circular cylindrical shell of constant thickness under the impact of a concentrated shock load distributed over an arbitrary region on its lateral surface is being studied. The shell material is assumed to be linearly elastic, anisotropic, and symmetrical about its middle surface. The KirchhoffLove model is employed to describe the shell motion. The motion of the shell is being considered in a cylindrical coordinate system associated with the axis of the cylindrical shell, and the soughtfor function of the normal nonstationary deflection is constructed by connecting the Greenrsquo;s function with the function of the operating load using an integral operator of the convolution type in spatial variables and time. The Greenrsquo;s function for an anisotropic shell is a solution to a special problem of the impact of an instantaneous concentrated load on the shell, mathematically modeled by the Dirac delta functions. Expansions in exponential Fourier series, integral Laplace transform in time and integral Fourier transform in longitudinal coordinate are being used to construct the Greenrsquo;s function. The inverse integral Laplace transform is being performed analytically, and the original integral Fourier transform is being found using numerical methods for integrating rapidly oscillating functions. The integrals of the convolution of the Greenrsquo;s function with the load function are being taken with quadrature formulas using the rectangle method. As an example, the unsteady dynamics of cylindrical shell was sstudied under the impact of arbitrarily timedependent concentrated load and load distributed over the finite area belonging to the lateral surface of the shell. Several options of symmetry of the elastic medium (isotropic, orthotropic and anisotropic) herewith were analyzed, which demonstrates calculated solution versatility both in terms of influence nature and shell material. For the considered symmetry options, the study of the unsteady vibrations propagation character, which allowed evaluating the solution adequacy, was conducted.The presented approach to constructing the unsteady deflection function while transition to the dimensional values opens opportunities for the analysis of the stressstrain state of the extended cylindrical shells with account for various options of the material anisotropy and law of distribution of the unsteady loading along both coordinates and time. 
Oreshkin V. I., Meleshin Y. M., Tsvetkov V. K. Digital antenna array signal bearing accuracy improving. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/ff8/i0xk2rnq45vxm1f397p05tt2fnyb8js2/Oreshkin_Melyeshin_TSvetkov_.pdf This article discusses technical solutions for the development of receiving device for a spacecraft with a possibility of direction of arrival (DOA) estimation. The device must provide DOA) estimation of the incoming signal with a given accuracy and statistical characteristics under typical conditions for a spacecraft (weak signal, low consumption, small size). To solve this problem, it is proposed to use wellknown sumdifference method of DOA estimation based on a smallsize antenna array with digital diagramming (DBF). DBF antenna is a type of active antenna array, each channel is a separate receiver with digital signal processing. The formation of the phase and amplitude distribution in the antenna aperture is carried out in digital form. If we have information about the signals in separate channels of the antenna array, it is possible to use correlation algorithms for DOA estimation. For example, MUltiple SIgnal Classification algorithm (MUSIC). The essence of the algorithm is to calculate the eigenvalues of the correlation matrix formed from signals in various channels of the antenna array. This algorithm makes it possible to use the total energy of a data packet, since the values of the correlation matrix contain the integral result averaging the thermal noise. However, this approach is computationally expensive. It is necessary to carry out several convolution operations to form the correlation matrix. Instead, it is proposed to use the phaseinterferometry direction finding (DF) method with use an only one convolution operation per antenna array channel to improve DF accuracy. The convolution operation is performed on the received signal, stored in memory, and the detected data to accumulate energy and reduce the effect of noise on the DF result. Due to the very weak signal against noise background, signal processing is carried out in several stages. The receiving signal is filtering and Doppler shift is compensating. Then an approximate DOA estimation is made. The resulting direction estimate is used to form the main beam of the digital antenna array. The detected signal data is used as coefficients to compress the entire packet and increase the energy of the signal to increase DF accuracy. 
Pavlov A. N., Pavlov D. A., Umarov A. B. Digital antenna array signal bearing accuracy improving. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/ec4/puy4du9yb39ilcweybn722b28m8bc791/Pavlov_Pavlov_Uvarov_.pdf In the course of the research and development works performing on a spacecraft creation and development (a small spacecraft in particular), the important and integral condition of studying the onboard systems capabilities of a small spacecraft consists in performing analysis and evaluation of its structural states architecture. These states reflect both functional and technological specifics of the small spacecraft control. One of the primary tasks associates with the necessity of structural and functional survivability evaluating of the subsystems and a spacecraft as a whole, which often has to be performed under conditions of uncertainty due to the impossibility of simulating the whole spectrum of the space medium conditions. With a view to the existing uncertainty, it is necessary to consider all possible modes of the system development or degradation while its separate elements failure, i.e. pessimistic, optimistic and intermediate scenarios. The structural analysis of the small spacecraft onboard system functioning begins, as a rule, with plotting a diagram of the object functional integrity, representing a logically universal graphical tool for the structural representation of the system objectsrsquo; properties under study. Functional integrity diagrams allow representing correctly both all traditional types of structural diagrams (block diagrams, fault trees, event trees, connectivity graphs with cycles) and a crucially new class of nonmonotonic structural models of various properties of the studied systems. The functional integrity diagram of the small spacecraft onboard system allows graphical representation of logical conditions for their own functions implementation by the elements and subsystems of the small spacecraft. It allows representing also the modeling goals, i.e. logical conditions for the studied system property implementation, such as, the system reliability or failure, safety or accident emergence, these or that operation modes implementation of the small spacecraft onboard control system, etc. 
Shkinderov M. S., Mubarakov R. R. Simulation of the noise immunity of an access control and management system under the influence of an electrostatic discharge. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/9cb/l4b6yvy4tqvvdpjwhau69x6sl902z4yo/SHkinderov_Mubarakov_.pdf An access control and management system is an important element in ensuring the security of access to a building. The effectiveness of an access control and management system is dependent on reliable used in an area of operation where electromagnetic interference may be present. One of the dangerous sources of electromagnetic interference for such systems is visitors to the building. They may have accumulated static electricity. During normal walking, a person can be charged up to a voltage of about 15 kV. Electrostatic discharge may occur when passing through the turnstile. Electrostatic discharge can cause induced interference in communication lines and secondary power lines. Induced interference can lead to a violation of the noise immunity of the access control and management system in the form of shortterm failures. The simulation model for investigating the induced interferences under the influence of an electrostatic discharge on the turnstile the paper proposes. The simulation results give an idea of the parameters of the induced interference in the wire lines of the access control system. On the basis of the parameters of the induced interference, the quality of the functioning of the system elements under the influence of an electrostatic discharge is assessed. For probabilistic assessment of noise immunity of system elements, a method based on calculating the probability of a single bit error is used. In this case, a temporary disruption in the functioning of the electronic elements of the system is possible. The results obtained are in good agreement with experimental data. 
Masyukov I. I. Method and device for arranging tasks in reconfigurable computing systems. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/2b2/kxm5csw8nv2pgibk692a9ve5jjt3f55c/Masyukov_.pdf In view of the growing complexity of the problems being solved, reconfigurable computing systems (RCS) have become widespread in various branches such as industry, aviation, instrument making, etc. The RCS distinctive aspect consists in the ability of the internal architecture changing for the task being solved, allowing productivity and energy efficiency increasing. The high degree of integration and hardware configuration allowed FPGAs application as the main computational element. When solving the information graph on the RCS, in view of the employed and available resources of the reconfigurable field, it is being divided into subgraphs, for which a configuration, describing the tasks locating among the FPGAs is being composed. Due to the complexity of the location search problem, which is NPcomplex, its execution on a host computer operating in real time seems impossible. The existing approaches are either inapplicable for the DCS configuration search, or being solved programmatically. Thus, the development of the tools reducing the search time for the RCS configuration is uptodate. An algorithm and a model, including the problem of the set covering, were created when developing a unit for the tasks location in the RCS. The model describes the unit construction, and four criteria. These criteria are being based on the ideas of tasks selecting from an adjacency matrix based on the number of links, the intensity of exchange between them and the occupied and available resources for location, allowing reduce the number of enumeration options, which made it possible to reduce the computational complexity of the algorithm. The algorithm developed on the basis of the model, in the set of selection, storage and assignment procedures, can be implemented on the current hardware. In the course of experimental studies of the tasks arrangement in the RCS, an analysis of the performance and the resulting final configuration was performed. It is shown that the developed unit is 5.17 times faster than the similar software. Thus, the inference can be drawn on the hardware implementation of the presented method and algorithm advantage. The developed unit is applicable in the RCS operating in real time, due to its productivity increase. 
Sudarenko D. A., Lyutov A. V. Development of a database management system for a structural and parametric description of LTCC technology using ADO.NET. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/d68/qc59hvg6fl562g90kuyfmf4tn905q8xc/Sudarenko_Lyutov_.pdf Low temperature cofired ceramic (LTCC) technology was chosen as the technology under study. Currently, LTCC technology has been widely used in various fields of electronics, especially for the production of microwave microcircuits of low and medium integration. This technology provides an inexpensive solution for mass production of electronic devices in telecommunications, medicine, automotive technology, military technology and other industries. During the implementation of LTCC technology, problems were identified related to the mutual influence of a large number of parameters at each stage of production on the quality of products. To improve the quality of the production of microwave components, a methodology of structuralparametric description (STR) of the LTCC technology is proposed. Based on this methodology, an MS Access database was developed. Access technology does not allow making multiuser, distributed systems; to solve this problem, it is proposed to use the database management system (DBMS) ADO.NET. Before Microsoft released the .NET framework, one of the main data access technologies used in applications was ADO (ActiveX Data Object). With the release of the .NET framework, ADO.NET became the successor to ADO. ADO.NET is a family of technologies that enable developers of .NET applications to interact with data using standard and structured approaches. ADO.NET manages both internal data (created in computer memory and used inside the application) and external data outside the application — for example, in a database or text files. Regardless of the data source, ADO.NET presents data in application code in tabular form, as rows and columns. When interacting with external data sources, ADO.NET can use disconnected data technology. With earlier technologies, developers typically created a persistent database connection and used various recordlocking techniques to safely and correctly modify the data. With the advent of the Internet era, the strategy of maintaining open connections for each of the many concurrent HTTP requests to a web application has proven to be ineffective. For ADO.NET, the preferred strategy is to open the connection before the database query and close it immediately after the query is complete. The article discusses the structure of the ADO.NET framework of the Microsoft Visual Studio system, its main parameters and features. The ADO.NET architecture and parameters for establishing connections with external data sources are presented. The process of creating a database in the ADO.NET DBMS for the production of microwave components based on LTCC MS SQL Server is shown. ADO.NET manages both internal data (created in computer memory and used inside the application) and external data outside the application — for example, in a database or text files. Regardless of the data source, ADO.NET presents data in application code in tabular form, as rows and columns. The article discusses the structure of the ADO.NET framework of the Microsoft Visual Studio system, its main parameters and features. The ADO.NET architecture and parameters for establishing connections with external data sources are presented. The process of creating a database in the ADO.NET DBMS for the production of microwave components based on LTCC MS SQL Server is shown. 
Popov E. P., Vereikin A. A., Nasonov F. A. Investigation of the physical features of aviation systems using mathematical modeling using the example of an air cooling system. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/944/ikytwd6wmmglnago3jx2ousoenu9hm8k/Popov_Vereykin_Nasonov_.pdf The relevance of the research issue lies in the need to check and adjust algorithms of aviation systems at each stage of their development. In connection with the expansion of the application scope of aircraft developed by PJSC laquo;Sukhoi Companyraquo;, a need arises to solve the problem of geometry optimization in joint hydraulic and thermal calculations. For this purpose, special software complexes are being employed that allow replacing real complex systems structures with structural schemes in the form of blocks, i.e. mathematical models that fully describe these systemsrsquo; structures. Practice has shown that, along with the existing methods for technical condition monitoring of the air cooling system (SVO) as part of a prospective unmanned aerial vehicle (UAV), there is a necessary to perform automated monitoring of the trend of product parameters during flight tests [1]. Let us consider how the method applied in the presented article will affect economic efficiency on the example of a PJSC laquo;Sukhoi Companyraquo; prospective unmanned aerial vehicle (UAV). The insurance cost of the aircraft equals to 1.3 billion rubles, the insurance cost of the ground control point of a promising UAV is designated at 145 million rubles. Thus, the total price of the manufactured goods is 1.445 billion rubles [1]. The price is determined based on the cost recovery principle, where no more than 20% is the cost of the head contractorrsquo;s work. In summary we get the price of the goods produced of 1.445 million rubles, and the cost of the goods produced of 290 million rubles (20% of 1.445 billion rubles) [2]. To achieve this goal, the following tasks were identified and solved by the implementation and development of the algorithms SVO in the SimInTech PC, which allowed improving the efficiency of the workflow and eliminating system shortcomings. The structure of the SVO mathematical model building in the SimInTech PCSVO is a complexbranched network of pipelines, including various units such as heat exchangers, dampers, dehumidifiers, check valves, overpressure sensors and temperature sensors. Calculation of such systems manually or with the stateoftheartn computational fluid dynamics software systems requires significant computational resources and labor intensity. Due to the laquo;Set conditionsraquo; block, various situations of electric fans operation (EV) are modeled, which ultimately allows apprehending of the system behavior in the situation being considered. It offers the possibility to simulate failure situations and timely detect and eliminate the system weaknesses. The method for creating the SVO mathematical model, which includes the physical processes, occurring in the system, and control algorithms, allows developing the basics for solving the problem of reliable control of the technical condition of the SVO as part of a promising UAV during operation. It allows as well detecting malfunctions occurrence, preventing thereby the irreversible process of the system destruction. The three considered cases of the SVO functioning simulation clearly demonstrate that application of the proposed method of working out allows identify the system operation shortcomings and increase the workflow efficiency. 
Apollonov D. V., Bibikova K. I., Gavrilova A. V., Shibaev M. V. Issues of choosing the architecture of the automatic control system of a convertible unmanned aerial vehicle – a tiltrotor. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/caf/isbidlageh0q6it1foxxqzqs0i6tv4fp/Appolonov_Bibikova_Gavrilova_SHibaev_.pdf The relevance of the research issue lies in the need to check and adjust algorithms of aviation systems at each stage of their development. In connection with the expansion of the application scope of aircraft developed by PJSC laquo;Sukhoi Companyraquo;, a need arises to solve the problem of geometry optimization in joint hydraulic and thermal calculations. For this purpose, special software complexes are being employed that allow replacing real complex systems structures with structural schemes in the form of blocks, i.e. mathematical models that fully describe these systemsrsquo; structures. Practice has shown that, along with the existing methods for technical condition monitoring of the air cooling system (SVO) as part of a prospective unmanned aerial vehicle (UAV), there is a necessary to perform automated monitoring of the trend of product parameters during flight tests [1]. Let us consider how the method applied in the presented article will affect economic efficiency on the example of a PJSC laquo;Sukhoi Companyraquo; prospective unmanned aerial vehicle (UAV). The insurance cost of the aircraft equals to 1.3 billion rubles, the insurance cost of the ground control point of a promising UAV is designated at 145 million rubles. Thus, the total price of the manufactured goods is 1.445 billion rubles [1]. The price is determined based on the cost recovery principle, where no more than 20% is the cost of the head contractorrsquo;s work. In summary we get the price of the goods produced of 1.445 million rubles, and the cost of the goods produced of 290 million rubles (20% of 1.445 billion rubles) [2]. To achieve this goal, the following tasks were identified and solved by the implementation and development of the algorithms SVO in the SimInTech PC, which allowed improving the efficiency of the workflow and eliminating system shortcomings. The structure of the SVO mathematical model building in the SimInTech PCSVO is a complexbranched network of pipelines, including various units such as heat exchangers, dampers, dehumidifiers, check valves, overpressure sensors and temperature sensors. Calculation of such systems manually or with the stateoftheartn computational fluid dynamics software systems requires significant computational resources and labor intensity. Due to the laquo;Set conditionsraquo; block, various situations of electric fans operation (EV) are modeled, which ultimately allows apprehending of the system behavior in the situation being considered. It offers the possibility to simulate failure situations and timely detect and eliminate the system weaknesses. The method for creating the SVO mathematical model, which includes the physical processes, occurring in the system, and control algorithms, allows developing the basics for solving the problem of reliable control of the technical condition of the SVO as part of a promising UAV during operation. It allows as well detecting malfunctions occurrence, preventing thereby the irreversible process of the system destruction. The three considered cases of the SVO functioning simulation clearly demonstrate that application of the proposed method of working out allows identify the system operation shortcomings and increase the workflow efficiency. 
Peshevets S. V. Methodology for substantiating additional requirements for the training of electronic warfare specialists. Trudy MAI, 2021, no 120, http://mai.ru//upload/iblock/3cb/7yjo5ubkqyigwkjqhkvoxdennxasog17/Peshevets_.pdf The article substantiates the expediency of improving the quality of training of specialists in the field of electronic warfare. A methodology has been developed to substantiate additional requirements for the training of electronic warfare specialists. The use of mathematical methods and models in the processing of expert information is substantiated in the interests of ranking the requirements for the training of specialists. Additional requirements for the training of specialists in electronic warfare have been formulated. It is shown that the most important requirements for specialists in electronic warfare are the ability to make decisions, organize and implement the use of forces and means of electronic warfare units against aerospace control systems. According to the results of the study, using the Rush model for evaluating latent variables and a model that takes into account the competence of experts, it was found that the most important requirements for the training of electronic warfare specialists to perform the tasks of disorganizing the control of airmobile robotic systems of foreign armies are such as: be able to make decisions on the use of forces and technical means of electronic warfare units, organize and implement the use of forces and technical means of electronic warfare units; be able to make a decision on the use of forces and technical means of electronic warfare units, organize their use of electronic warfare units and control them in the course of fulfilling the tasks of electronic reconnaissance and suppression in conditions of radioelectronic interference created by modern electronic means of leading foreign countries; know the features of the use of modern domestic samples of electronic warfare technology. 
Popov I. P. Classical mechanics methods application to electric charges. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/d3b/h1u5ro6yrzisvm0gqwl8opmqkk202dxe/01_Popov_rus_eng.pdf The article proves three theorems associated with studying accelerated electric charges on the basis and in terms of classical mechanics. Active development of aerospace ion and plasma engines theory touches upon a number of aspects, the two of which are being considered in the presented work, namely the charged particles dynamics and electromagnetic radiation at their acceleration. It is assumed that the charge moving along the circular path, i.e. with the centripetal acceleration, should necessarily radiate electromagnetic waves. It spreads, inter alia, to the cyclotron radiation.
The terms and methods of classical mechanics are being used, which spread, inter alia, to the electric charges dynamics in a part of forces, accelerations, displacements, work and energy. The starting point is a credible statement. A number of mathematically correct transformations is being performed with it. Thus, the result is necessarily reliable. Electromagnetic waves possess momentum and energy. The wave receives energy from the energy source, which leads to energy reduction of the source itself. At the same time, any decrease in energy is being necessarily stipulated by the corresponding work performing. Three theorems has been proved. Theorem 1. A tangentially accelerated charge does emit electromagnetic waves. Theorem 2. A normally accelerated charge does not emit electromagnetic waves. Theorem 2 formalizes a wellknown in mechanics circumstance that the centripetal force does not perform work (since the scalar product of orthogonal vectors must be zero). Theorem 3. Electric charge satisfies Newton’s second law. In view of Theorems 1 and 2, the cause of magnetron radiation should be sought in the tangential acceleration caused by the Coulomb interactions of the beam charges. 
Ekimenko A. A., Mikhailov D. Y. Investigation of the interaction of space debris particles with structural elements of a spacecraft. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/6df/6zc771qe0dj8wt3pcoszjg48ggxiy4ns/02_Ekimenko_Mikhaylov_rus..pdf During operation, spacecraft are constantly exposed to external factors that lead to degradation of the structure and external elements. As a result, such an impact leads to changes in the optical properties of materials, changes in the physical and mechanical properties of structural materials, the formation of craters and through breakdown of the walls, as a result of which the operation of both individual onboard systems and the spacecraft as a whole is disrupted, which is a very urgent task. One of the influencing factors on the spacecraft is the flow of cosmic dust particles and the pollution of outer space by space debris particles, which have different velocities. The size range of space debris and dust particles varies from a few micrometers to tens of meters. Solid particles with a size of less than 1 mm are considered as a constant influencing factor, characterized by the density of their flow. Also, an equally important parameter of space debris is the shape of the particles. The article presents the results of a study of the impact of particles on the design of the spacecraft. The process of crater formation with equivalent stresses at velocities of 1, 1.5, and 2 km/s is considered. Graphs of the total stresses over the thickness of the barrier and the change in the depth of the craters over time are presented. In this paper, as an object of research as an element of the spacecraft, the result of the interaction of a twolayer coating on impact with a particle of space debris, the size of which is much smaller than the thickness of the coating, is considered. The coating in the form of two plates made of a composite protective shield and an aluminum plate, are shown in Figure 1. The results of the numerical simulation are shown in Figure 3.The results of the evolution and the formation of craters at different points in time are shown. As a result of the collision of the particle with a softer barrier, the polymer coating substance is carried away. At the same time, a crater is formed on the aluminum barrier with an increase in diameter at particle velocities of 1.5 km/s and 2 km/s. Based on the results of numerical experiments, the impact effects of a steel particle on an aluminum barrier with a polymer coating are analyzed. Taking into account a comprehensive study covering the physical and mechanical, mathematical features of modeling a highspeed impact, a large amount of information about the interaction of a particle with an obstacle at different speeds of movement was obtained. The polymer coating is destroyed in all the studied variants, taking part of the kinetic energy of the particle. With an increase in the speed of movement, the amount of material entrainment and the diameter of the coating detachment from the aluminum barrier increases. After the destruction of the polymer coating, the particle hits the aluminum barrier. As the speed increases, the crater depth and stresses in the aluminum barrier also increase. The rate of increase in the depth of the crater is also proportional to the speed of movement of the particle. In all variants of the numerical experiment, the steel particle undergoes significant deformations, but significant mass entrainment occurs only at a speed of 2 km/s. The results of crater formation and stress in the barrier at different particle velocities of less than 1 mm in size allow us to create a foundation for further experimental studies to take into account the impact of particles on the spacecraft design elements. 
Win K. K., Temnov A. N. Angular oscillations of solid bodies with a twolayer liquid near the main resonance. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/682/d4uqroi1qlxft5j0v48kdeoa33is5m0m/03_VinKoKo_Temnov_rus_eng..pdf The development of rocket and space technology has led to the widespread use of cryogenic liquids, as a result of which it was proposed to create a certain stock of cryoproducts that are simultaneously in a twophase or threephase state, while forming layers of liquid, to increase their shelf life on board spacecraft or in tankers of future space refueling stations. Nonlinear problems of the dynamics of a solid body having a cavity filled with several liquids are of considerable applied and theoretical interest. Many important problems of the dynamics of mechanical systems, including liquid masses with timevarying boundaries, lead to the need to solve the problem of the interaction of liquid with absolutely solid bodies. In particular, the linear equations of motion of a solid body with liquids will allow us to determine the change in the characteristics of the stability of motion due to the deformability of the free surface and the interface of the layered liquid. The paper considers a problem in a nonlinear formulation about the vibrations of a solid body with an axisymmetric cavity around the horizontal axis OY and completely filled with two ideal and incompressible liquids. Nonlinear differential equations describing nonlinear oscillations of a solid body and the interface between two liquids in the vicinity of the main resonance of the vibrations of liquids are obtained. For a round cylindrical vessel, the hydrodynamic nonlinear problem is reduced to the sequential solution of linear boundary value problems. The obtained solutions of boundary value problems in the form of cylindrical functions were used to calculate linear and nonlinear hydrodynamic coefficients in the equations of oscillations of the mechanical system under consideration. 
Sposobin A. V. Meshless algorithm for supersonic inviscid gas flows calculating. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/fe4/b2rgni89anvhqo00yw970ntjvesazphn/04_Sposobin_rus_eng.pdf The presented work regards the problem solution of numerical modeling of blunted body flowaround by the supersonic inviscid gas flow [1, 2]. Such problem may be solved by rather wide specter of the wellknown methods. Cartesiangridbased immersed boundary method was successfully applied to solve this problem in the twodimensional setting [3, 4]. It was employed to study the flow evolution in the shock layer while largesize particle movement along the symmetry axis was performed within the framework of a series of works [57]. The above said studies continuation while a particle movement along various trajectories required the problem solution of the gas flow modeling in the 3D setting. Unlike the finite volume method, the meshless method does not divide the computational domain into mesh cells, but uses the cloud of points to represent the values of functions. The least square method is being used for spatial approximation of function derivatives. The article describes the HartenLaxvan Leer method in combination with the MUSCL scheme and Van Albada limiter as applied to Euler system solution in 3D space. The least square method is being used to approximate Neuman boundary conditions on the boundary of the surface [17]. The meshless method selection was stipulated by the possibility of gas flow modeling in the domains with complex geometry. This method is less fastidious to the computer memory compared with those on the Cartesian meshes, employed in the previous works [47]. The meshless method for Euler equations solving was adapted also to the 2D space for the flat and axisymmetric cases [14]. The software implementation of the described method is accomplished in the C++ programming language and employs the OpenMP parallelization technology [15, 16]. The series of computational experiments on the bodies flowaround by the supersonic flow was performed to test the method operation accuracy. The article describes in detail the problem of modeling the sphere flowaround by the inviscid gas flow at the incident flow Mach number of 3. The algorithm for the nodes set generation in the 3D space for the given problem is described. A good agreement with solutions obtained by the finite volume methods on Cartesian meshes [3] and reference data [21] is demonstrated. The next stage in the development of the meshless method is supposed to be solution of the NavierStokes equations in order to simulate supersonic viscous flows. 
Snazin A. A., Shevchenko A. V., Panfilov E. B., Prilytskiy I. K. Investigation of the interaction with a highspeed flow of an underexpanded gas jet injected out of the body. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/947/85y7966xg088miyo1xzql5ffanoy6vip/05_Snazin_SHevchenko_Panfilov_Prilutskiy_rus_eng.pdf The interaction of injected gas jets with an incoming highspeed flow is one of the most pressing issues today. The use of injected jets for motion control has a significant advantage over mechanical controls, especially with regard to high maneuverability. Calculations of the gasdynamic parameters of a highspeed flow near a conical surface at Mach number M_{∞}=1017 were carried out with the characteristics of the incoming flow P_{∞}=79.8 Pa, T_{∞}=270 K and the parameters of the injected jets T_{j}=293 K and J=4.95 — the coefficient of penetration of the gas jet into the incoming flow [1,2]. The object of study is a conical surface with gas injection holes located along the generatrix at a distance x/l=0.3, 0.6, 0.9 from the toe. When analyzing the distribution of the zones of increased pressure in front of the place of injection of the jet and low pressure behind it, it was found that the value of the pressure coefficient with an increase in the Mach number proportionally increases both in the zone of increased and decreased pressure, regardless of the place of injection. The maximum pressure coefficient difference between the zones of high and low pressure is observed during injection at a distance x/l=0.3. In this case, the injected jet interacts with the head shock wave, locally pushing it away from the model. As a result, the p ̅ on the surface before and after the jets is much higher than in other locations of the injection holes. It was found that an increase in the oncoming velocity leads to an increase in pressure before and after the injected jet. In this case, in front of the injected jet, the pressure increases more significantly than downstream of it. With an increase in the Mach number, the maximum p ̅ shifts closer to the injection site. The analysis of the efficiency of the action of jets with different variants of arrangement in highspeed flow is carried out. He showed that, while maintaining the parameters of the injected jets constant, an increase in the incoming flow velocity leads to a decrease in the J coefficient, since the pressure gradient at the shock wave increases. It was found that the magnitude of the Ky increases with an increase in the incoming flow velocity. The maximum is observed when the injected jet is displaced closer to the nose of the model (at М_{∞}=17), since in this place the injection of the jet is as close as possible to the head shock wave. The results of numerical experiments correlate well with the results of field experimental studies [2, 19, 20], carried out using the aerodynamic laboratory of the A.F. Mozhaisky MSA and contribute to a more complete study of the effect of highspeed flow on the elements of aircraft. 
Rotermel A. R., Yashkov S. A., Sevchenko V. I. Experimental study of aerodynamic characteristics in a supersonic wind tunnel ST3 using a software and hardware complex. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/f3d/zk6qpwidvcyy9yivr1189is4k6q500qp/06_Rotermel_YAshkov_SHevchenko_rus_eng.pdf The article considers the developed software and hardware complex for conducting weight experiments with the help of strain gauges, which allows automatically launching and measuring the forces acting on the model of the aircraft throughout the entire operation time of the supersonic wind tunnel. Experimental studies were carried out using a supersonic wind tunnel of the aerodynamic laboratory of the Military Space Academy named after A.F. Mozhaisky. Currently, the supersonic wind tunnel provides the most reliable data on the study of the force acting on the model when interacting with the incoming flow of aircraft of various geometric shapes. To ensure the study of the aerodynamic characteristics of aircraft in a supersonic wind tunnel, the question arises of the development, implementation and use of modern measurement technologies that will expand the range of experimental studies. One of the types of conducting aerodynamic tests is a weight experiment. This paper presents the results of the development, implementation and application of a software and hardware complex for conducting weight experiments in a supersonic wind tunnel using threecomponent strain gauges. The software package is implemented in the LabVIEW graphical programming environment, which is an application graphical programming environment used as a standard tool for conducting measurements, analyzing their data, and then controlling devices and objects under study. A computer equipped with measurement and control hardware and LabVIEW allows you to fully automate the process of physical research. Creating any program is very simple, because it eliminates many syntactic details. The system for measuring the forces acting on the model in interaction with the incoming flow, based on the software and hardware complex, allows you to determine the experimental values of the longitudinal X, normal Y and transverse Z forces, the value of which determines the corresponding dimensionless aerodynamic coefficients of the model (C_{x}, C_{ya}, M_{z}, K, X_{d}). Because of the conducted experimental studies on a supersonic wind tunnel with the use of a software and hardware complex, it has shown its effectiveness. The efficiency lies in the possibility of plotting graphs in real time, obtaining the values of the aerodynamic coefficients in tabular data. Because of the implementation of the software and hardware complex, it allowed to reduce the time for preparing, conducting and compiling the report of the conducted experimental studies by half. 
Vasilenko D. A., Dorofeev F. E., Dorofeev E. A. Developing neural network approximator for critical halfopening angle determining in the effect of lift coefficient sign changing for blunted conical bodies. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/afb/e4990ywoq6wayla2fl5a45aimtaqvy25/07_Vasilenko_Dorofeev_Dorofeev_2_rus_eng..pdf The sign changing effect of the lifting force while the angle of attack changing in the high speed flat streams for the wedge was first discovered in the V.S. Galkin and A.A. Gladkov work in 1961. This effect in a freemolecular flow was found by V. S. Galkin in 1962. He showed that while the wedge flowaround by the freemolecular gas flow such critical onehalf angle exists that at large angles the wedge lifting force became negative at any angle of attack. Moreover, this effect is being manifested at any gas velocities and the ratio of the wedge and gas surface temperatures. The presented work deals with this effect studying for the bodies in the form of squeezed blunted cones. The effect is being studied for the rarefied gas flow without supposition on the freemolecular flowaround mode. At present, neuralnetwork approximators application for fast computing of aircraft aerodynamic characteristics becomes one of new and promising trends of computational aerodynamics. The dependence of critical onehalf angle of the squeezed blunted wedge on the flow geometry and parameters was studied using the approximation based on the hypothesis of locality. The exact neuralnetwork approximator, allowing compute the critical angle at any set of parameters, was developed based on the computed examples of this functional dependence. Aerodynamic forces acting on the blunted squeezed cone in the rarefied gas stream are being calculated. The article demonstrates that there is such an angle of the cone onehalf angle, at which increase the lifting force becomes negative at an arbitrary angle of attack. The values of this critical angle were found for various geometries of the conic body and the Reynolds number of a highspeed flow. 
Park S. ., Grigoryev V. G. Stability of thinwalled axisymmetric coaxial structures containing liquid under multifactor loads. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/1df/sx9y70jsw5mzozy6708udi9ba7qh9iwo/PakSongi_Grigorev_isp_rus.pdf The presented work supposes that the structure consisting of two coaxial, liquid filled shells to be under both internal and external pressure. The internal distributed pressure is being applied to the internal cylindrical shell, while external pressure is being applied to the external shell, and both these pressures are independent and variable. The distance between external and internal cylinders may vary as well, and each of these variables affects natural frequency and stability of the structure. The purpose of this work is to develop a methodology for studying the stability of axisymmetric thinwalled elastic shell structures composed of two coaxial shells, the cavities of which can contain an ideal incompressible fluid. The stability domain boarder, which separates the domain, where the loaded structure keeps stable, fr om the domain, wh ere the structure loses its stability, is being determined on the coordinate plane of two parameters. Computations for this study were performed with the Visual Basic for Applications (VBA) system in the Excel spreadsheet processor medium. 
Gerasimchuk V. V., Telepnev P. P. Reducing vibration activity level by a damping coating with reinforcing layer. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/de4/d924nv1zg0vurnrobmg19zl970g7k89w/09_Gerasimchuk_Telepnev_rus_eng.pdf The article deals with experimental studies on the vibration level reducing of spacecraft electromechanical actuators by increasing the structure damping properties by application of a multilayer damping coating with reinforcing layer. A vibrationabsorbing selfadhesive coating made of multilayer aluminum foil and rubberbased polymer interlayers was being studied as a damping coating. A structural element bending at lateral vibrations causes cyclic tensilecompressive deformation in the damping layer and damping forces corresponding to them. The tests were being performed on a forcemeasuring testbench. A frame with a selfadhesive vibrationabsorbing coating was fixed on a multicomponent measuring platform, on which electromechanical devices with moving masses were being installed. While these mechanisms operation, besides controlling impacts of the orientation system, negative forces and moments transferred over the spacecraft structure to the precise equipment occur causing its improper functioning. The forcemoment reactions and vibration accelerations appearing herewith were being rasterized and processed by the special software. The authors revealed experimentally that damping coating with a reinforcing layer application could reduce the vibration activity level of a structure in the entire frequency range of electromechanical devices with moving masses (up to 7 %) operation. The levels more meaningful at the vibration activity reduction (up to 15%) were being registered in the peak regions of the highfrequency vibrations. The experimenters revealed that the damping coating operability directly depends on the fastening quality and correctness of the structure’s surface coating. Preliminary shapes determining of the vibrations of interest is required to determine the places of maximum stresses of bending vibrations occurrence. The damping coating should be fixed in the places of maximum stresses occurring at vibrations, so that temperature effect of mechanical energy into heat energy converting, and amplitudefrequency effect of the vibrations damping by the reinforcing layer manifest simultaneously and with maximum effect. At the authors’ opinion, different modes of vibrations with a broadband spectrum of disturbance frequencies will have a certain shape and frequency, into which external forces and moments «pump over» the main energy od disturbance, and it is this shape that will be optimal to ensure maximum reduction in vibration loading. The article suggests recommendations for locations selection for the damping coating with reinforcing layer installing. The test results may be applied to ensure the vibration loading level reduction of structural elements while a spacecraft design and pilot testing. 
Babaitsev A. V., Rabinsky L. N., Min Y. N. Method for evaluating residual stresses in AlSi10Mg alloy specimens obtained by SLM technology. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/747/4g4dq388cfuahe9c9o98cslg6gv4egjg/10_Babaytsev_Rabinskiy_YAnNaingMin_rus_eng.pdf Today, additive technologies are used to create physical models, prototypes, samples, tooling, and the manufacture of plastic, metal, ceramic, glass, composite and biomaterial components. Of greatest technological interest is the manufacture of final parts from metal alloys used in the aerospace industry, mechanical engineering, automotive, oil and gas, electronics, medicine and other industries. Selective laser melting (SLM) is one of the most advanced and popular 3D metal printing technology. When manufacturing products using SLM technology, complex geometric shapes, including internal cavities and channels, can be reproduced, as well as with wellthoughtout design solutions — to achieve a minimum amount of machining and eliminate expensive tooling. However, as a result of powder sintering and local uneven overheating, temperature residual stresses are formed in the synthesized parts. The level of which can significantly affect the performance of the resulting products. The paper presents a variant of the method for determining residual stresses in products made of PH1 stainless steel, obtained by the SLM technology. For this, a study of residual stresses was carried out on flat rectangular samples grown in 3 directions relative to the construction plane (parallel, perpendicular and at an angle of 45 degrees to the construction platform). The method for determining residual stresses is based on determining the deformation during drilling of the probe hole and subsequent numerical calculation to determine the residual stresses. Deformations were fixed using the image correlation method. Such a noncontact method makes it possible to determine with high accuracy the field of displacements and deformations using a drilling machine and a camera with a macro lens. The numerical calculation was carried out by the finite element method taking into account certain deformations from the experiment in the COMSOL Multiphysics environment. As a result of calculations, the distribution of residual strains and stresses was obtained for all samples for all its components. The most indicative results were obtained on a sample grown in the plane of construction. 
Volkov A. S., Solodkov A. V., Suslova K. O., Strelnikov A. P. Prototyping noise immune codes in communication systems with channels code division. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/db7/s1pr0df6l9y2jt5gvthrzzzsdrm9zhdn/11_Volkov_Solodkov_Suslova_Strelnikov_rus_eng.pdf The article discusses a modified RScode. The purpose of the work consists in developing a prototype of a shortened noiseimmune RScode using NI USRP2974 for a CDMAtype system. The CDMA system is intended for information transmission in the air from a base station to a mobile one and vice versa. The subscribers operation in this system proceeds in the common frequency band and on one carrier while separation takes place by various code sequences application, which are being assigned individually for each channel. A shortened modified RScode was selected for this partition. The article presents both coding and decoding procedures of the modified shortened RScode with both errors and erasure correction for the CDMAtype systems. The Euclidean algorithm was being employed for cutting computing time of the key equation. This algorithm automatically obtains a polynomial of error locators in parallel with the key equation solving. This algorithm was being executed with the predetermined initial conditions, and operational procedure was being changed depending on characteristic features of each iteration. The errors position search was performed by the Chen procedure, and their value by the Forney’s algorithm. The article demonstrated that the shortened modified RScode corrected errors and erasures being the part of signalcode structures in the communication systems with code division multiplexing under development. The codes are of maximal possible minimal distance for linear codes with similar length of both input and output blocks. The may be employed as well for the concatenated code creation with greater minimal distance. Prototyping of the shortened modified RScode was performed using the NI USRP2974 high performance standalone device with software defined radio communication (SDR) USRP for system design and deployment of next generation wireless radio communication systems. The discrepancy range of the bit error occurrence probability was found applying the RScode. Graphs proving effectiveness of the error correcting method of the truncated RScode by employing the binary channel with erasures were obtained . 
Demin D. S., Kononenko P. I., Lebedenko V. I., Prilutsky A. A., Reznichenko V. I., Sidorchuk E. A., Sysoev V. K., Khmel D. S. The concept of an onboard radar based on active phased array antenna employing reflector with solidsetting pneumatic frame. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/e50/qfectlykdncr9f0s32qufiw1f9ogn0qr/12_Demin_dr._Sysoev_KHmel_rus_eng.pdf The article considers a space onboard radar based on a hybrid mirror antenna for the L or P band and active phased array antenna transceiver modules, scanning along the forming surface of a cylindrical paraboloid of its reflector. The authors suggested using effective area of the reflecting surface of its reflector no less than 100 m^{2} for the L band, and no less than 160 m^{2} for the P band to obtain a high gain, and substantiated the requirements to the shape stability as well. For reflector of such a considerable size, the possibility of a light transformable structure development by forming a surface, employing flexible reflecting metallized grid, fixed on the frame being arranged under conditions of zerogrzvity by gas filling and hardening of the pneumoframe was substantiated with account for limitations imposed by the nose cone of a carrier rocket. On orbital injection the soft shells and flexible grid of the transformable reflector structure are being rolled up and packed in a container of relatively small dimensions and easily withstand acting vibration and dynamic loads as a part of a spacecraft at the stage of operation and at insertion. The article presents the layout of the onboard radar complex with hybrid mirror antennae for L or P band as a part of basic module of the «Navigator» support systems. The possibility of the reflector frame rigid structure creating from the composite material based on pneumoframe shells under conditions of the spaceflight was confirmed. Hardening technique for pneumoframe applying the infusion of a binder being solidified was tested on the example of the cylindrical thinwalled beam. The article presents the results of the transformable structure of the frame panel testing on functioning and strength, as well as verification of bending computations by stressstrain state modeling of a composite material. Its stiffness and weight evaluation is presented either. The transformable structure endurance to the cosmic space factors impact was estimated, and measures to its enhancing were being suggested. A number of passive methods have been proposed for stability ensuring of the reflector shape. Methods for the shape monitoring and correcting, and methods for the deformations impact compensating by hardwaresoftware means of the radar system were considered. In particular, the expediency of the mirror shape correction by mechanical actuators, as well as by phase correction of signals to align the front of the wave being radiated, was justified. The systematic approaches, substantiated in the article, such as deformation impact compensation; forming largesize reflector with rigid frame from composite materials by the gas filling and soft shells hardening under conditions of the space flight may find application for radar complex developing based the active phased array antenna with a hybrid mirror antenna. 
Masyukov I. I., Borzov D. B., Titov D. V., Sokolova Y. V. Mathematical Model and HardwareOriented Algorithm for Programs Placement Planning in Systems on a Chip. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/ff3/v6v3416x74j3t4x11oh08bmlfn3p7r9p/13_Masyukov_Borzov_Titov_Sokolova_rus1_eng.pdf A reconfigurable computing system () is a system that can be reconfigured after its manufacturing. A promising basis for such system constructing is an RCSFPGA. One of the tasks of building an RCS in real time mode consists in changing the internal FPGA modules organization. However, this leads to the increase in the switching delay time. This time reduction is achieved by the internal modules redistributing, which allows increasing the RCS speed. The article presents a mathematical model and a hardwareoriented algorithm for program scheduling in systems on a chip, which will allow reducing the time delay in computing the new topology of a reconfigurable computing system and increase its fault tolerance. To achieve the smallest total length of interconnections, the article proposes to employ two criteria: 1) The programs with a maximum number of related programs must have a minimum distance to their adjacent programs; 2) Adjacent programs with maximum loading among themselves must have a minimum distance; Thus, to achieve the minimum total interconnection length of the program configuration in the systemonchip, it is necessary to find such a mapping that would satisfy the above presented conditions 1 and 2. Based on the proposed criteria and method, a hardwareoriented algorithm was developed, which main advantages consist in the simultaneous selection and location search in the configuration of the selected programs. It reduces the total length of the obtained interconnects in the configuration being computed and the number of enumeration operations. The software modeling of the developed hardwareoriented algorithm and its results comparison with the algorithm program model, based on the ideas of the branches and boundaries method was performed. Comparison was performed for the following types of graphs: ring, fully connected, planar, Cayley direct product, star using the Halin construction, bipartite. It revealed that the hardwareoriented algorithm works more efficiently for a configuration search for the most of the presented graphs types: in configurations computing for all presented types of graphs (on average, the total length of interconnections is 8.4% less), and in operation speed in four out of six (6.6% faster on average). The presented method and the hardwarebased systemonchip configurationplanning algorithm developed on its basis are applicable in highavailability systems such as onboard aviation, tracking, surveillance, radar, recognition systems, etc. This approach application will reduce both the time spent on planning or design (compilation) of a new configuration plan, and reduce the switching delays of the system. 
Scriabin Y. M., Potechin D. S. Rational analyzing function for precise feature extraction from an electrostatic signal. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/8e3/72ds1dkt1q1o0b9rn02o92gxf9scxqbr/Skryabin_Potekhin_rus_prav.pdf The article is devoted to the problem of extracting features from an electrostatic signal. This problem becomes relevant when using an electrostatic monitoring system to detect unmanned aerial vehicles. The law of variation of the electrostatic field tenseness at a particular point on the earth’s surface depends on the landscape. In addition, the process of determining the parameters of the UAV flight requires the precise of determining the signs of an electrostatic signal. In the works of other researchers, the wavelet transform based on the Morlet function is usually used to extract the features of an electrostatic signal. The exact definition of the features is carried out from the analysis of the resulting threedimensional timefrequency distribution. In this paper, we consider another type of transformation of an electrostatic signal based on convolution with a complex rational function. We select a function that can provide a simpler timefrequency distribution. The simplicity of this distribution lies in the fact that the parameters of the electrostatic signal are extracted based on determining the intersection point of two twodimensional functions, instead of determining the peak on the threedimensional distribution in the case of the wavelet transform. The method under consideration has comparable noise immunity compared to the wavelet transform, in addition, it allows you to adapt the transformation to a specific electrostatic signal. 
Agayev F. G., Asadov H. G., Zulfugarli P. R. Studying optimal UAV functioning modes in wireless information transmission networks. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/473/obayd7eifdkhrp2e48xqdm4v5luxr68u/15_Agaev_Asadov_Zulfugarly_rus_eng.pdf The article deals with studying optimal UAV functioning modes in wireless information transmission networks. It considers two optimization problems of the UAV functioning in in wireless information transmission networks. The purpose of the study consists in (a) parameters determining of optimal transmission mode where the throughout C(t) is of constant value (i.e. the throughput is invariable); and (b) parameters determining of the UAV optimal functioning when the integral throughput value reaches its extreme at the constant value of the integral cost function being newly introduced. For the first task, conditions for the throughput constancy achieving were analyzed, and concrete condition at which fulfillment ensured this constancy was obtained. In the second task, conditions under which the integral throughput value reaches its extreme value is being determined with account for the requirements to the cost function. It was determined that such extreme in the form of the throughput minimum manifested itself at the following conditions fulfillment: (a) the presence of the cost function in the form of the functional relationship σ = σ(P(t)), where σ is a meansquare deviation of the white noise, and P(t) is the power of the signal being transferred, is conceded; (b) constraint of this integral function is conceded; and © the direct dependence between the above said indices was being ensured. 
Aslanova A. B. Mode indices optimization of battery powered unmanned aerial vehicles with differential payload shedding. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/208/pr8hgun55pjmce33imczk1hct0zdepiu/16_Aslanova_rus_eng.pdf The problem of provision of optimum flight regime of UAV with dynamically changing weight was considered in regard of UAV equipped with internal combustion engines. Expansion of the scope of application of UAVs equipped with electric motors and batteries (accumulators) may cause the need to take into account the factor of weight changes during the flight. Technologically, this may be caused by the need to remove used batteries or perform some specific tasks. These types of tasks performed by drones include differentiated delivery of payload (spraying chemicals to destroy agricultural pests, dumping water in the forest fire zone, dumping chemicals to form raindrops, etc.). In the long term, a section of the UAV flight path is also possible, where the weight of the drone increases due to the implementation of refueling in the air. Thus, the issue of optimizing the operating parameters of the UAV is being updated, taking into account the dynamic change in the total weight of the UAV during the flight. It should be noted that this question in regard of battery powered UAV is developed not completely. The article formulates and solves the problem of determining the optimal dependence of the UAV flight speed on the weight of a batterypowered drone in the mode of differential payload reset. The optimization criterion is the condition for minimization the average integral value of the aerodynamic drag overcoming force. The task is solved using nonconditional variation optimization method in line with Euler equation and Lagrange multiplier. It is shown that the optimal value of the flight speed of a batterypowered drone is directly proportional to 1/3 of the weight of the UAV and inversely proportional to 2/3 of the air density. 
Wai Y. S., Filippova A. S. On geophysical disturbances impact on the Earth’s pole wobbles with the lunar orbit precession frequency. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/941/6cn5y2dwo0764o8b5f4v21wi36bzl5y1/17_VeyYAn_Soe_Filippova_rus_eng.pdf The article studies the contribution of basic geophysical disturbances (atmospheric and oceanic) to the wobbling process in phase with the lunar orbit precession by the analysis and processing of the NCEP/NCAR data on atmospheric circulation and NASA/JPL data on the ocean angular momentum. For this purpose, numerical integration of the Earth’s pole motion equation with account for the kinetic momentum of the atmosphere and ocean angular momentum was performed. Combinational harmonics associated with the wobbling process under consideration were separated as well. As the result of the integrating, the Earth’s pole movement accounting for the basic geophysical disturbances was obtained, and contribution of atmospheric and oceanic disturbances to the wobbling process synchronous with the precessive motion of the lunar orbit was determined. Combinational harmonics, being obtained as the combination of the pole wobbling basic harmonics and harmonic with the frequency of the lunar orbit precession, were found. It was found that more than 50% of the energy of the wobbling process being considered, inphase with the lunar orbit precession, might be stipulated by the disturbance of the atmosphere and ocean. Wobbling with frequencies of cycle/year, caused by atmospheric and oceanic disturbances, coincide in phase with the corresponding wobbling of the observed motion of the pole. However, at least one third of this process is not explained by the disturbances being accounted for in the work. 
Protsenko P. A., Khubbiev R. V. The methods of ranking the Earth remote sensing spacecraft to ensure the operational monitoring of emergencies. Trudy MAI, 2021, no 119, http://mai.ru//upload/iblock/7a4/asjchezcu0agwtrboki10qpp278tayax/18_Protsenko_KHubbiev_rus_eng.pdf The article discusses the issues of ranking operational monitoring spacecraft of forest fires in order to determine the contribution of each spacecraft to solving the problem of monitoring for focusing the resources of the control complex on the most important spacecraft. For rapid response to emergencies is necessary to know the situation in the observed area. Since the area is large, it is impossible to fully reconnoiter it with one spacecraft flyby. In this regard, it is proposed to introduce a new criterion — the proportion of the observed area, showing which part of the area there is uptodate information. Intelligent information about the area is relevant only for a certain period of time, since an emergency situation can arise in the area at any random moment in time. Let us assume that the information about the area is relevant for a deterministic period of time Δτ, those to assess the situation in the area at time t, only the radio visibility zones of the Earth remote sensing spacecraft located in the time range [t–Δτ;t] are taken into account. Based on the proposed approach to assessing the observability of a given firedangerous area, the methods of ranking the Earth remote sensing spacecraft has been developed. The ranking of spacecraft is made taking into account the fact of information obsolescence and the nonlinearity of the area monitoring by a variety of spacecraft. As result of a comparative analysis of existing ranking methods based on the frequency of observation of a given area, and the proposed methodology, the fact of consistency of the results was established. At the same time, the proposed methodology makes it possible to single out that set of spacecraft, the use of which significantly increases the efficiency of monitoring areas of emergencies. The presented methods can be used to study the capabilities and ranking of both orbital constellations, consisting of the same type of Earth remote sensing spacecraft, and different types. 
Popov I. P. On parameters calculation of passive gravityassisted maneuvers of interplanetary spacecraft. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/b74/2ulabvezqf1iqjxcqiucy0mcq8zk7bwm/01_Popov_rus_eng.pdf The purpose of the study consists in analytical description of the ballistic trajectory section corresponding to the normal fall of the spacecraft on the surface of an atmospherefree planet. The motion of a normally falling body herewith is being characterized by an increasing acceleration of gravity. The problem of the speed, time and acceleration of the normal fall of a body on the planet’s surface in the absence of an atmosphere is being reduced to solving a secondorder differential equation, which is solved by the standard method. The solution specificity is the formal use of the table integral at an intermediate stage. It turned out, however, that his formula is inauthentic, namely, the derivative of the righthand side is not equal to the integrand. From this, It necessary follows that possible existing solutions to this problem based on employing the above said table integral are incorrect. The article presents correction of this table integral, which is an incidental result of the study. Temporal equation of a normal body falling on the planet surface in the absence of the atmosphere, as well as temporal equations of its speed and acceleration were obtained in this work. Expressions for the distance, speed and acceleration were obtained as implicit functions of time. The article presents a numerical example with regard to a planet with parameters of the Earth, according to which the period of normal fall of a body on the planet’s surface from the altitude of 629 km is 387.275 s = 6.455 minutes, while the body’s velocity at the planet’s surface is 3353.297 m/s. The results obtained may be handy for calculating the normal incidence of small celestial bodies and spent spacecraft structural elements. 
Khatuntseva O. N. On finding a generalized analytical solution to the HagenPoiseuille problem for a turbulent flow mode. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/88b/5zuy04z512dnjf98u1l3kb7eqq20cprk/02_KHatuntseva_rus_eng_ispr.pdf The modification of the NavierStokes equations by accounting for the additional degrees of freedom associated with the excitation of stochastic pulsations in the fluid flow allowed distinguishing two solutions to the fluid flow problem in a circular pipe (the HagenPoisel problem). One of these solutions is implemented for any values of Reynolds number and corresponds to the laminar flow regime, the second one is implemented only for large enough values of the Reynolds number and corresponds to the turbulent flow regime.
However, the boundary conditions, i.e. of the liquid «sticking» on the walls of the pipe with the of a linear velocity profile formation near the walls along the length of the viscous layer are V+ ~ y+. The zero derivative of the velocity in its center herewith allows obtaining a «smooth» solution to the problem for an arbitrary Reynolds number only in the case of a laminar flow regime.
Boundary conditions that arbitrarily «fixing» a solution at two or more points generally do not guarantee existence of a smooth solution to ordinary differential equations (ODE) or partial differential equations (PDE), even if these equations obey Cauchy’s existence and uniqueness theorem.
The absence of a smooth solution of the ODE or the PDE in the entire domain under study can be considered from the point of view of the existence of two or more asymptotes of the solution, as well as areas of uncertainty between them. A function of two summand, each of which is the product of two functions can be considered as a generalized (in the sense defined in the article) an ODE or a PDE solution. One function defines one of the solution asymptotes, while the other one defines the degree of this asymptote effect of the overall solution in each point of the area under study.
From this point of view, the presented work considers a generalized solution of the HagenPoiseuille problem for the turbulent flow regime of a liquid. One asymptote of the solution satisfies the boundary condition of liquid «sticking» on the pipe wall, while the second asymptote of the solution is a constant setting zero velocity derivative on its axis. A comparison with experimental data for the universal velocity profile in the nearwall flow region is presented. 
Panfilov E. B., Shevchenko A. V., Prilytskiy I. K., Snazin A. A. Evaluation of the control efforts of the aircrafts gasdynamic controls in hypersonic flight modes using the IT1M hypersonic wind tunnel. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/475/tur127njbnzyuiitds6plfcqwsbaqy9b/03_Panfilov_SHevchenko_Prilutskiy_Snazin_rus_eng_pravlenaya.pdf Improving the aircrafts aerodynamic characteristics (AC) in a wide range of speeds is a perspective trend especially with significant restrictions imposed on the shape of structural elements is flow and motion control, namely effect on the airflow to restructure its structure in accordance with the required change in AC and other airflow parameters. The most effective method is the gasdynamic method, implemented in gasdynamic controls (GDC) (longitudinal and normal injection of a gas jet fr om a body into a hypersonic flow).
On the experimental setup of the aerodynamic laboratory of MSA the A.F. Mozhaisky — the IT1M hypersonic impulse wind tunnel (HIWT), a series of experiments was carried out (with the parameters of the undisturbed flow: Mach number (M∞ = 17), Reynolds number (Re∞≈1.4 × 104) and pressure (p∞ = 200 Pa)) to determine the aerodynamic characteristics of an aircraft model using GDC.
The feature of HIWT is the ability to obtain experimental data on quasistationary processes in a time interval of 50 ms. Working gas — nitrogen (high purity, 1st grade, GOST 929374).
When a gas jet is blowing into an incident hypersonic flow, a complex shockwave structure arises, as evidenced by the experimentally obtained shadow patterns of flow around a body using GDC.
As an indicator of the effectiveness of the use of a GDC with a different location on the model, the amplification factor was selected (K_у=1+ΔY/P_y, wh ere P_y the GDC thrust; ΔY the increment of the normal force due to the presence of an area of increased pressure in the separation flow zone). A comparative analysis of the effectiveness of various combinations of the use of GDC on the aircraft model when moving in hypersonic flight modes is presented.
As a result of a series of experimental studies on the IT1M wind tunnel, the effectiveness of the usage GDC AC was investigated at hypersonic flight modes. The values of the aerodynamic forces (normal and longitudinal forces, as well as the pitching moment) acting on the aircraft model during hypersonic flight are obtained. It has been shown that the usage GDC significantly improves the main AC of aircraft. The most effective combinations of GDC for the model under study are options 2 and 3 (with J of the jet equal to 4.95 and 8.53) (Figure 8).
Experimental studies carried out with the use of the HIWT aerodynamic laboratory of the MSA named after A.F. Mozhaisky contribute to a more complete study of the behavior of aircraft elements in a hypersonic flow, as well as the verification of existing and newly developed computational codes for aircraft models with GDC. 
Eliseev A. V., Kuznetsov N. K., Eliseev S. V. Frequency energy function in dynamic states estimation of technical objects. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/d05/c280u9ffxs7ga9ilkegoos2et38ead4m/04_Eliseev_Kuznetsov_Eliseev_rus_eng.pdf The article proposes a new approach to the dynamic properties evaluation of mechanical oscillatory systems, as calculation schemes for technical objects operating in modes of intense vibration loading.
The purpose of the study consists in developing ideas of employing frequency energy functions representing potential and kinetic energies ratio in a specific form based on the application of relations of coordinates in the free oscillations mode.
Technologies of system analysis and structural mathematical modelling, within which framework the block diagram of the equivalent in dynamic sense automatic control system is being correlated in mechanical oscillatory system, are used.
The article demonstrates that the design schemes of technical objects, represented by design schemes in the form of mechanical oscillatory systems, allow detailing perception about systems’ dynamic properties, associated with the objects’ dynamic state, defined by the spectrum of natural vibration frequencies in a wide range. Growing attention to the reliability ensuring and operation safety of machines and equipment predetermines the attention to the frequency properties of the systems and accounting for the specifics of theif formation and manifestation.
The authors propose a method for dynamic properties evaluation of mechanical oscillatory systems based on the frequency energy function, which allows determining the frequencies of natural oscillations and their dependences on the system parameters, depending on the socalled cohesiveness coefficient of amplitudes by the coordinates of the system. 
Tolstikov V. G., Pykhalov A. A. Stressstrain analysis of aircraft airframe parts from composite materials based on scanning and globallocal problem solution. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/7ee/hkxihbkl7ipdfexcmv09uo3q1nfkdluk/05_Tolstikov_Pykhalov_rus_eng.pdf The article considers mathematical modeling of laminated polymer composite materials, being built basing on scanning parts with a computer tomograph with further mathematical processing of the obtained information and finite element models building. The main aspect of the work consists in determining the degree of the internal defects impact on the strength of the manufactured part by the results of the analysis of the individual finite element model.
The computed tomography technology allows determining the type of defect, its size and location relative to the base surfaces of the part under study. The resulting raster model is the scan data output. The wellordered packet of raster images with the defect in one of the of coordinates system axis direction of the object under study is being formed. The subsequent step consists in creating a wireframe model of the defect zone. The step consists of the following stages:
Further, the superimposition of the wireframe model of the defect on the 3D finite elements model of the part’s zone with the identified defect is being performed. The subsequent properties transformation of the finite elements that have fallen into the defect zone consists in the change (decrease) in the elastic properties of the material.
Detailed analysis of the stressstrain state of aircraft structures from composite materials may significantly increase the computational costs. To solve this problem, this article suggests employing the globallocal analysis of the elastic theory. This will allow considering the defect zone obtained after scanning with sufficient accuracy, without the part finite element model complication.
The presented approach application allows determining the suitability of the parts from laminated polymer composite materials with a high degree of adequacy, which consists in determining the real defects, revealed while the scanning process with the computed tomography, impact on the strength of the part.
the effect on strength the part real defects identified in the process of scanning on a computed tomography. 
Kazak P. G., Shevtsov V. A. Principles of design an energyefficient cellular communication system and wireless broadband Internet access for the Arctic. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/b1a/qqtxa51ngp0l1of1aaljvsmw3kiuc09v/06_Kazak_SHevtsov_rus_eng_Ispravl..pdf Currently, the Arctic territories of Russia are actively developing. For integrated development it’s necessary to create a modern telecommunications infrastructure accessible to remote sparsely populated areas which is capable of providing broadband Internet access and mobile communications.
The use of modern developing satellite communication systems («Starlink», «OneWeb», etc.) as such an infrastructure has a number of disadvantages: a long delay time for data transmission to a user and the need to use additional user equipment of large dimensions due to directional antennas. With the help of such equipment, it’s possible to organize only a stationary access point with a small service area which doesn’t allow the implementation of mobile communication using compact standard user equipment.
An alternative to satellite communication systems are cellular communication systems developed by 3GPP, which use cellular communication standards that provide broadband Internet access (LTE, LTEAdvanced, LTEAdvancedPro). The disadvantage of such systems is their unprofitability in the Arctic.
To date, integration with selforganizing networks with a dynamic AdHoc structure has already been considered as one of the ways to increase the profitability of cellular communication systems.
A new way of increasing the profitability of cellular communication systems in the Arctic is proposed. For this, cellular communication systems with capacity transfer, integrated with the Internet of Things LoRaWAN communication system are used.
The functions of the LoRaWAN communication system [12] are autonomous remote monitoring and site management which includes turning off the power supply of the site when there are no subscribers in the service area and turning it on when subscribers appear.
Reducing the energy consumption of the site due to the integrated equipment of cellular communication systems with capacity transfer and LoRaWAN communication system, as well as the proposed method for managing the power supply of sites allows the use of autonomous power sources, for example, using hydrogen, as the main ones to ensure the operability of sites.
This work is devoted to the study of implementation options and basic principles of operation of energyefficient cellular communication systems with capacity transfer integrated with the Internet of Things LoRaWAN communication system. 
Volkov A. S., Baskakov A. E. Bidirectional search procedure development for solving the the transport softwaredefined network routing problem. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/e97/jk0otm9xo3zyz0ibtdlculb6kdzn7l2n/07_Volkov_Baskakov_rus_1_eng.pdf Modern communication networks represent a complex architectural solution that performs a number of telecommunication tasks, which solution allows the most efficient transmission of large amounts of data through the network. The annual growth in the transmitted traffic volume makes the network technologies application for a long period of time without changes impossible, since the requirements for its processing grow, and increasingly stringent restrictions are being imposed on the network solutions and equipment along with it. One of the most important parameters of data transmission is the endtoend delay. It represents a set of time values required for an incoming network packet processing and transmitting it through the physical communication channels, as well as the operating time of the network protocols and technologies being employed, in particular, the time spent on of various tables’ construction and operation of algorithms software implementations.
Thus, the solution to the abovesaid problem can be reduced in the first approximation to the problem of finding a set of routes on a graph describing the a communication network topology.
The existing standard solutions to the problem of searching for the paths on a graph describe, as a rule, the solution to the single route searching per one algorithm iteration, or provide the ability to search for exclusively disjoint data transmission paths, which in some cases is not sufficient for solving the original problem. Application of the routes searching algorithm with the auxiliary graph constructing, allowing find a set of paths, including partially intersecting ones, on the graph from one vertex to another, or from one vertex to set of vertices, may alter the situation. This solution disadvantage consists in critical increase of the algorithm operating time while employing graphs of large dimensionality.
This problem can be solved by applying the bidirectional search method for the abovesaid algorithm with the auxiliary graph constructing. Thus, the original graph can be conditionally divided into two parts, being the subgraphs from the original graph, connected by the generated paths. A mandatory condition herewith is starting and ending points finding in the constructed subgraphs, then, the auxiliary graphs construction based on them will allow reducing the time complexity by up to two times, depending on the specific software implementation of the algorithm and the methods of the graph writing: adjacency list, incidence list, adjacency matrix etc. The calculated time complexity herewith for the tested network topology containing eight nodes and the connections between them will be 519.23 and 105.95 for the algorithm based on the auxiliary graph and its bidirectional variation, respectively. 
Ageev F. I., Voznuk V. V., Khudik M. Y. Technique of increase of noise stability of data transmission systems with binary phaseshifted noisetype signals in the conditions of action of noises with different spectral structure. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/ae0/6tys88fc2e9fspjvm7rjuye2s6wt1ylq/08_Ageev_Voznyuk_KHudik_rus_eng.pdf Relevance of this work decides by need of increase of level of noise stability of data transmission systems on phaseshift noisetype signals to noises with different spectral structure on the basis of purposeful modification of time structure of the pseudorandom sequence used when forming such signals.
The purpose of article consists in assessment of character and extent of influence on noise stability of data transmission systems with phaseshift noisetype signals of time structure of pseudorandom sequence in the conditions of influence of noises of different type, and also development of the general recommendations about ways of increase of noise stability of such data transmission systems on the basis of purposeful modification of structure of PSP of the used signals.
As object of research in article data transmission systems with phaseshift noisetype signals in the conditions of action of noises with different spectral structure are considered.
Subject in article is the technique of assessment of character and extent of influence on noise stability of data transmission systems with phaseshift noisetype signals of time structure of pseudorandom sequence in the conditions of influence of noises of different type, and also the recommendation about increase of noise stability of data transmission systems on the basis of purposeful modification of time structure of PSP.
The practical importance of article is that on the basis of the developed technique of assessment of extent of influence on noise stability of data transmission systems with phaseshift noisetype signals of time structure of pseudorandom sequence in the conditions of influence of noises of different type, recommendations about purposeful modification of time structure of this PSP which results in the maximum distinctions in ranges of signal and noise which finally leads to essential increase of the relation signal / (noise + noise) on output of the coordinated filter, and according to and to decrease in probability of bit error in the accepted signal are developed.
It is reasonable to use the offered technique at solution of problems of justification of technical requirements to data communication equipment with phaseshift noisetype signals, capable steadily to function in the conditions of difficult interfering situation. 
Dmitriev A. O., Moscatinev I. V., Nesterin I. M., Sysoev V. K. Options analysis of navigation systems for the Moon. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/01b/fuzdwpytcubn6zb338xscw03hqz87lu2/09_Dmitriev_Moskatinev_Nesterin_Sysoev_rus_eng.pdf Conducting a detailed study of the Moon and its further development should be based on a highprecision positioning system for objects located on its surface and in the circumlunar space. Currently, many space agencies and research centers are developing navigation systems for the Moon. The proposed projects stay at various stages from concepts to experimental work. Thus, conducting detailed analysis of these projects is an uptodate task.
Basic types of navigation systems, suggested to development by Russian and foreign researches, were outlined following the results of the analysis. Certainly, there is a number of concepts, such as navigation by pulsars, but they are even more complicated in realization and of less accuracy than those under consideration.
These are, in the first place, radionavigational systems, which can be conditionally split into three basic groups: — The systems based on constant contact with terrestrial systems; — Navigation systems autonomous from the Earth navigation (i.e., those not employing the Earth GLONASS, GPS, etc. as a support) with lunar reference points; — Autonomous systems without reference lunar based points.
All types of the systems have both their advantages and disadvantages: this is either the presence of a mandatory binding to the Earth (hence, there are delays in receiving any kinds of signals at such a distance), or either a large number of spacecraft or a complex lunar based segment.
Systems with gravitational measurements and the artificial intelligence application cannot fully perform the tasks of global lunar navigation.
Thus, we believe that the proposed lunar optical navigation system is uptodate and solves many of the problems and shortcomings of the abovementioned modern projects and proposals in the field of navigation on the Moon. 
Voronov K. E., Grigoriev D. P., Telegin A. M. Application of the direct propagation neural network for localization of the impact site of microparticles on the surface of the spacecraft. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/504/8vfhj8nsu02vsinek7p3zk4h9ep25qei/10_Voronov_Grigorev_Telegin_rus_eng.new.pdf The purpose of this article is to demonstrate an experimental method for determining the impact region of microparticles in the surface of a spacecraft, through a neural network, with information about time delays in the data set. The article briefly describes the main types of neural network architectures that are widely used in various tasks. The theory of operation of the architecture of the neural network of direct propagation with mathematical explanations is given. The fundamental operations of neural network training, such as the method of error back propagation, gradient descent of the loss function, the training coefficient and its optimization, are also considered. The task of detecting the impact site of microparticles on the surface of the spacecraft body is set. As input data for training and testing the neural network, we used the results of an experiment to measure time delays on an experimental model with four piezo sensors. The output data was the numbers of the areas of the plate that were subjected to a simulated impact with a steel ball. The neural network model itself was written in the python programming language, using the Keras library and TensorFlow. This article also provides a detailed method for constructing a neural network model in python. The neural network obtained in the course of the study showed good results in terms of predicting the impact area of cosmic particles. The accuracy reached almost 90100%. These results, as well as the advantages, disadvantages and prospects of the considered method, are given at the end of the article. 
Nenashev V. A. Features of classification of the underlying earth surfaces according to the characteristics of echo signals in onboard radars. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/ed8/rosrhejsezj6y0ius0e3s2334ht9oxqf/11_Nenashev_rus_eng.pdf Today, onboard radar monitoring systems are actively used as devices for observing the earth’s surface. They have great practical advantages. The main of these advantages are:
— implementation of monitoring of the earth’s surface in unfavorable weather conditions and at any time of the day, as well as in various seasonal conditions; — sufficiently long range of action; — high accuracy in determining the coordinates of the detected physical objects and outlines of the edges of the underlying surfaces; — the ability to cover large areas of the monitored areas in a short period of time; — implementation of the mode in real time, etc.
The work defines, analyzes and forms the corresponding parameters of echo signals, the space of information features of characteristics. The most informative classification parameters have been identified, the main of which is the radar cross section (RCS) value. In this case, the selected parameters of echo signals are stable under the influence of various destructive influences on the signal during its propagation.
The distribution laws of Weibull, Rayleigh, RayleighRice, Hoyt, etc. are used as a model for the fluctuations of the envelope of the earth’s surface echoes, as well as the lognormal law and the Kdistribution as the equivalent of the sea surface echo.
In this work, an algorithm for the classification of one information attribute, which is the RCS, has been developed. The block diagram of the algorithm is presented. The classification algorithm is implemented on the basis of comparing the RCS value taken from the corresponding base of classification features of objects and underlying surfaces with the RCS value calculated from the received values of the echo signal amplitudes observed in the receiver strobe of the onboard radar.
Through the use of onboard radar equipment, search, detection and classification of underlying surfaces is carried out, which makes it possible to perform these tasks regardless of weather, daily and seasonal conditions. In this case, the reliability of the classification algorithm depends only on the intrinsic fluctuations of the evaluated characteristics of the echo signals. The result of the work is the development of an algorithm for the classification of underlying surfaces by RCS. 
Tanygin M. O., Dobroserdov O. G., Vlasova A. O., Ahmad A. A. Technology modification for distance calculation between pairs of adjacent clusters in multilevel thresholding. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/844/teosk1jrde7cj263l0v5okxztk8ru2sc/14_Tanygin_Dobroserdov_Vlasova_Akhmad_rus_eng.pdf The purpose of the study consists in developing a method, algorithm and models of authenticity enhancing of the information packets source identification. This goal is achieved by extra checking the content of a special service word that is a part of the data packet for falling into the value range dynamically generated by the receiver. As the result, the number of packets, being analyzed by the receiver while identifying the source of the structured set of information packets, reduces. The article demonstrates that reduction of the number of packets being analyzed leads to the probability of identification errors origin reduction. Models for identification authenticity evaluation were developed based Markov chains apparatus. The process of information packs acceptance by the receiver from various sources is presented as a random process, in which a part of the states corresponds to the data packets processing errors occurrence, while the other part corresponds to the possibility of the reliable packets processing. The model parameters are the values range width, used for checking the data packet special word; the probability of a single data block inclusion into the structured set; the length of the structured set of data packets from the single source; the total number of data packets being processed by the receiver. The article shows that application of the method of limiting the analyzed packets set being analyzed allows enhancing identification reliability of the distributed information systems subjects, which exchange data packets of limited size. The probability of identification herewith of false source, which formed a certain structured set of packets, reduces by two or three times. In practical terms, it allows reducing the size of extra service margins in each data packet. This, in its turn, allows reducing information excessiveness of the processed data, increasing the data processing speed by the receiver, and reducing the size of both internal register memory and randomaccess memory of the receiver. 
Gavrilov K. Y., Kamensky K. V., Malyutina O. A. Trajectory signal modelling in the aperture synthesis radar based on optical images of the Earth surface. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/768/b901vylbdegcgrnbq25pgxlxf2bpotw9/12_Gavrilov_Kamenskiy_Malyutina_rus_eng.pdf The article deals with the development and research of algorithms for computer simulation of the signal trajectory in the aperture synthesis radar. It substantiates such modelling relevance, which is stipulated by the necessity to obtain radar images of one and the sane scene under various probing conditions. The radar images obtained thereby may be employed to analyze various synthesizing algorithms, trajectory instabilities, equipment errors and other factors affecting the quality of the resulting synthesized image.
These are the methods for direct and reverse forming of the trajectory signal. The first group of methods, in its turn, can use numerical methods of electrodynamics, or methods of geometric optics. The most appropriate approach is based on the methods of geometric optics, when optical images are used to form the amplitudes and phases of the trajectory signals of the probed scene, i.e. aerial photographs, photos from space, and etc. Based on this approach, trajectory signals and radar images synthesized on their basis were obtained when a continuous signal with linear frequency modulation was used as a probing signal.
The article presents the examples of the trajectory signals computer simulation and their corresponding synthesized radar images with high resolution (above 0.5 m). The trajectory signal simulation method based on optical images may lead to the synthesized images distortions, which appear in the form of alternating dark and light bands located horizontally and vertically. The conditions under which such distortions occur, as well as methods for their elimination, were determined. The reasons for the distortions appearance in the form of bands are, firstly, the discreteness of the reflectors’ location point in the optical image, and, secondly, the interference of the radio signals reflected from a group of closely located reflectors. In literature, the second phenomenon is called the speckle effect.
To eliminate distortion of the images synthesized on the basis of the described method for the trajectory signal simulation, the article proposes to adding a random phase component to the signals of point reflectors. This technique allows to forming the trajectory signals close to real signals.
The article also provides examples of the application of trajectory signal modeling to analyze the distortions of synthesized radar images in the presence of trajectory instabilities with different amplitudes. 
Khanykov I. G. Technology modification for distance calculation between pairs of adjacent clusters in multilevel thresholding. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/8ff/cd4v3tgnx48mx4jik18w1d5s0uftzm1p/13_KHanykov_rus_2_eng.pdf The article considers the multithreshold images processing technology, which consists in generating a series of partitions into clusters for the original grayscale image. Each image is being assigned to its own brightness histogram, which every column is a separate cluster of pixels. A cluster is being characterized by the number of pixels it contains and the average brightness value. All pairs of adjacent clusters are being browsed while traversing over the brightness histogram. The pair of clusters with the minimum distance between them is being selected for merging at the end of the histogram traversing. In general case, 256 partitions are available by the number of the gray levels. In a special case, when the image consists of K grey levels (K < 256), and there is a need to find a partition from t levels of grey, the necessity to generate K — t partition into clusters will arise. With the original version of the multithreshold processing method, the distance between the pairs of adjacent clusters was computed through the product of the intraclass and interclass dispersions, which requires considering the brightness histogram as a function of the probability density. The original technique is full of complex design equations. The modification proposed in the presented work allows computing the distance between the pairs of adjacent clusters by the increment of the total quadratic error. This modification is justified by a number of reasons. Firstly, the number of computational operations reduces twofold. Secondly, the accumulated value of the total quadratic error, expressed through the meansquare deviation, serves as the quality indicator of the image partitioning to clusters. Thirdly, the set of the total quadratic errors, characterizing the series of partitions into clusters, forms optimal sequence of partitions as evidenced by the convex curve. 
Grechishnikov V. M., Kuritsky A. A., Butko A. D. Principles of localization of shortcircuit defects in the pins of chips connected in parallel to the digital data bus. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/ce0/ltfr67obu15s0a6boypcqwa8m09fwckl/15_Grechishnikov_Kuritskiy_Butko_rus_eng.pdf To improve the reliability of the digital electronic modules of control systems in aviation, various redundancy schemes are often used, based on the parallel connection of the same type of functional elements to the data bus. The functionality of such channels is implemented on superlarge integrated circuits (SLIC), made most often in BGA (Ball Grid Array) enclosures and equipped with a JTAG interface in accordance with the IEEE 1149.1 standard. The JTAG interface is the basis for the development of hardware and software tools for boundary scanning, which are widely used not only for programming, but also for rapid contactless search, localization, identification and visualization of defects on assembled printed circuit boards
In the process of automated soldering of BGA chips, defects may occur in the form of a short circuit (bridge) between their terminals located in the subcorp space in the zone of physical inaccessibility to traditional electrical controls. Such defects can be detected using hardware and software boundary scanning. However, due to the parallel connection of chips in the presence of a short circuit only under one of them, the defect will be determined under all, including defectfree, chips at the same time.
The authors investigated the possibilities of the boundary scanning method for localization of short circuits under microcircuits in BGA enclosures connected in parallel to the digital data transmission bus according to the double «hot» redundancy scheme. The calculated values of the currents on the monitored sections of the communication lines were found experimentally, which make it possible to accurately determine the position of the defect under the microcircuits in the BGA enclosures.
The conducted experimental studies have shown that the implementation of the results obtained in the technological processes of production control and diagnostics will significantly reduce the time of searching and restoring the operability of products. 
Storozhev S. A., Khizhnyakov Y. N. A new status regulator adapting method employing fuzzy logic. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/4a3/3qhw0kiyqs270l90olcpnahrl2njmjgh/16_Storozhev_KHizhnyakov_rus_eng.pdf From the control theory point of view, an aircraft gas turbine engine (GTE) is a complex nonlinear object, which frame mathematical description is known a priori. While the GTE operation, continuous parameters monitoring, such as gas temperature behind the combustion chamber, rotor speed of a low pressure compressor (free turbine), rotor speed of a high pressure turbocharger (gas generator), is required. Further development of gas turbine engine control may be associated with the fuzzy control application. The goal of the study consists in upgrading control the fuel supplying to the GTE combustion chamber. The article proposes a new approach to the state regulator adaptation employing triangular terms with different bases, which vertices are being displaced depending on the arithmetic mean values of the input variables of the gas turbine engine, and the bases of the terms are attached to the current abscissas of the term vertices. There is a possibility to develop an adaptive fuzzifier from the analysis of the «traversed path» of each input variable, based on the proposed approach to terms adaptation. The grade of membership determining of the fuzzyfier was performed on the singleton base. Defuzzyfication was performed based on the weightaverage formula. This adaptive state regulator allows replacing the standard selector and ensuring adaptability to the GTE external operation conditions. The developed adaptive state regulator is being characterized by better values probability of nofailure of the engine electronic regulator (EER). The results of the study may be employed for the combustion chamber control. The obtained adaptive state regulator will allow significant reduction of the uncertainty in the combustion chamber operation, ensuring guaranteed thrust of the flying vehicle. 
Kolpin M. A., Protsenko P. A. Method for correcting the work plan of the ground automated spacecraft control complex based on the search for the maximum clique in sparse network graph of operations. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/2a0/ndc0wacvl0a4ua4zhugq552rikcr261z/17_Kolpin_Protsenko_rus_eng.pdf The necessity of automating the process of correcting the work plan of the ground automated spacecraft control complex in the interests of increasing the operativeness of countering emergency is reasoned. Method for correcting the work plan of spacecraft control agency is proposed. The plan in question can be represented as sparse network graph of operations. This circumstance makes it possible to reduce the problem of plan correction to the search for maximum cliques in independent subgraphs of the original graph using the known optimal and suboptimal algorithms of graph theory. This approach is implemented in two stages. At the first stage, the complement of the initial operations graph is constructed and a set of disconnected subgraphs is searched in it using known algorithms for finding the components of the graph’s connectivity (in depth or width). The advantage of these algorithms is the linear convergence time relative to the number of vertices and edges in the graph.
At the second stage, the search for maximum cliques of the found subgraphs is carried out. If the subgraph has less than 70 vertices, then the BronKerbosch algorithm is used; otherwise, suboptimal procedures that allow finding acceptable solutions in polynomial time are used.
The modeling of the process of correcting the work plan of the control agency using the developed method and heuristic procedures FIFO and LIFO has been carried out. It is concluded that the use of the developed method provides an increase in the correction completeness index due to optimization procedures when solving the problem of redistributing of the resources of the ground automated spacecraft control complex.
The method developed can be used for: — creation of software tool for automated correction of the work plan of spacecraft control agency; — conducting scientific research to assess the stability and operativeness of spacecraft control. 
Lebedev A. S., Dobrolyubov A. N., Bezrukov A. V., Yarigin D. M. Improving the information content of the system for detecting contamination of elements of rocket and space technology. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/252/0e3qp7hajl3nupn4ydfhcw66mh1sztis/Lebedev_Dobrolyubov_Bezrukov_YArygin_rus_eng.pdf The subject of the study is the methods of quality control of elements of rocket and space technology in production and operation. The aim of the work is to separate surfaces with various impurities (defects) due to an expanded dictionary of features based on secondorder statistics (combination matrices).
The method of identification (recognition) of various damage to the surfaces of elements of rocket and space technology is considered.
The initial data for generating signs of damage discrimination is a twodimensional array of intensities of electromagnetic waves reflected from these surfaces in the optical range. The reflection of light from the studied surfaces is recorded by the digital camera’s CCDmatrix when they are irradiated with a singlemode laser module S5 (Sanyo) of the visible (red) range with a continuous radiation power of 5 MW in the spectral range of 635 nm, which is the optimal source of coherent radiation for building control and automation systems, alignment and marking devices, as well as for scientific purposes.
The generation of a dictionary of surface recognition features is based on nonlinear transformations of the resulting images (textures). To do this, the twodimensional array is transformed into a secondorder statistic ‒ the spatial dependence matrix (the matrix of combinations) .
The description of class recognition in the language of newly generated features made it possible to eliminate areas of ambiguous solution when identifying surfaces that were present in the previously developed method based on the feature space (mathematical expectation, variance, skewness and kurtosis coefficients) formed on the basis of firstorder statistics (histograms of the intensity distribution of reflected signals). Thus, it is possible to separate the contamination (damage) of the surface of the studied elements from each other, eliminating the previously existing uncertainty.
The proposed methodology can be used to form expert opinions that exclude the «human factor» when assessing the condition of the studied surfaces of rocket and space technology elements at various stages of their manufacture and operation (at the manufacturing plant ‒ during production and in operating organizations during repair and maintenance work). 
Dorozhko I. V., Ivanov O. A. Decisionmaking support system model for spacecraft onboard systems diagnosing based on Bayesian networks. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/914/61em1ztxyytqrbhrrvdpid2aopht4umc/19_Dorozhko_Ivanov_rus_eng.pdf The article proposes employing Bayesian networks capabilities, based on nonuniform data as well as fragments of knowledge representation and posteriori inference for the incoming information accounting, to solve the problems of the spacecraft onboard systems diagnosing.
The developed model and technique are based on mathematical apparatus of Bayesian trust networks, as well as the basic concepts and relationships of the theory of reliability and technical diagnostics of systems. The initial data is information on the reliability (structural and logical schemes, failure rate of elements) of spacecraft typical onboard systems and diagnostic models that linking the types of technical conditions and diagnostic features. For causeandeffect relationships between the types of technical condition and diagnostic features, sets of conditional probabilities or densities of distributions are pointed, depending on the continuous or discrete type of diagnostic feature, respectively.
The results of the research are constructing technique and a model of an intelligent decisions support system for a spacecraft onboard systems diagnosing.
The article considers examples of new incoming information processing in a fragment of the Bayesian network at diagnosing spacecraft onboard systems. It quotes analytical calculations and posteriori inference results while new information incoming on the spacecraft blocks failures, as well as while incoming of discrete and continuous values of diagnostic features.
The model based on dynamic hybrid Bayesian trust networks includes discrete and continuous variables describing causal relationships of technical conditions and diagnostic features types, as well as relationships of blocks (elements) in terms of reliability. The results of the logicalprobabilistic inference allow control the values of the spacecraft operational state probabilities in the course of time, as well as predict possible failures and take proactive measures.
Mathematical models of diagnosing, considered in the article, account for the types of elements connection, reliability of elements, as well as dynamics of technical states types and their relation to the diagnostic features, which may be both continuous and discrete. 
Dement`ev A. N., Bannikov A. V., Arsen`ev K. V., Shiryaev A. A., Basak A. A. Quality control of the spacecraft onboard equipment functioning under the impact of the propulsion system radiation. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/256/ruwxxupdrfw1newexvnc05uskitah0ad/20_Dementev20_20_Bannikov_Arsenev_SHiryaev_Basak_rus.eng.pdf One of the concepts for the prospective space systems development consists at present in the spacecraft energy capacity enhancement through the space purpose neuclear reacotrs application.
The article presents computational models that allow radiation conditions determining created by nuclear reactors of advanced spacecraft (AS) in the locations of onboard equipment (OE). In addition to the ionizing radiation (IR) impact from the outer space (OS), the radioelectronic OE is exposed to the penetrating radiation of a nuclear reactor. The article shows that along with a number of operational characteristics increasing, nuclear reactors application as power systems involves stricter requirements for radiation resistance. The results of the absorbed doses’ modeling and calculation for the of the payload insertion vehicle model containing reactor are presented.
Presently, in the context of modernization and the transition to an innovative path of development, space nuclear energetics become uptodate again. The «Roskosmos» State Corpoation together with the «Rosatom» State Corporation propose developing a project of a spacecraft equipped with a nuclear rocket engine of a more than megawatt capacity for flights to the Moon and Mars 1.
The current requirements for the spacecraft consist in the active life increasing by the amount from10 to 15 years, which entails an increase in the requirements for ensuring the OE radiation resistance.
Among the numerous factors affecting the OE functioning, the IR CP impact may be distinguished due to the fact that both dose (DE) and single (SE) effects caused by the IR CP account for up to 50% of all OE SC failures.
Besides, the OE of a spacecraft with the onboard reactor should function normally in a stationary mixed field of gamma and neutron radiation, which characteristics’ values, as well as the ratio between the gamma and neutron components of the radiation field depend on the thermal power of the reactor, location of the equipment on the spacecraft relative to the reactor, the type and characteristics of the protection used, the reactor operation duration, as well as the presence of the residual gamma background of the reactor in the off state.
In this regard, when spacecraft systems designing, it is necessary to conduct studies on assessing the IR impact of various energies on the OE elements to ensure the required levels of radiation resistance.
The presented models account for the difference between the neutron and photon radiation interaction. The thechniqye for determining the neutron radiation propagation function in the form of the neutron radiation flux density in the the spacecraft structure materials depends greatly on the energy range, which affects significantly the physical processes of interaction. Besides, when neutrons propagate through the spacecraft structural elements, secondary gamma radiation occurs as a result of inelastic scattering and neutron capture. The quantitative characteristics of secondary gamma radiation depend on the type of material, its thickness, and the energy distribution of neutrons.
In the region of photon energies from twenty kiloelectronvolt to ten megaelectronvolt, to which the photons generated by the spacecraft nuclear reactor are being related, the main primary processes of gamma radiation interaction with the spacecraft structure materials are the photoelectric effect and Compton scattering of gamma quanta.
The article cosnsidered computational models, which allow determining the radiation conditions, created by the neuclear reactors of the advanced spacecreaft in the OE locations.
The authors show that the radioelectronic OE is being exposed to the penetrating radiation of a nuclear reactor in addition to the impact of the IR OS, and that along with the increase in a number of operational characteristics, the of nuclear reactors application as energy systems involves stricter requirements for radiation resistance. The models presented in the article allow the specific absorbed doses computing and, with account for the propagation function of the corresponding components of gammaneutron radiation, determine the absorbed doses at a given point.
The article presents the results of absorbed doses modeling and calculation for a model of a payload insertion vehicle containing a nuclear reactor. It should be noted that the proposed model of the gammaneutron radiation inpact from the reactor on the spacecraft OE elements is of an applied engineering nature and has no fundamental limitations on the linear dimensions of individual devices and structures when calculating the passage of the AI through the spacecraft elements, which allows it to be employed for calculating local dose radiation loads as well. 
Efanov V. V., Zakota A. A., Gunkina A. S. Probability assessing technique for a fighter guidance to the allowed guided missiles launches zone under conditions of incomplete instrumentation. Trudy MAI, 2021, no 118, http://mai.ru//upload/iblock/8d2/jdppxl0pemk1zca7bw6qa6ywd4m24fsp/21_Efanov_Zakota_Gunkina_rus_eng.pdf Confrontation of parties at ranges exceeding the range of visual visibility, and confrontation at visual visibility may be distinguished in modern air fight. In the first case, the longrange air fight, which represents a flight, detection, identification, closingin. maneuvering and is being performed applying the surveillance and sighting system (SSS) and with medium and longrange missiles. In the second case, close air fight is being carried out under conditions of maneuvering with highg, fully employing maneuvering capabilities of an aircraft, physical abilities of a pilot and with application of shortrange missiles and cannon armament.
Until the moment of target detection herewith by the onboard facilities or visually by a pilot, the taskoriented control of a fighter can be implemented by a higherlevel system. The system possesses the information on both the target and the fighter from the groundbased or airborne control points (CP) through the command radio link to bring it to the radar contact with the target.
After the SSS transition to the continuous direction finding" mode, the third stage of the shortrange guidance begins. The basic task of this stage consists in bringing the fighter to a certain area of space, which is restricted by maximum and minimum launching ranges of guided missiles and limiting values of the fighter angular coordinates relative to the target. For the shortrange guidance, the «direct closein» method, directed to achieving the final goal of guidance, is widely used as the basic one.
This method assumes that the target is not maneuvering and keeps its movement parameters of constant. The fighter is being guided along a straightline trajectory to the point of the intended rendezvous. The end of the shortrange guidance phase is the fighter’s stationing to the starting position for the attack. The main task herewith consists in ensuring the target lockon by the missile coordinator or its readiness for launch. Close guidance ends up with the attack of the target, i.e. applying the GM from the allowed launch zone.
In the incomplete instrumentation mode, the SSS performs target tracking only by the angular coordinates. However, the information on maximum and minimum range is necessary for launching conditions computing. The article suggests a technique for the probability assessing of the fighter guidance to the guided missiles launching zone under conditions of incomplete instrumentation. The gist of the technique consists in determining: — The probability of a target detecting and locking, under condition of absence of interference in accordance with the explicit dependence on time of identification, lockon, average time the target staying within sight of the SSS, depending on maximum and minimum range, aiming time and relative closein speed; — The probability jumpingoff in accordance with the formula dependence of the sector width and guidance errors. The fighter and missile maneuverability is being checked herewith, and in case of missile maneuver capability exceedance, the lockon sector width is being determined in accordance with the expression depending on the missile and fignter angular speed relative to the closein speed and average lockon range; — The rootmeansquare guidance error in accordance with the formula dependence on course meansquare deviation and spatial position meansquare deviation of a fighter and a target. Position measuring accuracy herewith is being determined according to the expression, depending on the fighter to target speed ratio, target speed, measuring time and average lockon range; — Additionally, the accuracy error of the fighter and target spatial position under conditions of the incomplete instrumentation based on the indirect target movement parameters determining method.
Simulation of process of the fighter guidance to the allowed launches zone under conditions of incomplete instrumentation allowed revealing that at the measuring accuracy of the target spatial position under conditions of instrumentation incompleteness form 2.6 to 7%, the probability of the fighter guidance to the allowed launches zone changes within the limits from 0.7 to 0.4. 
Popov I. P. Sources of force and velocity, resonances and antiresonances. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/91e/oomdtxrhgyfm8b6fvd6qn72vejvflv32/Popov_rus.pdf The article considers parallel and series connections of a mechanical system’s elements with a source of harmonic force, or a source of harmonic velocity as a source of the external mechanical harmonic impact. A crankandyoke drive and a flywheel with a large moment of inertia can be the source of harmonic velocity. The source of the harmonic force can be represented by the rod of the pneumatic cylinder, which cavity can be in communication with the cavity of another pneumatic cylinder, which diameter is immeasurably higher than that of the first one, and which piston performs harmonic oscillations. The mechanical harmonic impacts, described in the courses of theoretical mechanics, correspond to the source of harmonic force. The article describes the four modes, namely resonances and antiresonances of forces and velocities. The symbolic (complex) method implementation has significantly simplified the study of resonance and nearresonance phenomena, particularly, it allowed deeply unify and formalize consideration of various mechanical systems. The cumbersome and timeconsuming operations associated with the preparation and solution of differential equations have been replaced by simple algebraic transformations. This method is based on the mechanical analogue of Ohm’s law in a complex representation and the concept of mechanical reactance, resistance, impedance, susceptance, conductance and admittance. The classical consideration delivers one amplitudefrequency characteristic, while the symbolic (complex) method delivers eight ones with a significantly larger number of characteristic points and characteristic ratios. Resonance and antiresonance of forces, resonance and antiresonance of velocities were determined. Resonances stem from the combinations of parallel connection of elements and a source of harmonic force, or a series connection of elements and a source of harmonic speed. Antiresonances occur due to the combination of parallel connection of elements and a harmonic velocity source, or their series connection and a harmonic force source. 
Lazarev S. I., Lomakina O. V., Khorokhorina I. V., Kochetov V. I. Analytical studies of mechanical displacements in baromembrane apparatus elements. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/fff/5s5lmyn0nx30uyfsozcrny8oxomsroyq/Lazarev_Lomakina_KHorokhorina_Kochetov_rus.pdf Baromembrane devices of the flatchamber type are applied for separation, concentration and purification of solutions by reverse osmosis, nanofiltration, ultrafiltration and microfiltration processes. Operating under excessive pressure, they possess the following characteristics: ease of assembly and installation, a sufficiently high specific separation area, reliable operation, and a small pressure drop. The difficulty in operation of such devices, for example, for reverse osmosis, lies in the large values of working transmembrane pressure. To solve this problem, the authors proposed to employ end flanges, characterized by increased rigidity and strength. The purpose of this work is to study the stressstrain state of the structures of the end flanges of the flatchamber type baromembrane apparatus operating under high transmembrane pressure.
The flanges with shape of rectangular plates, are made of “caprolon” (dielectric material). There are holes on the cover for bolts, necessary for tightening the intermediate working chambers to seal them. To increase the strength characteristics, a metal plate in its structure, which is superimposed on the flanges is provided.
During this device operation, its individual working surfaces are being exposed to highly concentrated solutions. In the authors’ opinion, optimal dimensions selection, namely of flanges in this particular case, based on the strength and rigidity conditions is an urgent task. To study the stressstrain state of the flange, we use both analytical and numerical methods. Accounting for the strength parameters and stiffness, several options of the design scheme were considered to select the flange optimal dimensions:
– A flange without a plate and bolts;
– A flange with a plate but without bolts;
– A flange without both a plate and bolts;
– A flange with a plate and bolts.
Computations were performed using the SOLIDWORKS Finite Element Method (FEM) software.
Analyzing the data the displacements and stresses values computing, a good comparability of the results was noted. The conducted studies of the flange of the flatchamber type baromembrane apparatus, in terms of strength and stiffness allowed determining the design scheme reflecting the design of the real device. A comparison of the techniques for the flange calculating revealed the correctness of the design scheme selection and the method for calculating the end flange of the baromembrane device. 
Sysoev E. O., Dobryshkin A. Y., Sysoev O. E., Zhuravleva E. V. Modeling vibrations of a thinwalled cylindrical shell under uniform temperature impact at a variation formulation of the problem . Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/a30/qwm2sabanw4didy70gej4e2d7j3r9jrl/Sysoev_Dobryshkin_Sysoev_ZHuravleva_rus.pdf The purpose of the article consists in verifying mathematical model of thinwalled cylindrical shell vibrations under the impact of the uniform temperature based on variation formulation, and employing various methods, including the experimental one.
The stateoftheart construction often employs expressive and costeffective shapes of buildings and structures in the form of thinwalled cylindrical shells. These buildings herewith are being exposed to temperature impacts and external forces action, leading to technogenic accidents. To avoid these accidents, frequency responce of buildings and structures should be computed. Dynamic temperature variations of the shell lead to the elastic modulus of buildings changing, which affects the frequency response dynamics. The existing vibration analysis models for thinwalled cylindrical shells do not fully account for this fact, thus, improved analytical models development is required with confirmation of the high quality of the developed model. Experimental verification is one of the most common methods of mathematical models proofing. The new theoretical basis parameters are being verified with a realistic scaleddown model of the structure, and comparison of experimental and theoretical data is being performed.
The article presents a new design model for thinwalled cylindrical structures vibrations being exposed to the uniform heating, based on variation formulation. The obtained design model has been verified by experiment, and its application range has been determined.
The new verified mathematical model can be used for performing structural analysis, in design bureaus conducting vibration analysis for cylindrical shells.
Comparison of experimental and theoretical results of was performed. Convergence of the results is less than 5%. It was demonstrated also that the experimental data revealed a discrepancy with the results obtained while vibrations computing of the open cylindrical shells by the wellknown mathematical model. 
Blinkov Y. A., Ivanov S. V., Mogilevich L. I., Popov V. S., Popova E. V. Longitudinal waves in coaxial elastic shells with account for structural damping and with fluid inside. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/0cc/fcqp5a64mwrqynb1b364uhr1m1alukk6/Blinkov_Ivanov_Mogilevich_Popov_Popova_rus.pdf This article studies longitudinal deformation waves in coaxial elastic shells with soft cubic nonlinearity, containing a viscous incompressible fluid, both between them and in the inner shell. The structural damping effect of the shell material in both longitudinal and normal directions and the environment surrounding the outer shell on the wave amplitude and speed was accounted for. The article demonstrates that this leads to the need for numerical methods application to study the nonlinear wave process. The numerical study of the model obtained in the course of this work being performed employing a difference scheme for equations similar to the CrankNicholson scheme. In the absence of liquid inside the shell, structural damping in the longitudinal direction as well as surrounding elastic medium, the velocity and amplitude of the waves, propagated in the shells, do not change. Computations show that the waves’ movement takes place in the introduced moving coordinates system in the negative direction of the abscissa axis. This means that the found nonlinear addition to the wave velocities in the linear approximation (the speed of sound) decreases the waves velocities and they become subsonic. The result of the computational experiment in this case coincides with the exact solution; therefore, the difference scheme and the system of generalized modified Korteweg – de Vries – Burgers (MCdVB) equations proposed in this work are adequate. At accounting for the impact of inertia of the liquid motion in the inner shell, a velocity decrease of the deformation waves occurs, while the presence of the elastic medium surrounding the outer shell leads to their velocity increase. The liquid viscous stress in the inner shell and structural damping of the shells’ material in the longitudinal direction leads to the waves amplitudes decrease. Structural damping in the normal direction increases the wave amplitude by a constant value and decreases its velocity. 
Lokteva N. A., Ivanov S. I. Noiseabsorbing properties of a homogeneous plate with arbitrary boundary conditions under the impact of a plane acoustic wave in acoustic medium. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/d35/og8lkuizxp41ay17ririzmt5tjon15tf/Lokteva_Ivanov_rus.pdf The main purpose of the presented work consists in the displacements determining of the plate under the given boundary conditions. By reason of purely mathematical difficulties, such kind of problems consider, as a rule, a limited number of types of soundproof panels fixing, being reduced to the boundary conditions corresponding to the free bearing. Thus, obtaining techniques for solving the problems associated with interrelation of acoustic media and a plate is of significant scientific value. The approach used to solve problems with arbitrary boundary conditions is generally applicable to solving other problems, particularly, of the theory of plates and shells. It supposes a solution finding of a problem on sound absorbing properties of the homogeneous infinite plate. After this, strive for the fulfillment of boundary conditions in certain points of the infinite plate. The problem setting herewith is assumed related, where not only direct impact of the wave on the obstacle but also the acoustic media behavior prior to and after the noise absorbing obstacle are being accounted for. This formulation of the problem allows determining the noise level not only directly at the interface between the plate and the acoustic medium, but also at any distance from it.
The article presents the developed general approach to the solution of the problems with arbitrary boundary conditions for the plates. The problem of the plane harmonic wave interaction with the infinite homogeneous KirchhoffLove plate has been solved. The midline normal displacements were determined depending on the oncoming wave frequency. Influence functions for auxiliary forces, necessary to ensure the boundary conditions fulfillment in the specified points, were found for employing the method of compensating loads. The compensating forces values were determined based on the boundary conditions for rigid fixing of the plate edges. As an example, normal midline displacements, corresponding to the rigid fixing on the two edges and hinge attachment, were obtained based on superposition. The boundary conditions fulfillment in both cases was demonstrated. The sound absorption coefficient for a rigidly fixed plate has been determined. 
Kulygin S. V., Kazachkov V. O., Kochkarov A. A. Vehicular flows monitoring on toll road sections based on the GNSS employing. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/eb4/jzpg213gvpo0ge3nva55szmash1tgw1e/Kulygin_Kazachkov_Kochkarov_eng_.pdf Currently, the toll roads construction or organization of the toll roads on the already existing road network is a promising trend in the development of a highquality road system. In the context of insufficiency of the budget funds being laid out in Russia for the toll road infrastructure development, the issue of attracting private investment for road construction has become acute. For investments attraction, the toll road system should be organized so that it would guarantee refunding of the committed facilities and sufficient profit margin to the investor for account of toll operation of the object, as well as economic concernment of the society, which would employ this system.
The obvious disadvantage of toll drive way systems with toll gathering points is the costly maintenance of the systems, both in terms of the entry and/or exit checkpoints equipment, and the involvement of fulltime operators. The main disadvantage for the drivers is traffic jams creation at the entrance and exit of the toll road section.
To solve these problems, an electronic system of fees was implemented. With this technology implementation, the driver passes the toll plazas without stopping at a given speed. Payment is being made with special electronic systems. Today, the existing Russian systems have their drawbacks, such as inability to read heavily polluted or deliberately hidden license plates without transponders, as well as the lack of ontime payment guarantee of the drive way at the postpayment.
The purpose of the work consists in studying automated information systems that determine location of a vehicle by the Global navigation satellite systems GLONASS and GPS, to eliminate the above said problems peculiar to the electronic tolling systems.
Implementation of the ERAGLONASS automated information data systems and vehicle monitoring systems opens up an opportunity to the electronic tolling system improvement. For vehicles with the abovementioned systems, the approach does not require installation of additional equipment, and if the individual vehicle identifier is linked to the vehicle identification number (VIN) and its registration plate, it allows solving the problem of unreadable numbers. The absence of changes to the hardware on the car side allows also performing further modification of the system with device updates by simple flashing.
For this solution implementation, the machine (computer) code and previously released devices updating is necessary. The access point for vehicles registration at the entrance and exit of the toll road section are necessary to be installed herewith. Information transfer to the data processing center for the vehicles monitoring will be realized through the mobile GSM system. After data processing, a driver would receive a receipt for payment for the toll road section passage.
For the proposed solution verification, computation of the traffic being transferred from the vehicles to the GSM standard base station on weekdays and weekends/holidays based on the M/M/1 queuing system.
The article presents the obtained graphs of the distribution function of waiting time for a vehicle serving by a single station covering the toll road section. Inferences were drawn that the servicing waiting time would be less than 400 ms with probability of about 0.99 on both weekday and holiday.
The maximum number of vehicles served by one base station was computed as well. Thus, on a weekday, this number will be 118992, and on a weekend/holiday 161952 vehicles.
Thus, due to vehicles monitoring by the “ERAGLONASS” and monitoring systems, which receive code signals from the Global navigation satellite systems GLONASS and GPS to determine the location, the barriers at the toll roads entrance and exit can be discarded. The solution will lead not only to the electronic passage fare system maintenance cost reduction, traffic jams reduction at the entrance and exit when transition to the electronic paying system with minimum costs.
The proposed modernization can also act as an independent system, and allows also improving the existing electronic fare payment systems in Russia to reduce the likelihood of unpunished free drive way, which opens up an additional opportunity to attract investment for construction and maintenance of the toll roads. 
Bakhtin A. A., Volkov A. S., Solodkov A. V., Baskakov A. E. Development of an SDNbased network segment model for 5G standard. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/32d/grksi2nfea1trz8tcx2wnep2fgvo2ixo/Bakhtin_Volkov_Solodkov_Baskakov_rus.pdf The main effort of the scientific community in the field of telecommunications at present is focused on the development of the fifth generation mobile communication networks, which feature is an increased data rate up to 10 Gbit/s. An important requirement for the fifth generation mobile networks consists in ensuring flexibility of their architecture for various kinds of applications functioning, of which realization is also possible by employing technologies of softwaredefined network (SDN) and network functions virtualization (NFV). The article proposes a model for a network segment organizing under the OpenFLow protocol control, and packages format with account for the possibilities for data transmission level control. The delay and throughput characteristics of the modeled nework segment, demonstrating the SDN networks advantages when employing the proposed format of the control packages, were obtained. The 5G standard envisages wireless communications with the encreased wireless data rate and throughput; enhanced coverage area; significantly diminished total delay and reduced energy consumption. Data transfer rate should reach the values from 1 to 10 Gbit/s in real networks which is ten times higher than the theoretical peak data transfer rate in the LTE network, i.e. 150 Mbit/s. The symmetrical delay herewith was originally being planned at the level not more than 1 ms, i.e. nearly ten times less than for the 4G. Other key tenets of the 5G development are high throughput in terms of the unit of coverage area and a huge number of connected devices. With high requirements for the delay and limited bandwidth, a new paradigm for organizing a cell and a base station as a whole is being introduced. The increase in demand for wireless infrastructure capacity has changed the way the networks are designed, and shifted the focus to multiple small cells as opposed to the original hexagonal of the large areas coverage Changes in architecture and radio interface put emphasis on the development of the 5G standard for smaller cell sizes and an increased number of antennas. Configuring and maintaining numerous network equipment, servers and routers with such a dense of the deployed 5G network is a daunting task. The Software Design Network offers a simplified solution to this complex problem. The fundamental principle of the SDN is the separation of the network between the layers of control and data transmission, which ensures speed and flexibility in 5G networks, as well as employing the existed network architecture and reducing the requirements for computing power of the network equipment. The SDN concept decouples data and manages layers by the software components. The software components are responsible for the management layer, reducing thereby the hardware requirements for the network equipment. Interaction between the two layers is being achieved through the open interfaces, the most popular of which is Open Flow. The article considered the requirements of the 5G standard for the network infrastructure. It demonstrated the general tendency to reducing the cell size, moving digital processing to the core network level, and locating on sites only radio transceivers, operating on the SDR technology. It was determined at the network architecture level that the softwaredefined network ensusres the greatest convergence, reuse of current network resources and the easiest scaling and standard changing in the future. The article shows that the most successful solution to preserve the existing network infrastructure is the OEPC protocol. It presnts the of service messages formats, as well as proposes a frame format with fields that support GTP tunnels. The simulation results allowed establishing that the SDNconsept based network ensures low delays and, with the selected packages format application, uniform balancing of the network loading. It allows employing the suggested modification of the packages fields to create new algorithms for the communication means control.

Sentsov A. A., Nenashev V. A., Ivanov S. A., Turnetskaya E. L. Combining the generated radar images with a digital map of the area in onboard systems for operational monitoring of the earth's surface. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/550/n36va9lyrcxa0jg5sfzwbava7t2ju2n1/Sentsov_Nenashev_Ivanov_Turnetskaya_rus.pdf The article considers the problem of combining the radar image generated by the onboard equipment of a small aircraft and a digital geographical map of the area, taking into account the heights in real time. To solve this problem, we use methods of correlationextreme image matching, methods of highprecision onboard monitoring, methods of image matching and processing. To implement a system for the operational display of current location information received by radar equipment from the sides of small aircraft, it is necessary to combine radar and topographic (optical) images into a single information field. To do this, you need to find the appropriate functional transformation in order to overlay the actual data generated in real time on the geographical map. For this purpose, an algorithm for combining the radar image and a digital map of the area based on the correlationextreme method has been developed. To solve the condition of the algorithm for finding a small aircraft at a point from the confidence square, a criterion for combining four pairs of reference points is proposed. In the case of an insufficient number of reference point pairs, the algorithm provides for the use of a unique pair, which allows you to perform a primary comparison of the contours of characteristic reference points and calculate preliminary estimates of the components of the error vector of navigation data. The software implementation of the abovementioned algorithms on programmable logic integrated circuits can be performed using parallel calculations, which allows for a mode that is close to real time. The results obtained can be used to update topographic maps of the earth’s surface, for environmental monitoring of areas of high attention, as well as for the implementation of autonomous navigation of aircraft during operational search and rescue operations in areas of emergencies and natural and manmade disasters. The results of the work are adaptable for processing images obtained in different spectral ranges and combining them with a digital map of the area in order to increase the information content of the information obtained. 
Panteleyev A. V., Karane M. S. Application of hybrid multiagent interpolation search method to the satellite stabilization problem. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/ed1/9cdd018pgd0v97bx431njx1ebsg3wq8p/Panteleev_Karane_rus..pdf The article regards the problem solution of satellite stabilization using the algorithm for finding the optimal openloop control based on application of the expansion in terms of the system of basis functions and the multiagent method.
Multiagent algorithms are quite popular now and used in various fields of science. Multiagent algorithms are not rigorously justified and convergence guarantee, however they are successfully applied in practice and demonstrate acceptable results in reasonable computational time. The article proposes a hybrid multiagent interpolation search algorithm based on the Bezier, CatmullRom and Bsplines interpolation curves construction. The curves are being constructed based on information on the agents, form the current population, position. In addition, the algorithm needs to solve the problems of onedimensional parametric optimization to realize the exploratory and frontal search. Beyond that point, the described multiagent method employs the ideas of swarm intelligence and migration algorithms.
Besides, the algorithm under consideration for the optimal openloop control search is based on application of the expansion in terms of the system of basis functions. This approach is quite popular and actively used in the spectral method for nonlinear control systems analysis and synthesis. The authors propose to search for the optimal openloop control in the form of a saturation function, which argument is a linear combination of the given basis functions with some coefficients to be found. Particularly, piecewise constant, piecewise linear, quadratic and cubic splines are being used as basis functions. In addition, the saturation function should guarantee the specified constraints fulfillment on the parallelepipedictype control.
Based on the proposed algorithm, the software for the optimal openloop control search has been developed, and its algorithm efficiency has been studied when solving the problem of position stabilizing of a satellite driven by engines. Comparative analysis of the effect of basis system selection was performed as well. As it can be seen from the numerical experiment, the algorithm successfully copes with the problem of the satellite position stabilizing and finds a solution close to optimal when using all the abovementioned systems of basis functions. In addition, the interpolation method parameters were selected so that to achieve a high accuracy of the applied problem being solved. 
Ermakov P. G., Gogolev A. A. Comparative analysis of information integration architectures of strapdown inertial navigation systems for unmanned aerial vehicles. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/c31/xon4nnv6t4aum3wqzj4b7kfbsol369la/Ermakov_Gogolev_rus.pdf The article describes a comparative analysis of separate and loosely coupled architectures of navigation information integration in the case of the following sensors application:
– inertial sensors based on microelectromechanical systems (MEMS) technologies comprising accelerometers measuring proper acceleration, and gyros, measuring rotation speed of a body;
– barometer, measuring air pressure under certain conditions; and, finally,
– GNSSreceiver forming information on position and velocity of the unmanned aerial vehicle (UAV).
Let us pay attention to the fact that the MEMSbased inertial sensors exhibit large errors that can be compensated using data on the position (latitude and longitude) and velocity of the UAV from the GNSSreceiver, as well as on the altitude, being updated by the barometer using hypsometric expression. However, navigation information about the UAV from inertial system is basic since it possesses a high refresh rate and property of independence on the external interference.
In the case of a separate integration architecture, the algorithm of the strapdown inertial navigation system restarts with new initial conditions for the UAV position and velocity from the GNSSreceiver and barometer, respectively. This approach requires minimal hardware and software costs, though the precision of the integrated navigation solution herewith is getting worse with the restart time increasing.
A loosely coupled integration architecture employs the integrated Kalman filter to evaluate the UAV coordinates, velocity and orientation, as well as systematic errors of accelerometers and angular rate sensors. Computed estimates of the inertial system errors are being subtracted from its indications for errors compensation. Thus, this approach is being characterized by high precision and reliability of navigation solution, but, at the same time, tuning integrated Kalman filter is not a trivial task. 
Tanygin M. O., Alshaea H. Y., Mitrofanov A. V. Complexity of algorithm for data source determining. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/ce7/rpgg4mo5ts6zbgjx08bmyodtav4brdpf/Tanygin_Alshaia_Mitrofanov_rus.pdf The article deals with the problem of complexity assessing of the procedures for determining the incoming information blocks source. The algorithm for processing the blocks analyzed by the receiver, implementing the data source identifying method, is described. The method is based on incoming blocks unification on the receiver side into the structured sets, and checking for these blocks certain logic values, being computed on the assumption of these blocks content and certain a priori information, known to both the source and receiver. The blocks, incoming to the receiver, are being buffered and then unified into the structured intersected sets. This sets form a treetype structure in the receiver memory. Analyzing this structure, the receiver determines that structured set, which was formed by the target source.
The article shows how the number of these sets, being formed, affects the incoming blocks analyzing complexity. A mathematical model for assessing typical operations, executed by the receiver while the incoming blocks checking and their appending to the corresponding side branches of the tree structure, was developed based on the theory of probability.
Functional dependencies between the probability of the side branches of the tree structure forming and their length and parameters, used while organizing interaction between the source and the receive were determined.
Mathematical expectation of the number of operations executed by the receiver to analyze the contents of the information blocks service fields was estimated, based on the obtained probability estimates. The dependencies between the characteristics of the information systems, in which the considered identification method is implemented, the service information fields size and the number of elementary operations were determined. Based on the obtained results, the space of receiver operating parameters was partitioned into the ranges, in which the dependence of algorithmic complexity on the number of data sources can be approximated by various functions. The range where complexity increases linearly with the number of interacted elements of the information system growth was determined as operating range. This makes the studied method more preferable compared to the known ones with power and factorial complexity, especially when identifying the sets of large the data blocks. 
Borzov D. B., Koshelev M. A., Sokolova Y. V. Modeling a reconfigurable realtime system with a decrease in the time spent on processing information. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/743/8oic1zsuswk0c27bnfsojn6mpulz4881/Borzov_Koshelev_Sokolova_rus.pdf The purpose of the research is to reduce the time spent on processing information, contributing to an increase in the speed of a reconfigurable realtime system, by creating a methodology and an algorithm for distributing an array of computational tasks.
The research methods of the work are based on the definitions of set theory, graphs, probability theory and mathematical statistics. With their help, a mathematical model and a system of criteria for a reconfigurable realtime computing system, built on a wireless protocol, was created, which allows placing tasks according to the minimummaximum time estimate. And also an algorithm for placing tasks in a computer complex is proposed, which allows increasing the performance of the system by reducing the time of data transfer.
As a result of the research, a method was developed for the distribution of computational tasks in a realtime reconfigurable computing system, which makes it possible to reduce the time of data transmission within the system, which increases the performance of the complex. A methodology for distributing computational tasks to individual processor modules has been compiled. The work of the proposed methods is simulated. And a system of criteria is proposed that describes the final state of a reconfigurable realtime computing system. As a result, the resulting system gave a gain in time of about 2.5 times. Placing connected problems in dynamic systems reduces the payoff coefficient linearly.
The resulting model can be used in distributed computing. The work of the proposed methods is simulated. Their analysis confirmed the increase in system performance as a whole. 
Nikulin V. S., Khizhnyakov Y. N., Yuzhakov A. A. Virtual adaptive meter of deleterious substances in combustion chamber of a gas turbine engine based on the RBFnetwork. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/4c6/7tbkrv3j1n5kw3v177oyz6m0uoe6j8z5/Nikulin_KHizhnyakov_YUzhakov_rus.pdf The soft computing technology toolkit is based on fuzzy systems, probabilistic models, neural networks, genetic algorithms, etc., which have their own advantages and disadvantages. This toolkit application was considered for an aircraft gas turbine engine (GTE) operating under conditions of uncertainties such as regulating hardware elements aging, variable ambient environment parameters, and variable fuel parameters.
Combustion chamber, ensuring the process of the airfuel mixture (AFM) burning, is one of the basic parts of the gas turbine engine. Today’s progress in aircraft building development imposes requirements to the aircraft and engine softhardware facilities integration simplicity, as well as reduction of deleterious substances exhaust to the environment.
The purpose of the presented study consists in the following:
– developing method and algorithm for the adaptive virtual measurer of the deleterious substances exhaust by the GTE combusting chamber based on the RBFnetwork;
– adaptive control of air consumption into the combustion chamber;
– adaptive control of the gases temperature behind the combustion chamber employing fuel consumption regulation by the homogeneous collector.
The following research techniques were used in this work:
– graphoanalytical method for the RBFnetwork architecture building as an alternative to the Kohonen algorithm;
– an algorithm for oxidizer feeding control with the RBFnetwork;
– creating an algorithm for the current total value of deleterious substances correction at the specified value exceedance;
– creating an algorithm for the fuel consumption control in the homogeneous collector while temperature control behind the GTE combustion chamber by the adaptive fuzzy regulator
Based on the total computing of the deleterious substances, the following conclusion can be made on the exhausts requirements, which is 18 kg, as well as improvement of control system of the remote guiding device (RGD), and combustion products temperature behind the GTE combustion chamber.
The results of the research confirmed the decline of the combustion process uncertainty impact, and exhausts reduction in the airfield vicinity. 
Knyazev A. S. Joint use of the XPlane flight simulator and the SimInTech program to investigate the operation of aircraft systems. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/f20/qerbbtq2m4vf6z145helx0jjs4mbkhm4/Knyazev_rus.pdf The work shows the relevance of using the XPlane flight simulator as a research program. From the existing programs allowing to realize interaction with XPlane such as Microsoft Visual Studio, Builder C ++, Delphi, Matlab Simulink, LabView, etc., many are import therefore their use in the Russian enterprises and universities is undesirable. Besides, it doesn’t allow students, teachers and engineers to conduct researches without license for these products.
In this regard, for interaction with the XPlane flight simulator, it is advisable to use the Russian modeling program SimInTech, which is not inferior to imported analogues in terms of functionality and calculation quality, and also has some advantages and can be provided to Russian universities and enterprises for free. To interact SimInTech with the XPlane flight simulator a set of primitive blocks is used. Ready demos projects with all necessary blocks which are adjusted for interaction with XPlane are available to the user. When developing the project it is expedient to use ready decisions to start work.
Interaction of the user with XPlane for the research purposes is carried out by receiving data from the simulator and sending data to the simulator. For an example it is considered the «Damper» blocksubmodel. It’s work is described and it’s elements are considered. The mechanism of interaction of the project in SimInTech with the XPlane flight simulator is described. With use of primitive blocks in SimInTech the implementation (reproduction) of schemes of various aviation systems is possible. Sharing of SimInTech also XPlane allows to accept from the flight simulator data which in real aircraft can be received from various onboard sensors and systems.
To interact with the XPlane flight simulator, the program SimInTech developed demo examples that implement all available methods of sending and receiving data, so it is in no way inferior to other programs that can be used for the same purposes. References to documentation containing detailed instructions for use of SimInTech and XPlane are given. 
Zulfugarli P. R. Indicators computing technique for energyinformation effectiveness mode indicators of unmanned aerial vehicles for remote sensing functioning. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/60d/6p6t06b5vp3khvq3okxyywytfpk2iqvp/Zulfugarly_rus.pdf One of the major UAV shortages is limitation imposed on its energy provision. This shortage necessitates optimal distribution of the UAV energy balance by optimal selection of its flight trajectory and communication order. Alongside with that, the final product of the reconnaissance type UAV is the information volume collected while the performed flight. The main inference from the above said is that the UAV should operate in the energyinformational effective functioning mode. The purpose of the presented work consists in developing the technique for optimal mode parameters computing, ensuring energyinformational effective mode of the UAV functioning.
The suggested technique is based on the UAV representation of as a cyberphysical system fed by electric battery, and envisages performing a twostep optimization of the UAV functioning. The first step implements optimization of energy consumption optimization based of the battery discharge model. The optimization criterion at the first step is the indicator of the distance covered, defined as a product of the optimal speed of the cyberphysical system and the flight time during which the battery discharge was minimum at the minimum computed load current and specified battery capacity. At the second stage, the optimization criterion is the quantity of the procured information at the fixed length of the passed flight track.
The authors formed and solved the problem of the remote sensing UAV functioning optimization, performing the flight in energyinformational effective mode. Quadratic equation, which solution allowed determining the optimal load current value was obtained. Formulas for computing the stages optimality criteria of the suggested twostage optimization method of the remote sensing UAV were obtained as well.
The obtained results may be employed in developing highly effective UAV implemented with a view of remote sensing information collecting and processing in the extended time functioning.
The major outcome of performed study consists in the possibility of the UAV energyinformational functioning implementation intended for of information collecting and remote sensing. 
Efanov V. V., Zakota A. A., Gunkina A. S. A technique for accuracy evaluation for airborne target movement parameters determining under condition of its covert observation based on iteration method application. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/1cf/mov0wgg6jr00sg1h0kum0il3h1l6ykmw/Efanov_Zakota_Gunkina_rus.pdf The article presents the analysis of the two approaches, namely positional and positionalrapid ones, for target movement parameters determining based on its track angles. It was revealed herewith that methods based the above said approaches are not employed at present.
With the positional approach application, only absolute or relative coordinates characterizing the target space position are being employed, while the positionalvelocity method allows determining both velocity and acceleration of the moving target, enabling dynamics evaluation of its spatial movement. Within the framework of the latter approach phase coordinates of the target, mother aircraft and measurement are being represented as vectors in multidimensional space of states. The coordinates’ estimates herewith may be formed either in both Cartesian and polar coordinates based on either real or artificially generated measurements.
The positional approach to the coordinates’ evaluation is being realized based on the azimuthalelevation, triangulation and kinematic methods. The azimuthalelevation method employs the results of azimuth and elevation angle simultaneous measurements of the stationary ground target. The slant distance to the target is being determined based on the values of altitude and elevation angle. The scope of its application is restricted.
With the action against stationary ground targets, both triangulation and kinematic methods are used. The triangulation method for the target position determining employs analytical dependencies between the sides and angles of a triangle, which vertexes are associated with the target and radar station. This method implies solving algebraic equations. However, its application is restricted due to problems associated with the targets identification, staying at the same angular position. The simplest kinematic method rests upon the notion of the equations describing the process of reciprocal motion of the aircraft and the target including a motioning target. The stateoftheart kinematic method, which might be named dynamickinematic, is based on mathematical description of reciprocal movement of a target and radar carrying aircraft in the state space.
The positionalvelocity approach to estimating the target coordinates is being realized base on the pseudo triangulation and kinematic methods. The kinematic method is inapplicable due to the impossibility of nonlinear filtering of Markov processes implementation.
The authors propose a mathematical model for indirect parameters determining of the airborne target based on description of the objects rendezvous procedure in the form of linear equations corresponding to various options of the situational scenery while rendezvous. The article demonstrates the process of the system of linear equations preparation to the iteration process. Estimation of degree of convergence of system of linear equations, describing the rendezvous process of the objects at various values of the input parameters, was performed. It was revealed herewith that:
The degree of convergence for the system of equations which describe the process for objects approaching each other with different values of input parameters has been estimated. The results obtained show that:
– In case of the exact input parameters the degree of convergence is high, and the number of iterations achieves k = 55 for the meansquare values of range and velocity of correspondingly from δ_{D1} = 1.5% to δ_{D1} = 4.2% and δ_{Lt} = 11.8%;
– In case of inaccurate input parameters (the error Δβ = ±0.1°, Δβ = ±1´,
Accuracy evaluation of the range to the airborne target and its velocity can be increased with multiple measuring of angular coordinates (using a «bunch» of measurements). Practical computations revealed that with n = 20–25 the error in the range determining was from 15% to 20%, and in velocity determining was 20%—25%. 
Mingalev S. V., Kazimardanov M. G. Application of numerical method in improvement of fuel atomization characteristics of combustion chamber. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/e14/25np8aznb44xi9uz6sbf7qiecybwy9cz/Mingalev_Kazimardanov_rus.eng_.pdf The article is devoted to the research of approach to getting the dropdiameter distribution, the spray angle and the localization of kerosene flow inside an airassisted atomizer by simulations performed with the coarse meshes, which are not fine enough to accurately imitate turbulence and with the level of mesh refinement that are not high enough to make the value of drop diameter independent on the mesh cell size. The simulation of fluid in the airassisted atomizer, which was patented under the number RU2615618, was performed using ANSYS Fluent by the volume of fluid method in two configurations: 1) The fivedegree sector on the mesh with minimal sell size 25 μm and 2time, 3time and 4time adaptive mesh refinements at the gasliquid interface, 2) The full geometry with fuel channels and swirlers on the mesh with minimal sell size 125 μm and 2time adaptive mesh refinement. The last approach is the main way to simulate the atomization of fuel in airassisted atomizers in UECAviadvigatel JSC. Comparison of the results reveals that the value of spray angle doesn’t substantially depend on the minimum mesh cell size. Regarding the diameters of droplets, it plunged by more than 70% with the reduction of mesh cell size. Consequently, the simulation of atomization with coarse meshes gives the upper estimate of droplet radius and this result can be of practical use, if the value is so small, that its reduction wouldn’t substantially influence emissions of NOx and the gas temperature after combustion chamber being yielded by the combustion simulation. 
Golyakov A. D., Richnyak A. M. Investigation of the fault tolerance of the optoelectronic navigation system of an autonomous spacecraft. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/282/6yxbs1m933e7kbohbd12t23n8mgtjhg4/Golyakov_Richnyak_rus.pdf The relevance of the topic of the article is due to the need to increase the autonomy of solving the navigation problem of promising spacecraft with a long period of active existence in the conditions of uncertainty of the existing disturbing effects of outer space. A promising way to combat these disturbing influences is the development and manufacture of faulttolerant onboard systems of spacecraft, including onboard systems designed to solve problems of autonomous navigation.
The article provides a solution to the problem, the essence of which is to study the fault tolerance of the opticalelectronic navigation system of the spacecraft, which can be used as an additional source of autonomous determination of the parameters of its orbital motion. The study of fault tolerance is carried out on the example of an optoelectronic navigation system of an autonomous spacecraft with a long active life, based on the zenith navigation method and containing two astronomical sensors, a local vertical builder, an altimeter and an onboard computer.
The main results of the work are the proposed indicators that allow us to assess the fault tolerance of the onboard systems of spacecraft. Using the method of mathematical modeling, the article shows the possibility of quantifying the fault tolerance of an onboard optoelectronic navigation system. The classification of fault tolerance indicators of onboard systems of spacecraft is developed, the ratio for calculating the conditional fault tolerance indicator is obtained, which allows us to evaluate the fault tolerance at known values of the failure probabilities of the components of the onboard system, and quantitative estimates of the fault tolerance indicators of the optoelectronic navigation system of an autonomous spacecraft are given.
The results obtained in the article are based on methods for assessing the fault tolerance of technical systems for various purposes, the theory of autonomous navigation of spacecraft, and methods for processing the results of navigation measurements.
The results of the conducted research can be used when it is necessary to justify the appearance of onboard systems of spacecraft with a long active life and the requirements for the fault tolerance of their optoelectronic navigation system, as well as when evaluating and monitoring fault tolerance indicators during the development and operation of these systems. 
Kornilov A. V., Korchagin K. S., Losev V. V. Development of Complex Measurement Navigation System Algorithms of Aerial Application Based on Domestic Hardware Components. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/2e2/6mdjn5sub3naq6fgtb7afkq7tnw9438s/Kornilov_Korchagin_Losev_rus_.pdf The article is devoted to the development of new methods and improvement of existing methods as well as analysis means of data processing in aircraft navigational systems. Particularly, are present an analysis of results of theoretical and applied data processing method development and research as a part of Comprehensive Measurement Navigation System are considered in the article.
The concept of the system is developed: taking into consideration application specifics, available limitations and level of accuracy and functionality requirements, hardware component is realized completely on electro and radioarticles of Russian production. As raw data sensors the following sensors are used: inertial sensors (compensating silicon accelerometer, solid state wave gyroscopes), pressure transducers (static pressure transducer, total pressure transducer), navigation satellite system receiver and analogue magnetometer.
The system structure synthesis is performed, main data communications between data sources are determined in terms of available constraints and level of accuracy and functionality requirements for Comprehensive Measurement Navigation System. Possible data interconnection is conducted; as a result, methods and algorithms are established for quality improvement by means of measurement error reduction of flight and navigation parameters:
– autonomous compensation algorithm of gyroscope error;
– method of data fusion from inertial and barometric sensor;
– method of data fusion from inertial sensors and satellite navigation system.
The results of abovementioned method researches are performed using mathematical and semirealistic simulation, as well as by ground tryout of the Comprehensive Measurement Navigation System test item.
Research data showed that developed solutions and methods of data processing allow to produce measurement navigation system of aerial application with required specifications based on Russian hardware components. 
Agayev F. G., Asadov H. G., Aslanova A. B. Multifunctional unmanned aerial vehicles. Optimization and synthesis with account for noise effect. Trudy MAI, 2021, no 117, http://mai.ru//upload/iblock/b91/6a4ao0wdr2m9mp0fgyeuzmn6z61gwtv0/Agaev_Asadov_Aslanova_rus.pdf The article deals with optimization and synthesis of multifunctional unmanned aerial vehicles (UAV) with account for the noises impact. The purpose of the work consists in of multifunctional UAV functioning optimization intended for sequential implementation the tasks of load delivery and making a terrain reconnaissance by remote probing technique. The necessity for this task fulfillment in military art is explosives delivery and release, as well as explosion aftermath assessing.
The authors employed the wellknown results of the UAV navigation provision task using local radiotechnical navigation system, allowing achieve high accuracy in the UAV delivery to the specified target no less than the satellite radionavigation systems accuracy. The article considered the cases absence of radionavigation signal suppressing, as well as multichannel Doppler signal processing and pulsetopulse phase manipulation of navigation signal under conditions of radioelectronic counteraction.
The task of the multifunctioning UAV functioning optimization, performing functions of the load delivery to the specified point (a) and (b) making reconnaissance in the vicinity of this point under conditions of local radionavigation system (pseudo satellites) application was formed and solved.
As the result of the UAV functioning optimization at the relatively small distances, the optimal functional dependence of the UAV positioning at the specified point probability on the flight distance was obtained.
The results obtained in the article can be implemented while developing and operating the multifunctional UAV of the similar purpose. The authors formulated and solved the problem of the multifunctional UAV functioning optimization, sequentially performing the functions of (a) load delivery to the specified point, and (b) making reconnaissance in the vicinity of this point
The results of the multifunctional UAV operating mode optimization at relatively small distances demonstrated the presence of the optimal functional dependence of the probability of the UAV positioning at the specified point ono the UAV flight distance value. 
Popov I. P. Vibrations computing for ramified mechanical systems in the field of complex numbers. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/1ee/019rea4ppdqqxghq08d46320mmcsm3fa/Popov_rus.pdf The article considers both parallelseries and seriesparallel connection of consumers of mechanical power. The purpose of the work consists in developing compact algebraic methods for ramified mechanical systems computing at forced vibrations in the steadystate modes. Speeds of mechanical systems’ elements and forces applied to them are being determined algebraically through the known systems parameters and disturbing harmonic impact. A complex representation of harmonic and related mechanical quantities is used. This approach is widely used in electrical engineering. The main research methods within the framework of this work are methods of mathematical modeling and analysis. It is not the physical object itself herewith, which is being studied, but its mathematical model, namely the object “equivalent” reflecting its major properties, i.e. the laws it follows, connections peculiar to its constituent parts etc. As for the considered ramified mechanical systems, classical methods based on solving the second order differential equations are being multiply complicated and require solving the systems of equations, which are being reduced to the systems of higher orders. Symbolic (complex) description employing for the mechanical processes and systems allows apply instead simple and compact algebraic methods, which labor intensity is tenfold less.
A relation between mechanical values for various types of elements connection of mechanical systems was established. Being an unnecessary component of mechanical systems studying, vector diagrams are of great methodological value, since they demonstrate quantitative and phase relationships between systems’ parameters. 
Gorodnov A. O., Laptev I. V. The effect of the wall heat capacity on the temperature stratification and pressure rise during natural convection of hydrogen vapor in a vertical cylindrical vessel. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/aa3/sk2zfcj4mjdydrgzz23lpgsi0qtv0lo1/Gorodnov_Laptev_rus.pdf As of today, Russian space industry announced several projects of new launch vessels, such as super heavy class rocket and the rocket with reusable stages, operated on liquefied natural gas as a fuel. Moreover, other countries, such as USA, China and the ESA members, announced plans of future missions to Mars and Moon. A considerable part of the future space missions depends on the possibility of effective longterm storage of cryogenic fuel components under lowered gravity conditions. The important role of cryogens in space flights is being determined by their widespread application as a fuel and in life support systems.
Due to cryogens’ very low temperatures, the tanks for their storage are extremely sensitive to the thermal flows from the environment caused by solar radiation, aerodynamic heating and conductive transference from the other parts of a spacecraft. External heating and the presence of microgravity lead to pressure raise and freeconvective motions in the storage tank. The pressure rise rate is being accelerated by temperature stratification effect. This effect has been demonstrated in many ground and space experiments.
One of the most important problem in experimental cryogenic storage studies is scale factor. Most of experimental data was obtained with smallsize fuel tanks. This leads to the problem of geometric similarity violation of the fuel tank wall thickness compared to the real rocket storage tanks. To estimate the impact of this dissimilarity, the article considers the problem of the wall’s thermal capacity and thermal conductivity impact on temperature stratification and pressure rise at the vapor nonstationary thermal convection in the closed cylindrical vessel.
Low Mach numbers approximation is being used to describe evolution of the vapor temperature, velocity, density and other parameters. Boundary conditions, defining parameters range, physical properties of vapor and a wall material simulate conditions of the experiment on drainagefree hydrogen storage.
A series of computations at various wall thickness values was performed using numerical method proposed by Quazzani and Garrabos. The computation data demonstrates considerable reduction in the pressure rise rate, temperature stratification value and convection intensity with the wall thickness increase. The obtained results demonstrate the possibility of considerable underrating of the pressure rise rate and other heat exchange parameters on the steam blanket of the tank, when the wall’s real thermal capacity and thermal conductivity are not being accounted for. 
Antufiev B. A., Sukmanov I. V. Dynamic behavior of thinwalled structures with elastic filler under the action of a moving load. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/565/82rlje2ajd99shraepiacdg4o8zjm7eo/Antufev_Sukmanov_rus1.pdf The problem of dynamic deformation of a cylindrical shell with a collapsing elastic base under the action of internal pressure on the free part of the cylinder and a movable radial load is solved. The deformation of the structure is considered to be axisymmetric and is described by the equations of the moment classical theory of shells, and the filler obeys the Winkler hypothesis. Similar problems arise in the design of solid propellant rocket engines (solid propellant rocket engines). In this case, the destruction of the filler is explained by fuel burnout, and the internal pressure is due to the action of combustion products. A movable radial load simulates a pressure wave, as a result of which the problem of determining the critical speed of its movement arises, at which the solid propellant rocket walls lose stability. We will consider the solution of the problem in tw o versions – quasistatic and dynamic, which will allow us to compare solutions and choose the optimal one. In the quasistatic version of the solution, the deformed state of the shell, determined by its deflection w, does not depend on time t, but changes only along the xaxis. Examples are considered and parametric studies are carried out. In the dynamic version of the problem statement, we assume that the deformed state of the shell depends not only on its longitudinal coordinate x, but also on the time t. We will consider two types of pinning the ends of the shell – hinged pinning and rigid pinning. From a comparison of the graphs obtained, it can be seen that with rigid pinching of the ends of the shell, the natural vibration frequencies are higher than with their hinged support. 
Shishkin S. V., Boikov A. A. Tightness analysis method for flange connection of pipes with metal Zshape seal during the influence of external axial force. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/e16/xj7ow6q5yb4skl0xexn6afyestn17jup/SHishkin_Boykov_rus.pdf The most common problem in flange connections of pipes is to ensure their tightness during the functioning. At the same time it is unacceptable to design constructions of flange connections too strong and heavy, because it can lead to increasing of loads, acting on a flying vehicle. That’s why it is necessary to have a method of tightness analysis. In this article connection with Zshape seal is estimated during the phase of loading by external axial force. The problem is – to obtain relations, which allows to calculate increment of contact pressure between edge of the seal and surface of flange. It allows to calculate total contact pressure and use it in tightness analysis of connection by means of KozeniKarman’s theory of equivalent porous layer. According to this theory, flanges and seal are estimated as rings with high curvature and modeled by means of theory of axisymmetric deformation of K.B. Bitseno. Problem is solved by using of system of equilibrium equations of flanges and equation of displacements’ compatibility of contact points of flanges and seal. Influence of the pipe on flange was taken into consideration by means of using of system of equations of displacements’ compatibility, applying to the profile of connection of flange and pipe. Displacements of pipe are estimated by means of moment theory of shells, displacements of flange are estimated by means of theory of axisymmetric deformation of K.B. Bitseno. As a result, universal tightness analysis method was obtained, which can be more useful in this case, in comparison with relations, obtained by means of theory of axisymmetric thin plates, applied to flanges, because a lot of flanges in vehicles can’t be modeled as axisymmetric thin plates because of their constructions. 
Bykov A. P., Piganov M. N. Quality indices prediction of onboard radioelectronic devices. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/fb8/5bsmz2wro4ofv4n90ewfdebuoemo0ynk/Bykov_Piganov_rus.pdf The article presents a technique for developing predictive mathematical models and quality indicators individual forecasting of the spacecraft onboard radioelectronic devices by the results of autonomous tests. For forecasting, Extrapolation method, based on the quasideterministic models application, was selected. Transient resistance between electrical circuits of the microprocessor based temperature controller, which installed on the honeycomb panels in the spacecraft unpressurized compartments, was selected as the predictable parameter. The training experiment data, obtained after the second cycle of the testing impacts, served as initial data for the prediction.
The second cycle of tests included checking the device functioning in normal climatic conditions, a low pressure effect test, and a higher humidity effect test. Linear, parabolic, logarithmic, and exponential models were proposed. When these models developing the predictable parameter normalizing by the mathematical expectation was used. The forecast models selection was based on minimum average dispersion criteria, computed at the reference temporal points of tests and minimum values of the erroneous solutions probability and consumer’s risk. The study of the above said models was performed.
Probabilistic characteristics of their efficiency were obtained. It was established that the logarithmic model ensured minimum average dispersion values and the manufacturer’s risk, as well as acceptable erroneous solution probability value, i.e. consumer’s risk minimum value. The parabolic model allows obtaining zero value of the manufacturers risk and acceptable level of erroneous solutions probability. 
Bydanov E. V. Radio line resources managing technique, employing spacetime signal processing, for situational centers. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/3b7/qh3o3p4di7izxqrzpimz3b2mkwcejabw/Bydanov_rus.pdf Active information development all over the world has predetermined the nature and methods of warfare. If the firepower in the recent past was the basis of success in any armed conflict, as of today, the basis of success is the reduction of the combat control cycles, fr om the target to detection to the decision of its hitting. Modern technical equipment of all management levels, situational centers in particular, allows achieving this. The most problematic side herewith is provision of stable, highspeed radio communication with the units staying in the field conditions, seaborne and airborne, wh ere fiber optic communication lines laying out is impossible.
One of the ways of solving this problem consists in equipping the physical level of the radio lines in use by the technology involving the timespace signal processing. This will enhance the radio line capabilities, and, besides conventional resources managing, allow managing the number of the antennae elements in use on both receiving and transmitting sides.
Analysis of works devoted to the transmitted data security at the physical level of radio links with similar technology revealed negligible attention to the issue. In this regard, the issue of developing a methodology for controlling a multiantenna radio line is relevant.
A technique for resources managing of a radio line that employs spacetemporal signal processing for data transmission and provides operators with modern communication services in in places where the fiberoptic communication lines layingout is complicated or impossible, has been developed. The proposed approach allows operators data transmission by the radio line more secured from radio monitoring and noise immune. The power consumption herewith of the subscriber terminals of the presented radio line is much less. This is being achieved by a lower signal emission power, compared to subscriber terminals of similar technology, radio lines, and linearly depends on the distance to the subscriber terminal of the subscriber. 
Volkov A. S., Solodkov A. V., Tsymlyakov D. V. Developing programhardware interface for polar codes characteristics studying. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/1c3/eecr0gkns381s95r1agxbgorwsz8ujzd/Volkov_Solodkov_TSymlyakov_rus..pdf Polar codes are the new generation of noise immune codes, employed in the standard of a new generation of mobile communication. Since these codes are not algebraic and, hence, do not have precisely specified characteristics due to the soft reception, all results shuld be obtained only through mathematical modelling, or by the testbench testing. which allows giving the code effectiveness evaluation in certain conditions without mathematical calculations.
This article describes the work on the test bench development according to the principles of rapid prototyping for performing fullscale modeling of various types of signalcode structures based on the polar noiseimmune codes being employed in the new generation communication systems. An overview of decoding techniques of polar codes being tested is presented, and mathematical foundation of these techniques is described to to a small extent.
Several development tools were used for the test bench development: Vivado, Matlab, and Verilog language. The hardware part of the test bench is the Diligent Zedboard PCB based on the Zinq7000 of the Xilinx Company.
The article describes the key points of the test bench creation. It demonstrates the evaluation technique for the signal coding effectiveness at the white noise impact.
Data on the effectiveness and hardware costs for various types of decoders were obtained.
The polar codes in the control channel and LDPC codes in the data transmission channel were selected as basic polar codes for the 5G Standard. The polar codes, initially proposed by Erikan in 2009, are the first type of the structural channel codes, for which maximum throughput capacity of a binary symmetric channel without memory was proved, i.e. the case of reaching the Shennon boundary while employing the soft decoder of sequential exclusion. This decoder is of low hardware complexity compared to the brute force methods such as Chase's algorithms.
The basic idea behind the polar coding is to convert pairs of identical binary input channels (each bit of the input word is called a channel) into two sundry types of channels of different quality, when one is better and the other is worse than the original one. This will allow using nearly ideal channels for transmitting data to the recipient of the message, with this, presetting the bits (e.g., zero) in noisy channels so that decoding relies on values known to the receiver. Noisy and noiseless channels are called frozen and unfrozen, respectively. Only unfrozen channels are transmitting data. Selection of channels partition technique and the set of frozen channels fully determines the polar code.
There is a problem of optimal dynamic allocation of timefrequency resources to subscribers. It takes on a special character with their high mobility. The 5G next generation communication systems imply extremely high users’ mobility, and frequent switching between the base stations. For timely power adjustment, devices need to transmit information quickly to the base stations, and this, in turn, requires application of short code structures in service channels. These are exactly the polar codes, which demonstrate the best noise immunity at the same length compared to the other types of codes.
The same problem is the case when data transferring between drones or in selforganizing networks, and it can be solved using the specified class of codes.
Since the discovery of polar codes, several algorithms have been proposed for decoding polar codes. The two most popular of these algorithms are sequential exclusion decoding, which was suggested in the original article, and list decoding. The first method consists in data bits decoding one by one, and each decoded data bit together with previoiusly decoded bits is being used for the next data bit decoding by means of the received signal. This results in extremely long time for all bits decoding. Thus, the polar decoding seems unsuitable for the real time applications. Let us consider the main stpes of polar codes decoding. 
Podstrigaev A. S. Improving the efficiency of a matrix receiver in a complex signal environment based on a fiber optic delay line. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/607/6voy6vhide5ylj2o8x0co5jctm1z0x8h/Podstrigaev_rus.pdf A matrix receiver and receivers based on it are used to analyze signals over a wide instantaneous bandwidth. However, in a complex signal environment (CSE), the receiver input pulses are overlapped in time. This leads to errors in determining the timefrequency parameters of the pulses. Therefore, the article aims to improve the efficiency of the matrix receiver in the CSE conditions. For this, it is proposed to connect a broadband fiberoptic delay line to the receiver input. A circuit of the delay line with a delay duration tunable in accordance with the duration of the received pulse is considered. Using the example of the electronic environment generated by pulsed radars, an increase in the number of signals processed simultaneously without errors is shown. The increasing is at least 2 times when using one delay line and at least 3 times when using two delay lines. In practice, the signal environment is formed by radio emission sources with different duty cycles. So, the number of simultaneously processed signals can be orders of magnitude higher. An important for practice advantage of the considered technical solution is the possibility of modifying an already existing matrix receiver without significant design changes. Additionally, when increasing the number of simultaneously processed signals stored main advantage of the matrix receiver – high sensitivity as in narrowband scanning receiver with a broad instantaneous bandwidth of operating frequencies, like a multichannel receiver. The presented approach to increasing the throughput due to one or several delay lines can also be used for other receivers used in broadband analysis tasks. 
Barkova M. E. Radionavigational support of space solar power plant. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/4a3/tzv6571ujmo708dm3o3nnox1efwkjljz/Barkova_rus.pdf The main problem of article is accumulating and transmitting the solar energy to the receiving device with minimum power losses.
The purpose of this work is radionavigational provision developing of the solar space power plant (SSPP).
This work relevance consists in increasing the number of the engaged renewables, including solar energy, and in the fact of the transmitting beam holding techniques deficiency.
The main shortcomings of the existing projects are excessive attention to technical issues to the detriment of energy transmission ensuring with the minimum losses.
The SSPP consists of the transmitting and receiving segments. The SSPP transmitting segment represents a one spacecraft (S) or the Ssystem. The receiving segment can be presented by a spacecraft in need of energy or the rectennaes, which represent nonlinear antennas for f the laser transmitted radiation transforming into electricity.
By the type of provision the SSPP are being divided as follows:
 Technical provision (the SSSP space segment parameters technical parameters);
 Radionavigation provision (trajectory and spacecraft movement selection, on account of its structural specifics, coordinates determining of the points with rectennaes, segments synchronization).
The obtained results can be applied while spacecraft development and operation.
The author concludes that parameters determining of the SSPP radionavigational provision allowed creating the energy transmitting modes.
The author’s unconditional credit consists in creating the invention named “Solar Space Power Plant”, and its technical and its radionavigational provision.
Some algorithms of the SSPP parameters, and modes selection found application in the JSC “Russian Space Systems”. 
Balaban I. G., Balaban A. L. Telemetric system for parameters control of chemical current sources. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/d4d/e80l8ij8cemay0gq11plmjhjbmehxe1x/Balaban_Balaban_rus.pdf The paper outlines the basic principles of building a telemetric system for monitoring the parameters of chemical current sources. A method of noncontact current measurement is proposed for ensure galvanic isolation, a distinctive feature of which is the use of three load resistors (shunts) in order to reduce the error in measuring currents of various magnitudes. The method allows to measure currents up to 120 A. Voltage measurement range: from 0 to +40 V, temperature: from 0 to +100 ^{o}C, capacities: from 0 to 511 A⸱h, insulation resistance: from 0 to 5 MOhm. The error in measuring current and capacity is not more than 5%, voltage and temperature is not more than 1%, insulation resistance is not more than 10%. The system operation algorithm is developed and implemented programmatically. The method for protecting telemetry information when monitoring the parameters of chemical current sources (CCS) is developed. Within the framework of the implementation of the strategy of import substitution in the economy of the Russian Federation, in the development of a telemetry system and control of parameters of chemical current sources, only domesticmade electronic components is used.
The research results can be used in the development of CCS condition monitoring devices used for power supply of autonomous devices for which there are no maintenance procedures during operation. The use of such monitoring tools will make it possible to analyze the operation of CCS in order to increase their reliability, determine ways to improve the equipment and establish the causes of its failures. 
Nikulin V. S., Storozhev S. A., Abdullin D. M., Khizhnyakov Y. N. Adaptive virtual meter of harmful substances in the combustion chamber of a gas turbine engine using fuzzy technology. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/4d6/3io77gx8ajcw920e104zhha3jtcbbv20/Nikulin_Storozhev_Abdullin_KHizhnyakov_rus.pdf The toolkit of soft computing technologies is bas on fuzzy systems, probabilistic models, neural networks, genetic algorithms, etc., which have their own advantages and disadvantages. The application of this toolkit is considered for an aircraft gas turbine engine (GTE) of aircraft operating under conditions of uncertainty. The distribution of fuel between the manifolds is performed using a fuzzy regulator, the inputs of which are the pressure in the combustion chamber, temperature in the combustion chamber, fuel consumption in the diffusion manifold. Fuzzy controller output – calculation of the current value of the coefficient of the combustion chamber or the content of the oxidant in the combustion chamber. The calculation of the amount of harmful substances is carried out using a fuzzy regulator, the inputs of which are the temperature in the combustion chamber, the fuel consumption of the diffusion manifold, the consumption of the diffusion manifold in percent and the current value of the coefficient of the combustion chamber. Fuzzy regulator output – calculation of the current value of harmful substances in the combustion chamber for further calculation of the total emission of harmful substances for the takeoff and landing mode of the aircraft. Оn the basis of the total calculation of harmful substances, it is possible to draw a conclusion on the fulfillment of the emission requirements, which is 18 kg. The research results have confirmed the reduction of the influence of the uncertainty of the combustion process and the reduction of emissions in the airfield area. 
Diukov V. A. Technological process optimization of complex shape composite aviation structures autoclave molding with prior correction of their geometry. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/43e/9za4qbwxbaca09w48iot0fv7r96lynny/Dyukov.rus.pdf The article presents geometry correction methods for the complex shape thinwalled composite structures. Topologically correct prepreg and shapegenerating rigging models were developed. New prepreg theoretical models obtaining is being ensured by edges sectioning of the original parts by parallel or radial planes and creating surface by the intersection lines of the specified planes and associated facets. For parts creating, the surfaces were being truncated, thickened, and corresponding moulds were being built. The obtained parts and moulds were placed in assemblages.
Thermophysical parameters of the composite prepreg were assigned to the models, and then the coupled problem of heat transfer and polymerization was being solved. Kinetic equation, which structure and parameters depend on the binder properties, is being employed to describe the dependence of the degree of polymerization on time and temperature. The type and parameters of the kinetic equation are determined from the results of materials analysis by the Differential Scanning Calorimetry (DSC) using various numerical methods for these parameters identification. For the specified technological system, the heat injection method, namely autoclave molding, was selected. The law of temperature variation was selected in the most commonly widespread stepwise form: heating – isothermal dwelling – heating – isothermal dwelling – cooling.
As the result, both temperature and time optimalи regimes of the twostage autoclave molding cycle were selected, which ensure achieving the required degree of polymerization value of the carbon fiber reinforced polymer (CFRP) prepreg, and minimizing temperature differential and binder degree of polymerization in the polymerized volume. Temperature and time regimes of cure affect the structure and quality of the material.
The results of the molding process simulations demonstrated a significant dependence of both the average temperatures and the degree of prepreg polymerization, and their spread in the prepreg and mould, on the characteristics of the technological process and technological limitations. 
Trusfus M. V., Abdullin I. N. Marker images detection algorithm for the unmanned aerial vehicle vertical landing. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/89f/ckfysnaup5je0ve4kiz6b0fzac7y94f6/Trusfus_Abdullin_rus.pdf The primary task while drones application consists in automatic landing ensuring. Most of the existing autolanding solutions ensure accuracy up to three meters. For a more accurate landing, accurate distance measurements are required. Methods, ensuring accurate camera images, require accurate identification of the marker image points.
The marker image consists of two black rectangles situated in the center of each other at the angle of 90 degrees. The rectangles are applied on a white surface. Their detection is based on the objects’ contours detecting on a monochrome image with further test for compliance to marker geometric shape. The dependencies of distances between the points of the geometric shape equivalent to the claimed structure are presented.
This study considers the methods of adaptive binarization and the Canny boundary detector to perform camera image conversion to monochrome one. Detection of the outline of each object is being performed on the monochrome image. A convex hull of minimum area is being built for each outline in such a way that all the object points be inside. The search for the points corresponding to the marker’s apexes is being performed according to the presented dependence of distances on the convex hull. Checking of all points of the initial outline on the correspondence to the marker’s geometry shape by checking if each point lays on the corresponding side is being performed for the marker image identification.
Software was employed for conducting experimental study of the described algorithm. One of the programs employs binarization method, while Canny boundary detector is used in the other one. Photographs in 640 ´ 480, 800 ´ 600 and 1920 ´ 1080 resolution were used while conducting the study.
According to the results of the study, the highest detection accuracy and speed were displayed by an algorithm based on the use of the Canny boundary detector. False detection of marker images was not detected in any of the algorithms. The algorithm based on the adaptive binarization revealed the best performance in detecting marker images in «blurry» images. A conclusion was made by the results of the study that the developed algorithm allows detecting all points of the marker image of the vertical landing site designation without errors in false targets detecting. 
Zaitceva I. S. Pilotinduced oscillations prevention through the nonlinear correction method. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/bdc/uy47fjr06zkpa8asfqv5zz4ae7dfl21j/Zaytseva_rus_2_.pdf The purpose of this article is to solve the problem of nonlinear correction device synthesis to prevent the pilotinduced oscillations in a compensatory tracking system. The oscillations discussed in this article introduce a negative phase shift into the system. Thus, a simple and effective solution to this problem consists in embedding a nonlinear correcting device into the control loop. The pilot actions in the compensatory tracking task are aimed at ensuring the cutoff frequency of the closed system, at which the control error will be minimal. The aircraft–pilot system optimization, based on the pilot’s ability to adjust his control performance parameters, is illustrated by the software developed with the MAtLAB/Simulink tools. The goal function is given numerically in the form of the cutoff frequency of the closedloop pilotaircraft system, which corresponds to finding maximum system performance. Frequency quality indexes, control accuracy, and pilot model parameters are numerically limited. The pilotinduced oscillations prevention is demonstrated by the example of an unmanned aerial vehicle control system. The human pilot is described by the McRuer “at the cutoff frequency” model. The values of a pilot model and nonlinear corrective device parameters were obtained. Frequency and transient responses of the corrected ratelimited actuator system are presented. Handling qualities of the optimal system were assessed using the bandwidth criterion and the index of the transient process performance. The proposed method can be employed in the flight control system design and flight performance assessment. 
Wai Y. S. Refined lowparametric model of the terrestrial pole motion. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/63a/e2a61prsbfp9n6gc6zxu18kefjfk8erd/VeyYAnSoe_rus.pdf The terrestrial pole oscillations approximation refinement considered in the article allows approximation refining and propagating implementation of the smallparametric doublefrequency model of the pole movement to the longer time intervals. Approximation accuracy improving while keeping the same number of the model parameters is of great significance. As far as it is impossible for the time being to predict the amplitudes relationship changing, as well as determine it in real time, the effect will always be detected behind the time, and it will fall on the approximation period for a considerable time, which will negatively affect prediction based on the basic model.
For the modified model, there is no need for the exact definition of the oscillation mode changing, and it is possible to be limited by the analysis of the resulting parameters of the pole modulation process without its subdivision into harmonics to solve the set problem. Establishing of the occurred changing of the average frequency over the harmonics modulation period with the delay to the extent, which is allowed by the ψ(t) function analysis is quite sufficient. For the modified model, there is no need for the exact definition of the oscillation mode changing, and it is possible to be limited by the analysis of the resulting parameters of the pole modulation process without its subdivision into harmonics to solve the set problem. Establishing of the occurred changing of the average frequency over the harmonics modulation period with the delay to the extent, which is allowed by the ψ(t) function analysis is quite sufficient. 
Myo Z. A. On the polar tide impact on the Earth pole steadystate movenemt. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/485/lfibeh2kmrzki326jp4vka1rfn81n5hm/MoZoAung_rus.pdf A small displacement of polar tide and a phase shift of coefficients of the tesseral harmonic of geopotential relative to the Earth pole oscillations is the result of the Earth mantle viscosity. This displacement is quite small, and insignificant for practical tasks, such as satellite navigation. However, it presents considerable interest for studying the Earth pole since it determines the steadystate mode of Chandler wobbles, as well as amplitude of the necessary external disturbance for Chandler wobble excitation of the Earth pole.
The expressions of the tesseral harmonic coefficients variations, stipulated by the polar tide of the viscoelastic Earth model, were obtained in this work by methods of nonlinear mechanics with infinite number of degrees of freedom. A viscoelastic solid body, consisting of the axisymmetric hard core and viscoelastic axisymmetric (in nondeformed state) shell, being subjected to deformation according to the KelvinVoigt model, is being considered as a simplified model of Earth. There are no displacements on the inner boundary of the shell, and the outer boundary one is free. It is supposed that the deformation process of the Earth can be assumed as quasistationary.
These expressions are being compared with the ones recommended for accounting by the International Earth Rotation Service. The steadystate oscillations mode of the Earth pole are being studied based on the Eulerliouville dynamic equations, with account for variations in geopotential coefficients due to the tidal deformations of the Earth mantle. The article demonstrates that the polar tide model selection significantly affects the parameters of the steadystate oscillatory process of the Earth pole and the amplitude of the necessary disturbance with the chandler frequency to excite the observed chandler oscillation of the pole. 
Chigrinets E. G., Rodriges S. B., Zabolotny D. I., Chotchayeva S. K. Numerical modelling of thermal fields in a polymer composite. Trudy MAI, 2021, no 116, http://mai.ru//upload/iblock/ff6/z2flno67mbdvftdlk15i2m098ptjlmrr/CHigrinets_Rodriges_Zabolotnyy_CHotchaeva_rus_.pdf Polymer composite materials (PCM), having reinforcing glass fibers in their content and named glassfiberreinforced plastics (GFRP), are the most widespread composites applied in the industry. Due to their high strength and stiffness at low specific mass, the PCM more and more widely employed in aircraft building and space industry, superseding conventional metal alloys. One of the glassreinforced plastics machining specifics compared to metal materials consists in different heat balance ratio, since up to 90% of heat released while cutting transfers into the tool, whereas up to 70% of heat goes to the chippings while cutting metall.
In the especially loaded structures under study from polymer composite, the reinforcing packs from titanium foil placed between the reinforcing glassfiber tape layers are used.
This layered material of the “glass plastic  titanium” type is employed in manufacturing spars of the main and tail rotors of MI28 and MI35 helicopters. MS 6530 infrared pyrometer is used for the temperature control in the cutting zone. Maximum acceptable temperature of the machined sample, which does not cause PCM thermal defects formation, is determined by the differential scanning calorimetry (DSC). The DSC 200 F3 Maia equipment of the NETZSCH Company was employed. Finite element modelling was performed with COMSOL Multiphysics CAE system.
Pyrometric data on average temperature registering in the cutting area allowed performing finite element modeling of thermal processes while a multilayer fiberglass plastic drilling, as well as revealing the sources and direction of heat flows. Mathematical model realized with the COMSOL Multiphysics software allowed revealing spacetime regularities of temperature fields’ proliferation and values of critical temperatures inside the composite.
Cutting temperature rise in the process of titanium foil layers cutting leads to the composite layers warming up, which degrades polymeric matrix properties and intensifying thermal defects formation. Finite element modelling allowed upgrading technology of fiberglass spars of the helicopter main and tail rotors machining. 
Popov I. P. Calculation of mechanical oscillations in the field of complex numbers. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/1b0/Popov_vol.pdf It was noted that traditional calculation of complex mechanical devices at forced sinusoidal oscillations is, as a rule, a rather difficult task. Most often, calculators, designers and technologists are interested in steadystate oscillation modes. The goal of this study consists in significant calculations simplifying by replacing the need to solve differential equations with simpler algebraic methods. The author employs complex representation of harmonic values and the values associated with them. Such approach is widely used in theoretical electrical engineering. The main research methods within the framework of this work are methods of mathematical modeling and analysis. With this, a mathematical model, i.e. the object “equivalent”, reflecting its basic properties, namely the laws it obeys, bonds peculiar to its constituent parts, etc., is being studied, rather than the physical object itself. The article considers the scheme of parallel connection, in which the speeds of all mechanical system elements iare equal, while the forces are different, as well as the scheme of series connection, in the forces applied to the mechanical system elements are equal, while speeds differ. Application of symbolic (complex) description of mechanical systems at forced harmonic oscillations (in the steadystate mode) allowed abnegate the extremely cumbersome and laborious computational algorithm, associated with differential equations solving, and replace it by the much simpler algebraic operations. Due to this fact, the computation time was reduced manifold. Being an unnecessary component of the mechanical systems studying at harmonic impact, vector diagrams are of significant methodological meaning, since they demonstrate quantitative and phase relationships between the system parameters. 
Dobryshkin A. Y., Sysoev O. E., Sysoev E. O. Temperature impact on the elasticity modulus of structural materials. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/a02/Dobryshkin_Sysoev_Sysoev.pdf Elasticity modulus of a material, to be more exact Young’s modulus, significantly affects the figures while any operation of the material. Thus, the attention to this indicator long since cases interest. It should be noted that a significant u of research has been conducted in this area. There are indicators of the Young’s modulus of all structural materials, as well as its indicators at various operating conditions, including those at various temperatures, e.g. above and below zero Centigrade. The presented study was conducted with the purpose of solving the problem of buildings and structures strength and stability under the temperature effect. To do this, the review of the wellknown data in the Young’s modulus area was performed, and revealing the most advantageous materials for implementation with the purpose of buildings and structures strength enhancing.
Not a single branch of human activities can do without employing the elements in the form of closed and open thinwalled cylindrical shells. These are, for example: hangars, pipelines, missiles, submarines, boats, aircraft and other elements. There are quite a few elements in the form of open and closed shells in the form of machine parts and mechanisms. This form of structures has become widespread due to their higher efficiency compared to the others such as, rectangular structures and parts, since less material is spent on their manufacturing. Besides, it is is easier to manufacture such elements, for example, by rolling. Often these parts, such as aircraft engine nozzles, or aircraft skin, are affected thermally. This phenomenon creates many difficulties, since the exposure temperatures are often above 1000°C. The Young’s modulus herewith is being significantly reduced, the same relates to the strength as well. 
Averyanov I. O. Prediction of dependability for soft landing system with air dampers with Monte Carlo method. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/8b6/Averyanov_voll_.pdf There are a lot of researches related to soft landing systems with air dampers (System). Today it is a trend to use numerical simulation with LSDYNA Airbag module or fluidstructure interaction methods. But almost all of the researches are related to single landing process simulation. The article describes the developed dependability model of landing process for soft landing systems with air dampers.
This dependability model is based on physical model of landing process for soft landing systems with air dampers; it consists of mathematical model of fabric air dampers comes from and equations of rigid body motion – from. This physical model allows to get gradient landing area and position of the System in 3D space as initial conditions.
Monte Carlo method is used to realize mathematical experiments with random values of applied load factors. These factors are: landing area gradient angle, vertical velocity and mass of the system, horizontal velocity vector. Reliability function is used as a dependability measure. The following failure modes are considered: excessive acceleration, temp acceleration growing, final vertical velocity, system overturn of its excessive vertical jump, air damper failure.
Several thousand cases of mathematical landings with random initial conditions are considered to get statisitcs of their failures. It allows to get the reliability function of the whole landing process.
The case of air dampers efficiency improvement with the use of the developed model is considered. The idea is to use reliability function of the landing process as an optimization criteria for air damper structure – number of release valves and their combination in the air damper chambers are considered as target function.
Presented results show that the use of the developed model may be useful in design study of soft landing systems with fabric air dampers. 
Nakhatakyan F. G. The impact of clearance in roller bearings on the power contact between its elements. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/95c/Nakhatakyan_voll.pdf The presented work studied thoroughly the problem of radial clearance impact on a number of roller bearing loading parameters. It is indicated herewith that the source of the clearance is of no importance. It forms as the result of wearing, or it is a preliminary, i.e. deliberate clearance from technical considerations. The problem was solved analytically, based on the proposed method, employing herewith the author’s technique for determining the pliancy of a “bearing” with a single rolling body.
Two characteristic schemes for a bearing loading with a radial force were considered. The first scheme describes an option, in which the radial force passes through the center of the maximally loaded roller, and the second one touches upon the case when the radial force passes between such rollers.
The problem has been solved with both absence of a radial clearance and its presence. The following parameters were determined: the bearing stiffness (pliancy); the number of loadbearing rollers; the maximum load on the roller, as well as the functions of these parameters on the radial clearance.
The main results of the work are as follows:
– bearing stiffness in the absence of radial clearance in both loading schemes is almost constant;
– with the clearance increase, the stiffness in the second loading scheme decreases more rapidly than in the first scheme, which can cause fluctuations in the rotor systems.
The obtained results can be employed while solving a number of problems, for example, when designing and studying the dynamics of the aircraft turbine mechanisms, or when evaluating the wear and performance of rolling bearings, as well as their durability. 
Khmarov I. ., Egozhukov R. A., Markushin G. N., Koshelev A. V., Kanivets V. Y., Kondrashov N. G. Measuring laserlocation characteristics of aerial object. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/2fc/KHmarov_Eguzhokov_Markushin_Koshelev_Kanivets_Kondrashov_voll.pdf Experimentaltheoretical and experimental studies of the laserlocation characteristics (LLC) of aerial objects are uptodate scientific and practical tasks while creating promising and modernizing conventional active optoelectronic information devices, as well as in solving the problem of optical visibility reducing of objects.
Direct measurements of the objects LLC herewith are important for of experimental and theoretical methods, as well as mathematical models verification, and for information capabilities of laser devices evaluation. Of special importance is the study of objects’ reflection characteristics in the presence of various factors in the structure, associated with the objects application conditions (physical phenomena concomitant with the flight, the adverse effects of environment, physical fields and etc.) in the presence of the objects onboard opticalelectronic devices (OED) and a translucent spacescattering of fragments (not amenable to the rigorous mathematical modeling).
However, when performing seminatural and fullscale measurements on open routes there are difficulties associated with calibration (standardization) of locational signals reflected from remote targets, with the technical difficulty of creating laser measurement channels (LMC) with rather large linear dynamic range, and with measurement estimating inaccuracy.
The authors consider the methodological apparatus and devices solving these problems. They provide fullscale measurements of the air objects LLC in flight employing a nearinfrared (IR) laser measuring complex (LMC) as a part of a multichannel optical measuring system (MCOMS).
As the result, the authors developed and tested a method that implements of measuring and signals calibrating processes with a large dynamic range on open routes. Techniques for aerial objects’ laserlocation characteristics measuring on open routes using LMC as part of the MCOMS have been developed and tested. Measurements of the effective scattering area (ESA) of four targets were performed with the LMC as part of the MCOMS. Dynamic measuring range of the EAD data is no less than 0.01–30 m^{2}. The LMC as part of the MCOMS is capable of measuring the targets laserlocation characteristics with meteorological visibility range of 20 km at the distances of 0.2–20 km. Under favorable weather conditions, the relative inaccuracy of the ESR of aerial objects measurements was 15–30%, depending on the target type. The results of measurements obtained using the LMC as part of the MCOMS meet the requirements to this class of measurement systems. 
Baskakov A. E., Volkov A. S. Resources managing algorithm for transport softwaredefined communication network. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/5d6/Baskakov_Volkov_voll.pdf Transport SDNs represent the imposition of actively developing concept of network resources centralized management on transport reconfigurable packet networks, including optical ones. The main parameters and principles of the PCS herewith are not only preserved, but also extended to the lower levels, including the level of physical resources management.
The basic stage ensuring the possibility for developing solutions to manage the resources of the communication network, along with the network protocols realizing their operation, consists in developing
– Mathematical base of the communication network under study;
– Processes of resources allocation;
– computation of the necessary paths, including application of the existing developments in the field of standard telecommunications networks, softwaredefined networks, communication networks of unmanned aerial vehicles or selforganizing communication networks.
Following the principles of the SDN concept, the resources of the optical network from the viewpoint of the higher layer (IP) will be considered as a set of virtual transmission paths with a certain bandwidth, and all the detailed information on the structure will be available herewith only to the lower optical layer. Such approach will allow outlining the two subtasks within the framework of the resources managing task of a packet optical network: the optical network resources managing to create a virtual IP topology, and managing the pool of virtual channel resources at the IP level.
The requirement for dynamic and optimal control of transport resources of a packet optical network, defined by the PCN concept, presupposes a rigorous mathematical formalization and optimization statement of this problem. The attention is worth paying to the network models represented in the form of differentialdifference equations of state. Such models are successfully employed for solving routing problems at the IPnetwork level, regarding it as the problem of channel and buffer resources allocation between incoming IPpacket flows.
With a view to the developing trend of energy saving, minimum of electric energy consumed by the network was selected as the optical networks resources control optimality criterion.
Electric energy consumed by the network directly relates to the number of devices involved in it, which in turn is also determined by the choice of the method of overlaying the packet network atop the optical one. Among all possible options, from the viewpoint of economy, attention should be paid to the «transparent» architecture of the IPowerWDM, in which establishing of light paths exclusively at the optical level is possible without transit routers engaging.
The of the upper control level task consists in resources distribution of the available virtual topology between the incoming IPflows, which e initial data is routing variables: the known structures of the virtual topology of the IPnetwork, and the volumes of the transmitted traffic. Besides, it is necessary to form the requirements for the virtual topology of the IPlevel, namely, for the number of light paths between pairs of routers and their bandwidth.
It is possible to avoid additional complication by applying as the initial data the packet flow rate from the ith to the jth router with the given requirements for the average IP packet length and bandwidth, rather than the transmitted traffic volumes estimation.
The presented algorithm allows describing the process of managing the resources of the transport PMS by an aggregate of computational procedures. All levels of management herewith are linked by a single target function, namely by the minimum of total energy consumption, and their solutions are coordinated with each other. 
Chistyakov V. A. Monopulse radio direction finder using digital antenna array . Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/b6e/CHistyakov_voll.pdf Digital technologies development at present allows improving radar systems, which opens possibility for application of complex modern methods of digital signal processing. It allows, in the first place, achieving the best results in radar systems operation, improving therewith weight and size characteristics of the systems under development.
Thus, application of digital phased antennae arrays for direction finding problems solving allows employing mathematical tools for angular characteristics estimations of the object under study.
The article deals with a monopulse direction finder with the sumdifference directionfinding method, accomplish based on the sixteenelement flat digital phased antennae array. The idea of the sumdifference monopulse method consists in generating both sum and difference signals to compare their amplitudes and angular coordinates estimation of the object. In addition, there is a necessity in directionfinding characteristic estimation of the antennae system to realize the said method.
Digital phased antenna array allows both sum and difference signals generation at the expense of correctly selected weight factors, avoiding herewith the waveguide converters application. The weight factors represent complex numbers able to change amplitudephase characteristics of the signals.
To gain the possibility to estimate the azimuth and elevation angle of the place, the elements of the flat antennae array should be represented in the form of rows and columns, which will be nothing else but the linear antennae arrays. The two linear antennae arrays will form two pairs of both sum and difference signals for the azimuthal plane and elevation plane.
The result of the works was the monopulse direction finder simulation with the abovedescribed digital antenna array, during which the monopulse response curve and radiation pattern were estimated. The sum and difference signals were generated, and the corresponding weight coefficients were obtained.
The dependence of the rootmeansquare deviation of angular coordinates on the signaltonoise ratio was plotted for more illustrative estimation of the direction finder with digital sum and difference signals generation. 
Ivanov S. A. Inertialsatellite observations monitoring by combined goodnessoffit criteria. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/b47/Ivanov_voll.pdf GPS is the most widespread and advanced global navigation satellite system (GNSS). However, the GPS signals are the subject to a large number of different types of interference, both natural (the GPS signal can be weakened by trees, buildings, and antenna orientation), and imitation (intentional) interference. Intentional interference, also called spoofing, allows entering false GPS information into the navigation system.
Powerful jammers are easy to detect and neutralize due to the high intensity of radiation. Less powerful sources of interference are harder to find. It is important to deal with them by employing improved antiinterference technologies in receivers, improving the antenna, or integrating with an inertial navigation system or other devices insensitive to interference.
Inertial navigation systems (INS) are not affected by artificial interference. The main sources of errors in the INS are the errors in inertial sensors (gyroscopes and accelerometers), incorrect initialization of the navigation system, and imperfection of the gravitational model used for calculations.
The presented work is devoted to the problem of monitoring and violations localization reliability improving, namely, to the problem of detecting and parrying simulated interference in inertialsatellite navigation systems (ISNS).
The proposed solutions to the problem are based on the diagnostic ISNS models decomposition, and application of combined statistical criteria. The BINS error vector estimation and the reasons for the difficulties of satellite support for BINS are being considered. The technology of sequential processing of observations allows forming diagnostic parameters by the sample of residuals on a sliding time interval. The article presents and analyzes the results of field experiments with a typical BINS. Conclusions are drawn on the need for adaptiverobust processing of inertialsatellite observations.
The scientific novelty of the proposed work is associated with the addition of procedures for detecting and parrying anomalous inertialsatellite observations based on the combined statistical criterion x^{2}/ϑ^{2} , with account for the fact that anomalous signals associated with the SNS are usually pulsed. Such procedures can be performed in both real time and according to the data from the onboard registration devices. 
Kasmerchuk P. V., Vernigora L. V. Linearization method in the problems of spacecraft with electric propulsion power plant transfer to geostationary orbit. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/a7d/Kazmerchuk_Vernigora_voll.pdf The work “Optimization of noncoplanar lowthrust flights by the linearization method” by P.V. Kazmerchuk and L.V. Vernigorа solved the problem of noncoplanar flight from a high elliptical orbit to a geostationary orbit (GSO) within the minimum time (the task of optimal response) employing modified linearization method. In this task, the thrust acts continuously, with a constant level, and control is performed by the thrust vector turn. Another important class of optimization problems of transferring the spacecraft (SC) with electric propulsion power plant to the GSO are the problems of the final mass maximization under the limitations on the transfer time (the problem with the fixed time). The flight time increase relative to the optimal response problem allows reducing fuel consumption and increase the final mass by disabling the propulsion system at the trajectory legs with less efficient control. The article considers the nonadjustable EPPs, which thrust can be either zero, or maximum.
Maximum principle is widely used to solve the tasks of the EPP SC flight optimization. Application of the Maximum principle allows reducing the original optimization task to solving a boundary value problem. When solving such boundary value problems, researchers face convergence problems, the initial approximation selection, stipulated by the locality of the Maximum principle, and the existence and uniqueness of solutions to the systems of nonlinear equations. To overcome the above said difficulties, the authors use various approaches, such as the continuation method, sequential refinement of motion models, combinations of numerical methods, and others. A specific feature of the fixed time task consists in the presence of a large number of local extrema, which further complicates the solution of the boundary value problem of the Maximum principle. This happens due to the fact that partial derivatives matrix of the discrepancy of a boundary value problem by its unknown parameters, one way or another used in all indirect methods, degenerates at the boundaries of the domains of attraction of local extrema.
Being a direct method operating in the controls space, the MLM belongs to the class of gradient methods (first order methods), which stipulates its large convergence domain. It turned out to be possible to use trivial initial approximations in the task of optimal response that allows expect its successful application for the tasks with a fixed time as well.
MLM also belongs to the class of local methods, but it is desirable to have an algorithm that allows getting solutions close to global ones. Looking ahead, we note that it was possible to parameterize the task with only two quantities: the initial value of the true longitude of the flight and the initial value of the EPS thrust. The resulting twoparameter family can be easily studied by direct enumeration to find the global minimum without the need to invoke global optimization methods.
The main problem when trying to use MLM for solving a task with a fixed time consists in determining the number of thrust switching points and their location on the trajectory, since there is no explicit information about the switching function. The solution algorithm should automatically determine the optimal values of these parameters along with the thrust vector direction optimizing at the active legs of trajectory. The article proposes an algorithm that allows regularly solving the tasks of EPP SC flight to the GSO with a fixed time. 
Tugolukov V. A. Arranging measurements while shipborne aerial vehicles testing under nontestground conditions of the open sea. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/96b/Tugolukov_voll.pdf The article considers methodological issues arranging external trajectory measurements of the shipborne aviation systems’ parameters while the shipborne aerial vehicles testing under the open sea conditions and absence of the lack of the route measuring testground within the water area for the State testing of aircraft carrier. The author suggested a differential measuring method based on navigation parameters correction of the shipborne aerial vehicles relative to the aircraft carrier, and transmitting the set of corrections to measurements of all navigation satellites to the definable points. These corrections can be used at the satellite observations at the definable points with measuring at the coastal geodetic station with known coordinates of pseudorange to all “visible” satellites and computing its measured coordinates, and then the measured ranges as well (according to the measured coordinates of both station and satellites). Then further processing information on computing the rootmeansquare error of lateral and vertical deflections of the shipborne aerial vehicle while takeoff and landing on the ship, and at combat control from an aircraft carrier ship and / or from a shipborne radar patrol and guidance aircraft is proposed is being performed. The accompanying monitoring of the achieved values of the aircraft carrier efficiency levels is being performed, and the accuracy characteristics of the shipborne aircraft is being obtained to assess the feasibility of the requirements for the carried aviation systems and for the aircraft carrier ship as a whole.

Bagretsov S. A., Chernaya T. E., Karpenko K. A., Tarasov A. G. Techniques for determining rational time for specialists training in automated training systems. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/858/Bagretsov_CHernaya_Karpenko_Tarasov_voll.pdf It is necessary to combine theoretical and practical drill in the process of specialists training. However, the balance between these two types of training may differ drastically for various sphere of activities. The material of the article allows determine the rational learning time with known and unknown level of losses associated with operator errors. The proposed techniques allow predicting with fairly high degree of accuracy the required number of practical classes in special disciplines for this of that training period to increase the specialists’ level of training.
The proposed methods are based on the fundamental concepts and relationships of probability theory, utility theory, and fuzzy logic. The interval measure obtaining method is based on the concepts of a hypothetical game (pseudogame). The interval boundary values usefulness is being coordinated based on the expert survey.
These methods allow determining the rational period of the training course studying by the student from the initial time instant, which ensures an optimal combination of the loss function indicators and costs in the sense of the minimax criterion. The obtained results can be used while the educational process planning to ensure the necessary level of students’ preparedness and minimize the learning process costs.
A rational combination of theoretical and practical stages of training allows prepare a specialist with professional knowledge, skills and abilities at a level guaranteeing the functional activities tasks fulfilling in any conditions of situation. The proposed scientific and methodological approach is advisable to be implemented while organizing the specialists training process when the necessary level of knowledge and skills is known for the correct functional duties performing with the required probability.
The proposed methods allow determining the specialists training period, which minimizes training the costs and the necessary level of a specialist training, which is defined as the probability of timely and errorfree solution of problems related to his future professional activity. The technique allows accounting for specifics of the trainees’ further practical work, and defining criteria of the professional training levels and resource constraints on performing sales professionals training. 
Nevolin A. O. Internetprotocols obfuscating encoding algorithms effectiveness measurement methods. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/4a2/Nevolin_voll.pdf Data encryption is not always possible today. In some situations attacker does not actually need to decode information – he just can organize DDOSattack and turn attacked system off for a some (maybe long) time. If information system uses encryption protocols, it’s always a good hint for security analyst – if data is encrypted, that means than there is something important.
There are some ways to protect data and whole system – by alternative methods of secure data processing, digital steganography for example. A new method is protocol masking. In this way we encode some protocol so it looks like another. So attacker does not actually know what kind of information is transferred through channel that he is listening.
While encoding one protocol as another we must remember to keep it’s basic characteristic similar to referenced protocol. If we don’t, attacker can easily not only detect fact of masking, but also find out which protocol we used originally. So we need some metrics to describe measure of information “protectiveness”. These metrics can be, for example, statistical characteristics of protocol. If we keep them the same, the fact of protocol change will not be discovered by security analyst.
This article describes offered model of whole system. Also it proposes a models of attacker and legal user. Some strong mathematical measures of encoding efficiency are then introduced. They are based on statistical characteristics (commands or their parameters probability and other). Finally, some methods of XMLbased protocols obfuscation are described and analyzed at the point of view of proposed characteristics. 
Spevakov A. G., Kaluckiy I. V. A unit for unique sequence generating employed while personal data impersonalizing. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/3b2/Spevakov_Kalutskiy_voll.pdf A problem of data impersonalizing occupies special place in automated information systems while data processing. Such methods and algorithms are employed to improve the system security and reduce material costs for information security tools purchasing. One of the tasks consists in developing specialized units that will allow increasing the speed of data conversion during impersonalizing. Such units can be employed not only in large data processing centers, but also in information systems with a small number of personal data subjects, but demanding data processing speed. This allows performance improvement, as well operating costs and product weight reduction. The purpose of this work consist in the speed increase of the unit for generating a unique sequence for personal data impersonalizing by parallel computing and FPGA based implementation. The problem solution of increasing the speed of forming a unique sequence for impersonalizing personal data is achieved by implementing a method and algorithm for data impersonalizing that allows their FPGA based implementation employing parallel computing. The developed unit novelty lies in the fact that a method for introducing identifiers using hashing critical data and a private key was proposed. This allows increasing the of data privacy level, bating requirements for the security level of the information system, and increasing the of data processing speed by convolving critical data into a hash identifier by parallel computing employing the developed specialized device. The results obtained consist in the development of a unit for generating a unique sequence used for personal data impersonalizing. This unit implements the proposed method. The experiments confirming the proposed mathematical model adequacy in comparison with the software implementation were conducted. The proposed device allowed increasing the speed of hash identifiers computing by more than a thousand times, with power consumption decrease by 11.7 times. The results of the experiment allow recommending the proposed unit for implementation in automated information systems for personal data processing at the design stage or optimization of existing systems. It will reduce the information protecting system cost. The authors propose the presented solution implementation in the form of a FPGA based unit, which will allow increasing speed and reducing operation costs. 
Borzov D. B., Basov R. G., Titov V. S., Sokolova Y. V. Processor load scheduling device in multiprocessor systems of critical purpose. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/774/Borzov_Basov_Titov_Sokolova_voll.pdf The need to prompt response from the computing system side emerges in the stateoftheart multiprocessor critical systems. The systems, which failures lead to the losses (economic, physical, human etc.) are defined as critical systems. In the event of failure, such systems are the subject to high requirements for operability, reliability, safety, security, etc. All costs herewith associated with introduction of changes to such system or its replacing (direct, indirect, etc.) are more important that the losses occurred in the case of the multiprocessor system failure itself. It is obvious that minimization of both time and hardware costs, necessary for the multiprocessor system response to the hazardous situation is of most importance.
The failures occurring in the internal processor modules, such as aircraft cockpits, surveillance systems, targeting, atomic systems etc., can be assigned to the critical situations. In case of the multiprocessor system failure herewith, its performance and response decrease, which is unacceptable in critical systems. One of the options for this issue solving may be processor loading planning in multiprocessor systems. In this case, the multiple loading of several processors by the same task (routine, subroutine, algorithm, file, etc.) can be avoided, and, with this, the queue of the incoming tasks can be planned in such a fashion that they are being fed simultaneously. This allows reduce unplanned operation downtime and, at the same, time increase its availability factor along with increased performance.
The presented work is devoted to critical multiprocessor systems, to which high availability objects, which operability is critical for any kind of activity, can be assigned. In such cases, a person, country, enterprise, organization, etc. is distinguished. A failure in this case leads to in the system response time decrease and a further decrease in its performance, and, thus, the availability. In this case, the application of the software for solving this issue is unacceptable, which means that it is necessary to use specialized hardware load scheduling tools. 
Chigrinets E. G., Rodriges S. B., Chotchayeva S. K., Sorokin A. V. The experience of CAD/CAM systems application in educational process at the basic department of “Aircraft engineering”. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/c59/CHigrinets_Rodriges_CHotchaeva_Sorokin_voll.pdf Computer engineering gains more and more importance in the modern world due to the 3D solidstate modelling, analysis and simulation integration. In this aggregate of methods and means for the engineering problems solving, the groundbreaking role is being assigned to creation and application of the socalled digital twins, which are based on digital representation of separate real components, products, technologies and processes, allowing performing a wide specter of analysis and virtual simulations. The object location herewith does not matter.
Practical application training of the CAM systems is a weak side of the DSTU (Don State Technical University) compared to the theoretical preparation.
This article demonstrates the application example of the NX computeraided manufacturing system by Siemens PLM Software in the engineering personnel training for an aircraftbuilding enterprise.
In the framework of their practical training, the students collected information that has become the initial data for the machining process simulation of the especially critical helicopter parts employing the NX CAM. Managing routines for the fiveaxis HURON K2X8 FIVE machining center were developed applying the «Machining» module, analysis of various cutting strategies was performed, visualization of the material removal was carried out, and the machinetool operation simulation was demonstrated
Verification of the developed managing routines allowed revealing overcuts and and rough surfaces on the completed part, collisions of the machining center actuating devices with rigging and workpiece, tools contact during rapid feed, excessive and insufficient machining allowances. The revealed defects were corrected prior to program run on a CNC machine.
The demand for graduates of the engineering specialties are largely determined by the knowledge of modern CAD/CAM system at the technological preparation of production and the ability to employ them. The increased interest of today’s young people in computer technologies raises the interest of the students in the study and improves apprehension of the educational material. However, introduction of computer engineering methods into educational process faces certain difficulties as well. The main one is the insufficiently equipped laboratories of the University. Very often, the such programs implementation is being supported exclusively by the enthusiasm of individual tutors and department staff members.
This publication was prepared based on the cooperation between the department of Aircraft engineering of Don State Technical University and the division of Computer Aided Manufacturing of “Rostvertol Helicopters Co.” within the framework of “The new personnel of the militaryindustrial complex” project. 
Malshakov G. V. Studying search alphabet distortion impact on entities identification based on data frequency analysis. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/0f9/Malshakov_voll.pdf The article recounts the results of studying the impact of the alphabet tokens degree of occurrence in the entity objects of the subject domain on the identification of entities based on data frequency analysis with various strategies for tokens exclusion.
The following dependences are shown:
– Dependence of autocorrelation on minimum allowable number of characters in tokens for various samplings (as a percentage of the initial data);
– Dependence of covering the entity objects alphabet of the subject domain on limitation on the number of characters in the alphabet tokens;
– Dependence of the number of correctly recognized entities of the subject domain for various samplings volumes on the limitation of the number of characters in lexemes of the alphabet of the subject domain entity’s frequency identification at unfavorable strategy for the subject domain entity objects exclusion;
– Dependence of the number of correctly recognized subject domain entities for various samplings sizes on the limitation on the number of characters in the lexemes of the alphabet of the frequency identification of the subject domain entity at a favorable strategy of excluding objects of the subject domain entities.
The impact of the degree of occurrence of alphabet lexemes in the entity objects of the subject domain and the strategy of excluding alphabet lexemes on the entities identification based on data frequency analysis was established.
The above said studies allow reducing the number of errors in identifying domain entities based on the data frequency analysis while ensuring the interoperability of the applied software. 
Zakota A. A., Efanov V. V., Gunkina A. S. Evaluation technique for motion parameters determining accuracy of aerial target under conditions of covert surveillance. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/02b/Zakota_Efanov_Gunkina_voll.pdf The object of the study is the system for parameters determining of aerial target motion under conditions of covert surveillance.
The subject of the study is a technique for accuracy evaluation of indirect target motion characterization system.
The objective of the study consists in accuracy improving of aerial vehicle motion characterization based on recommendations elaboration for creating conditions to perform measuring process and measurement data processing.
In the process of this work execution analysis of existing approaches to target motion characterization was performed. It revealed that advantage of pseudotriangulation technique lies in nonlinear equations reduction to algebraic system of equations. However, under certain conditions it does not ensure target motion parameters determining. The approach eliminating this drawback through introduction of the closingin with aerial target law is proposed.
This technique ensures aerial target motion simulation, namely computing its coordinates arrays; measuring process simulation, i.e. computation of arrays of precise and containing accidental errors of locating angles values. Besides, this technique ensures preliminary measurement smoothing and angular velocity evaluation of aerial target sightline. It allows:
 Define approximately potential value range for approximation dependence coefficients;
 Perform parameter identification of aerial target motion at various approximation dependence coefficient values within the established range;
 Select approximation dependence coefficient estimation value by minimum variance of inadequacy in calculated values of aerial target horizontal range;
 Characterize aerial target range motion with selected approximation dependence coefficient; measurement error assessment by spread in calculated values at different number of bearing measurements;
 Computation cycle repetition with increase in number of measurements in the case of exceeding spread in range estimations of its preset error value.
While computation performing the initial data is aerial target motion trajectory characteristics; the carrier acceleration value; the number of grouped measurements; total limit number of measurements, rootmeansquare deviation in aerial target bearing measurement results.
To check capabilities of the said algorithm a series of numerical experiments was performed.
It was assumed while testing that the time interval between measurements wass , and . Results smoothing revealed the following:
 with rational choice of approximation coefficient value (in accordance with the specified procedure), discrepancy between approximation and real dependences was insignificant;
 approximation errors were by an order lower than the measurement errors.
It should be noted that the low error level while smoothing aws achieved at essential variances of approximation dependence coefficients caused by differences in measurement process implementations.
With the intent of justifiability check of the supposition on keeping the closingin velocity constant, preliminary studies were being performed, during which parameters of the carrier flight were being determined by its flight simulation at the afterburning turningon. This data shows that owing to the carrier considerable thrusttoweight ratio, constant acceleration maintaining of a ≈ 4–8 m/s^{2} within quite a prolonged period of time is possible.
The technique testing results revealed that with the measurements number increase the range determining error fell and achieved the value of about 10% with the initial structure of the algorithm, and less than 10% at extra smoothing of the stored total data per each second of the measurement process.
The strongest impact on the results of the range determining is imposed by the carrier acceleration value and the interval between measurements.
The results of refinement and studies of еру fundamental algorithm for estimation of aerial moving target range are indicative of its high sensitivity to accuracy and amount of information being used. The relatively small size of the synthesized range linear interval (“rangefinding baseline”) should be considered as physical reason of this effect.
The aerial target range and velocity estimation accuracy increases with adding to the number of notches. However, this technique requires significant time increase up to 2025 sec per problem solution operation. Nevertheless, at present the passive sensors appeared, which are capable of measuring angular coordinates of aerial target with the time interval of t ≈ 1 – 10–^{2}...0.5 – 10–^{2 }sec.
With account for this, it is possible to perform multiple measurements of the desired data (angles) using “cluster” of indications when measuring angles of discrete angles.
Based on these results recommendations for creating conditions to perform measurement process and measured data processing were worked out. The proposed technique was employed for developing the method for air ordnance delivery in the environment of covert target observation. 
Anan’ev A. V., Rybalko A. G., Ivannikov K. S., Klevcov R. P. Dynamic model of temporarily fixed ground targets hitting process by a group of smallclass attack unmanned aerial vehicles. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/e03/Ananev_Rybalko_Ivannikov_Klevtsov_voll.pdf The article presents the dynamic model of the fixed ground targets hitting process by the by group of smallclass attack unmanned aerial vehicles. Considering the said process is probabilistic both in states and in time, the dynamic model is based on the Markov’s random processes theory with continuous time and discrete state, and on the theoretic basis of the simplest flows.
A scenario for groups of smallclass unmanned aerial vehicles application for hitting temporarily fixed ground targets, revealing the order of actions at each stage of the process under study, was employed as initial data for determining states of the dynamic model.
New dynamic model differs from the known ones by inclusion of the additional blocks. The first one realizes probabilistic parameters computing of wind disturbances due to the special maneuver, and the second computes the cycles of the unmanned aerial vehicles groups’ flights from the Uturn point to the target to the ammunition discharge point with account for its hitting probability with acceptable direction deviation.
Studying the model allows determine conflicting variable parameters of smallclass unmanned aerial vehicles’ combat maneuvering and calculate their rational values. On the one hand, these parameters affect the discharge accuracy and, consequently, rational ammunition consumption. On the other hand, extra maneuvering may significantly increase the hitting time, which is utterly critical for the temporary fixed targets, which can be removed out of strike.
A statistical model was being studied initially in this work to solve the set problem on hitting temporary fixed targets in a specified time. Further, having solved numerically the system of linear inhomogeneous differential equations with constant coefficients, developed for the dynamic model, the authors obtained time dependencies for various states of the process under study.
The conclusion to the article presents the result of the impact estimation of the sought probabilistic parameters of a group of strike unmanned aerial vehicles combat maneuvering on the probability of the task accomplishment at various time instants. The most significant probabilistic parameter, which increasing requires extra operations while actions planning, was defined.
The most significant probabilistic parameter, which is to be additionally increased during the stage of operation planning, is detected. 
Maskaykin V. A. Numerical method for studying temperature regimes of an inhomogeneous, structured body. Trudy MAI, 2020, no 115, http://mai.ru//upload/iblock/821/Maskaykin_voll.pdf In the aviation industry, thermal insulation mineral, fiberglass and polymer materials are employed for operation in extremely low temperature conditions. In certain cases, the structures, which perform the function of absolute isolation of gases from the external thermal impacts, are being created to obtain thermal isolation. If thermal isolation materials are being considered, the thermal isolation life span of such materials does not always satisfy the needs for temperature retention, and being regarded as a secondary subject operating in temperature regimes. The presented work solves two dimensional thermal conductivity problem of the element serving as a thermal insulator. It includes as well the study of heat transfer at the interaction of various materials between each other and their structural distribution in the element.
To solve the set problem, let us consider a conventionally selected segment (element) of the heatinsulating sheathing. The requirement consists in ensuring thermal isolation of the specified element in conditions of low temperatures by means of various materials and their structural distribution in the element. This problem solution is being performed by creating mathematical model and solving it numerically based on an implicit difference scheme. Computations of the mathematical model include the thermal conductivity problems of homogeneous body, a heterogeneous body with the structure of materials stratification, and the structure of the chess distribution of materials.
The results of the study show that the interaction of different materials in the element and the structural distribution of materials in the element play an important role in increasing thermal insulation properties. Interaction in heterogeneous bodies of various heatinsulating materials with each other has a low thermal insulation index, in contrast to the interaction of a heatinsulating material with the other, having the opposite thermal conductivity characteristics. An increase in thermal insulation in such body is accompanied by thermal insulation of a material with high thermal conductivity properties. A mutual substitution, “balancing” of the processes of thermal conductivity of materials with each other occurs. 
Korovaytseva E. A. On some features of soft shells of revolution static problems solution at large deformations . Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/265/Korovaytseva_rus.pdf The presented work demonstrates specifics of thinwalled structures mechanics at strong nonlinearity problems solution computational algorithms realization by an example of soft shell of revolution static inflation at the large deformations problem. The problem solution algorithm under consideration realizes the method of differentiation by parameter. The feature of the algorithm consists in using specific method of nonlinear Cauchy problem solving with righthand side given on discrete mesh of variable step. Studying the properties of the system of equations under consideration revealed the necessity for solution regularization preceding of the suggested algorithm realization. Thus, the initial stage of solution construction uses the wellposed system of equations of technical theory of soft shells, as its solution is close to the solution of the problem being considered, but without having a poor stipulation. Analysis of various parameters of computational algorithm or properties of soft shells theory equations impact on calculation results cannot be performed in analytical form. Thus, for these issues studying numerical experiments concerning solution of hemisphere bloating problem with different conditions of the edge fixation are used. Physical properties of shell material are supposed to be described by Treloar relations. For the obtained results illustration only loading diagrams as pressuredeflection curves are used. The effect of the following parameters of the computational algorithm on the computational results was studied. These were the preliminary internal pressure magnitude, solution continuation parameter selection; the magnitude of initial and maximum allowable solution continuation parameter step; the number of parameter steps on which solution regularization was used; the ways of stress state calculation at developing the resolving system of equations. It is worth mentioning that in the presented work, apparently for the first time, the author managed to obtain the value of deflection of the soft hemispherical shell, being inflated, w_{0}=35R (where R is the radius of the nondeformed shell) only in 60 solution continuation parameter steps. The maximum value of deflection herewith obtained prior to the loss in calculation stability reaches 10^{8}R. In this case the solution error is equal to 5%, and the number of solution continuation parameter steps is 280. A significant, difficulttopredict dependence of computational results on the algorithm parameters mentioned above was revealed, up to obtaining wrong results. Thus, setting a miniscule value of the preliminary pressure may lead to the convergence problem of the solution correction right at the first step. An excessively large value of the step by the parameter leads to significant distortion of the results, while a too small one leads to the computation stability loss. Conclusions on the effect of basic stress state computing method and a number of steps by the parameter, at which the system of equations regularization is performed, may appear different for various boundary conditions at sphere equator and various methods of the solution continuation parameter selection. Thus, judging by the performed studies, when solving problems of the stressstrain state, being followed by large displacements and deformations analysis, applicability checking of any `previously developed recommendations concerning calculations in each concrete case is necessary. Realization of the selected solution algorithm or parameters assignment should not be restricted by only one method. Studying the problem solution behavior in a wide range of possible changes of the algorithm parameters is necessary; and in the absence of analytical solution, the repetitiveness of the results at various values of the assigned parameters can be the indicator of the obtained results certainty. Probably, such numerical experiments may and should be performed by the technique similar to the methods of experimental mechanics, and properties determining of this or that algorithm in application to the solution of this or that type of problems is similar to determining mechanical properties of materials at various types of the stressstrain state. 
Baklanov A. V., Krasnov D. S., Garaev A. I. Gasdynamic computation of experimental installation for gas turbine engine section testing. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/e93/Baklanov_Krasnoa_Garaev_rus_1_.pdf When designing test benches for of the combustion chamber sections testing performing it is necessary to perform gas dynamic calculation to determine parameters and characteristics such as the rate of fuel gas and air, the air velocity at the section inlet, and operational time of the experimental installation when employing a limited number of liquefied gas cylinders. It is necessary as well to know the range of a gas rate measurement and pressure on the measuring area of the gas main of the experimental installation to sel ect appropriate measuring devices
The combustion chamber section represents a 1/14 part of a full sized combustion chamber and consists of an outer casing, inner casing, a flame tube with a frontend device, in which the nozzles are installed. The fire tube is bounded by side cooling walls on both sides. Nine nozzles are being installed in the combustion chamber section.
The test bench includes a source of compressed air and a central main line leading to the section. Gas is being fed to the section collector through the fuelfeeding system and then to the flame tube head, which distributes it among the nozzles.
The following was determined fr om the computation results:

Krauzina M. T., Sidorov A. S., Burkova E. N. Magnetic fluid application as a heat carrier in cooling systems under spaceflight conditions. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/934/Krauzina_Sidorov_Burkova_rus.pdf This article presents the results of numerical simulations and experiments on studying mechanisms of heat and mass transfer in magnetic fluids. These substances belong to the class of nanofluids and are being employed as a heat carrier in cooling systems. The interparticle interactions effect on diffusion processes in magnetic fluid was studied. Numerical experiment has demonstrated the possibility of convective cooling in the absence of gravitational field.
The flows’ modes and structures in a magnetic fluid in a vertical thin layer being heated from the one wide side, as well as a spherical cavity, being heated from below, were studied. The interaction of thermomagnetic and thermogravitational convective flows in a vertical magnetic fluid layer placed in a transverse magnetic field was being considered. A flat rectangular shape selection for the study is associated with a model of the simplest heat exchange device, as well as for comparing the results with known theoretical calculations in this problem. To study behavior of the inhomogeneously heated magnetic fluid in gravitational and uniform magnetic fields, experiments in a spherical cavity were performed. Besides, with this geometry, the simplest movement is being realized near the stability threshold of mechanical equilibrium when heating from below in the form of a sole whirl, rather than the system of interacting shafts as in the case of the flat layer.
The article demonstrates that thermogravitational and thermomagnetic tramsport mechanisms interaction under laboratory conditions leads to the complex behavior of the convective system and, as a consequence, to the heat and mass transfer processes complication. The authors propose the possibility of application of active and passive cooling systems with magnetic fluids onboard a spacecraft under conditions of microgravity. For this, numerical modelling performing of the cooling system is being planned to give estimation of its energy efficiency, as well as performing the fullscale space experiment. 
Firsanov V. V., Pham V. T., Tran N. D. Strainstress state analysis of multilayer composite spherical shells based on the refined theory. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/eca/Firsanov_Fam_CHan_rus.pdf Nowadays, due to such advantages as high strength and low density, multilayer composite shells are widely used in various fields of mechanical engineering, including aerospace engineering. Theoretical and experimental studies have shown that when determining the stress condition of plates and shells, especially in the areas of joints (flanged, welded), local and rapidly changing load, as well as those made of nonhomogeneous materials, the classical theory is not in line with the practice.
For multilayer composite shells, reliable determination of normal and shear stresses corresponding to lateral deformations represents an urgent issue. This article presents an option of the refined theory of the strainstress state calculation of spherical shells made of layered composite materials. When creating mathematical model of the shell, the threedimensional equations of linear elasticity are used. Components of the required displacements are being approximated by polynomials at a coordinate normal to the middle surface of the shell by the two degrees higher than the classical Kirchhoff–Love theory. A system of differential equations of equilibrium and corresponding boundary conditions have been obtained using the Lagrange variation principle. The formulated boundary value problem is being solved by successive application of finite difference and matrix sweep methods. The calculations were performed using a computer program.
A multilayer composite shell, rigidly pinched at two edges was considered as calculation example. The numerical results of the calculation of dimensionless shells deflection under the action of symmetric and asymmetric loads are practically identical to the published results of researchers, employing the other methods, which confirms the validity of the proposed refined theory.
The thickness impact on the stress condition of the shell is being studied. The article presents the graphs of the continuous stress distribution over the thickness of the shell are presented, which is of great importance for the composite materials. It has been established that lateral, normal and tangential stresses of significant value occurred in the edge zone of the multilayer shells. The authors recommend employing the proposed refined theory for their determining. 
Shlyapnikov P. A. Determining limiting amplitude of hardened parts cycle with stress concentrators with compressing average stresses. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/36a/SHlyapnikov_rus.pdf The purpose of this work consists in developing a technique for the limiting amplitude quantifying of hardened samples with stress concentrators at various compressive average cycle stresses.
To confirm the previously obtained theoretical solution on predicting the maximum amplitude of parts with stress concentrators, hardened by the surface plastic deformation (PPD) methods at the central tensioncompression cycle asymmetry and compressive average stresses of the cycle, an experimental study of cylindrical samples made of 45 steel with semicircular profile incisions hardened by pneumatic blasting was performed.
Both nonhardened and hardened cylindrical samples with concentrators applied to them in the form of an annular incision of a semicircular profile were subjected to studying. Incisions were being applied on the hardened sample after pneumatic blasting of a smooth cylindrical sample. As the result, the increment of the maximum amplitude of samples with stress concentrators due to surface hardening, as well as the redistribution of residual stresses of a hardened smooth sample as a result of applying the concentrator to the hardened surface of the sample were being determined.
Experimental limit amplitude determining of nonstrengthened and hardened samples was performed with the UMM01 testing machine, allowing implementing both tensile and compressive average cycle stresses. The results of the endurance limit determining are summarized in a table. For comparison, the table shows the calculated data obtained earlier by the computer modeling.
The author proposes to perform estimation of the hardened samples and parts with different asymmetry degree by the cycle limiting amplitudes diagrams with account for residual stresses. The limiting amplitudes diagram is based the modified Gann diagram.
A limiting amplitudes diagram of a cycle with average compressive stresses was obtained for an asymmetric cycle, where a hardened sample with a concentrator and a nonhardened sample with a stress concentrator were employed.
Fr om geometrical considerations, the equation for the coefficient of of residual stresses effect on the limiting amplitude at various compressive stresses of the stretchcompression cycle was obtained. As the result, a technique for the limit amplitude of hardened samples and parts estimating employing the lim it amplitudes diagram of the stress cycle of parts, with account for residual stresses was proposed. A simple equation for calculating maximum amplitude of hardened parts with concentrators at different degrees of cycle asymmetry was proposed. The obtained scientific results can be used in strength calculations without lengthy and costly tests. 
Belyaev B. V., Golicov I. O., Dobrolyubov A. N., Lebedev A. S. Mathematical model for operability diagnosing of flying vehicles at cracktype faults . Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/4cd/Belyaev_Golikov_Dobrolyubov_Lebedev_rus.pdf Recently, the acute issue of the possibility of orbital space vehicles flight prolongation after colliding with the object of technogenic origin, which may lead to sealed structures damaging in the form of surface microcracks arises.
The urgency of this problem will enhance in the oncoming years due to the current tendency of nearEarth space contamination increasing by technogenic particles. In this regard, failures diagnostics of flying vehicles with the damages if the form of cracks becomes of vital importance, since it will allow substantiating terms of space vehicles staying in orbit to fulfill the set task.
The article studied the issues of diagnostics of the flying vehicles’ sealed compartments with through microcracks functioning. The authors obtained equations allowing describe regularities of changing of the working medium leakage from sealed compartments through the through cracks, depending on their changing geometry. The algorithm of plotting regularities of the working medium leakage from the sealed compartments change in the presence of developing the through cracks in their shells was developed. The article presents typical regularities of the working medium leakage through the through cracks in time. Computational results of the compartment depressurizing depending on the through crack length, the degree of its opening, as well as free volume of the sealed compartment are presented.
The results, obtained in this work, allow solving the inverse problem for the instrument and habitable spacecraft compartments. Having the telemetry data on the gas state parameters (pressure and temperature) inside the compartment and these parameters changes with time, a possibility of diagnosing microdents characteristics under conditions of the orbital flight emerges. This, in its turn, allows assessing the time margin for the leakiness localization, or taking decision on the emergency landing of manned spacecraft.
The results of this work allow more quick failures diagnostics of flying vehicles operating under conditions of of the nearEarth space clogging with objects of natural and artificial origin. 
Kostin A. V. Design procedure for computing printed circuit conductors on metal base for AC spacecraft devices. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/d4d/Kostin_rus.pdf The article suggests the technique for the design procedure of printed conductor (PC) width of the printed circuit board, being installed of the metal base, for the onboard spacecraft devices, depending on the flowing sinusoidal current of various frequency. The technique accounts for nonuniform current distribution in the PC volume due to the skin effect. The following problems were solved while this technique developing:
The article presents the dependence of the PC active electrical resistance on frequency. This dependence was obtained under the condition that the PC width is much greater than its thickness. This condition is most often being fulfilled in practice. Such assumption was made with the purpose of simplifying the search for the dependence. As long as active resistance equation turned out to be rather complex even with account for the assumption, the article presents the graph of the reduced active resistance dependence. To obtain the active resistance value, the value of the reduced active resistance should be multiplied by the PC length value and divided by the value of its width. The active resistance value is being determined graphically for the specified AC frequency. It simplifies the PC width calculation while printed circuit boards design.
Analysis of active electrical resistance dependence on the frequency was performed. It was established in the course of the analysis that at the frequencies up to 100 kHz active electrical resistance weakly depended on the frequency. The skin effect can be ignored at these frequencies. At the frequencies above 1 GHz, the active electrical resistance does not depend on the PCB thickness. This allows making a number of simplifications, and calculate the active resistance by the thickness of the skin layer.
The previously developed technique assumes the presence of heat removal only through the printed circuit board on the metal base. The article references the publications recounting its gist.
According to this technique, the thermal resistance of insulation material layers is determined by both the geometry of their part, located under the PC, and thermophysical properties of the materials themselves. When the current flows through the PC, the dissipated power is determined as the product of the square of current and the PC active resistance. This power will be equal to the thermal flow. Then the overheating will be equal to the product of the thermal flow and the thermal resistance of the insulation material layers. Refinement for the AC consists in the electric resistance dependence on the frequency.
Analysis of temperature distribution in the PCB volume due to the current distribution nonuniformity and heat dissipation from the one side only, was performed analytically by solving thermal conductivity equation. Calculations revealed that the skin effect would not be affecting the temperature distribution in the PCB volume significantly. Analysis of the frequency impact on the temperatures distribution was performed.
It was noted that the temperature distribution law became close to the linear with frequency increasing. This is associated with the fact that the AC is being pushed out to the PC surface, and heat sources inside PCB disappear.
It was noted that other assumptions made while developing the technique for the DC affect the calculation result for the AC as well. It is associated with the fact that the proposed technique is based on the previously developed one. First of all, this concerns the edge thermal fluxes effect to the PC temperature. The article stipulates that the method can be applied even if the PC width is not much great than its thickness. If the condition is met, the current flows along the lateral surfaces can be ignored. Nonfulfillment of this condition will lead to the situation when these currents will significantly affect the result. However, the presence of additional currents means that the larger PCB section will be employed while the current flowing. This will lead to the situation when actual active resistance will be less that the calculated one. Consequently, actual PCB temperature will be less than the calculated one. This will no degrade the PCB reliability, but even increase it.
The actual PC power will be less than the calculated one. And as a result the actual PC temperature will be less than the calculated one. This will not decrease the reliability of the PC and increase it instead. 
Podstrigaev A. S., Smolyakov A. V. Signal spectrum studying at double frequency conversion. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/f36/Podstrigaev_Smolyakov_rus.pdf The article performs the harmonic composition analyzes of the output signal of the signal relay device with injection of Doppler frequency shift. Functional models of mixers and bandpass filters were developed in MATLAB. Mixers models are based on intermodulation tables. Bandpass filters models account for parasitic passbands. Powers of fundamental and spurious components of the output signal of device with double frequency conversion were determined by the developed models. The results were obtained for various device bandwidths. Simulation was performed for a singletone input signal. The article considers three cases of the input signal location in the passband of the device, namely in the center of the band and at its borders. General patterns of changes in the device output signal while the device bandwidth changing were highlighted. Thus, with the device bandpass increasing, the power and number of spurious harmonics increase in its output signal. In each separate spectrum herewith, corresponding to the fixed value of the device bandpass, the power and number of spurious components decreases with the frequency increase. The cases, when the spectrum does not correspond to the above said patterns were considered in detail. The article demonstrates the possibility in principle to imitate Doppler frequency shift in the wide frequency band of the input signals with the relaying device of the signal with double frequency conversion. Thus, such device can be an integral part of a broadband simulator of radar targets.

Vernigora L. V., Kasmerchuk P. V., Sysoev V. K., Dmitriev A. O. Method of lunar landing stations’ coordinates measurements using spacecraft optical television means. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/c25/Vernigora_Kazmerchuk_Sysoev_Dmitriev_rus.pdf The paper describes use of optical laser beacons, with the help of which it is possible accurately and uniquely to determine the location of lunar landing stations when they are observed by optical television means of orbiting spacecraft. The optical beacon installed on the lunar landing station will be detected by the onboard television camera of the orbiter on the basis of a significant excess of light flux above the level of background noise.
Three coordinate systems are used to construct the method of lunar landing stations’ coordinates measuring: the International Celestial Reference System (ICRS), the Bound Coordinate System and the Instrument Coordinate System.
The presented technique is based on the quaternion algebra (RodrigueHamilton’s parameters). RodrigueHamilton’s parameters are widely used in analytical mechanics and they are closely related to Euler’s angles and an endturn vector. They clearly determine the orientation of the solid body in space and do not degenerate by any parameters of rotation. Practice shows that calculation using RodrigueHamilton’s parameters provides the lowest computational efforts compared to other methods, when the same accuracy characteristics are provided.
The accuracy of the optical laser beacon localization depends on the accuracy of determining of the orbiter’s orientation according to the measurements of the star sensor, the onboard TV camera resolution and the altitude of the orbiter’s orbit. The correlation between the spacecraft orbital parameters and the mutual position of the optical laser beacon is achieved by equalizing of a large array of observations. The equalization method takes into account all measurement errors: from errors in determining of the onboard TV camera orientation to satellite’s orbit deviations caused by irregularities of the lunar gravity field.
The presented technique will allow to locate the position of the lunar landing station with an optical laser beacon onboard with an accuracy of units of meters.
Thus, the integrated use of the orbiter onboard equipment and the binding of its measurements to the World Time Scale allows to determine the selenographic coordinates of lunar terrain points in the LRS system. This will allow to use it as a reference point for establishing of a highprecision grid of selenodetic coordinates, and to bring mapping of the lunar surface to the accuracy corresponding to the detail images of the lunar relief. 
Borzov D. B., Dyubryuks S. A., Sokolova Y. V. Method and technique of wireless data transmission in multiprocessor systems for nonstationary exchange objects. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/9c8/Borzov_Dyubryuks_Sokolova_rus_5_.pdf The article considers data transmission improving in multiprocessor systems for movable objects using wireless data transmission between processor objects (software). The authors developed method and techniques for wireless data transmission with the ability to account for the movement in space of objects of exchange, which ensures increase in the multiprocessor systems performance and a reduction of the communication delay total value. With account for the task specifics, the authors perform the tasks place (programs, subroutines, files, etc.) between multiple software of a multiprocessor system, accounting for the current distance between the software, thus reducing the total communication delay, increasing the productivity and speed of the entire task performing en masse. The proposed ideas are supposed to be employed in critical multiprocessor systems (tracking, observation, aiming, control systems, etc.), when the extraordinary situation time in the system should be minimal. The proposed method and technique for wireless data transmission in multiprocessor systems for movable objects of exchange allows make conclusion on the possibility to design an appropriate algorithm and a specialized device for application in critical purpose multiprocessor systems. It contributes to the reduction of the communication delay total value and concurrent increase in multiprocessor systems performance.
The authors accounted for the problem of computing systems (CS) compatibility and its architecture with the structure of the processed tasks, manifesting itself in the fact that any CS performs the assigned task only for a certain class of algorithms and methods. The assumption was made that the structure of the task and the architecture of the system did not correspond to each other, and the performance of the entire CS was minimal. As far as there is no structure that processes the tasks of various types equally well, several types of topologies, matching up a certain type of algorithm, are used while computing systems developing. Thus, both the CS topologies and methods of their accommodation should be considered within the framework of this work to achieve maximum performance. The authors of the presented work account for the fact that the CS is based on wireless technology. Thus, the performed analysis of such communication methods’ protocols allowed revealing compatibility of their connection with topologies. 
Chernetskaya I. E., Spevakova S. V. Multispectral electronic device for autonomous mobile platform of ecological monitoringMultispectral electronic device for autonomous mobile platform of ecological monitoring. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/067/CHernetskaya_Spevakova_rus.pdf A special place in robotic systems application is occupied by the task of developing specialized devices for orientation controlling of the autonomous mobile platforms (AMP) operating in constantly changing observation conditions. One of the tasks consists in developing an optoelectronic control device for controlling autonomous mobile platform for ecological monitoring. Such platforms can be used under conditions dangerous to human health, for analyzing radiation, chemical, and bacteriological contamination, as well as for roundtheclock monitoring of geographically remote places. However, operation of these devices involves employing them on the territories not prepared in advance, with complex landscape, or presence of obstacles, both temporary and permanent. The points for data collection for analysis may not be provided with access ways with road marking. A promising trend is optoelectronic sensors application to obtain information on the elements of the work stage, along the AMP path, which in its turn leads to the in the computational complexity increase of the image recognition algorithms and imposes additional requirements on the performance of the control device element base. This leads to the increase in weight and decrease in the criterion of the AMP autonomy. The purpose of the presented article consists in the performance improving of the device for the autonomous mobile environmental monitoring platform. The authors propose to employ multispectral video sensors that allow obtaining an image of the work scene in several spectral ranges, and hybrid image processing methods that will reduce computational complexity and improve the results accuracy. The problem solution of improving the speed of selection of the objects located on the path of the autonomous mobile environmental monitoring platform is achieved by detecting heterogeneous objects in various spectral ranges, by color and classification based on the albedo value. The developed device novelty consists in calculating threedimensional coordinates of the geometric center, and the size of the objects highlighted in space by a sequence of images, obtained in drastic conditions in various spectral ranges from video sensors and lidar, from the mobile surveillance system. It allows adjusting the AMP original route, formed by positioning systems, based on the detected obstacles, increasing thereby the speed and precision of the AMP spatial reference. As the result of experimental studies, a comparative analysis of the devices, processing the multispectral imagery to search for the objects located in the field of view of video systems of observation was performed. A structuralfunctional diagram of multispectral mobile device for environmental monitoring platform was proposed. The article presents the description of the softwarehardware testbench employed for the experimental study by simulating the FPGAbased device. The authors were able to analyze the speed performance of individual blocks, which allowed realize even blocks loading and the FPGA internal resources optimization, as well as confirm mathematical substantiation of the proposed hybrid methods and assess the key characteristics of the device. As the result, it allowed reducing computational error at the distance of up to 100 m to the object, the RMSE up to 0.447%, MAPE — 0.397, and increase speedperformance. The object selection and its coordinates determination required 0.04 seconds.
The authors propose the presented solution implementation in the form of a device for autonomous mobile platforms control based on the FPGA. This will allow increasing performance of such platforms and reliability of the obtained results. 
Tanygin M. O., Alshaea H. Y., Dobritsa V. P. Evaluating buffer memory organization impact on the message source detection procedures speed. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/22f/Tanygin_Alshaia_Dobritsa_full.pdf Rather strict requirements to the control cycle duration are being laid in certain types of information systems, such as mobile objects control systems, robotic systems and other realtime systems. Thus, the bit capacity reduction problem of messages transmitted between controlling, monitoring, switching and executing devices is urgent for them. One of the approaches to this is size reduction of the additional service information fields, intended for data integrity and authenticity control. The purpose of the work consists in obtaining numerical dependencies between the required buffer memory volume of the receiver and the execution speed increasing of analysis operations, as well as determining conditions of the memory organization option, being under consideration, application.
The authors established the relationships between the probability error value of the data placing in the receiver buffer and the number of interacting devices, the buffer memory size, and the length of the fragmented message. The article demonstrates that with buffer memory organized as isolated areas, the speed of memory attribute analysis increases proportionally to the length of the fragmented message transmitted between the source and receiver.
The article shows that with a small number of interacting devices, buffering messages from various sources in isolated memory areas can increase the speed of analysis of attribute information by a factor determined by the fragmented message length. The ratios between the buffer size and the interacting devices number were determined, which reduced the probability of errors in data placement in the buffer up to a value not exceeding 0.1. 
Solomatin M. S., Mitrofanov D. V. Biometric authentication methods application for automated control systems employing keyboard handwriting. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/8b8/Solomatin_Mitrofanov_rus_4_.pdf Information technologies development in many areas of human life activity led to the necessity of automated systems for any process control. The task of information protectiveness, which enters, processes and stored in these systems, becomes uptodate as well.
Earlier, it was noted in the works that, in our opinion, application of the intellectual detector of the information protecting system in the automated control systems, was uptodate.
One of the intelligent detector subsystems is the authentication subsystem within the information system. Let us take a closer look at the biometric authentication. These systems are based on unique biometric specifics of the particular person. They can be divided into dynamic ones, which are subjected to changes with time, and static, remaining unchanged.
They can be divided into dynamic, which are subject to change over time, and static, which remain constant.
With authentication in the automated control system, we suggest employing user’s keyboard handwriting, which refers to the person’s dynamic characteristics.
Under the keyboard handwriting we understand a set of dynamic characteristics of the working with the keyboard. The standard keyboard allows measuring the following timing characteristics: the time of holding the pressed key and the time interval between keystrokes.
With this authentication technique employing there is no need to purchase extra expensive equipment. It becomes possible to read user’s dynamic characteristics, using a conventional keyboard that comes with a personal computer, and special software.
At present, three basic authentication algorithms based on the keystroke handwriting are being employed. These are analysis while password entering, analysis, based on entering extra text fragment or phrase, and constant covert monitoring. Each of the algorithms has its pros and contras. System development complexities, operation time, and requirements to the computer speed can be highlighted as the common differences.
Operation of each algorithm is based on comparison with the reference behavioral model.
During operation in the system training mode the user enters certain test phrases, which were prepared in advance and should be changing with the with the passage of time. The text phrases selection is an important stage, since it is necessary to collect sufficient amount of statistic information close to real operation.
After the learning mode, the estimates calculated based on statistical information are compared with the reference ones during the period of the system normal operation at the stage of identification. On their basis, a conclusion is made on the keyboard handwriting parameters match or mismatch.
When statistical data obtained in the course of work differs from the reference behavioral model by more than the value set by the protection system, the user gets a refusal to work, and protection system generates a warning message.
Thus, in our opinion, the user authentication application in automated control system employing the keyboard handwriting is prospective. 
Shavnya R. A. Mathematical model of icecovered wires galloping phenomenon. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/7f9/SHavnya_rus.pdf The article considers the problem on aeroelastic fluctuations of power transmission line icecovered wires under the wind loading (this phenomenon is also known as wires galloping). The sought quantities are the generalized coordinates of the problem: the coefficients of the approximating functions of the Ritz method and local displacements. A rigid connection between cross section of the ice and cross section of the wire is assumed. It is regarded also that while moving the wire cross section remains in the same plane. The equations describing the process dynamics are being obtained using the D’AlembertLagrange principle equations. The summarizing system of nonlinear differential equations, obtained by grouping the terms at variations of work and latent energy, describes the process dynamics. The system should be integrated numerically using appropriate methods (Runge–Kutta, linear multistep methods in case of high stiffness of the system, etc.). Initial conditions for the dynamics problem integrating may be obtained from the solution of the statics problem. The equations for the static problem can be obtained by excluding all inertial terms (terms with a time derivative) from the equations of the dynamic problem. The problem of statics is also being solved numerically, for example method of continuing by the parameter. The phenomenon described in the article is similar to the aviation flutter phenomenon, and, correspondingly, the described model with certain addons can be applied to solve this type of problem. Besides, the model of the elastic tensile wire, described in the article, can be employed in other tasks with tether systems (aircraft fuel hoses, space tether systems, etc.). 
Kriven G. I., Makovskii . V. On damping properties whiskered layer of modified fibre composites. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/63c/Kriven_Makovskiy_rus.pdf In this work, for the first time, the effective dynamic properties of a whiskerized layer in modified composites are studied taking into account the structural characteristics of the interphase layer – the length of whiskers, the volumetric content of whiskers, and their mechanical properties. In the case of pure shear along the whiskers, the effective dynamic properties of the interphase layer obtained by the threephase method and the Reuss method are estimated. In the calculation, we use two types of interfacial matrix: epoxy and viscoelastic polymer at temperatures below the glass transition temperature. Comparison of the obtained plots indicates the effect of a significant increase (by about an order of magnitude) of the effective loss modulus of the whiskerized layer if a viscoelastic polymer is used at a temperature below the glass transition temperature instead of an epoxy matrix. We will also show that an increase in the stiffness of whiskers has a positive effect on the effective characteristics of the interfacial layer, however, we note that this effect manifests itself only at very low volume fractions of the binder in the layer, in the rest of the range the effect is not so pronounced. high effective dissipative properties are realized, which opens up prospects for modeling and predicting modified fiber composites with abnormally high damping properties at the same time sufficiently high mechanical characteristics.
Note that the use of a more accurate procedure for calculating the effective properties, based on the threephase method, gives somewhat large values for the effective characteristics of the loss modulus, but does not fundamentally change the dependence for the loss modulus. It is important to note that the proposed new procedure for modifying a fiber composite leads to a significant increase in the effective loss modulus, when the effective loss modulus can be significantly increased in comparison with modified composites obtained on the basis of only an epoxy matrix and even in comparison with the loss modulus of the epoxy matrix itself (more than 40 times compared to the loss modulus of an epoxy matrix). At the same time, we note that the effective mechanical properties change insignificantly, and all the useful characteristics and features of the modified fiber composites remain invariably high. 
Filimonov I. A. Experience of developing personal bibliographic retrieval system, oriented on specific area of scientific or engineering knowledge. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/5a9/Filimonov_rus.pdf The article regards a case of personalized bibliographic retrieval system, as well as the examples of its application. The system is accommodated with the resources of the AI Corpus scientific publication, established at the Pole Allen Artificial Intelligence Institute. It complements such retrieval systems, as Google, and by engaging of certain open components can be extended by the functions of searching, referencing and analyzing of a higher level. The author proposes an approach, allowing perform a twostage information retrieval, i.e. by the search in the Global Information Bank, and thereafter by the fine search within the boundaries of the information asset being retrieved with regard to the special areas of the system user interests.
To clarify of the problems of this article, a partial classification of informational systems by the nature and role of the informational retrieval being performed in them was proposed. The basic requirements to the implemented system were formulated. A technique for scientific documents passports cataloguing was proposed. The author performed comparative analysis of the implemented system with the generalpurpose retrieval systems. Systems of information analysis services for a specialist in the area of software engineering are the research objects, dedicated to the problem under discussion. Physical purpose of the study consists in implementing experimental individualized bibliographic retrieval systems for both scientific and technical workers. The implemented system can be employed as well by the scientific and technical personnel for search, selection and analysis of scientific documents in the field of aerospace engineering. 
Simonov A. S., Zhabin I. A. Fault tolerance insuring technique for communication network of multidimensional torus topology. Trudy MAI, 2020, no 114, http://mai.ru//upload/iblock/799/Simonov_ZHabin_rus_eng_.pdf The article describes a method for fault tolerance ensuring of a communication network with a multidimensional torus topology, tested while developing the Angara highspeed interconnect router. The highspeed data transmission is associated with a number of difficulties that should be overcome by the hardware designer to achieve acceptable fault tolerance. Problematics of the issue becomes especially acute with an increase in the number of nodes in the system, since the probability of failures is greatly enhanced with expansion in the number of connections.
The work on the fault tolerance ensuring was performed in the following areas:
– quality improving of the transmitted signal by parameters finetuning of the highspeed transceivers;
– automated control of the parameters of the signals eye diagram and optimal parameters selection of the transmitting and receiving sides of the data transmission channel;
– developing a faulttolerant link integrity control algorithm with the ability of the damaged data retransmission;
– developing a data flow control mechanism to control the credit information of the virtual channels;
– developing network layer algorithms for network state monitoring, and quick routing tables rebuilding.
The algorithms and mechanisms described in the article continuity ensuring f the transmitted data flow and their guaranteed delivery over the communication lines between the nodes, exclusion of losses, duplications and distortions of packets during transmission. The conducted measurements have shown that the bit error rate (BER) was about 1012, which corresponded to the permissible values.
The methods described in the article allow obtaining the availability factor of more than 0.99 for large computing systems. At present, they are implemented in the equipment of the serially produced Angara network equipment, and are also widely applied in the design of the second generation Angara high speed interconnect router. 
Dobryshkin A. Y., Sysoev O. E., Sysoev E. O. Effective test benches for studying natural vibrations of open cylindrical shells and plates. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/5bf/eu3x3irzb3eunv15jztvqycnjwdabk3b/Dobryshki_Sysoev_Sysoev_rus.pdf A need for experimental test benches, with which one or several parameters can be measured with high accuracy, arises for conducting tests of thinwalled shells. One of the most significant factors is exclusion or minimization of measurement errors. The purpose of this work consists in identifying a new regularity able to eliminate or physically reduce the calculation error when determining numerical oscillations characteristics of the thinwalled open shells of various curvatures. It was confirmed in the course of the research that a significant number of factors affect the accuracy of certain characteristics of the oscillatory process. Description of all physical laws, affecting measurements accuracy while experimental set up, touches on a significant time period. Thus, on the assumption of the conducted study a technical device, named a test bench, was manufactured in the course of this work. Test benches allow significant measurement quality increase. A test bench for contactless study of natural and forced oscillations of open cylindrical shells was developed in the engineering structures laboratory of the KomsomolskonAmur State University. This test bench is metallic and rigidly attached to the base. Its small size allows measuring numerical characteristics of thinwalled open shells vibrations with high fidelity while measuring their width, height and curvature, as well as mounting methods. The studies aimed at revealing effective devices improving measurements quality, were conducted for its creation.
The scope includes all thinwalled shells employed in aerospace technology, submarines and ground structures. In the course of shell structures operation accidents occur, sometimes with casualties. This circumstance necessitates improvement of technical and scientific aspects of calculation, as well as mathematical and physical models. Experiments setting and conducting for confirming and correcting the developed mathematical models is an integral part of these studies. Since human casualties take place while shells operation, the studies in this area should certainly be continued. Flights of spacecraft and other delivery vehicles, for which the shell is the only possible structural solution, make relevant the studies in the field of shells vibrations. 
Arutyunyan A. M., Kuznetsova E. L., Fedotenkov G. V. Plane unsteady contact problem for a rigid stamp and an elastic halfspace with a cavity. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/e73/Arutyunyan_Kuznetsova_Fedotenkov_rus.pdf Plane nonstationary contact problems are being considered for absolutely rigid bodies with rectangular sections in plan (stamps) and an elastic halfspace with recessed cavities of arbitrary geometry.
The problems setting includes the equations of plane motion of an elastic medium (Lamé’s equations), Hooke’s law, Cauchy relations, zero initial conditions, boundary conditions of the free edge on the boundary of the internal cavity in a halfspace, conditions of contact between the boundary of the halfspace and the stamp. To close the problem, the equations of translational motion of the centers of mass of the stamp are added. Cases of free slip and rigid adhesion are considered as contact conditions. We assume that outside the contact zone, the surface of the halfspace is free of stresses. All equations and relations of the mathematical formulation of the problem are written in a Cartesian rectangular coordinate system.
At the initial time instant, a vertical load is applied to the stamp with a predetermined law of changing in time, which resultant is passing through the center of mass of this body.
The dynamic work reciprocity theorem is used to solve the problem. Application of the reciprocity theorem of works leads to the twodimensional boundary integral equations, which kernels of are the transient functions. These functions represent solutions for a nonstationary problem for an elastic plane under the impact of concentrated mass forces. Integral Laplace transforms in time and Fourier transforms in spatial coordinates are used to build a solution to this problem.
The direct boundary element method with discretization in time is used to solve the twodimensional boundary resulting integral equations. The linear interpolations in time herewith are used for displacements, and piecewise constant approximations for stresses. Special quadrature formulas based on the canonical regularization method are employed for singular integrals calculation.
As the result, a statement is presented and a method for solving new plane nonstationary contact problems for absolutely rigid stamps and an elastic halfspace containing a recessed cavity with a smooth boundary of arbitrary geometry is developed. A resolving boundary integral equation is built and its discrete analogue is proposed. 
Baklanov A. V., Krasnov D. S., Garaev A. I. Studying torch parameters behind the atomizer with jet and swirled fuel feeding. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/23b/Baklanov_Krasnov_Garaev_rus.pdf The discharges level of deleterious contaminants concentration in combustion products is one of the basic parameters, characterizing the combustion process effectiveness in combustion chambers.
The article being presented considers the impact of fuel feeding technique, realized in the atomizer, on the above said parameter variation. One of the considered atomizers ensures jet feeding of the fuel with the perforated atomizer, while the other one ensures swirled fuel feeding by the swirler integrated into the fuel passage. Basic geometrics of the atomizers, such as swirler sizes, the number of blades and the outlet nozzle diameter, are presented as well.
The flame tube simulator design, in which the tested atomizer is being placed, is regarded. The article presents the test bench installation designed for the atomizers testing in the flame tube simulator, as well as modes at which these tests were conducted. The results were obtained in the flame tube simulator with installed jet atomizers and atomizers with the swirled fuel jet. The analysis, by which results the inferences on the jet atomizers application efficiency were drawn, was performed. According to the performed studies, parameters of the atomizer with swirled fuel jet are being characterized by the presence of high values of CO and CH level in the combustion products, which is explained by the low mixing quality of fuel with air and, consequently, extremely low effectiveness of the fuel combustion. The atomizer with jet fuel feeding demonstrates low CO and CH values, which is indicative of the good quality of fuel mixing with air and high efficiency of combustion process organizing. 
Gorelov S. L., Nguyen V. L. Rotation body of minimal aerodynamic drag in hypersonic rarefied gas flow. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/e5d/Gorelov_NguenVanLam_rus.pdf Equations obtained from local models gained wide proliferation for assessed calculations of forces acting on a body while its highspeed motion in a gas. The basis of these models is the assumption that each element of the body surface interacts with the gas flow independently from the other segments of the body, and the force acting on it depends only upon the element orientation relative to the motion direction. Such representation of the forces acting on the bodies in the hypersonic flow allows rather simple solution of variation problem on searching for the shapes of the bodies of minimal drag.
The drag force in the hypersonic rarefied gas flow for a rotation body with powerlaw generatrix is being computed based on several local models.
In this case, the drag factor value is being computed analytically. The variation problem is being reduced to the problem on the extreme value of the onevariable function, i.e. the degree of the rotation body generatrix.
Apart from the classical Newton aerodynamic problem, the problem of a rotation body with minimal drag for a freemolecular hypersonic gas flow is beings also solved as well. To determine the degree in the rotation body generatrix at the arbitrary Reynolds numbers the wellknown local model for the approximate determination of pressure and friction on the body surface in a hypersonic rarefied gas flow is being used. In all cases, the problem is being solved for bodies of arbitrary elongation.
At Reynolds numbers tending to zero and for large elongations, the degree in generatrix of the rotation bodies of minimal drag tends to 2/3, and for Reynolds numbers tending to the infinity it tends to ¾. This is consistent with the wellknown results for the freemolecular flow mode, as well as for the continuous medium (Newton formula), respectively. 
Kartovitskiy L. L., Levin V. M., Yanovskiy L. S. Analysis of gasdynamic compression based on modified Crocco pseudoshock model. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/b75/Kartovitskiy_Levin_YAnovskiy_rus.pdf The article proposes a Crocco pseudoshock model modification allowing evaluate parameters distribution while supersonic flow transition to the subsonic flow in the structure of the mathematical model of the supersonic ramjet power plant with the deceleration zone.
Numerical simulation of the gasdynamic parameters in the of the prechamber diffuser (isolator) channel of a specified geometry was performed. As part of modified Crocco’s model, the pressure distribution can be approximated by the orthogonal Laguerre decomposition
where coefficients b_{j}
are determined by the numerical solution of the variation problem of minimizing entropy producing. For the adequacy testing of the modified Crocco pseudoshock model, experimental data was obtained from experimental testing of a dualmode ramjet engine combustor with a prechamber diffuser. Verification of the calculated pressure distribution along the pseudoshock development zone using the principle of minimum entropy producing was performed by comparing with the generalizing experimental dependence. A certain discrepancy between the experimental and computed data can be explained by no accounting for the entropy producing processes, as well as by the effect of the heatmass transfer processes on the parameters changes in the pseudoshock structure. The original Crocco model employs the condition of constancy of the total pressure p* = const, which means
. This assumption does not produce an adequate result. Thus, the solution of the original Crocco model for the compression zone leads to the values of M>2.0  2.5 in the cross section of the dissipation layers confluence. From physical estimation, the Mach number should approach 1.0 in the confluence zone of the dissipation layers, which can be achieved by modifying the Crocco pseudoshock dissipative model. The model is intended for parametric studies as a part of the ramjet mathematical models. 
Timofeev P. M. Methods comparison of returning the first stage of the reusable rocket. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/41f/Timofeev_rus.pdf The article considers in detail the basic types of the first stages returning, such as returning along the ballistic trajectory to the launching site or another prepared site through the reusable engines, operating on the onboard fuel reserves (vertical landing); landing, employing parachutejet systems; the first stage returning employing the aerodynamic quality, lifting wings and a turbojet engine.
The main disadvantages of each method of the first stages returning were considered in detail. Comparison of the method of the first stage returning employing the aerodynamic quality, lifting wings and a turbojet engine with the method of returning along the ballistic trajectory through the reusable engines operating on the onboard fuel reserves was performed. Both stages had equal remaining mass of m_{r} = 0.38; specific thrust parameters of r_{sp} = 300 s for the turbojet engine; flight range of L = 300 km; and initial return speed of 
Maklashov V. A., Piganov M. N. Mathematical Model of Active Jamming Station Functioning. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/84d/Maklashov_Piganov_rus.pdf
The article regards a model of the onboard active jamming station (AJS) functioning, algorithms for penetrating jamming suppression in a «compensation» way, compensation and modulation control algorithms while the penetrating jamming suppression in conditions of incomplete information on the radio waves propagation channel characteristics.
The AJS generalized mathematical model describes the operation of the radio waves radio channel along the object of the station location, the received useful signals and penetrating jamming. The following assumptions were accepted while the model developing:
— radio channel of the radio waves propagation is linear, since nonlinear electrophysical effects, caused by the object surface irradiation are smallish and can be neglected due to relatively small values of the AJS radio signals
— radio wave propagation along the object from transmitting to the AJS receiving antenna occurs over a number of ways (a multipath propagation character);
— the number of ways, electric length, damping and phase incursion are a priori unknown, and changing rapidly;
— while radio waves propagation along the object of the AJS accommodation, it is being delayed at each way of propagation proportionally to its length, which leads to the uncontrolled changes of the penetrating jamming phase and amplitude.
The article presents equations describing time and frequency properties of various realizations of the useful receiving radio signal. It is shown that amplitude and initial phase of the received radio signal fluctuate randomly due to the changes of radio waves propagation conditions.
When mathematical model developing of the penetrating jamming suppression mechanism, the fact of the low efficiency of classical algorithm, stipulated by the fact that compensation occurs at the very high carrying frequency of the radio wave radiated by the AJS, was accounted for.
The authors proposed to reduce the effect of negative facts on the effectiveness of penetrating noise suppressing by synthesizing a compensation oscillation from the components of the AJS’s emitted oscillation at frequencies arising due to its additional modulation. For this, penetrating jamming was separated into such components. To eliminate spectrum distortion of the receiving signal, when the filter extracted the jamming components, a criterion for modulation frequency selecting was introduced. This allowed utilizing a system of the 2n bandpass filters separating the penetrating noise into the components. To isolate the receiving radio signal from the received mixture containing penetrating noise, the authors proposed to employ a separate filter with central frequency matching the tuning frequency of the AJS receiver. The output signals are converted by a quadrature (synchronous) detector to obtain complex envelopes of interference in each filtering channel.
The article proposes the algorithm for synthesizing a complex envelope of the compensated oscillation from the complex envelopes of frequency components of the penetrating jamming. Compensating oscillation is being restored from the complex envelope by modulating harmonic oscillation in the quadrature modulator. A generalized structural diagram of the compensation method for the penetrating jamming suppression is described.
The algorithm for compensating oscillations forming was presented in the matrix form. Equations for the generalized linear algorithm for forming both the compensation oscillation and a value of power of the noncompensated residue of the jamming were suggested. This algorithm can be implemented in digital form using an ADC and a signal processor.
To optimize parameters of the proposed algorithms, the authors propose to develop a computer mathematical model of the penetrating jamming suppressing process at the input of the AJS receiver. 
Gusev S. N., Miklin D. V., Moroz A. V., Sahno I. V., Sherstuk A. V. Seminatural modeling of digital data transmission channel in the ultrasonic wavelength range. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/2ff/Gusev_Miklin_Moroz_Sakhno_SHerstyuk_rus.pdf The presented work describes the laboratory installation for seminatural modeling of the data channel in the ultrasonic wavelength range. Seminatural modelling is understood as a study of a system on the simulating installation with real equipment elements inclusion into the model structure (in this case it is software algorithmic support of the digital receivertransmitter track). The laboratory installation is meant for transmission line simulation of radar and optoelectronic information to the data receipt and processing point at the design stage. The purpose of the work consists in transmission quality improving of the spacecraft trajectory signal by the radar with the synthesized aperture antenna (SSAR). In the following, the SSAR laboratory breadboard will be developed, which will include the breadboard of ultrasonic SAR and ultrasonic data transmission system (UDTS).
The installation includes the hardware (PC, amplifiers, power supplies, ultrasonic sensors) and the software part. To create the Doppler effect in the channel, the possibility of linear or nonlinear (with or without acceleration) movement of the transmitter or receiver was realized. The receiver is implemented based on software signals reception and processing.
The result of the work is the developed laboratory installation of the OSPA integrated into the SAR layout based on the location acoustic complex, which allows obtaining the quality assessment of information packages transmiting.
The laboratory installation can be applied in scientific research and training when studying radio engineering disciplines. 
Aung K. T., Babaitsev A. V. Studying geometrics impact of cylindrical shell under pressure clamped between rigid plates on the contact zone width. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/d1c/3AungCHzhoTkhu_Babaytsev_rus.pdf The presented work studies the impact geometrics changing of the elliptical crosssection cylindrical shell under pressure clamped between two rigid plates on the contact zone width. The study is being performed by the analytical modelling of the method with Wolfram Mathematics software. The dependence of contact zone width between the shell and rigid impediment changing on acting pressure was obtained in the course of analytical modelling. The study of major and minor semiaxes impact, as well as the shell thickness on the contact zone width changing depending on the acting pressure was being performed for the obtained solution.
The performed modelling results revealed that the minor axis increase entailed the contact zone reduction, while the major axis increase resulted in the contact zone width enhancing. The shell thickness increase reduces the contact zone of the shell with the rigid plate. Analytical dependencies of the contact zone width on the geometric parameter were obtained by approximation for studying the process of the contact zone width. Analytical alignment method was used as approximation. The obtained functions were being differentiated to determine the speed and speedup of the contact zone width change while changing each of geometrical parameters. 
Nagornov A. Y. Flutter of the unmanned aerial vehicle from composite materials with WingTail Boom Configuration. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/e35/8Nagornov_rus.pdf A mathematical model for calculating the flutter of a composite unmanned aerial vehicle (UAV) with a wingtail boom configuration is presented. The mathematical model is built in the Nastran software with a finite element method (FEM). The elastic model of the device is represented by a set of beams connected through flexible joints. The aerodynamic model is constructed using the doubletlattice method (DLM). To obtain the critical flutter speed from the rotational natural frequency of the control surfaces in the finite element model varied stiffness elements «CELAS2» modeling actuators of the controls. The design features of the device under study are considered. Calculations of flutter shapes are presented and the results are analyzed.
From the results obtained, it can be concluded that a UAV with a wingtail boom configuration is subject to flutter of control surfaces, which is due to weight unbalancing of the controls.
The considered design scheme of the UAV has low natural frequencies of tail due to the elasticity of the tail beams and the wing, as well as the elasticity of the wing joints in the fuselage.
NX Nastran software package can be successfully used to calculate the flutter of composite aircraft. The advantages of the finite element method implemented in NX Nastran include the possibility of high detail of the computational model in order to more accurately simulate real aircraft structures. However, when verifying a computational model developed using FEM, difficulties may arise: the higher the model detail, the more difficult it is to correct the constructed model based on the results of the experiment. 
Nguyen T. N., Podstrigaev A. S., Leonov I. E. Mathematical model of signal modulation type recognizing algorithm in the autocorrelation receiver for radio engineering monitoring means. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/97e/NguenCHongNkhan_Podstrigaev_Leonov_rus.pdf The article presents a mathematical model development of the algorithm for recognizing the signal modulation type (linearfrequency modulation (LFM), phaseshift keying (PSK), and simple ones) in the autocorrelation receiver. Analysis of the algorithm implementation possibility on the FPGA basis is presented as well. Mathematical model adopts the assumption that the transfer gain of the autocorrelation receiver equals to one, and various distortionless filters pass the signal loworder components at the multipliers outputs. The article presents analytical description of the LFM, PSK simple signals processing in the autocorrelation receiver. Based on the developed model, the applicability boundaries of the algorithm were substantiated: 1.5 MHz bandwidth for the highpass filter; up to 50 MHz for the bandwidth filters; and up to 100 KHz for lowpass filters. The time delay in the correlator of the autocorrelation receiver herewith lies within the 10 ns to 1000 ns range. Besides, based on the developed model, the effect of the delay time on the signal detection characteristics, which allows defining the optimal delay time for tuning the autocorrelation receiver while effective radar signals detection, was evaluated. Sequences of actions for analyzing the possibility of the developed model FPGAbased realization were proposed. The algorithm resourceintensity evaluation was performed. Evaluations of the resourceintensities of the filter system and spectrum obtaining devices, realized on the fast Fourier transform basis, were conducted. The evaluation result revealed that no less than 900 000 logic gates were required for the entire algorithm implementation. The appointed requirements are feasible for the majority of modern FPGAs, such as FPGA on the VU095 chip of the Virtex UltraScale family, which contains 1.176 million logic gates.
These requirements are true for most modern FPGAs. For example, it can be used the FPGA VU095 of the Virtex UltraScale family, which has 1.176 million logic gates. 
Markarian A. O., Churkov I. S. Control tasks in the decisionmaking system in case of failures of automated workplaces. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/a99/12Markaryan_CHurkov_rus.pdf Automated workplaces are an integral part of any enterprise, including those in the aerospace industry. Errors that may occur at the automated workplace exert a negative impact on the activities of an individual company, as well as on the industry as a whole. At present, there are solutions to this problem, but they are being realized manually using software utilities to rectify some of the identified problems.
The purpose of this work consists in creating the structure of the decisionmaking system in case of automated workplaces failures and the formulating the decisionmaking criteria.
The following errors and failure factors were revealed while the errors statistics analysis process. The conducted studies allowed developing a mathematical model of the decisionmaking system and its subsystems.
The effectiveness criterion is optimization of the working places users activities by reducing the time spent the failures detection and elimination.
The following results were obtained.
The study of the failure statistics, allowing identify and describe statistical dependencies in the form of a mathematical model, was conducted.
A conceptual model of the decisionmaking system in the event of automated workplaces failures, consisting of four interconnected subsystems, has been developed. Management tasks for each of the subsystems were formulated. This is the scientific novelty of the presented results.
The system functioning allows ensuring the smooth operation of the automated control system, or reduce to a minimum the amount of the time spent on solving the problems of failures, which defines its practical meaningfulness. 
Pogosyan M. A., Vereikin A. A. Automatic landing systems of aerial vehicles: analytical review. Information support. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/9e6/13Pogosyan_Vereykin_rus.pdf The article demonstrates that the basic problematic areas of aerial vehicles (AV) automatic landing systems (ALS) developing are information support and automatic control.
The purpose of the work being presented consists in studying the issues of information support, actual for the ALS of both manned and unmanned aerial vehicles, identifying the basic problems, hindering the AV ALS development with regard to to the information support and technical solutions, which can be employed while the AV ALS developing.
The article considered radio and satellite information support systems for automatic landing (AL) ensuring, technical vision systems (TVS), as well as a number of other systems. The authors suggested a multilevel classification of tools for the ALS information support.
The ALS radiotechnical information support systems, capable of ensuring the ALS prior to the instant of the AV landing on the runway, assume high material costs on both installation and operation. Satellite navigation systems (SNS) with functional augmentations seem to be their alternative. However, in the case of largescale warfare the satellite signal accessibility remains in question. Application of systems, ensuring autonomous navigation, such as TVS, correlationextreme systems, etc., which also, in their turn, are not free from disadvantages and can depend significantly on the external conditions, can be the wayout to the situation.
Inertial navigation system (INS), corrected by the information received from the satellite navigation system with functional augmentation (differential navigation) and radiotechnical navigation system (as a backup source of information), may be suggested as the core of the AL information support.
While the ALS designing, It can be recommended to develop information support based on the complex information processing by the following systems: INS, the ILS radio beacon system, global SNS with additional augmentation, and TVS. When designing the ALS for military purpose aerial vehicles, we recommend information support developing based on the computer processing of the information from the following sources: : INS, landing radar, global SNS with additional augmentation, VS, correlationextreme navigation system using onboard radio systems.
The nearterm prospects for the ALS development with regard to information support are associated with employing information received from the INS, radio navigation systems and global SNS with additional augmentation. The mediumterm prospects of the ALS are associated with the widespread application of the capabilities of information complexing from external sources of various physical nature (mainly SNS, VS and correlationextreme navigation systems using onboard radio systems) and increasing the accuracy characteristics of onboard INS. The longterm prospects of ALS are associated with autonomous navigation systems employing capable to operate in nondeterministic conditions, including the resources of control degradation. 
Tabakov E. V., Zinina A. I. Automation of operation normativity analysis of the spacecraft onboard computer. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/814/14Tabakov_Zinina_rus.pdf The main block of the spacecraft control system (CS) is the onboard computer. In the process of the CS operation, it executes the onboard software modules (OSM), which define its behavior. Thus, correctness of the entire CS functioning depends on the onboard computer operation normativity. That is why thorough checkup of its operation in all possible operation modes on the test benches is of utter importance. Normativity control technique is the spacecraft telemetry information analyzing with regard to the signs, which characterize various aspects of the onbooard computer functioning and the OSM operation.
The existing analysis technique lies in decryption of the initial binary file of telemetric information (TMI) by the special program tool. As the result of its operation, a new text document, which content is presented in the form recognizable by a human, is being formed. Further, personnel of the enterprise extract the required information and analyze the obtained data. Despite of this approach simplicity, it has a number of significant disadvantages, such as:
Thus, automation of the detailed analysis performing presents interest. The similar work was already being conducted, though only as a part of the normativity control of the program modules execution times. The purpose of the presented work is development of the approach created earlier by adding the analysis as regard to the criteria characterizing the onboard computer operation.
The source data for the new algorithm represents normative values of the signs, which characterize the onboard computer state for its various operating modes, the cyclogram information and TMI. The analysis procedure itself is proceeding in three stages. These are:
Special program tool for performing automated analysis was realized based on the proposed algorithm. Its special feature consists in the possibility of operation with both graphic interface (manual mode) and automatic mode (at interaction with the existing automation tools). As the result of this work, the analysis of the onboard computer functioning while conducting test bench testing has been significantly simplified. 
Zaretsky B. F., Kurmazenko E. A., Proshkin V. Y. Spacecraft crew life support control: systems approach. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/ef1/15Zaretskiy_Kurmazenko_Proshkin_rus.pdf Automated control system (ACS) of life support systems complex (LSSC) is being described from the system approach position. The ACS and LSSC constituent parts are being regarded in aggregate and interaction between each other. Accounting for external surroundings, such as systems operating in conjunction with the LSSC, environment, the spacecraft sealed bay, crew and groundbased flight following services, is mandatory.
The effectiveness of the LSSC ACS developing and functioning is being defined by the great number of controversial criteria. The article suggests splitting all criteria into the three groups, so that criteria inside each group would not contradict each other. Three generalized global effectiveness criteria (GEC) were formed on this base. They are
– survivability, incorporating local criteria (LC), such as resource, reliability, etc;
– cost value, incorporating the LC such as energy consumption, weight, servicing time, material costs, etc;
– comfortability, incorporating the LC such as live environment parameters, interaction with crew, accommodation, operating modes, etc.
While extremum searching per each GEC, restrictions are imposed on the two remaining GECs.
The systematic approach sequence while the ACS developing:
– analyzing connections with higherorder system and external surroundings;
– analyzing the variety of effectiveness criteria, and developing the GEC;
– creating hierarchical structure of effectiveness criteria;
– system decomposition by the subsystems of less complexity; optimal solution search for subsystems in the LC structure, following from the hierarchical structure;
– optimal solution search for the entire complex system with ensuring extremum on GEC.
The first and second rank of importance criteria, such as sustainability, cost value and comfortability, were considered in the hierarchical structure of each GEC.
The suggested approaches to ACS for LSSC are realized while the new test bench design. The test bench is universal, and adapted (with minimum necessary changes) for refinement and maintenance of any life supporting system (based on physicchemical regeneration processes) from the LSSC content. The test bench is described as applied to the oxygen regeneration system. The “ElectronVM” system is based on the oxygen obtaining by the water electrolysis technique, and it has been functioning onboard the International space station since 2000.
Simulation modeling of the ACS functioning, based on the “MARS500” data, was conducted as a part of the suggested approach presentation.
The considered approach presents a technique for developing the LSSC ACC for a manned space object. 
Dorozhko I. V., Osipov N. A., Ivanov O. A. Technical state prediction of complex technical systems by the Berg algorithm and Bayesian networks. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/4ea/16Dorozhko_Osipov_Ivanov_rus.pdf The purpose of the presented work consists in predicting the diagnostic characters changes and correlating them with possible type of technical state for undertaking preemptive measures while complex technical systems diagnosing.
The approach being proposed and models are based on the basic concepts and relations of reliability theory and technical diagnostics of systems. The source data represents information on the reliability (failure rate of elements, structural and logical schemes) of complex technical structures and diagnostic models linking the types of technical states and diagnostic features. The sets of conditional probabilities or distributions density are being pointed for the causeandeffect relationships between types of technical states and diagnostic features, depending of continuous or discrete type of the diagnostic character.
The algorithm for predicting the values of diagnostic features proposed in the article is based on the Berg linear prediction algorithm. It is adapted and studied herewith for the main functional dependencies of diagnostic features. The results of diagnostic characters predicting are considered on the specific examples, and estimates of the forecast accuracy are given. The model based on dynamic hybrid Bayesian trust networks includes discrete and continuous variables, which describe the causeandeffect relationships of types of technical states and diagnostic features, as well as the relationship of blocks (elements) in terms of reliability. The results of the logicalprobabilistic inference indicate that the decision on the type of technical condition of a complex technical structure changes significantly when accounting for the forecast estimates of diagnostic characters.
The proposed scientific and methodological approach can be employed to create diagnostic software for modern complex technical structures with artificial intelligence elements.
Mathematical models of diagnostics considered in the article account for the connections types, elements reliability, as well as dynamics of technical states types and their relationship with diagnostic features, which can be both continuous and discrete. the Technical condition predicting allows implementing the proactive management concept, parry possible failures, changing the operating modes in advance, switching to backup elements, etc. 
Pankratov I. A. The fastest reorientation of the spacecraft's circular orbit plane. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/af7/17Pankratov_rus.pdf The article considers the problem of the fastest reorientation of the spacecraft’s circular orbit plane in quaternion formulation. The spacecraft orbit terminal position is not being fixed in the orbit plane. Control, i.e. the acceleration from the jet thrust vector, orthogonal to the orbit plane, is a piecewiseconstant function, limited in absolute value. The spacecraft center of mass motion is described by the quaternion differential equation of orientation of the orbital system of coordinates. The article presents an original genetic algorithm, developed by the author, for finding the number of active section of a spacecraft movement and their duration. While this technique application there is no need in searching for the initial values of the unknown initial values of conjugate variables. To solve the Cauchy problem at one of the algorithm operation stages, a wellknown partial solution of the quaternion differential equation of orientation of the orbital system of coordinates was used. Examples of the problem numerical solution are presented. A case, when the difference between initial and final orientations of the spacecraft orbit is units of degrees in the angular measure is considered. The final orientation of the spacecraft orbit plane herewith corresponds to the orbit plane of the satellites of the Russian GLONASS orbital grouping. Graphs of components of the quaternion of orientation of the orbital system of coordinates, angular variables, describing orientation of the spacecraft orbit plane, and optimal control are plotted. Specific features and regularities of the optimum reorientation process of the spacecraft orbit plane are established. 
Bortakovsky A. S., Uryupin I. P. Routes optimization of continuousdiscrete movement of controlled objects in the presence of obstacles. Trudy MAI, 2020, no 113, http://mai.ru//upload/iblock/fdc/18Bortakovskiy_Uryupin_rus.pdf The objective of the research consists in developing techniques for optimal routes forming of the aircraft flat motion in the presence of obstacles. The problems of aircraft control routes planning and optimizing are being studied currently with increasing intensity. The relevance of these studies is determined by the need for effective automated control of unmanned aerial vehicles (UAV) for various purposes.
The article regards the models of the flat motion of control objects along the specified map with obstacles with various quality functionals. The map represents a connected graph, which arcs correspond to the continuous movements of the object, its vertices correspond to the discrete changes of its state (switches), and the path connecting several vertices of the graph describes the continuousdiscrete nature of the motion trajectory.
The first section considers the control object movement along the rectangular grid. The movement between two grid nodes is either uniform of uniformly accelerated. The movement direction changing in the grid nodes (turn) is considered to be switching. A number of the grid nodes is inadmissible for the movement due to the obstacles contained in them. The problem on minimizing the number of switches, response time or response time with account for the number of switches is being set.
The second section solves the problem on the flat movement optimization of the unmanned aerial vehicle (UAV). The MarkovDubins model was selected as the model of motion. The feature of the response time problem consists in the presence of intermediate conditions, i.e. the points on the map, through which the UAV trajectory should pass. This problem is being reduced to solving an aggregate of MarkovDubins problems with additional finitedimensional minimization.
The third section combines the two problems discussed previously in the first two sections. The UAV rational trajectory is being formed in two stages. Initially, the optimal polyline, i.e. the trajectory of movement on the rectangular grid with obstacles, is being synthesized. Then, the optimal MarkovDubins trajectory is being built «atop» this polyline, and the vertices of the polyline serve as intermediate points for the UAV trajectory.
The result of this work is algorithms, allowing build rational routes of the UAV’s flat movement with many obstacles, such as in the city. It is difficult to solve the optimal control problem under such phase restrictions. Thus, application of the proposed rational control patterns seems righteous. 
Khatuntseva O. N. Is the dynamic chaos a stochastic process in the autonomous systems of differential equations of the Lorenz system type. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/ff2/vinm4krx17odh4qeguz5qv2an75p39wb/KHatuntseva_rus_.pdf At present, there are no stability criteria similar to CourantFriedrichsLewy criteria for systems of autonomous differential equations (SADE). The instabilities, manifesting themselves as a computational chaos, occur while the numerical integration of SADE. Moreover, the time step decrease does not lead to this instability elimination. Commonly, the studies on determining the sensitivity of solutions to the initial conditions setting are being conducted to explain the deterministic chaos phenomenon. These studies demonstrate exponential divergence of initially close solution trajectories, and impossibility of selecting such small computational error to «conquer» the uncertainty in the Lorenz type SADE.
The conclusion is drawn from this circumstance that since the principal difficulties do not allow achieving the necessary accuracy, there is no need to muse about determinism. However, such approach does not resolve the problem of solutions determinism, irrespectively to the possibility or impossibility of obtaining of the information regarding the evolution of the considered system. The issues of predestination in the closed systems, in particular with such closed system as Universe, conjugate with these issues.
The studies conducted in the presented work demonstrate that the deterministic chaos occurring in SADE of Lorenz type may be associated with the stochastic process and is not, in essence, the deterministic chaos for any finite time step.
The article discusses the issues associated with the possibility of turbulence modelling based on the NavierStokes equations via direct numerical simulation technique.
The problems related with the feasibility for modeling of the turbulence on the basis of NavierStokes equations via the direct numerical simulations are also addressed in the paper. 
Baklanov A. V., Krasnov D. S., Garaev A. I. Studying parameters of combustion chamber section with jetinjection nozzle. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/21e/elkwhl750jdhal6g464ajkqbx7803au8/Baklanov_Krasnov_Garaev_rus.pdf Pressure losses, combustion completeness, temperature field unevenness at the outlet and hazardous substances release are one of the main parameters of a combustion chamber. The article presents a fuel combustion technique, in which an air jet is fed along nozzle axis, and the fuel is being inserted into the main flow by means of the radial trickles. The effect of the jetinjection nozzle setting into the combustion chamber section on the above listed parameters changing is being considered to estimate this fuel burning technique. The structure of the bench installation for the combustion chamber section testing, as well as modes at which these tests were being conducted are presented. Equipment, employed for measuring such parameters as flame temperature and concentration of hazardous substances in combustion products was described as well. To perform analysis and comparison of the obtained data, the experiments were conducted with the jet nozzle and the jetinjection nozzle being installed into the combustion chamber section in number of nine pieces. The section represents the 1/14 of the fullsized combustion chamber and consists of the outer and inner cases, and a flame tube with the with a frontend device, in which the nozzles are being installed. The flame tube is bounded by the side cooling walls on both sides. Nine nozzles are being installed in the section. Analysis of the component content (CO, NOx, CH) and combustion products was conducted, and combustion completeness was computed according to the obtained data. From the analysis results the inferences were drawn on the jetinjection nozzle application efficiency, and recommendations were given on the nozzles of selected type installation in the fullsized combustion chamber. 
Budanova S. Y., Krasavin E. E., Nikitchenko Y. A. NavierStokesFourier model options for supersonic and hypersonic flows. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/1a6/i6seav0s9r1djsj6y7tm8yquyjay287v/Budanova_Krasavin_Nikitchenko_rus.pdf The flows of the highdegree nonequilibrium are of considerable interest at present stage of the engineering development. Such flows are being realized, for example, while the hypersonic flying vehicles flowaround, reentry spacecraft, in vacuum installations and other technical devices.
The basic physicomathematical model of a gas medium flow is the NavierStokesFourier (NSF) model. This model is theorybased for weakly nonequilibrium flows, but it can be applied for the flows of a highdegree nonequilibrium. In such flows, the NSF model coarsens the solution. For example, when computing shock waves, the disturbance area is narrowed. The model is short of viscosity. The opposite sign effects are being observed while the gas intensive expansion.
The presented work analyses the processes of the nonequilibrium stresses and heat flows forming at the shock wave front, employing the model kinetic equation (MKE). The hypersonic flow at the Mach number of M_{∞}= 5 is under consideration.
The article shows that the heat flows gradients, absent in the NSE, contribute mainly to the nonequilibrium stresses forming process. The basic factor of the heat flows development are the fourthorder gradients, which are missed in the model as well.
Several options for improving the viscous properties of the NSF model are under consideration. It is known that in the case of multiatomic gases a significant effect can be achieved by accounting for the voluminous viscosity in the equations of nonequilibrium stresses. Besides, the voluminous viscosity coefficient allows computing the temperature of the translational degrees of freedom molecules in the first approximation. Defining the shear viscosity coefficient by this temperature, will improve the viscous properties of the model.
The Stokes’s friction law can be obtained by using the moment stress equation as its strict first approximation. If one accounts for the terms of the second order of vanishing in the equation terms, containing gradients and divergence of the flow velocity, , then the shear viscosity coefficient will take a tensor form. The NSF model with this shear viscosity coefficient describes better the processes of viscosity and heat conductivity.
The article demonstrates that the improved option of the NSF model allows obtaining rather wide area of disturbances on the example density, velocity and temperature profiles in the flat shock wave. The profiles shapes differ slightly from real ones. This, probably, is a consequence of the artificial approach to the model improvement. 
Duong M. D., Gidaspov V. Y. Computational algorithm for calculating composition of combustion products of hydrocarbon fuels in the presence of a condensed phase. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/927/elljufig6o5ai8l07gt845g3sd8ggrou/Zyong_Gidaspov_rus.pdf The article describes the computational algorithm that allows computing the equilibrium composition of combustion products of hydrocarbon fuels in the presence of condensed components. The mixture of combustion products was considered as an isolated system of ideal gas without energy interaction and mass exchange with the environment. Numerical methods and computational algorithms, based on the thermodynamic potentials extremum search, are employed for the thermodynamic equilibrium search. The composition of the combustion products of hydrocarbon fuel in the air may include about 150 possible compounds of chemical elements C, H, O, N, Ar, with condensed phases of C(с) and H_{2}O_{2}(с) among them. The article presents specifics of the algorithm implementation with regard for thermodynamic functions at the temperature of the phase transition T_{p}.
Without this, in many cases, when the temperature value passes through the point T= T_{p}, the monotonous iterative process is disrupted, which may lead to the algorithm divergence. The results of numerical simulation of stationary equilibrium flow of combustion products of kerosene with the air in a Laval nozzle are compared with reference data. The effect of pressure on the composition of combustion products in excess of fuel was studied. Analysis of the computational results and reference data confirms the reliability of the developed algorithm. The impact of pressure (p = 1–100 atm) on the composition of combustion products in an adiabatic reactor with an excess of fuel was studied. It follows from the obtained results, that the condensed phase (p = 1–100 atm.) is a part of the combustion products at the air excess coefficient α < 0.36, the dependence of the soot concentration on the pressure changes qualitatively with the air excess coefficient changing. 
Selim R. S. Eigenvalues of the Squire equation for laminar and developed turbulent boundary layers. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/f21/gsxsy06n2xy7g92qhl5y04v5n5proqhr/Selim_rRamiSalakhSaber_rus_.pdf The stability of the eigenvalue problem for twodimensional laminar and turbulent external flow over a flat plate was numerically studied using the theory of time linear stability. That is, the classical as well as the efficient approach are considered in detail for the eigenvalue problem: two different methods are studied for deducing the spectrum of eigenvalues, namely the finite difference method and the collocation method based on basic functions. The first approach of the physical model discretizing leads to algebraic equations with large matrices that are difficult to solve efficiently, while the second one creates matrices that are usually complete and have a large number of conditions. This problem is being discussed here in the Appendix to the Squire equation, which describes laminar and turbulent boundary layers. The average velocity profile of laminar boundary layers is obtained numerically. The dispersion ratio as a function of the wave number α and other flow parameters for the problem (such as, the Reynolds number) is being defined for two different velocity profiles. The algorithm is realized in Mathematica, and the calculated eigenvalues are being compared between the two different methods.
The linear stability of a small class of engineering problems can be studied by solving the OrrSommerfeld equation. The most famous examples of this are the Blasius Boundary layer and the plane of the Poiseuille flow. While the plane flow of the Poiseuille is strictly parallel, in the first case, an irrational argument relative to the parallel mean flow must be called in, in such a way that the system of stability equations, obtained by substituting small wavelike perturbations in the NavierStokes equations and linearization of the Blasius profile, will be reduced to the OrrSommerfeld equation. A numerical method for solving the OrrSommerfeld spectral equation in a twodimensional boundary layer (β = 0) was studied by the Chebyshev collocation method for laminar and boundary layers. To obtain the spectrum of eigenvalues of the Squire equation for the background field of a developed turbulent boundary layer, a collocation method (pseudospectral) based on Chebyshev polynomials was used. The technique was debugged on the profile of Blasius and Mucker. It is obvious that an increase in the number of Chebyshev polynomials has a significant impact on the accuracy of determining eigenvalues for the Blasius and Miskeg profiles. The impact of Chebyshev polynomial degrees on the accuracy of determining the real and imaginary parts of the eigenvalues of the first mode for laminar and turbulent boundary conditions was considered. 
Krioukov V. G., Abdullin A. L., Nikandrova M. N., Gasilin V. V. Generation of reduced reaction mechanisms for heterogeneous flows in nozzles. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/66c/sd2so2hwo52cpg3bfqzprefd5bloxk46/Kryukov_Abdullin_Nikandrova_Gasilin_rus_2_.pdf Mathematical modeling of chemically nonequilibrium heterogeneous flows in nozzles of both solid engines and directflow engines with solid fuel is an urgent task of rocket engine theory. Such flows have a significant fraction of the condensed phase (possibly variable along the length of the nozzle), and are being initially described by huge reaction mechanisms. These features prevent the nozzle problems solution in a modern multidimensional formulation. These predicaments are being overcome in this article in two ways:
a) The condensed phase is being imitated by the “Large Molecules”, which allows consider it a gaseous substкance and include reactions with its participation in the initial reaction mechanism.
b) The initial mechanism is a priori redundant and includes many reactions that exercise minimum impact on the composition of the working fluid. They can be excluded practically without loss of accuracy in the characteristics computing. For this, various methods for reactions reduction can be used.
The presented article proposes a reduction procedure, consisting of two methods: DRGEP (Directed Relation Graph Error Propagation) and a method of linking with an adaptive threshold. The DRGEP method is focused on searching and removing from the reduced reaction mechanism only the substances with reactions engaging them. If insignificant reactions still remain in the mechanism, they are removed by the engagement method. The degree of the mechanism reduction depends on the reduction threshold ζ_{L}. The developed procedure requires a small amount of calculations and allows reducing the initial mechanism to a certain acceptable size, ensuring a controlled error in predicting the flow characteristics.
This procedure was applied to the task of reducing the reaction mechanism in the stream of combustion products of metallized fuel C + O + H + N + Al + Cl. The initial reaction mechanism included 33 substances and 68 reactions. The reduced mechanisms were generated at various thresholds of value of ζ_{L} = 0.02–0.12. For small ζ_{L} values, the reduction rate is = 5.0–6.5 with high accuracy in the flow characteristics predicting. Further, with an increase in ζ_{L}, the indicator increases significantly, but forecasting errors significantly rise. In the presented example, the most acceptable mechanism was generated at ζ_{L} = 0.08. 
Popov V. V., Sorokin F. D., Ivannikov V. V., Degtiarev S. A. Developing a spatial model of a gear transmission with separate storage of the accumulated and extra turns for solving nonlinear problems of aviation transmissions dynamics. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/94b/h33dcseu8ih7mvkw73o4qu8uqe62uiso/Popov_Sorokin_Ivannikov_Degtyaryev_rus.pdf Aviation transmissions ensure the torque transfer from the rotor to propeller or fan, and accessory box drive in the engines of various types, from the engine to the shaft of the main and tail rotors of the helicopter etc. [13]. Aviation transmissions should ensure high strength properties at small size. The dynamics analysis performing seems to be the best tool for these requirements compliance ensuring.
Many scientific papers deal with the gear transmission dynamics. The most meaningful and interesting gear transmission models are represented in the works of Cardona [9], Spitas [12], Qiu [13], Margielewicz [14], and Kubo [19]. Nevertheless, most of them do not account for the linear wheels movement, variable stiffness, interaction between gears and other machine elements, and unfit for the nonstationary dynamics studies.
The article presents a spatial model of the gear transmission capable of accounting for the aforementioned limitations and applicable for the nonstationary dynamics problem solving. The model is based on the Cardona’s model [9].
The model employs Euler vector and the rotation tensor associated with it as rotations description. The final rotation is being decomposed into the accumulated rotation and a small incremental one. This technique allows avoiding the problems associated with achieving exceptional points near the 2p angle [1517].
The presented model can be employed for performing analysis of the wide spectrum of gear transmissions, such as spur gears, helical gears, conical gears and internal gears. The model allows accounting for the gear mesh stiffness, gear mesh damping, kinematic error of the transmission and backlashes. The gear transmission model can conjoin with the models of other machine elements such as shafts, bearings, cases etc.
The proposed model was verified by several wellknown tests. 
Yudin D. A., Firsanov V. V. Computational and experimental study of the strainstress state of product structural elements at the impact against a solid obstruction. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/e92/0w3q317s5ytljq4p0s6rqo6121tw3git/YUdin_Firsanov_rus_2_.pdf The article presents the results of computational and experimental study and mathematical modelling of product structural elements while the impact with the solid impediment. The problem of developing effective technique of numerical modelling of threeor dimensional dynamic impact problems.
The finite element method was used for the impact problem solving.
The results of strains and stresses computing were compared, using numerical modelling, with the results of the fullscale test, which demonstrated their validity.
The impact load tests are an obligatory part of the general complex of preliminary field tests of the prototypes of engineering products at the experimental development stage. The basic requirement to the field tests consists in ensuring the equivalence of the impact loading under the field conditions of the product loading while operation.
The validity of the impact loading tests ca be increased by improving testing and measuring equipment, as well as testing technique due to determining impact loads as close as possible to the operational ones.
To reduce the volume of the cost intensive field tests of the products, they are being replaced by mathematical modelling with modern software. The basic requirement for numerical computations consists in ensuring the equivalence of the impact loading while mathematical modelling to the loading under conditions of the field tests. Usually, the correspondence of the testing modes on the velocities and impingement angles, as well as overloads levels in the characteristic zones of the structures are being accepted as the equivalence conditions. 
Timoshenko A. V., Koshkarov A. S. Comparative analysis of entropic metrics of space objects optical images informativity. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/c2f/tag0635rxlofmfd0dh7req9cftebjsmq/Timoshenko_Koshkarov_rus.pdf The existing tendency to the intensity increasing of nearEarth space employing by everincreasing number of states, expanding spectrum and increasing complexity level of the space operations, the expected deployment of the extralarge satellite systems for group space missions are increasing the risks for the space activities associated with technogenic contamination. Optical images are the most informative type of information on the situation in outer space. The article brings up issues concerning preliminary images rejection obtained by the groundbased optical means, unfit for the human operator recognition. Specifics of the space objects surveillance by the groundbased optical means with account for dangers for national space vehicles and manned flights safety are considered. Estimation of the conventional network of optical means is performed. The necessity of performing preliminary rejection of the images, being obtained, prior to the analysis performing by the human operator is substantiated. It is shown that the main postdetector processing method is blind deconvolution of images. The work with the functional of the entropy of the image being restored is required while deconvolution operations performing. Entropy metrics by Shannon, Tsallis, Capture and Rennie were selected for the study. A comparative analysis of the entropy metrics of informativity, which application is in demand when computing the deconvolution functional, was performed. Test images with different visual quality were selected. On the example of real images a possibility of their employing with account of images visual perception by the human operator was estimated. Within the framework of the conducted studies inferences were drawn on the applicability of employing various entropy metrics and the degree of their consistency with the structuralsemantic approach of visual perception of images by a human operator. The trends of future studies on determining the generalized metric for the images of such class, as well as applicability of entropy metrics to the processing satelliteobtained data on the remote Earth monitoring were determined. 
Gusev S. N., Miklin D. V. Model of the test radio signals simulator for aviation systems of the Earth surface surveying . Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/982/z7izd4un45ie2n69h78u789y8zt74wgn/Gusev_Miklin_rus.pdf The article presents description of the model of the test radar signals simulator designed for calibration problems solving of air borne synthetic aperture radar systems (SAR). Control algorithms, employed in the simulator, for forming simulating trajectory signals, which reproduce virtual objects on radar images, are being considered as the subject of the study.
The necessity of solving this problem is stipulated, firstly, by the complexity of SAR calibration for complex objects, employing calibration polygons; secondly, by the lack of a uniform approach to the calibration means development based on simulators, employing the retranslation principle of the SAR probing signal. Thus, the purpose of the article consists in developing a model of the test radar signals, allowing reproducing the target environment with the specified set of object of various structure on the radar.
The proposed model is based on application of the theory of spatial and temporal signal processing in SAR and computer modelling techniques, from which the viewpoint the target simulating trajectory signal is the sum of the reflected signals from the point reflectors in a complex concentrated target. Each echo signal from the point reflector herewith should be computed with account for the position and the nature of the reflection in the specified direction.
The developed model peculiarity consists in frequency correction procedure integration into the algorithm for simulating trajectory signal formation. It allows compensating the geometry violation of the wave front and the change in Doppler frequency spectrum, caused by the objects reproduction at the certain distance from the simulator location.
The result of the work represents the model structure of the test radar signals simulator and the algorithm used in the model for computing the simulated trajectory signal of a complex concentrated target with account for the time delay, amplitude and frequency correction.
The developed model was tested while seminatural simulation of the reproduction process of virtual objects on radar. The seminatural simulation results presented in the work proved the approach correctness and the adequacy of the developed model.
The proposed model can be employed at:
– SAR calibration at different stages of development and design;
– developing of simulators for the signals programming;
– substantiating the trends of methods and means developing of radar systems calibration for the Earth’s surface observing. 
Kartukov A. V., Merkishin G. V., Nazarov A. N., Egorov V. V. Object images employing for air medium parameters analysis near moving objects. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/3ad/q8wxnt03upb0dty97xv2rzl211h9yidh/Kartukov_Merkishin_Nazarov_Egorov_rus.pdf The tasks of monitoring, position assessing of the aircraft and interacting with the environment are of great importance in the aviation technology. At large distances, they are being solved mainly in the radio range (radar). At short ranges, the optical range methods are very effective near aircraft, since the wavelength is several orders of magnitude smaller and allows one to achieve high accuracy of the measured parameters.
Movement of various objects, such as a car, and plane, or a helicopter, is accompanied by their interaction with the air. The aerodynamic parameters of an object are necessary for calculating its speed characteristics and determining the possibilities for their improvement. Typically, the aerodynamic characteristics measurements are performed in wind tunnels employing the reduced models of the objects. The wind tunnel has a rather large and complex structure, requiring highly qualified service.
Registration of the aerodynamic parameters of the air medium occurring while the object moving is possible. Similar methods are used for the fuel quality analysis.
Employing the object images distortions allows obtaining all necessary information on the air medium parameters as well as the «clean» sky turbulence by relatively simple technical realization.
Further, a new technique for the fast and qualitative estimation of the moving object aerodynamic properties by distortions of the reference object image under the action of the turbulent wake. A set of reference objects installed along the path of movement allows determine the size of the turbulent wake, the impact of the structural elements of the object and evaluate their role in creating aerodynamic drag.
The illustrations to the article show the effect of a turbulent wake after a car travels on an image of a straight rail mounted on a track of movement. The white rod image blurred in its lower part, which is stipulated by the laminar layer transformation into the turbulent, is shown as well.
Compared to the known technique of wind tunnels application, the described technique: 1) does not require manufacturing of a highprecision model of the object being studied;
2) does not require highly qualified servicing;
3) in some cases, an experimental study is possible, wich cannot be implemented in a wind tunnel (for example, for a helicopter);
4) does not require presence of the fastening and information retrieval elements in the working area, distorting the flow;
5) allows building 3D models of the “atmosphereobject” structure using a set of reference rails. 
Romanov A. M. Accuracy Estimation and Synthesis of Nonlinear Direct Mathematical Operations on Bitstreams. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/576/20vjy14a8g7vidr4zgp3dt3tq2rqdavq/Romanov_rus_.pdf Field programmable gate arrays (FPGA) are widely used in the aerospace industry, both for onboard devices and ground equipment. This paper is devoted to accuracy estimation and synthesis of nonlinear direct mathematical operations on bitstreams (DMOB). DMOB or direct processing of sigmadelta modulated bitstreams is a promising method to reduce the resource area consumption of the FPGA designs which allows to implement complex digital signal processing algorithms on the basis of radiationresistant FPGAs as well as FPGAs produced by Russian vendors, the logical resources of which are significantly smaller than those of foreign counterparts in commercial versions. The estimates of nonlinear DMOB accuracy which were previously obtained were empirical and covered only a small set of mathematical operations in a limited range of possible implementation parameters. This paper proposes a new approach to accuracy analysis and synthesis of nonlinear DMOBs which allows to implement a wide range of nonlinear digital signal processing algorithms directly on sigmadelta modulated bitstreams providing a given accuracy. The key point of this paper is that nonlinear DMOBs implemented by combining input averaging filters and nonlinear mathematical operation perform linear interpolation of this mathematical operation, and the number of interpolation reference points depends on the filter window. This statement supported by a number of assumptions is analytically proved for a onedimensional case, and it is experimentally confirmed with regard to a multidimensional case. All the assumptions used in the proof are analyzed in detail, and the conditions of the proposed method of applicability for real projects are formulated on the basis of the assumptions. Solutions described in this paper allow to achieve a flexible compromise on the nonlinear DMOB FPGA core area usage and the computation accuracy. The example of the implementation of bitstream multiplier demonstrates that the proposed solution is superior to the previously known and widely used analogue. 
Radin D. V., Makaryants G. M. Developing and experimental studying of dynamic characteristics of adaptive pressure pulsation dampener for the gas turbine engine fuel system. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/5d0/netjdjrn1umuywb05v7zsqynzlq305d3/Radin_Makaryants_rus.pdf One of the key trends for the environmental and cost performance improving of modern gas turbine engines is the development of lowemission combustion chambers, which realize the concept of lean homogeneous mixture combustion. Pressure pulsations in the gas turbine engine fuel system can lead to unstable combustion in lowemission combustion chamber. The pump rotation frequency varies greatly depending on the engine operation mode. Thus, it is necessary to employ the adaptive Helmholtz resonator, being adjustable to the pump rotation frequency, to suppress the pulsations. In the work being presented, the adjustable element of the dampener was represented by the cavity volume. This study focuses on the developing and experimental studying of dynamic characteristics of the adaptive resonanttype pressure pulsations damper in the frequency range under consideration., An automatic design system was developed in the C# programming environment to perform theoretical studies. The experimental test bench consisted of a pump, a fuel cooling system, a resonator with a piston to change the cavity volume, and the imitation the fuel system. The pressure pulsations prior to and behind the resonator, as well as behind the pump, when the resonator was not installed, were being measured while testing. The resonator volume was being varied from minimum to maximum value. The efficiency of the adaptive Helmholtz resonator was being evaluated with the insertion attenuation factor, which represents the ratio of the pressure pulsations amplitude in the circuit without resonator to the pressure deviations amplitude in the circuit with the resonator. The frequency characteristic of the adjustable resonator efficiency represents the monotonically decreasing curve. The efficiency of the adjustable dampener increased by more than three times at the subresonant, and by more than half times at the superresonance frequencies compared to the nonadjustable one. The experimental data verified the theoretical computations with high accuracy. The adjustable Helmholtz resonator ensures much higher pressure pulsations damping than the nonadjustable one in the entire frequency range. 
Efanov V. V., Zakota A. A., Volkova A. S., Izosimov A. V. The aircraft weaponry control technique in conditions of covert target surveillance. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/a6f/sjmxrnzfo1thxkg5nr4at1nl3qr2zwh4/Efanov_Zakota_Volkova_.Izosimov_rus.pdf The military aircraft weaponry includes both guided and unguided weapons, radar and optoelectronic surveyingandguidance complexes intended for striking both airborn and ground targets and ensuring aircraft defense.
There are known technique and devices for aircraft weaponry control, which perform the target detection and capture, determine its parameters, choose the weapons and perpetrate its preparation and launch.
The disadvantages of the abovedescribed systems consist in the fact that the weapon control in conditions of the covert target surveillance is not being ensured.
Selection of the channel with the passive type radar means as a leading channel of the weaponry control system ensures discrete operation mode for the active type radar means of the slave channel of the weaponry control system. The mode of periodical measuring of the range on target herewith, being followed by the radar means of the leading channel of the weaponry control system, with transition to the continuous position finding at achieving the preset range or by the crew command. It ensures the possibility of covert target attacking at its capturing.
Identification of the targets being followed by the radar means of both leading and slave channels of the weaponry control system is performed, in the absence thereof the reset mode of capturing by the radar means of the slave channel of the weaponry control system is set. By this, the probability of the target tracking and the aircraft interference immunity is increased.
Targets identification is realized by comparing the absolute value of the angular coordinates difference of the target viewfinding by the radar means of the leading and slave channels of the weaponry control system with the preset threshold. With this, exceedance of the above mentioned threshold is conceded only during the set time interval.
The stealthiness of the passive radar stations operation ensures higher viability under combat conditions due to the hampering of their detection and jamming.
However, unlike the active detection and ranging, active detection and ranging does not allow obtaining the object range by the data of receiving signas from the single station. This is undoubtedly a serious disadvantage.
Analysis of the methods ensuring indirect determining of the targets’ range and motion speed was performed. It is necessary to utilize the joint results of several (more than two) tracking stations, removed from each other by the known distance, and any of the
The kinematic distance measurement method (KDMM) being used while working with only a single target is known. The KDMM is realizing one of the information restoring methods, and it comes into action if other information restoring techniques are unavailable. The information about a target is being by the angular coordinates in the vertical or horizontal planes with the supporting height. The results of the KDMM modeling show that the absolute error of distance measurement makes up from hundreds of meters to several kilometers.
The purpose of the work is consists in accuracy increasing of the the range and speed of aerial target movement determining in the covert surveillance mode.
To eliminate the KDMM shortcomings the method of covert determining the target motion parameters is proposed. Its essence consists in obtaining the target motion parameters based on solving the vector equations that associate the range, speed, and bearing of a fighterinterceptor with a target. To obtain herewith the parameters necessary for the equations solving the interceptor should perform certain maneuvers.
The modelling results analysis of the proposed method and algorithms realizing it allows making the following conclusions:
— the method ensures the much more accurate distancetoatarget computing;
— the maximum error value is below the resolution range level of the onboard distance measuring devices.
The suggested algorithms for determining the target range and motion speed are approved with the seminatural complex composed of the thermal direction finder, target simulator, microcomputer, interface with the personal computer, and the programmedmathematical support.
The technique for evaluating the effect of measuring resolution of the track angle, flightpath angle, and velocity variation dynamics on the target motion parameters determining accuracy is suggested.
While seminatural tests conducting it was determined that the suggested technique and algorithms are efficient in general. Practical computations on determining the range to a target demonstrate that the errors introduced by the computing process significantly increase, if the Gauss method is being used for the task on the forward motion and the rational selection of the reference element is not accounted for. At the same time, the instrument errors impact can be significantly reduced by the reference element rational selection at each step.
A technique for target detection was suggested for the case of decoy flares employing. The technique consists in
– the airborne target detection,
– selection of angular speed of optoelectronic module (OEM) guidance by the crosshair superimposition on the target on the screen,
– transferring the OEM to the automatic target guidance mode,
– measuring current target range,
– converting the digital code of range into the video signal, displayed of the screen in the form of the digital caption.
The following factors are additionally determined:
– angular velocities of the target motion by measuring the time intervals of the target shifting relative to the preset angular positions;
– angular accelerations of motion by evaluating dynamics of the target angular velocities;
– dynamics of angular accelerations changing by subtracting the subsequent and previous values of the angular accelerations of the target.
With this, the following factors are recognized:
– the target tracking, if the values of change in dynamics of the angular accelerations of the target motion are less than the set value;
– the decoy flare tracking, if the values of change in dynamics of the angular accelerations of the target motion are more than the set value.
In this case a manportable weapon complex gunner receives the information capturing the decoy flare. 
Dmitriev V. I., Zvonarev V. V., Lisicin Y. E. Justification technique for rational control methods of unmanned flying vehicle. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/e0d/ax3zgb7anvjlogpp1222rdz8bexo2y8s/Dmitriev_Zvorarev_Lisitsyn_rus.pdf The purpose of the article is efficiency increasing of the unmanned aerial vehicle (UAV) application based on the feasible selection and realization of rational control method.
The article considers the UAV application as the object of research. The subject of research is the UAV control methods.
The relevance of the topic in the modern militarypolitical situation is determined by ensuring the State security in the field of military development, on the assumption of the existing threats. At present, UAV is the most important component of weapons, military equipment, automated reconnaissance and information transfer systems. Its application can significantly increase the efficiency of troops command and control, increase combat capabilities and combat means effectiveness.
The article presents a methodology for the UAV application effectiveness evaluating and a technique for the UAV control methods forming. The dependence of the orrect frame reception probability on the signaltonoise ratio for a system with addition and with autoselection is demonstrated. Recommendations on the UAV control method selection are given.
The practical significance of the article consists in the following:
– the developed technique for evaluating the UAV application effectiveness describes more accurately the conditions for receiving messages and allows compare radio channels with various characteristics (type of modulation, type and parameters of the noiseimmune code, etc.) at the information receiving point, and perform the performance indicator computing of the UAV control methods;
– in supplement to the known methods, the developed technique for rational UAV control methods substantiating allows accounting for the dynamic characteristics of a random process, determine the exact parameters of the radio channel, and increase the reconnaissance depth (ensuring herewith the required survey resolution of the required probability of the correct frame reception and the given stealth).
It is advisable to use the obtained methodology when planning the use of UAVs with the aim of transmitting information over the radio channel with signal fading. 
Philatov V. I., BonchBruevich A. M., Khokhlachev E. N., Borukaeva A. O., Berdikov P. G. Parameters formalization of adaptive protection system for automated communication control system. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/117/p8ny9ett8fwh0w779uoms40f12vyxl94/Filatov_Bonch_Bruevich_KHokhlachev_Borukaeva_Berdikov_rus.pdf The article analyzed the theoretical model of the system for protection of the automated communication control system (AССS) against accidental hazardous impacts, representing a threat to the aircraft control systems. The tasks for realizing systematic approach to solve the problem of ensuring the ACCS adaptive protection.
The simulation model for the AССS protection against hazardous impacts, employing the queueing theory, is considered. The article analyzed the properties of simulation modelling systems, namely GPSS World. The article presents also a mathematical model of the protection system and reviews the functions of its components.
The article used KendalBasharin representation for formal presentation of various options of the AССS protection organization against hazardous impacts. Model restrictions, which represent a function of loss for the untimely users requests compliance were considered
The task of the most rational organization of the ACCS functioning was put forward in the article.
From the performed analytical work the inferences were drawn that it was not rational to use the method of simple sorting of all possible options to obtain the optimal option of the ACCS adaptive protection system. There is a necessity to employ a combined algorithm of the directional search with the penalty of randomness together with static tests.
The topic of this work relevance is stipulated in the first place by the necessity to develop new methods and ways for the ACCS protection from the hazardous impacts, used for the aircraft control, for example, in case of the control interception prevention. 
Lebedev A. S., Dobrolyubov A. N., Mikhaylenko A. V., Bezrukov A. V. Searching for diagnostic features for controlled surfaces contamination recognition system at the optoelectronic monitoring. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/d6c/de3u6cval9jl66jjmt4inekqiz0fz633/Lebedev_Dobrolyubov_Mikhaylenko_Bezrukov_rus.pdf 
Anan’ev A. V., Rybalko A. G., Lazorak A. V. A technique for target runin direction justification based on theory of risk when striking groundbased objects by aircraft complexes. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/34c/2q9s6jik4wrw1tnaoybs7x1tsktf356l/Ananev_Rybalko_Lazorak_rus.pdf This technique allows performing application planning of:
 The new militarypurpose complexes, namely, smallclass unmanned aerial vehicles (UAV SC),
 New weapons, such as freefalling unguided containers (FFUC), charged with the small caliber and capacity ammunition for damage inflicting to easily vulnerable ground objects.
The FFUC application specificity is its discharging from the carrier as a largecaliber ammunition, which requires special attention while the targeting point selection. The presence, in its turn, of asymmetrically located and different by their importance elements as parts of the ground target contributes to the several targeting points’ selection and, hence, determining rational direction of the approach.
Thus, for example, when employing largecaliber weapons against long narrow targets, it is necessary to select a certain rational angle of approach. At the same time, if the smallsized ground based objects are being attacked with the weapons, which scattering characteristics do not commensurate with the target size, the approach direction selection makes no difference, and targeting is being performed to the center of a target. The FFUC specifics and scattering parameters allow recognize “an aircraft on the open flying line” as a stretched areatype target with asymmetric location of the unequal by the damage probability and damageinflicting scale vulnerable areas, rather than a smallsized single ground object.
Thus, the newly revealed property of the object of striking should be accounted for while rational selection of the target approach direction by the UAV CS and target striking by the FFUC.
The gist of the developed technique consists in the following:
 The ground target decomposition on n vulnerable zones, when the areas of these zones fit into the total area of the object;
 Criterion selecting (recovery time of the damaged units of vulnerable zones), and indicators defining (labor costs required to replace units of vulnerable zones) of damage inflicting risk for a ground target;
 Risk weight factors determining for each vulnerable area by the expert assessment method (Thomas Saati hierarchy analysis method);
 Determining probability of vulnerable zones hitting with the FFUC, with account for the targeting point disposition in range and direction, and the UAV SC accuracy characteristics;
 Employing the analytical expression of integral risk (the first multiplier is probability of the FFUC hitting the vulnerable zone, and the second one is the risk weight factor for each zone) for risk value determination when targeting point shifted by one step in range and direction for each iteration;
 Creating threedimensional dependence (surface) of the integral damage risk on targeting point position on range and direction;
 Selecting rational direction of target approach as the result of revealing several local extremes of the integral risk function.
Thus, the target approach at the angle to the central axis of the groundbased target justified by the proposed technique ensures 20% increase in the inflicted damage compared to the target approach along the central axis only. 
Kalyagin M. Y., Voloshin D. A., Mazaev A. S. Quadcopter flight control system simulation in Simulink and Simscape Multibody. Trudy MAI, 2020, no 112, http://mai.ru//upload/iblock/5cc/zat6f015cvto2wv7cqyaasx0lcouajy0/Kalyagin_Voloshin_Mazaev_rus.pdf Currently, the unmanned aerial vehicles (UAV) are widely used throughout the world as means for monitoring, creating maps, optimizing agricultural activities, monitoring fire being dangerous areas, power lines surveillance, logistics, etc. The multirotortype UAVs are widely proliferated due to their structural simplicity and the ability to both flying at near zero speeds and maneuvering with high frequency.
One of the most important tasks at the early stages of the UAV design consist in studying dynamic characteristics of alternative design options of the vehicles with account for their design characteristics. The stateoftheart computer engineering systems are able to implement the endtoend process of designing and linking solidstate UAV models with adaptive dynamic models and their operation in various modes by transferring design parameters obtained in CAD systems, directly to the simulation environment of the flight control systems. Of particular interest is the set of tasks associated with control algorithms developing to ensure the UAV normal operation under the impact of external disturbances.
The article proposes an approach to the solidstate and dynamic computer models linking of the unmanned aerial vehicle of the “quadcopter” type at the early stages of the design using Solidworks and Simulink/MATLAB software packages. The model designed in the Simulink/MATLAB environment allows evaluating the developed systems for an aircraft stabilization and control for the UAV, implemented according to the “quadcopter” aerodynamic scheme without starting the quad copter itself.
The discrepancy between the results of 