# 2016. № 89

## Mechanics

### Theoretical mechanics

Skorobogatykh I. V.

The problem of the satellite, consisting of axially symmetric solid and deformable parts, motion relative to the center of mass is studied in the case, when its center of mass is moving in a circular orbit around the center of gravitation attraction. The Voigt-Kelvin model is used for deformable material description. Equation of deformations and motion around the center of mass is obtained using d’Alembert-Lagrange variation principle. The elastic displacement vector is expanded in series of free oscillations nodes of deformed part of the satellite. These nodes are orthonormal. The deformations are considered as quasi-static. This is used for obtaining of approximate solution of deformation equations. These solutions are substituted in equations of rotation. The special case of plane rotations of satellite is considered. Two series of the satellite equilibrium positions in orbital coordinate system are found. The first is the case when the satellite symmetry axis is directed along the radius vector of the center of mass, and the second is the case when the satellite symmetry axis is orthogonal to the radius vector of the center of mass. The first series of equilibrium positions is asymptotically stable, and the second is unstable. The work shows that the evolution of every plane rotational motion tends to the first equilibrium position. Thus, it is shown that the satellite is captured in a stable equilibrium position, in which the satellite symmetry axis is directed along the radius vector of the center of mass in the orbital system coordinate.

Keywords: attractive center, axisymmetric satellite, linear theory of viscoelasticity, the evolution of rotary motion

Bardin B. S., Chekina E. A.

We deal with the stability problem of a resonant rotation of a symmetric rigid body about its center of mass in an elliptical orbit. The motion of the body can be described by canonical system of differential equations with Hamiltonian

where , and are the satellite's equatorial and polar moments of inertia respectively; is the eccentricity of the orbit; ν is the true anomaly.

If the parameters α, satisfy the relation then the canonical equations with Hamiltonian has particular solution [2].

The resonant rotation is a planar motion such that the body completes three rotations in absolute space during two orbital revolutions of its center of mass. In this paper we study the stability of the resonant rotation in an extended formulation taking into account both planar and spatial perturbations.

Let us introduce perturbations by means of the formulas

The equations of perturbed motion have canonical form, that is the variables satisfy the equations

By analyzing linearized equations of perturbed motion there was found eccentricity interval , where the resonant rotation is unstable. Outside this interval a nonlinear stability study has been performed and subintervals of formal stability and stability for the most of initial data have been found. The conclusions on stability were obtained by an analysis of coefficients of the Hamiltonian normal form normalized up to terms of fourth order. A nonlinear normalization of the Hamiltonian was performed by using an approach based on construction of symplectic map generated by the Hamiltonian system.

Table 1. Results of the stability study in nonresonant case

 Subinterval Conclusion on stability stability for the most of initial data formal stability stability for the most of initial data

Keywords: Hamiltonian system, symplectic map, normal form, resonance, satellite, stability

### Deformable body mechanics

Yershova A. Y., Martirosov M. I.

Composite structures are introduced into the aircraft industry very rapidly, ranging from small nonessential components to the most important systems. This tendency is associated primarily with the possibilities opened by the implementation of new materials, which in aerospace industry cannot be done without significant volume of research effort on studying physical and mechanical features of the composites, and methods for evaluating their performance. In this regard, the study of granular composites based on unsaturated polyesters requires a separate study, development of techniques of carrying out experiments to determine the mechanical characteristics and properties, selection of appropriate constitutive equations for describing the features of the mechanical behavior of the material.

Due to its properties, and mechanical properties one of the most interesting and promising types of polymer composites is injection molding artificial stone, which is a structural composite material, which main components are unsaturated polyester resin and inert granular filler. The article presents an experimental study of the mechanical properties of casting artificial stone, namely, equipment selection for the experiment, developing methods and conducting experiments to determine mechanical characteristics of the material.

The results of mechanical tests allowed, firstly, define elastic characteristics of a new class of granular composites based on unsaturated polyesters — artificial injection-molded stone. Factors of compliance and calibration the fracture toughness experimental values are the intensity of energy release G1С and critical value of stress intensity factor К1С. A comparison of the mechanical characteristics of the material obtained with different types of tests was made. The obtained values of the mechanical characteristics appeared to be comparable with the characteristics of natural stone.

It is shown that the material properties strongly depend on the type of stress state. The technique of determining the parameters of the equations is adopted to describe the established dependence of the elastic characteristics from the type of stress state. The obtained values of the parameters defining relations allow solve wide range of problems on stress-strain state and health products of the artificial injection-molded stone.

Currently this material is used in aviation and aerospace, as non-radioactive and light finishing material.

Keywords: experimental studies, elastic properties of a material, polymeric composites, granular composites, artificial injection-molded stone

### Fluid, gas and plasma mechanics

Nikitin P. V., Tushavina O. V.

The presented work performs the analysis of energy balance equation in the interaction zone of hypervelocity heterogeneous stream with solid surface. The problem is solved analytically and aims at revealing the physical entity of the kinds of energies realized while interaction of a heterogeneous stream with a flat impediment. The necessity of solving such problem associated with the study of impact mechanism of «k-phase» when forming various functional coatings on the surfaces of low-temperature structures by high-speed heterogeneous flows. A particle temperature and the surface temperature in the impact area play decisive role when forming high-quality coatings on the surfaces of the structures. In this regard, one of the problems of the present work consists in determining the levels of the said temperatures.

In this work, we obtained the equation of energy balance in the impact area of high-speed particles and a hard surface. Solution of this equation allowed us to derive the relationship to calculate the instantaneous temperatures of the particle and the solid surface in the impact area.

Keywords: heterogeneous stream, the impact mechanism of the particle-phase balance of energy, ethno functional coating, the deformation energy upon impact, the degree of deformation of particles, deformation of the substrate under high-velocity impact

### Dynamics, strength of machines, instruments and equipment

Shakirtov M. M.

The connection between the external load cycle asymmetry coefficient and the characteristics of loading cycle of the material at the apex of crack-like cut is observed.

The cyclic loading of a flat specimen with central crack-like cut is observed. The specimen is made of cyclically hardening material. The external load cycle asymmetry coefficients differ from 0 to 0.9. The problem is solved by finite element method in two-dimensional formulation. The specimen is in plane stress conditions. The finite element model is analytically verified. It is confirmed that the proposed model produces nonlinear static simulation with sufficient accuracy.

For cycles with different values of the asymmetry coefficients stress values at the tip of the cut have been tracked throughout loading history. It was found out that the stress state evolution process radically changes when reverse plasticity takes place at the crack-like cut tip.

It was illustrated that any asymmetry coefficient of the external load produces symmetrical loading cycle at the tip of the crack-like cut. The amplitude of this symmetrical loading cycle increases from cycle to cycle. Moreover, the closer the external load asymmetry coefficient value comes to the unity, the smaller the loading cycle amplitude rate of increase becomes.When its value is close to unity, reverse plasticity does not occur. In this case material around the tip undergoes asymmetrical loading cycle with constant amplitude.

Keywords: crack-like cut, cyclic loading, the asymmetry coefficient, plastic zone, stress concentration

## Aeronautical and Space-Rocket Engineering

### Aerodynamics and heat-exchange processes in flying vehicles

Popov S. A., Gondarenko Y. A.

Purpose of the work is investigate of the influence of a condition of a tear-off and vortex flow around a maneuvering aircraft with external suspension on his aerodynamic characteristics.

Methods of the work are the analysis and numerical experiment.

Results of the work. Currently the of a condition of a tear-off and vortex flow in the mathematical model of the aircraft is taken into account by entering the internal variable x. The behavior of this variable can be described by the equation:

, (1)

where τ1, τ2 — time constants, caused by a lag effect of the processes of development of separated flow around or recovery non-separable flow.

In the simplest case, the variable x may be regarded as the relative coordinate of the point of separation of flow from the upper airfoil surface or the point of destruction (explosion) of vortices above the upper surface of the wing. For a full layout of the aircraft with the wing of complex shape in plan, including external suspension, a of a condition variable x has a different more complex form and appears in the form of a generalized variable.

It is known that the parameters characterizing the state of a tear-off and vortex flow, can be used:

— coordinate of the point of separation of flow in each section of the streamlined surface;

— number and area zones of separated flow;

— the coordinates of these zones on the streamlined surface;

— parameters characterizing the symmetry (asymmetry) of zones of separated flow on a streamlined surface.

The analysis of the above parameters suggests that they all depend on the location along the wingspan of the points of separation (R) and reattachment (S). The locus of these points for various sections of the wing will determine the position of the lines of of separation (lR) and reattachment (lS). In this case, a generic variable x can be represented by parameters which determine the position of the lines of separation and reattachment.

To determine lines of separation and reattachment with the use of the software Ansys Fluent, the authors investigated the process of flow airflow around the maneuverable aircraft at high angles of attack with various embodiments of external suspension. The results of the research are:

− a field of condition of a tear-off and vortex flow of profiles of a wing and the stabilizator of the maneuverable aircraft airplane with different options of placement of external suspension brackets and without them;

— analysis of the impact properties of the external mounts on the condition of a tear-off and vortex flow around of the maneuverable aircraft;

− analysis of influence of a status of a tear-off and vortex flow on aerodynamic characteristics of the maneuverable airplane;

− a mathematical model of influence of a status of a tear-off and vortex flow on aerodynamic characteristics of the maneuverable airplane with external suspension brackets.

Application area of results. Results of this work can be used in scientific and design organizations engaged in development of aerodynamic configurations maneuverable aircraft and control systems, and also in aviation institute of higher education for educational process improvement.

Conclusions.

Thus, the mathematical model of influence of a status of a tear-off and vortex flow on aerodynamic characteristics of the maneuverable airplane with external suspension brackets includes two-dimensional fields of condition of a flow of profiles of a wing and the stabilizator for different sections to which each point there corresponds a certain value of lift coefficient . Such dependencies allow using known types of interpolation with the required degree of accuracy to calculate the values of aerodynamic characteristics for any arbitrary state of flow, which depends, including the availability of external suspensions. This eventually makes it possible to solve equation (1), in which the dynamic variable x will be used for the data status field of the flow profiles for stationary cases .The result of solving equation (1) will be state field of the flow profiles for non-stationary cases .

Keywords: aerodynamic characteristics, tear-off and vortex flow, the mathematical model, external suspension brackets

### Design, construction and manufacturing of flying vehicles

Arutyunov A. G., Dydyshko D. V., Kuznetsov K. V.

Design of a new aircraft starts fr om collecting and analyzing of the data on aircraft created earlier, being in operation prospective models. It allows understanding the position of the aircraft under design, evaluate its competitiveness, and identify the areas wh ere the breakthrough technical solutions are required.

This article presents a brief analysis of the history of initiation and development of the transport airplanes. It outlines the aircraft, which can be considered the most generic for the given class. The article presents and analyzes the data on certain transport and passenger aircraft characteristics, and describes the transport aircraft most distinctive features.

Transport aircraft existing in the world are necessary to classify according to their purpose as follows: military transport aircraft, civil transport aircraft with cargo ramp, freighter aircraft and special transport aircraft.

The development of the transport airplanes can be traced by the examples of the following aircraft, characterizing each of these stages:

Arado Ar.232 — the first airplane designed for special military transport assignments;

Me.323 — the first serial military transport aircraft;

Lockheed C-130 Hercules and Antonov — the first mass military transport aircraft;

Antonov An-22 — the first heavy-lift transport aircraft;

Lochheed C-5 Galaxy and Antonov An-124 Ruslan — the first super heavy-lift transport aircraft.

Some parameters dependencies of these airplanes, characterizing their transport capacities, presented in this article, reveal that the advanced transport airplane (ATA) will not probably have the cross-section of its cargo bay more than 27 ... 30 m2. The ATA’s useful-to-takeoff load ratio will be not less than 65%. There are no preconditions for the ATA cruising flight speed growth, and most likely it will remain at the level of ≈800 km/h. The commercial transport airplane will most probably be equipped with two turbojet bypass engines with higher bypass ration ≈ 10. Takeoff thrust of currently existing engines allows create transport aircraft with take-off weight of about 280...300 tons.

Keywords: transport aircraft, cargo ramp, cargo bay, advanced transport aircraft, military transport aircraft, special transport aircraft

Platonov I. M., Bykov L. V.

While performing mathematical modeling, it is imperative to have in mind the inherent inaccuracy of numerical methods and the precision of the solution, which depends on the finite elements discretization. In this paper the influence of mesh quality on results accuracy will be studied based on the case of fluid flow over a swept wing NFL(2)-0415. A series of experiments were performed on a wing with above mentioned profile in the Arizona State University.

To perform a mathematical modeling a system of Navier-Stokes equations and a turbulence model were used. In this instance the turbulence was modeled using the intermittency model.

To estimate mesh quality the location of boundary layer transition along the chord length was determined by the intermittency parameter. When intermittency equals 0 the flow is considered laminar, when it equals 1 — it is fully turbulent. Results acquired during CFD modeling were compared to experimental data.

An important factor to consider is the local wall distance y+, a parameter which signifies the normal distance fr om the surface to the center of first cell. The correct description of boundary layer highly depends on such parameter, which, consequently, affects flow regime and aerodynamic parameters, such as lift and drag.

Three different sizes of mesh were reviewed. A mesh independent solution was achieved, wh ere the results stopped improving with increasing mesh size. These sizes were 1.4 and 2.3 million elements, with the appropriate local wall distance y+<10.

It is a good practice to always perform mesh independence studies whenever mathematical modeling is involved. Mesh quality criterion such as y+ must be applied to cases of near wall flows, i.e. the boundary layer flow.

Keywords:

Vershkov V. A., Kritsky B. S., Makhnev M. S., Mirgazov R. M., Trebunskikh T. V.

The results of numerical flow simulation around the helicopter rotor have been obtained in commercial programs FloEFD, Ansys Fluent, RC-VTOL are presented in article. The program RC-VTOL was developed in TsAGI.

The main aim of the article is to compare the program’s features and requirements. The conclusions are made about the software usability to solve problems concerning the helicopter rotor.

The main features of the program FloEFD are the automatic grid generator, which build a Cartesian grid adapted to the body, and the turbulence model using a «Two-Scale wall functions.» RC-VTOL is based on the nonlinear vortex blade theory. The blade is modeled as infinitely thin surface. Vortices are trailed from the sharp trailing edges of each rotor blade. Therefore, for the calculation it is not necessary to build a three-dimensional grid, which may cause a numerical error.

The validation of the program FloEFD was made at the first stage of calculations. For its validation the Caradonna and Tung benchmark for rigid two-blade rotor are used. The hover mode with the rotation frequency n = 2500 RPM was considered. The numerical data were compared with the results obtained in the program NUMECA FINE/Turbo. The comparison shows satisfactory agreement between calculations in commercial programs and experiment.

The horizontal flight regime (V∞ = 11.5 m/s) was discussed at the second stage. The experiment was made by L.S. Pavlov in a wind tunnel TsAGI T-105. The rigid one- and four-bladed rotor with a frequency n = 348.5 RPM was considered as the object of experiment.

Calculations were made in three different software packages: FloEFD, ANSYS Fluent and RC-VTOL. Analysis of the results, based on the calculation of the speed and accuracy of the results, shows the advantages and disadvantages of each program. The RC-VTOL program required 10 minutes for creating a numerical model of the rotor and the numerical grid and 20 minutes for the calculation of each case. The calculation in ANSYS Fluent took about 48 hours to simulate each case and about seven days to set up the project and the calculation mesh. Setting up the model and generating the mesh size of about 2.7 million cells in the program FloEFD took about 35 minutes and about 36 hours for the calculation.

The results show satisfactory and in some modes good agreement with the experimental data in all software its mean about their suitability for the calculation of the helicopter main rotor.

Keywords: main rotor, aerodynamic characteristics, numerical methods, CFD software

### Thermal engines, electric propulsion and power plants for flying vehicles

Avdeev A. V., Metel'nikov A. A.

There are no open articles about air-based continuous chemical HF(DF) laser for space debris combat. However, air-based laser installations are operate and maintain easier than space laser installations. This point makes their use attractive for solving space debris problem.

The subject of research is the system of laser air-based power plant (LAPP) — spacecraft (SC) — a fragment of space debris (FSD). The object of research is performance characteristics of major subsystems LAPP for space debris combat. The aim of the research is to define the basic performance characteristics LAPP for space debris combat. In this work carried out LAPP system study. Also functional system diagram and working algorithm of the unit are designed.

There are basic LAPP subsystems:

• sensor channel;

• laser channel;

• acquisition and tracking subsystem;

• control subsystem.

The main factors which affect LAPP performance are defined. There are LAPP optic system disalignment caused by aircraft vibration and transmitted energy decrease caused by effects of aero-optical disturbances.

In this work was defined permissible guidance system error for space debris combat. Also the transferred energy and the minimum aperture of the laser channel were evaluated in this work.

The calculation was made for system features:

LAPP characteristics:

•  altitude — 20 km;

•  pulse energy— 1,35 J;

•  pulse duration — 10 ns;

SC characteristics:

• altitude — 250 km;

• collecting aperture — 15 m;

In summary, the minimum aperture of the laser channel was defined as 0,08 m. The maximum guidance system error was evaluated as 7’’. The maximum guidance accuracy was 3’’.

Keywords: space debris, laser air-based power plant, DF-laser

### Dynamics, ballistics, movement control of flying vehicles

Matyushin M. M., Lutsenko Y. S., Gershman K. E.

The paper is devoted to spacecraft and space groupings control and functioning issues systematical consideration at large. For the first time, the authors present in this paper the structural diagram of the existing spacecraft (space grouping) flight control system, reveal space grouping flight operating control, control tools and control objects. Flight control processes were analyzed within the framework of the existing system, and flight control generic methods shortcomings were considered. The paper is focused on the issues of flight operating control developing and space grouping flight control formation. The paper shows that the adopted nowadays control structure has rather complex arrangement. Besides, flight controls computing and forming space groupings flight control vectors are scattered in space, and each of them computes only the part of the common space groping flight control vector. This, in its turn, leads to the iteration process of flight control vector searching. It does not allow solving the problem of space grouping flight optimization and necessitates multiple conformances. Consequently, the process of flight control vector computing has low efficiency and the occurrence of conflicts when operative treatment of the decision-making personnel is required. Based on the analysis of space grouping flight control procedures the authors proposed new flight operating control structures, allowing increasing its quality. In the authors’ judgment, the last version of space grouping flight operating control structure is the most adequative to modern requirements on the efficiency, cost and reliability of space grouping flight control vector developing, and complies with modern technical capabilities. Space grouping operating control optimality index quantitative analysis can be obtained based on the flight control technologies models. Such models allow developing flight operating control cost estimation, time-dependent and reliability models. The results of the studies on these issues will be presented in subsequent publications.

Keywords: control system, flight control of the spacecraft and space groups, structure of the system of calculation of parameters of flight control, flight control center, flight control tools

Barkova M. E.

The main problem of solar space power plant (SPS) consists in energy transfer to the Earth with minimum losses. The paper aims at the SPS space segment orbit parameters selection. It presents the SPS space segment orbit selection technique development and modified mathematical model of movement with account for perturbing factors associated with the energy transfer. The problem is reduced to obtaining the exact provision of the SPS space segment in an orbit, determination of rektenn ground segment coordinates and their synchronization. The paper deals with the problem of SPS space segment provision definition. The obtained results can be applied to SPS design and operation.

The author comes to a conclusion that the SPS space segment should be low-orbital. The results of the perturbing factors associated with SPS operation impact are summed up at the end of the paper. The paper reveals that the perturbing factors associated with SPS operation do not affect SPS space segment movement.

The merit of the paper consists in developing the SPS space segment orbit selection technique, and revealing the perturbing accelerations caused by the solar space power plant operation.

Keywords: Solar Power Satellite, Solar Power Satellite space segment, Solar Power Satellite space segment orbit, spacecraft

Vereshchikov D. V., Kuznetsov A. D.

Now there was a requirement of landing of heavy cargo. In the course of the movement of cargo on a cargo cabin of the military transport plane at the time of dropping arises indignation. It considerably complicate piloting and create danger of an exit of parameters of flight out of limits of operational restrictions. The mean of landing from extremely small altitude provides the highest precision of a landing of freights. Extremely small altitude is called transport plane flight altitude at distance between wheels of the released chassis and the Earth’s surface of 5±2 m. Piloting even more becomes complicated because of need of parrying of the destabilizing moments of the earth in close proximity. Now development of digital computer facilities at the high level. Therefore there was an opportunity to solve the specified problem by partial automation of flight control of the military transport plane when landing with use of an adaptive mean of control. For development of a way of adaptive management and carrying out imitating modeling the mathematical model of the difficult dynamic system «plant — cargo» has been created. This model considers mutual inertial interactions of her elements. The mathematical model is realized in the Matlab@Simulink program. Comparison of results of modeling with materials of flight tests has confirmed reliability of the created model. The mean of adaptive management is based on the principle of compensation of external indignation because of fast by change of position of the center of masses when moving cargo. Direct measurement of the revolting moment is inaccessible. It is estimated at rate of control on change of the parameters of flight bearing information on indignation. This assessment is carried out by parametrical identification of aerodynamic characteristics of the plane by means of reference model. Identification of unknown aerodynamic characteristics is made by a recurrent method of the smallest squares. Indications of sensors of parameters of flight are used. Thus the new way of adaptive management of military transport plane at a stage of direct dropping heavy cargo is developed. The mean consists in formation of correcting elevator deviation on the basis of the current identification of aerodynamic characteristics of the plane. The way provides automatic stabilization of angular provision of the plane. There is compensation of the revolting moment. Results of mathematical modeling confirm operability of this way of adaptive management of plant when landing heavy cargo from midget heights. Due to compensation of the revolting moment throwings of kinematic parameters of flight are reduced. It facilitates work of the pilot and will allow to increase maximum weight. Level of safety of flight will be high. This way is offered for realization for the first time as adaptive control algorithms are applied only by maneuverable planes now.

Keywords: adaptive control mean, the non-parachute landing of a heavy cargo, identification, recurrent least squares method

Evdokimenkov V. N., Kim R. V., Yakimenko V. A.

This paper presents an approach for operational control and post-flight analysis of pilot’s activity features, which would increase the level of safety and efficiency level of modern aircraft. The presented approach is based on usage of individual-adapted neural network models, which characterizes individual piloting style. The designed models might be used in so-called pilot’s support systems which main function is generating recommendations during the flight. These recommendations may increase the pilot’s control actions efficiency.

The considered models provide an opportunity for determining the prediction of accuracy of bringing the aircraft to the terminal point of the trajectory on the basis of the current ergatic system “pilot-aircraft” state, which includes components that describe technical state and pilot’s activity features. The structure, parameters and set of neural network models inputs are determined based on data recorded by flight data recorders in previous flights and continuously refined as new data become available. The multilayer perceptron (MLP) might be used as an example of considered artificial neural network model. The main property of MLP is an ability to approximate any functional relationship between current state of ergatic system “pilot-aircraft” and the prediction of accuracy.

We calculate the information signal value, which is displayed, on the basis of the difference between the predicted and required state in a terminal point. The given results confirm the efficiency of presented approach.

Keywords: Artificial neural network, pilot’s activity model, pilot’s support systems

## Instrument making, metrology, information and measuring equipment and systems

Vavilova N. B., Parusnikov N. A., Subkhankulova G. A.

In the article the navigation problem for an autonomous underwater vehicle (AUV) is under consideration. In AUV’s navigation the following sensors are usually used: transponders that measure the distance from the AUV to transponders in known locations, velocity sensor, depth sensor, gyroscopic course sensor. A peculiarity of this work consists in the usage of Strapdown Inertial Navigation System (SINS) of medium accuracy together with mentioned above sensors. AUV’s navigation problem is posed as SINS correction problem with aiding measurements. Principal possibilities of this approach are investigated on the basis of the analysis of covariance with experimental data.

AUV are used in a wide range of scientific and applied research of ocean, such as a marine geological research, a study of the seafloor, ecological research of water environment. The value of the data provided by the underwater vehicle depends on the accuracy of a navigation system used. That is why the development of high-precision AUV’s navigation system is relevant today.

The presented paper differs from previous investigation in this domain by taking SINS of medium accuracy into consideration. Furthermore, data provided by SINS is regarded as the main data. Resulting navigation solution is based on SINS integration with aiding measurements delivered by special sonar beacon with known location (by means of GPS), sensors of velocity and depth. The estimation algorithm is based on technique of Kalman filtering. Mathematical models take into account specific peculiarities of AUV motion (low speed, relatively short distance between a vehicle and a beacon). The two typical types of the AUV’s motion were taken into account. The research method was based on analysis of covariance analysis with implementation of real data.

The experimental data was provided by scientific educational center «Underwater robotics», Far Eastern Federal University and IPMT RAS. Marine Autonomous Robotic System «MARK» has two main hardware parts — an autonomous underwater vehicle and an afloat vehicle. An equipment of a shore control center is also included. The afloat vehicle is a mobile beacon with a transponder. The location of the latter is determined by GPS. Vehicles have radio links with hydroacoustic communication system.

The presented article studies two representative mechanical trajectories of MARK’s motion. In the first case AUV moves rectilinearly with the constant depth, an afloat vehicle moves along a «zigzag» path with the side 200 m, intersecting the AUV’s trajectory. In the second case AUV moves along a square path clockwise with the side 100 m, an afloat vehicle moves along a square path counterclockwise with the side 200 m. In both cases the direction on the beacon was being changed and as a result the problem of position’s estimation became well-conditioned.

Derived results show that the standard deviations of the position’s estimation errors are less than 3 m.

The results of the preliminary analysis that was done give evidence the proposed algorithm can improve the accuracy of aided AUV’s navigation system in several times.

Keywords: strapdown inertial navigation system, calibration, high-precision turntable

Tarygin I. E., Kozlov A. V.

The paper treats the modification of previously developed inertial measurement unit (IMU) calibration technique [1-3, 8] that uses a single axis turntable of a low grade with horizontal axis of rotation. It allows multitude of parameters to be determined in a simple experiment which requires neither to meet any strict conditions nor to obtain any measurements fr om a test bench. Originally, the method was designed to estimate null biases, errors of scaling factors and sensitive axis misalignments of IMU sensors. Having been tested in industry for IMUs of different grades for a long time, this method proved its suitability and shows a great potential for extension. Previously it was shown how calibration method can be modified in order to account for sensor error model parameters variation over temperature [3]. The present work aims to include temperature time derivative variations as well.

Temperature time derivative variations in sensor output are commonly observed in fiber optic gyroscopes [4, 5]. Conventional approach considers conducting a special experiment for these variations to be determined. We suggest an extension of the method mentioned above that treats the introduction of the coefficients of temperature time derivative variations of instrumental error parameters into sensor measurement model. The calibration experiment left the same, except that temperature time derivative is expected to be non-constant to ensure the observability of these coefficients. Our study is intended to understand which temperature variation patterns establish good observability of desired coefficients, which of them do not and so on.

The paper provides analytical investigation of the observability of time-temperature derivative coefficients and investigation via covariation modeling. Two different temperature experiments are considered: the self-heating of the IMU and a calibration experiment carried out in a thermal chamber wh ere temperature is automatically controlled and decreases and increases linearly over time. Both of these two modes are examined in terms of possibility to determine coefficients of inertial sensor error variation due to the change of temperature time derivative.

Keywords: strapdown inertial navigation system, temperature calibration, fiber optic gyroscope

Matasov A. I., Tikhomirov V. V.

The paper considers the calibration of a strapdown inertial navigation system (SDINS) while the vertical axis turn around. The system measures the location and relative velocities of an object. To implement the parameter estimation the Kalman filter is employed. The turn is required to obtain the estimates of the additive constant errors of the accelerometer unit and angular velocity sensors with sufficient accuracy. The problem is studied in a unified experiment that includes the axis turn around and two static positions of the system during certain time intervals. The main difficulty consists in the presence of the derivative of the angular velocity in the system matrix. In order to overcome this circumstance, the sampling is executed by analytical calculation using the integration by parts. Such approach allows us to exploit all experiment data more fully. In traditional setting, the analysis is partitioned into two independent steps, which are related to the SDINS case positions before and after the turn. Besides, due to the alignment procedure, the initial covariance matrix is not diagonal. A mathematical formalization is presented, the corresponding software is developed, and the results of simulation are described. The obtained results verify the efficiency of the proposed approach. The system accuracy is really improved by the inclusion of the turn into the active part of the calibration experiment.

Keywords: strapdown inertial navigation system, alignment, instrument errors, instrument trihedron, exhibition, Kalman filter

### Instruments and control methods of environment, substances, materials and products

Rybin Y. M., Ageev I. M., Bubnova M. D., Shishkin G. G.

The paper presents the long-term fluctuations of the distilled water conductivity obtained experimentally. It shows that those fluctuations presents the cause of water conductivity temperature coefficient values variations in primary information conductometric water transducers.

The method is based on the earlier discovered phenomenon of water electric conductivity properties changes under magnetic field impact. The experimental study of various physical factors affecting water presents significant difficulties. Thus, at this stage of study the most important task consists in improvement of instrumentation and measuring technique to provide measurement repetition and obtain accurate and reliable experimental data.

The measured values of the distilled water conductivity temperature coefficient in the conductometric cell is largely dependent on the rate of temperature change in the course of measurement process. The lower the speed herewith, the greater the deviation from the TAP table value of 2%/°C. With classical linear temperature dependence of water electrical conductivity superimposed by large enough statistically significant long term variations thereof observed at temperature changes speeds of dT/dt less than 0.1°C/h, and possibly due to fluctuations in the basic mobility of charge carriers in water — hydrogen ions. The time dependence of the distilled water electrical conductivity at slow changes of its temperature has a pronounced cyclical abnormity.

The presented study provides a starting-point for further research.

Thus, the developed water electric sensors and instrumentations allow measuring and studying weak ELF magnetic fields excited in near-Earth space. The measuring problem of ELF weak magnetic fields caused by ionosphere phenomena and associated with solar activity effect on Earth space is of great interest for both scientific and practical applications. The study of magnetic field impact on water is very important for magnitobiology, water physics, as well as for solar-earth connections and solar activity effect on biosphere and noosphere. From a practical standpoint, this problem is very important for determination of ELF wave effect on space radio channels parameters of aerospace information system.

Keywords: conductometric cells, water sensor, temperature coefficient of conductivity, long-term fluctuation hydraulic conductivity, water sensors, thermal conductivity coefficient, long-term fluctuations of water conductivity

Stepanova M. A.

Compression electrical solderless connections are widely used in electronic systems, including devices designed for extreme operating conditions, such as automotive and aerospace equipment. The contact insertion gained such popularity due to a number of advantages over conductive pastes, welding and soldering. It demonstrates the rapidity of execution, relative ease of performance, efficiency and reliability. In most cases, forging connections are made in the holes of the PIN contact pressing mounting basic — the printed circuit board.

This article presents solderless connections, namely, press-in connections. Their advantages, basics of contact formation and application fields of this type of connections are shown.

One of the fundamental criteria for ensuring the reliability of press pin connection is the force hold contact in the hole of the PCB. This paper shows how high temperature affects the force hold contact in press-fit connection. The conducted experiments revealed clearly that the high soldering temperature could not significantly reduce hold force of the connection.

Keywords: avionics; solderless connections; printed circuit boards; press-fit; forging connections; connectors; tolerances and fits; the combination of tolerances

### Information and measuring and control systems

Kokuev A. A., Makarov K. V., Timoshenko A. V.

The paper aims at vindication of the necessity to account for radar stations blind areas while controlling airborne meteorological monitoring systems.

The paper analyzes radar station operating within the metrological system and develops radar station mathematical model. It also reveals detection areas zonal limitations, stipulated by the radar station design principle, and elucidates metrological monitoring figure of merit, consisting in a of single aircraft detection area width.

The authors hypothesize that accounting for radar station blind areas will allow provide non-occurrence of such monitoring areas sections, where convective clouds areas would not be detected. Based on the analysis the authors performed numerical modeling of meteorological monitoring figure of merit value, namely, the single aircraft detection area width, in relation to the angle at which the watch in monitoring area is performed. Modeling is performed either with accounting for the blind area, or neglecting it. The obtained difference in a single aircraft detection area widths reaches 14% for certain search angle values. It allows consider the above said hypothesis on the necessity to account for blind area impact confirmed.

A mathematical model of the radar system was supplemented according to the necessity of considering the blind areas. Hypothesis of the necessity of accounting for radar stations blind areas of the airborne meteorological monitoring systems was put forward and confirmed by numerical modeling.

### Radio engineering, including TV systems and devices

Gazizov R. R., Zabolotsky A. M., Belousov A. O., Gazizov T. T.

This work emphasizes the signals maximums along the PCB multiconductor transmission lines study topicality. As long as import substitution and technological independence achievement are of great importance, we decided to employ domestic electromagnetic compatibility computer modeling system. The paper presents the results of analyzing the spacecraft autonomous navigation system real PCB bus in time domain, using various combinations of loads and active conductors. The analysis was performed by quasi-static approach embedded into TALGAT system. Cross-sections of every conductor were plotted. Ultrashort pulse of trapezoidal form with amplitude of 1 V, rise and fall times of 1 ns was selected as an excitation. Simulation was performed for 40 cases, but only six are presented as revealing the most meaningful results. Time response at 20 points along each transmission line was calculated for each of those 40 cases. This study topicality consists in revealing both maximums and minimums of the signal. Autonomous navigation system radio receiving unit PCB bus parameters were calculated. We revealed and localized voltage maximums 1.2 and 2.7 times greater than the signal amplitude at the input. In two cases, the voltage maximums were localized at the points near the lower layer conductor. The coupling between these conductors may appear to be critical. The case where two peak values presented (maximum and minimum) was revealed. It was shown also that maximum localization was not constant.

Keywords: simulation, printed circuit board, signal maximum localization, electromagnetic compatibility, autonomous navigation system

### Systems, networks and telecommunication devices

Klebanova I. V.

The article describes the functionality of the Mine Fleet Management Systems (MFMS), and basic requirements for the selection of wireless radio systems to ensure their effective functioning in the conditions of the mining companies.

In surface mining the most widely used for dispatch tasks are the following wireless communication systems: VHF, trunking system (TETRA), GSM and broadband systems and technologies for wireless data transmission: WiFi, WiMax, specialized standards providing MESH networking.

Organization of the reliable communication system is the core element in deployment of MFMS for solving the following tasks: operational management of the mining equipment and optimizing scheduling of vehicles, reliable transmitting data to the dispatch center without delays, interrupts and data loss.

Wireless systems for MFMS should provide:

• transmission of telemetry from each vehicles to dispatch center, control commands and text messages from the dispatch server and users to mining equipment;

• transfer of updated application files to the mining equipment and vehicles;

• Remote connection to control panel of operators of mining equipment;

• Transmission of differential corrections from the navigation receivers using RTK mode.

Conclusion:

1. Today’s broadband communication system with MESH technology and high-precision positioning are widely used in solving problems of operational management of mining equipment for surface mining.

2. The article gives examples of practical implementation of the MFMS with different communication systems. Experience in usage of wireless systems for dispatch tasks in mining industry is useful in the implementation of similar projects in other industries.

Keywords: broadband radio systems, communications, wireless, GLONASS / GPS, Mine fleet management systems, dispatch, the access point, the MESH technology, wi-fi, open pit mining

Matveev A. M., Novikov S. V.

The advent of on-board high-performance radio-electronic systems featuring high sensitivity; considerable resolution; long range; small size, weight and power consumption, capable of transferring large amounts of information; as well as high performance and small-size computers provided the capability for helicopters and airplanes to perform detection and identification of various objects tasks, including the ones of rather small size. Realization of such systems involve new design principles, implementation of highly integrated electronic components, maximally digitized equipment, which provide high reliability level and interspecific unification.

The compact radar system-MBRLS-MF2, developed at the Moscow Aviation Institute, is targeted for installation on-board aircrafts and other carriers. It provides round-the-clock and all-weather information of the required detail level (up to detailed, which allows not only detecting, but, if necessary, identifying the kind and type of an object).

The MBRLS-MF2 can be used for monitoring or performing specific tasks in the interests of law enforcement structures, agriculture and forestry, borders and closed areas protection; reconnaissance while anti-terror and drug control operations, as well as in the interests of national defense during tactical and educational and training activities carrying out.

Due to excellent weight and size characteristics the station can be mounted on practically any man-carrying and unmanned flying vehicle with takeoff weight starting from 40 kg.

Keywords: high-tech production, scientific-technical project, radar, innovation, electronic industry enterprise

Agapov O. A.

The presented work deals with useful signal detection algorithm synthesis against the background of active jamming Gaussian interfering signals under known radar station inter-channel correlation matrix, operating at full polarizing receiving and emission. Operation at full polarizing receiving and emission means the possibility to emit various signals at various kinds of polarization (such as horizontal and vertical), as well as distinguish various components in the polarizing basis of the impinging wave. As an example this work analyses the radar station, which antennae represents a certain antenna array, consisting of similar elementary emitters. Each of these elementary emitters is cross-shaped and consists of two independent orthogonal dipoles. In the process of emission each dipole radiates the signal on the same carrier frequency but with different envelopes. While receiving a signal each dipole is connected to its receiving channel.

Synthesis of the algorithm was carried out in the framework of an adaptive Bayesian approach [8]. The algorithm is reduced to the decision rules of a useful signal, which is defined as a comparison of the crucial statistics value with a certain threshold determined for a given probability of false alarm Z > h0 . The logarithm of the crucial statistics is determined as:

where U — matrix of dimension 2P × 2 (P — the number of channels), defined by the relation:

— factors of the phase distribution of the useful signal by the aperture array, wherein ;  — matrix of N × 2 dimension (N — a number of time samples in the reception interval) of the desired signal. Its columns represent the expected signals from the first and the second polarizer. Each of the signals herewith is normalized R — inter-channel correlation matrix; Y — observation matrix of 2P × N dimension. The first row of the matrix corresponds to a sequence of complex time samples received from the first receiving unit and a first polarization channel. The second line corresponds to the sequence of time samples received from the first receiving unit and the second polarization channel. And it is true for all the rows. This work allows obtain performance evaluation of the presented algorithm. It shows that if active jamming signal circularly or linearly polarized, this algorithm allows detect the useful signal even of the same direction, from which the jamming signal comes.

Keywords: full reception polarization, full polarization radiation, Bayesian adaptive approach, Bayesian approach, interference, correlation matrix, polarization

Kalashnikov V. B.

The purpose of the paper consists in obtaining the answer to the question: implementation of what detection algorithms of objects with unknown polarization scatter matrix (PSM) is most effective from the practical point of view.

To achieve the object in view the author compares characteristics of optimal and empirical algorithms. The paper considers herewith either classical detecting procedures (optimal and quasi-optimal), ignoring PSM of an object, or detecting procedures accounting for such uncertainty factor in received polarizing channels as PSM of an object. Detecting characteristics evaluation is carried out using the Monte-Carlo technique. The author considers the cone and cylinder at various aspect angles as typical observed objects models. Based on the carried out analysis, the inference on the effectiveness of the procedures, accounting for the a priori unknown PSM compared to classical procedures, is drawn.

The carried out analysis revealed that optimal detecting rules under complete polarization analysis (CPA), accounting for such uncertainty factors in received signal as PSM, are certainly more effective than the classical ones. Among these rules, accounting for a priori unknown PSM, the optimal detecting rule with CPA and uniform space distribution of the PSM elements appeared to be the most effective. Moreover, despite rather complex technical realization of this rule, its implementation is justified by high efficiency compared to classical detecting rules.

Keywords: complete polarization analysis, polarization scattering matrix, the optimal detection, detection characteristics, Monte-Carlo method, modeling

Borodavkin L. V., Bondarenko A. P.

The paper outlines the differential frequency refined equation derivation for correlation-filter processing of a linear frequency chirp modulation signal. The signal with linear frequency chirp modulation commonly used for radar-location. Single slope linear frequency chirp modulation is considered. The universally accepted formula does not provide the necessary accuracy of the differential frequency measurement processing for large time-bandwidth signals and high-speed spacecraft. The refined equation provides range referencing to the emission commence and accounts for target offset during exposure time. The accounting for the signal propagation in this equation provides exact targets’ range and range rate time reference. The refined equation accounts for range and range rate time variations on the interval between emission commence and signal reflection at the target. The target offset during emission time leads to Doppler’s dispersion effect, which can be accounted for in the equation. This effect should be considered while forming heterodyne signal parameters. Neglect of this effects results in residual linear modulation while signal compression.

The authors obtained the complete equation derivation and carried out numerical analysis of the summands for long-range radar parameters. The refined equation is reduced to classical formula, used for the low-speed targets and small time-bandwidth signals. The summands additional to the classic equation cannot be omitted for the signals with linear frequency modulation and large time-bandwidth. The refined equation is more flexible to account for transmitter and receiver parameters values. Such an approach can be implemented for more compound signals. The range acceleration should be taken into account for super-large time-bandwidth signals, or the targets with high radial acceleration value. The paper considers the practical features of the obtained equation, and suggests an approach to obtaining derivative transformations.

Keywords: linear frequency chirp modulation signal, Doppler shift, Doppler shift distortion

## Informatics, computation engineering and management

### System analysis, control and data processing

Nemychenkov G. I.

The work regards discrete systems of automate type (SAT), which serve as mathematical models of control units in the form of an automata with memory. Discrete system of automate type models the switching control of complex dynamic systems operating modes, and is one of the hybrid systems components [1]. A discrete system of automate type is described by recurrence equations or containments, and serves as a control units mathematical model in the form of an automata with memory. It is one of the components of dynamic systems with automata part [2, 3], as well as logical-dynamic [4, 5, 6] and hybrid systems [1, 7]. A hybrid system means a system where the processes have several levels of heterogeneous description, while the system state is characterized by ever changing or discretely changing components [8]. One can encounter such systems solving applied problems concerning mechanical and electric power control systems, as well as control problems of aircraft, technological processes, and computer network traffic and in many other areas.

The aim of this work is development of software and algorithmic support for the synthesis of positional control based of sufficient optimality conditions.

The software and algorithmic support for the synthesis of one-dimensional and two-dimensional systems of automate type was developed. The algorithm operation was analyzed using academic examples with known analytical solution.

Certain restrictions on the number of switching count occur very often, while solving the aircraft movement control problems.

For example, a satellite transfer from a low circular orbit to higher (geostationary) one, requires the upper stage «breeze-M». The permissible of the upper stage cruise engine firing should not exceed 10. Thus, if the engine state (on/off) is described by a discreet system, the total number of system switching would, naturally, be limited. Such restrictions can be accounted for during switching systems synthesis [9, 10]. Implementation of switching systems for satellite active stabilization problems to describe the jet engine operation allows accounting for inefficient fuel consumption while its firing and cut-off [6].

The author developed the discreet SAT synthesis algorithm, described by recurrence containment, and consisting in conditional cost functions construction. The bundled software for SAT with single or repeated switching synthesis. An academic example was solved for 2-dimensional discreet SAT synthesis.

Keywords: discrete system, optimal control, optimal control synthesis algorithm

Zakovryashin A. I., Koshelkova L. V.

Efficiency of application of modern technology can be significantly enhanced through the use of elements of artificial intelligence. Technical condition of a complex object depends on the States of its essential parameters. The availability of diagnostic tools allows you to collect and process measurement information in the parameters object. Solved the problem of individual forecasting and smoothing of the trajectory parameters on the basis of joint processing of the measurement and a priori information. When processing data, we used the method of least squares on the small sample sizes. Individual prediction of relevant parameters allows us to estimate the time points for which the probability of the option beyond the boundaries of the tolerance field reaches a specified level. Joint processing of the measurement and a priori information allows to assess the maximum allowable time to use the object as intended.

If you have multiple of the same objects with the same maximum time of application is their ranking. dual performance capacity. The ranking of objects is performed on the residual performance capacity. The supply of object the estimated by the quantitative estimation of the technical state. The obtained results can find application in the on-Board operative advising expert system as well as the ranking of the same objects before applying them to their destination.

Keywords: complex object, significant parameters of the object, prediction of small sample sizes the maximum application time facility appointment ranking the same objects by the residual performance capacity

### Computing and control systems elements and units

Busurin V. I., Korobkov V. V., Kazaryan A. V., Naing T. L.

In this article the impact of destabilizing factors on the characteristics of acceleration transducer based on optical tunneling effect of the optical transmitter is discussed and an error analysis of the acceleration transducer based on optical tunneling effect is conducted to obtain more accurate information about acceleration. The error analysis of the acceleration transducer is conducted, showing the possibility of construction with small-sized and heat-stable devices for control and correction of gyroscopes. . For the acceleration measurement, a sensor, based on optical tunnelling effect, with the «prism-total internal reflection-plate», can be designed. Under the influence of the acceleration, the central part of the sensing element is deflected and maximum deflection is 0.21µm. This deformation is detected based on optical tunneling effect. To improve the linearity of the conversion function the serves the use of two independent channels of output optical signal detection using an additional prism disposed symmetrically relative to the central part of sensing element. It has been shown that a change in the ambient temperature range from −40 ℃ to + 60 ℃ acceleration transducer error is less than 0.7%. It is shown that the proposed implementation of the acceleration transducer slightly affected by lateral acceleration as well as the maximum lateral force is much smaller than the critical Euler force (within a given range of transverse acceleration). The effect of gas damping for the structure under consideration sensing acceleration transducer element is investigated.

Keywords: acceleration transducer, four-beam sensing element, tunneling, lateral acceleration, temperature, gas damping, errors

### Computing machinery, complexes and computer networks

Brekhov O. M., Balyan A. V.

The widespread use of computer networks in all spheres of human life, including the areas related with the risk for life, such as aviation and cosmonautics, medicine, etc., increases the need to ensure the reliability and fault tolerance. Errors in the functioning of such complex and distributed systems can not be avoided. Consequently, the actual objective is the study of the system behavior under the influence of faults. In order to solve this problem it was decided to apply fault injection.

Existing works in fault injection are strictly connected to one of the OSI network model levels. They make it possible to implement faults and analyze the functioning of computer networks with reference to a specific level. This fact seriously limits networks analysis capabilities. Faults and failures that occur at low levels, parry at higher levels and vice versa. However, fault injection and analysis of the reaction only at one level do not give a complete picture of the system functioning under the influence of faults and failures.

In this paper, we propose a method of multi-level fault injection. The method is based on the injection of faults at all levels of OSI model and analysis of the system reaction. The obtained data can be used to detect levels of the OSI model, which have the greatest influence on the reliability and fault tolerance of the computer network. The application of the obtained data in order to improve the degree of fault tolerance will allow to increase the efficiency of the network functioning. This paper presents the main types of faults occurring at different levels of TCP/IP protocol stack.

Following results were obtained:

• Formulation of the task of networks functioning analysis based on multi-level fault injection.

• Definition of the main types of faults and their causes at each level of the network model.

• Proposition of a multi-level fault injection method for the computer networks functioning analysis.

Keywords: computer networks, fault injection, fault tolerance

Belkin V. D.

Research work is devoted to the study of the principles of organization and functioning of the wireless sensor network (WSN) and creating tools for its implementation. The main goal of this work is to create a software platform to enable the application of WSN.

The first task of the research is devoted to the development of a tool for configuration of a workplace of the programmer on a UNIX-like operating systems that provides: 1) the development of applications for WSN nodes, 2) reprogramming the central microprocessor of the node, 3) debug your application. The result of solving the first problem is the first module of the software platform.

The second objective of the research is dedicated to the creation of the second module, the elements of which govern the functioning of the hardware components of the experimental nodes EVB8871. Collectively this module allows you to manage the components of WSN: to run the program a central microprocessor host to control power modes, to configure the timers, clock switches, LEDs, sensors, etc. in Other words, this module performs the basic functions of the operating system.

The third objective of the research is dedicated to the creation of a third module responsible for the transceiver. As transceiver nodes EVB8871 equipped with a chip Texas Instruments CC2520, which is a ZigBeeTM/IEEE 802.15.4 transceiver of the second generation, specially designed for RF applications in the 2.4 GHz band. This chip is an independent processor, which should be controlled to perform the desired action. The third module includes configuring a transceiver and an implementation of a stack of communication protocols which are the basis for the organization and functioning of WSN. From all levels of the protocol stack is of particular interest for the network because it is responsible for initializing the network, the interaction between the nodes and the further functioning of the network, i.e. its ability to self-organize.

Thus, a software framework for application development of BSS includes three modules that are implemented during the research work.

Speaking about the results, it should say on their broad spectrum of applications: aerospace, automation of buildings, transport infrastructure, medicine, defense and security. Part of the work aimed at conceptual development of the ideas applied projects aimed at solving acute problems in one area or another.

Keywords: wireless sensor networks, sensors, radio transmission, IEEE 802.15.4

### Mathematica modeling, numerical technique and program complexes

Volkov V. A., Kudryavtseva I. A.

The idea of particle filters dates back to the fifties. However, rediscovering particle filters occurred in 1990-s with the paper by Rosenbluth M. N., Rosenbuth A.W. «Monte Carlo calculation of the average extension of molecular chains». An important resampling technics was discovered. The progress in research became visible in 2000-s due to the growth of computational powers. Particle filter technique is becoming involved in many spheres of science: stochastic control theory, signal and image processing, satellite-based navigation system.

Particle filters became the very popular method for solving filtering problems in non-linear and non-Gaussian cases. The algorithms combine Bayesian approach with Monte-Carlo technique. Moreover, particle filters don’t involve local linearization or another functional approximation.

The solutions of stochastic discrete filtering problem by using Bootstrap Particle Filter with Residual Resampling, Bootstrap Particle Filter with Roulette wheel Resampling, Monte-Carlo Particle filter, Unscented Particle Filter are presented. Described task is solved by developed Software solution, based on MATLAB and Microsoft Visual Studio C# 2010 platforms. The results are compared to the results obtained earlier by other authors.

Keywords: nonlinear filtering problems, particle filters, bootstrap particle filter with Residual Resampling, Bootstrap Particle Filter with Roulette wheel Resampling, Monte-Carlo Particle filter, Unscented Particle Filter

Morozov A. Y., Reviznikov D. L.

Studying applied problems, we frequently encounter systems of ordinary differential equations that contain uncertainty or ambiguity of initial conditions or parameters. A natural demand for such problems is obtaining an outer interval enclosure of the solution by the known values of initial conditions or parameters. In particular, such problems arise in applied mechanics, thermodynamics and chemical kinetics.

There exist a number of Taylor series-based numerical methods for solving an IVP for ODE systems with interval parameters, such as Moore’s direct method, the parallelepiped method and Lohner’s QR-factorization method. All these methods represent a certain extension of the classical Taylor series method that takes into account the interval set up of the problem. Applying rigorous interval methods, which include the class of Taylor series methods, to more real-life systems often gives unsatisfactory results due to excessive lengths of the obtained intervals. This effect (excessive overestimation of intervals’ lengths) is usually called the wrapping effect or Moore’s effect.

The methods at hand are based on representing each integration step as some transformation that deforms the solution region using an interval Jacobian matrix. In the majority of cases, the wrapping effect appears due to the usage of this matrix, which implies deforming every volume element by all real Jacobian matrices in the region of interest. The suggested approach consists in computing the interval Jacobian matrix only in some discrete points of the region, which allows us to significantly reduce the wrapping effect at the cost of the fact that the obtained enclosure is now slightly less guaranteed to contain the solution. In this paper, we present the test results of applying the suggested method to model problems, which show its efficiency and give evidence of the fact that this approach can be used for finding solution to the problems in the class of interest.

Keywords: Taylor series-based interval methods, Moore’s method, parallelepiped method, Lohner's QR-factorization method, wrapping effect, Lotka-Volterra model, interval ODE systems

Kondrashin M. A., Arsenov O. Y., Kozlov I. V.

This article considers the approaches to developing complex distributed simulation systems for conducting experiments on test subject using up-to-date methods and means of virtualization and cloud computation organization.

Simulation means modeling performed with computers. It allows automatization of experiments conducted on a tested system. Distributed modeling is the modeling employing multiprocessor computers and/or computer network. The main requirement, defining the necessity of distributed modeling architecture implementation is complex simulation systems integration. The main advantages of the distributed modeling systems are as follows: the possibility of multiple stand-alone hardware sets integration while conducting an experiment; a new sample development verification by one of the distributed system element substituting; developing simulators for teaching personnel, operating the real system. Labor consuming process of preparing for conducting an experiment and original setting of the interconnections between the system elements; requirement of the exact notion of necessary computing resources at the stage of modeling system design; the need for implementation of special algorithms for hardware computing resources balancing can be referred to as the drawbacks of distributed simulation systems while developing complex simulation systems.

Today, in the age of computer technologies we suggest using the virtualization and computing clouds technology when developing distributed modeling complexes. Such technology helps you to get rid of the most of the disadvantages when building the distributed systems for modeling. Virtualization is a hardware-software opportunity of computer/server physical resources (processor, memory, storage and network adapter) utilization optimization through their representation in the shared access between units (virtual machines) logically isolated from each other.

The paper suggests an approach for the distributed modeling systems developing, using the virtualization and computing clouds technologies. We provide the description of the technology and its advantages, foremost among which is an easily scalable distributed modeling systems creation.

The simulation complex of the SC GCC elements and SC GСС in general under development at TsNIIMash (Central scientific research institute of mechanical engineering) is described.

The paper shows that the virtualization and cloud computation methods utilization when building the distributed modeling systems allow get rid of the most of the problems emerging from building analogous systems in a traditional way.A description of the developed applications allowing automatize the virtualization platform control process is also presented.

Keywords: simulation, distributed system, virtualization, computing clouds