2016. № 86
Mechanics  
Dynamics, strength of machines, instruments and equipment  
The paper contains the description of the computer program SNCalculator meant for fatigue endurance of aircraft components with geometric stress concentrators computation. SNCalculator is integrated into finite elements computation bundled software Femap. It allows significantly increase the degree of computations automation. As an initial data, the program uses material constants, stress history mask, parameters of calculation theories and mechanical stress level. Stress data is automatically loaded from Femap model after accomplishing its static analysis. Libraries allow reuse of materials and stress history mask. SNCalculator posesses postprocessing features, such as results saving, export of the results to Excel spreadsheet, export of the results to Femap FEM, stress cyclogram viewer. Fatigue endurance calculations algorithm is based on three most widely spread in aviation industry techniques: quality of design analysis (developed by Loim V.B.), similarity theory analysis (developed by Kogaev V.P.) and fatigue rating theory analysis (developed by Strigius V.E.). The first two methods employ conception of effective stress concentration coefficient. The first method implements «quality» as a parameter, which is identified by experimental data and study of analogous structures data. Effective stress concentration coefficient is calculated for the second method by Kogaev’s theory of similarity. The third method uses fatigue rating, which is defined as maximal normal stress of zerototension cycle for which fatigue life is equal 10^{5} cycles with 50% probability and reliability level equal 0.5. The paper describes the main steps of the abovementioned methods and presents schematic algorithm of fatigue life calculation realized by SNCalculator. Keywords: fatigue life, stress concentration, airframe, automation 

Aeronautical and SpaceRocket Engineering  
Design, construction and manufacturing of flying vehicles  
Considerable success has been achieved in the Venus exploration. Specifically it concerns planet’s atmosphere and surface study by contact methods. Thirty years ago descent vehicles of the Vega mission spent record breaking time, about two hours, on the Venus surface. For the first time in the history of planetary studies balloon probes drifted in Venus atmosphere for two days. They conducted atmosphere properties studies by means of the scientific instruments designed and developed by the institutes of the Russian Academy of Sciences in cooperation with science community of other countries. It slightly opened secrets of the planet, in particular an enigma of the atmosphere super rotation. Vega (Venus — Halley comet) mission activities could become a perfect example of the international cooperation. The scientists from eleven countries participated in this project realization. Various Venus exploration mission scenario alternatives are currently being developed after a long break in the Venus research. A modern and perspective Russian spacecraft VeneraD project intended for the longterm planet study is thought to consist of an orbiter, subsatellites, a lander and balloon probes. Proposals of the international mission organization with distribution of the responsibilities for the various spacecraft components between parties and probable usage of various launch vehicles are under consideration. The international cooperation in the implementation of the Venus research complex program shall enable to significantly increase the scientific performance of the projects with simultaneously high cost effectiveness. Keywords: Venus, exploration program, international cooperation, spacecraft 

Methodical bases for predictive research on perspective spacecraft (SC modifications) as a part of the space system (SS) of remote sensing (RS) were considered when upgrading with a given point in time. They allow to define rational (optimal) planning and design solutions for the future technique sample taking into account implementation of the project (dynamics of the external technical, economic and organizational connections (restrictions)), also, it is possible to determine the rational parameters of an object and its subsystems, in which the required tactical and technical performance can be obtained. The concepts of multilevel management of developments and implementation of multilevel design model are the basis of the created method. A twolevel model of project management and correlated statistical method for twolevel optimization are used. The statistical method involves solution to the main problems of the planning stages for the project as whole and replaceable subsystems, as well as the tasks of directed adaptation of project dependencies of top level. Design problems statements of upper and lower project management and twolevel optimization of the SC target hardware module parameters are given. Algorithm of research project involves the sequential solutions to the tasks for the developments on the upper and lower levels of management with the implemented design solutions. On the one hand, this approach makes it possible to take into account the peculiarities of design solutions to spacecraft subsystems without the expansion of the project model, on the other hand, optimization of the subsystem parameters unit on the lower level of management (with the detailed design model) is carried out taking into account the dynamics of functional limitations (weight, size, information and power). The implementation of such approach makes it possible to organize a multivariate study (when restricted with periods of work) and provides a definition of sustainable design solutions by expanding the range of possible solutions. The developed methodical bases for predictive studies allow to carry out optimization of performance modifications of spacecraft and its subsystems, to form a efficient algorithm of coherent optimization, to evaluate the effect of the key technologies parameters on the performance of advanced equipment. The key (basic) technology refers to forwardlooking design and technological solutions (DTS) to the basic subsystems implemented while creating spacecraft and their modifications in the planning period, on which the scientific and technical level, the competitiveness and efficiency of equipment are depended. In turn, such studies (during the inverse problem solving) allow to highlight the key (basic) DTS and find their rational parameters. The effectiveness of a new technology created in the planning period depended, mostly, from the implementation of key technologies. Keywords: Earth remote sensing, modernization, modification, predictive researches, methodical bases, technicalandeconomic model, algorithm, parameters 

Strength and thermal conditions of flying vehicles  
This article is directed on assessment of variability thermalphysic characteristics of constructional and the heat protection materials on aircraft construction heating. It is including the materials’ thermalphysic characteristics variability of temperature. It uses compact, fastacting calculation procedure. It is examining heat extension coherently thermal conduction. The task is reducing to calculation about skin onedimensional heating (along thickness). It supposes that thermalphysic characteristics depend on temperature. Therefore the thermal conductivity coefficient of the material is variable along thickness. The thermal conductivity onedimensional differential equation writes down as derivative of two functions product. The skin thickness is splitting into several calculation points with defined step. The thermal conductivity differential equation is producing in the difference form by way of central finite differences. This expression use only adjacent points temperature value. Thusly it is creating algebraic equations set with three diagonal coefficients matrix. The fastacting sweep method is using for the equations set finding . The boundary conditions equations are using for the skin confines points. The supply and divert heat transfer rate balance equation is using for the external and internal surfaces. The heat transfer rate equality as boundary condition equation is using for the different materials meeting surface. The analysis of constructional and heat protection materials thermalphysic characteristics achieves appreciable relation their value from temperature. Especially it is exhibiting for the heatresistant materials, which works in wide temperature range. Also it is very considerable the thermalphysic characteristics variation of radome materials and some of the heatinsulating materials. The calculation results is achieving, that the using of the thermalphysic characteristics value, achieved at room temperature, for greatly heating constructions can give great inaccuracy (to 50%). The disregard of value thermal conductivity coefficient variableness along material thickness can give great inaccuracy too (to 29%). The suggested determination scheme permits to correctly simulate the heat conduction process in sandwich structure with consideration of thermalphysic characteristics relation to temperature and without additional admissions. It distinguishes suggested determination scheme from «the heat balance equation» method, which used in some methodologies. Keywords: temperature field, multishield skin, aircraft, material characteristics, adequacy, intercomparison 

This article presents the analysis of effect of the hypervelocity dust impacts on the thermal state of the solar probe and the destruction of its thermal protection during the flight at close vicinity to the Sun. The relevance of this problem is caused by extremely high velocities of dust impacts on the structural components of the spacecraft, which are expected to be as high as 350 km/s depending on the perihelion distance; significant mission duration (~ 7 years) and greater values of cumulative particle density in comparison with the nearEarth environment. The main information about the density, composition and dynamics of dust particles at the close vicinity to the Sun is presented. In accordance with the described dust distribution model the cumulative density at different distances from the Sun and the cumulative flux of particles acting on the spacecraft following the orbit with a low perihelion during the period is calculated. These results suggest that the impacts of dust particles with mass > 10^{6} g are rather rare events. Thus, the main damage to the surface of thermal protection shield cause the impacts of grains whose mass is ranging between 10^{16} and 10^{6} g, moving in the opposite direction of the Sun. A 100 mkm particle with average density of 2.5 g/cm^{3} (with mass 1.3·10^{6} g) moving at 100 km/s will create in solar probe heat shield material a crater of diameter 0.18 cm and depth 0.22 cm. The diameters of craters formed in the spacecraft’s shield material by the collisions with the dust grains with a smaller mass (10^{16} <m <10^{6} g) will not exceed 2 mm. Due to the small size of the particle the period of highpressure action is limited by 10^{11} — 10^{13}sec, so the shock wave in the material decays rapidly and the energy transmitted to the material becomes insufficient for evaporation and melting. At some distance from the point of impact only local temperature rise to several hundred K is possible, that has no appreciable effect on the equilibrium temperature of the shield. Keywords: spacecraft, Sun exploration, thermal protection, hypervelocity impact, dust particles 

Control and testing of flying vehicles and their systems  
The creation of promising LPE for upper stages and upper stages of launch vehicles working on the components of rocket fuel (CRF) (liquid oxygen and hydrogen, kerosene, liquefied natural gas, etc.), requires a large amount of offline testing of units and systems in experimental units (EU) of the test bench.
When performing serialparallel connection of the cylinders to the reservoir pressurization and issue of uneven development will decrease in 2 times and will amount to ~ 12.5 %, which would increase the duration of test at 12 — 15 % when the feed system. On the basis of consideration of processes of heat exchange of a cylinder with a cryogenic component and the environment, and the generalized dependence of the Nusselt criterion from the criteria of Reynolds and Prandtl justified method technologies balloon filling systems for increasing the length of the test combustion chamber. Thus, the expediency of application of a seriesparallel configuration of the cylinders in the PFS and the technology fueling systems cryogenic component in three stages: charging, exposure, refueling. Keywords: components of rocket fuel, combustion chamber, experimental units, pressurefeed system, tests 

Dynamics, ballistics, movement control of flying vehicles  
This article describes the software development of Synthetic Vision System (SVS) prototype, which provides enhanced situational awareness for flight crew and decision making assistance during approach and landing phases of flight in nonvisual flight conditions for future civil transport aircrafts. The SVS uses as initial data the known aircraft present position and terrain elevation map database (map size, map grid intervals Δ_{1} and Δ_{2}, and Х, Y, Z coordinates of grid reference). As the sources of such data in this article respectively appears the flight management system (FMS) and the terrain awareness and warning system (TAWS). For 3Dmodeling of initial data it is necessary to express the coded topographic data in terms of primitive solids. Tin the most simple way the terrain region of consideration could be approximated as set of rectangular parallelepipeds, the bases of which are the terrain elevation map squares and the heights of which are the corresponding maximum terrain elevation. After 3Dmodeling of terrain region of consideration it is also necessary to cut off the unfaced lines and surfaces. To solve this the zbuffer method is chosen by reason of its most suitableness to implement on airborne equipment of civil transport aircraft and central display system architectural features. The SVS generates an image of the terrain elevation in region of consideration in 3D view for displaying it on the primary flight display combined with the other flight and navigation information in real time mode. Based on the proposed algorithm the software developed. Simulation results confirms the adequacy and applicability of the proposed approach to improve the situational awareness of the crew during approach and landing phases of flight in nonvisual flight conditions for transport category aircrafts. Keywords: aircraft, synthetic vision system, 3Dsimulation, landing 

Mathematical modeling is acknowledged method by analyzing the wide range of problems in the air traffic control purview. One of the actual problems in this scope is an estimation of the maximum throughput capacity (MTC) of the airport that can be expressed as an ultimate count of movements that can be performed on the runway system per a time unit in the presence of continuous demand. ICAO recommends using one hour as a most suitable time unit. The critical overview of the models that includes the solving of the mentioned problem demonstrates that they are not able to consider the whole range of factors, which exert one’s influence on the MTC value, in particular lateral separation minima for the aircrafts following the same route or moving crossing tracks in the airport area. This research expands the approach based on the spacetemporal sampling (quantization) of the investigating process. This allows take in consideration the restrictions imposed by lateral separation minima by the estimation of MTC value. The offered analytical calculation of the saturation capacity value in dependence of the topology of SID/STAR takes place in terms of macrocharacteristics that significantly reduce the dimension of the problem. One of these characteristics is topology «complexity» — the system of constraints imposed by separation minima on SID/STAR intersection. These characteristics could be expressed as scalar value. This paper investigates the impact of this value on MTC of the airport. As a second macrocharacteristic is proposed to use the occupation numbers which are defined by analogy with quantum mechanics and represents the quantity of aircrafts which may be in the airport airspace without creating conflicts. The evolution of air situation is described with Markov processes in discrete state space. The system of hypotheses allows us to express conditional probabilities of transitions between states of stochastic process in analytical form. An assessment for MTC of the airport and study its dependence from topology «complexity» provide on the basis of steadystate solutions. There is the software developed that allows to estimate the MCT for the real airports using the logic of the macrocharacteristic model. As an example the capacity for three Moscow airports is estimated. According the results the topology of SID/STAR can reduce the MCT up to 10 percent of the full runway capacity. Keywords: maximum throughput capacity, airport airspace quantum model, airport airspace topology 

Instrument making, metrology, information and measuring equipment and systems  
Navigation instruments  
The research subject matter is functioning mathematical models of inertial navigation system (INS) in standalone mode operation and of inertial sensor’s errors. The aim is to increase the accuracy of coordinates determination of the aircraft location under the conditions of absence of information from navigation radio engineering systems. The relevance of the work consists in continuous toughening of requirements to modern inertial navigation systems regarding increase of their precision parameters, reliability and improvement of operational characteristics. Feature of the standalone mode of functioning the INS is accumulation during all operating time of an error of coordinates determination and angular position of the aircraft. Reduction of rates of increase errors can be executed due to increase accuracy of the sensitive elements of INS, and also accuracy of installation and adjustment. It leads to the essential growth of cost of all flight and navigation complex and labor expenses at INS service. Methods of autoequalization provide such creation the scheme of INS which compensation of the revolting influences and reduction errors due to not essential changes of the design and modification of algorithm of the functioning system is provided. Development of onboard computing systems and algorithmic providing the strapdown INS allows to receive high precision of aircraft coordinates determination using gyroscopes and accelerometers of average accuracy. The results of research of possibility of INS aircraft accuracy increasing are presented in the offered article. As the main tool during simulation modeling was used the package of applied programs MathLab, by means of which were received optimum parameters of uniform and periodic laws of rotation the block sensitive elements and precision characteristics INS with autoequalization of errors. The results of the comparative analysis of two offered rotation laws are presented. The changes entered into design of INS are proved. The results of research can be used at modernization of the existing strapdown INS for the purpose of obtaining high precision characteristics of the aircraft coordinates determination with the minimum financial and labor expenses. Keywords: strapdown inertial navigation system, block of sensitive elements, law of rotation, gyroscope, accelerometer, simulation modeling 

Optical and opticalelectronic devices and complexes  
There is a probability of blades approach up to their collision and following crashing during some flight modes connected with dynamic maneuvering on coaxial rotortype helicopters. Safety of such helicopters can be increased by blades’ realtime control with account for their attained pose. The task of helicopter blades configuration measurements at realtime is considered to research effectiveness and safety of helicopter coaxial rotors operation. An optical measurement system is proposed. It is based on image processing from a high speed camera to indicate blade tip’s position in helicopter coordinates. The measurement equipment and its position are fixed. The problem of shooting frequency count on the assumption of measurementsystem specification was considered. Two things have negative influence on estimation of the helicopter blade tip position: low contrast between the blade and the background, and background texture, which makes difficult to detect blade’s edges. The first problem is thought to compensate with the help of blade’s LEDhighlighting, the second by using a contrast display towards the blade. One of the key moments of blades behavior on different modes research is blade identification, because they don’t have visual differences. However, the unique motion trajectories may differ critically. It is proposed to layof a contrast highlighter towards blade face. Developed an optical method of measuring the blade tip position of the helicopter including the structure of the experimental measurement setup, a set of algorithms and associated software for allocation, determine the position and identification of blades. The used algorithms for blade’s detection and identification are described. The research results confirm the operability of suggested approach. Keywords: helicopter blades, optical measurements, highspeed camera, image processing 

Radio engineering and communication  
Antennas, SHFdevices and technologies  
The object of this work is to develop a manufacturable design of the monopulse slottedwaveguide array for threecoordinate radar with frequency scanning in the elevation plane. To achieve the specified technical and design characteristics, numerical methods of electrodynamics and automated software packages for electromagnetic field simulation of threedimensional microwave structures was used to perform the following tasks: development of antenna block diagram; synthesis of the antenna and its main elements, carrying out the numerical analysis and the parametrical optimization of the electrodynamic models; a consideration the constructive and technological realization of the antenna. The main results are as follows. The practical implementation of the advanced design of the monopulse waveguideslot antenna array with frequency scanning showed that it achieves higher values of technical characteristics in comparison to the wellknown analogues. The features of serial beam forming network (BFN) was explored to eliminate the typical deficiencies of BFN. Obtaining a low level side lobes in the plane of the frequency scanning without insertion of additional loss in sumdifference BFN was proven. The effective techniques of numerical analysis and parameter optimization of electrodynamic model of BFN was developed. The issues of constructive and technological realization of an antenna were considered; they allow to simplify the manufacturing process by minimizing the influence of manufacturing tolerances of electrical parameters and to improve weight and performance characteristics. The application of such antennas in modern radar systems will increase the accuracy of aircraft altitude measurement and the maximum detection range, improve radar immunity and its performance characteristics. Keywords: monopulse antenna array, frequency scanning, pattern, beam forming network, electromagnetic simulation, numerical analysis 

Systems, networks and telecommunication devices  
In airspace areas over the aerodrome environs complex and critical tasks of air traffic control, such as takeoff, formingup, enroute flight and landing are solved. Communications and flights radio technical support (RTS) are the only sources of objective information for flight crews concerning their location on the ground and in the air, and the air situation in area of responsibility for mission control groups. Thus, a number of contradictions occurs, on the one hand the increased requirements to communication and radio aircraft flights technical support, and on the other hand — the need to identify communication and radio technical support performance indicator, characterizing meeting of the specified requirements. On this basis, the problem of communication and flight RTS performance evaluation indicators selection, characterizing the information exchange quality of aviation control system arises. The basis for the selection of indicators to measure the effectiveness of communication and aviation RTS forms the target destination, realized by the communication system and RTS through meeting its requirements for timeliness, reliability and security. As a generalized indicator of communication and RTS efficiency one can use the probability of task, completion with the desired quality at all stages of the aircraft flight. The offered approach to the selection of communications and RTS efficiency evaluation indicators will allow highgrade and effective development of proposals on decision making associated with the organization of communications and radio technical support at the state aviation aerodromes. Keywords: communications, radiotechnical flight support, aircraft, efficiency, indicator, system survivability, information exchange 

Radiolocation and radio navigation  
Research and development of radio systems, which allow to determine position of a mobile objects originate in the mid20^{th} century. At present time, global navigation satellite systems (GNSS), allowing precise positioning are widely used. However, the positioning task arises not only in the open air environment, but in areas where the satellite signals are severely distorted or are not available, for example, in shops, hangars, deep pits, office buildings, etc. High positioning accuracy by using GNSS becomes difficult in the presence of severe multipath fading or shadowing. But there are local positioning systems that can complement of completely replace the GNSS on a limited area or indoors. Typically, these systems use time division multiplexing techniques (TDMA) for system transmitters. Currently, the relative or local positioning systems are used widely in practical tasks, which require differential precise positioning from a knowing point. In this paper a mathematical model, describing the local positioning system with TDMA, is presented. Based on this mathematical model the prototype is developed. Prototype is based on softwaredefined radio technology using Universal Software Radio Peripheral hardware from Ettus Research company. This hardware allows to down or upconvert signals, perform filtering and stream a very high amount of data to or from general purpose computer. To process this data the stateofart multithread software was developed for use with Intel Core i7 central processing unit. The experiments with prototype was conducted at the test site. Results of experiments confirm the efficiency and precision of the proposed algorithms of generation and processing signals in the system. Keywords: local positioning, prototyping, softwaredefined radio 

Research on the impact of spoofing interference on the equipment of navigation information consumers
This experimental research confirms the vulnerability of geodetic user equipment of global navigation satellite system (GNSS) to spoofing attacks. The functions of user equipment are based on the receipt of radio frequency signals transmitted by navigation satellites. The structure of the signal for civil consumers is made up of unencrypted code, which is accessible by the general public and lets one deceive a GNSS receiver by broadcasting counterfeit GNSS signals, structured to resemble a set of normal GNSS signals. As part of this research, spoofing signals are created by a multiGNSS constellation simulator that has 24 channels, supported signals GPS ranging code C/A radio frequency link L1 and GLONASS standardprecision signal in L1 band. Spoofing signals are added to the authentic signal ensemble and impact the reference station receiver Topcon NETG3A. When the spoofing signal ensemble is at low power, positional accuracy decreases. When the power of the spoofing signal ensemble increases the number of satellite signals suitable to determine position decreases. If the threshold level of power of the spoofing signal ensemble is reached, then there is inaccurate information from the user equipment and the receiver plots erroneous coordinates. The disadvantage of this type of spoofing signals is the anomalously high value of signaltonoise ratio that can detect spoofing signals and can be used to create systems counteracting spoofing signals. The absence of detection subsystems for deceptive spoofing signals is revealed by user equipment in automatic mode. Keywords: global navigation satellite system, vulnerability, spoofing 

Informatics, computation engineering and management  
System analysis, control and data processing  
This article is devoted to the software complex of automatic planning of using facilities of Ground automatic Control Complex (GACC) and the results of its trial experiment. The way of software complex design includes formulation of complex creation problem, development of requirements and solution to the existing problems, structure definition and the conduction of the trial experiment of software. As a result of work there has been created a new software complex which allows solving the problem of the automated task of plan creation, its automated verification, resolution of conflicts, forecast of the state of the system «Orbital Group of Satellites — Facilities of GACC» depending on the management decisions. The trial experiment of the software complex in the modes of its functioning has shown an ability to perform software complex functions in accordance with the forecasted dynamics of system «Orbital Group of Satellites — Facilities of GACC» On passing the test the designed software complex will be implemented in the hardwaresoftware complex of the Center of situational analysis, coordination and planning.
The proposed automated planning facilities of GACC software complex can be applied in the management of automatic satellites of scientific and socioeconomic purpose. The methodological basis of the software complex is built on the earlier developed models and methods, which have improved the efficiency of the formation of the plan of using the facilities of GACC. On passing the test the designed software complex will be implemented in the hardwaresoftware complex of the Center of situational analysis, coordination and planning. Keywords: software complex, planning, satellite, Ground Automatic Control Complex 

CAD systems  
The article discusses the layout automation products, highdensity layout (especially aircraft equipment). Layout Automation is one of the most difficult tasks of design automation. Therefore, the aim of this study is the development of intelligent algorithms and automated layout relevant special mathematical and software. The paper shows that with an abundance of computeraided geometric models to describe the geometric shape of any complexity, their use in automated layout tasks, does not provide a solution to the problem the most dense placement. The mathematical formulation of the problem as a layout optimization problem, indicating its objective function, constraints and performance criteria. In this setting, the efficiency criterion adopted most dense arrangement of composable objects in a specific confined space. An approach (using geometric models receptor), which is a sampling space for placing individual elements (receptors) having discrete values of «0» or «1» depending on whether this receptor belongs to a specific object or not. This approach allows for the creation of geometric models of the automated layout pass from exhaustive search of accommodation composable objects to intelligent algorithms, the automated placement. This is due to a unique easy to determine cases of mutual intersection composable objects, both among themselves and with the prohibition. The article shows the results of approaches and the use of geometric models of the receptor at the automated layout aircraft. In particular, we show their use to address such trivial tasks automated layout as void spaces, bodily tracing software service areas have arranged objects. The results of the study the accuracy and performance of the proposed methods. Simulation possible to estimate the CPU time and costs, which are also of the expected size increasing with decreasing d receptor and a corresponding increase in the accuracy of the model by a parabolic relationship between a few seconds to about 3 minutes. This means that the amount of the receptor, for example, 0.2 mm form submission error is 0.06 mm ± 0.18, which is sufficient for conceptual design stage is a reasonable compromise between the expected accuracy of the algorithm and the cost of computing resources for its implementation. Application of the results — the creation of new methods and algorithms in the library automated layout methods. It is shown that the use of geometric models of receptor has both its advantages and its drawbacks, one of which is the need to block the conversion of geometric models’ parametric model ↔ receptor model "that brings some additional difficulties in the interpretation of the results of the automated layout. Rapid growth performance computing makes discrete receptor models more attractive and increasingly popular practice in the design of hightech equipment. It is shown that the receptor geometric models provide sufficient accuracy and performance at the stage of conceptual design of aircraft. At the same time that there is considerable scope for reducing the computing power required and the implementation of receptor geometric models (for example, by the use of adaptive size of the receptor). Keywords: design automation, layout, geometric modeling, receptor geometric models, shape recognition, connecting trails, service area 

Mathematica modeling, numerical technique and program complexes  
Gravitational waves are known to be one of the most wonderful predictions of Einstein’s Theory of General Relativity. In this theory the possibility of propagation metric tensor perturbations as waves follows from the hyperbolic Einstein’s equations. However, for a long time, no attempt to detect gravitational waves or any trace of their existence succeeded. Therefore, in scientific literature, time to time, some doubts had been expressed about the existence of gravitational waves. The situation changed dramatically after the observation of the double pulsar system PSR 1913+16 which began in 1975 and showed that the power is leaving the system for gravitational waves, as it had been forecasted in the General Theory of Relativity. However, the most convincing proof of the existence of gravitational waves was demonstrated in September 2015, when the LIGO Observatory registered a sufficiently powerful pulse of gravitational radiation. Therefore, nowadays, the most significant task in the theory of gravity is the theoretical analysis of the processes which leads to emission, detection of gravitational waves, and finding the ways to practical mastering the gravitationalwave channel of communication. In this paper we construct a mathematical model of the electromagnetic process for the emission of gravitational waves, generated during propagation of electromagnetic waves in a constant magnetic fields. According to the mentioned in the article calculation, such processes lead to the high frequency gravitational waves emission and can be used to find a practical mastery of radio, microwave and optical frequency gravitational — wave channel. A direct calculation shows, that taking into account the curved shape of the front of electromagneticwave changes substantially the amplitude asymptotic (wavefunction) which has been created by the gravitational waves. This fact should be taken into account for assessing the efficiency of an electromagnetic wave transformation into a gravitational one on astrophysical conditions, as well as in the calculation of laboratory sources of gravitational radiation. Keywords: mathematical modeling, gravitational waves, electromagnetic waves, Einstein equations, gravitational – wave channel 

Methods and systems of information protection, information security  
The research aims at creation of an authentication system based on the traditional password protection with biometric addition, providing security indicator improvement compared to the original version. This addition is a dynamic handwritten digital signature authentication based on neural networks and Bayesian classifier combining. The paper considers the possibility of combining classifier based on neural networks with Bayesian classifier by linear combination of outputs to reduce the overall probability of error classification regardless the error types. Within linear combination, neural network plays the leading role, since the results of neural network match those of linear combination. Results similarity was confirmed by comparison with expected values. It means that a linear combination without using errors of types 1 and 2 taken into account separately does not make sense because of the possibility of implementing neural network instead of linear combination. Thresholds of authentication for using errors of 1st and 2nd types taken into account separately accounting were created. The systems based on modified naive Bayes classifier and neural network, depending on the thresholds of authentication, was implemented. Software module for calculating errors of the 1st and 2nd type in neural network and Bayesian classifier was developed. The behavior of user dynamic parameters within signature recognition systems was presented. Performance evaluation of authentication system in the form of probabilities of errors of 1st and 2nd types was obtained. Keywords: identification, signature, Bayes classifier, neural network, integration, linear dependence, type I and type II errors 