# 2015. № 84

## Mechanics

### Theoretical mechanics

Mukhametzyanova A. A.

The paper considers the task of plane motion control of a two-mass parametric pendulum. The purpose of the work is to build new control laws with specified properties that implement processes of excitation and damping the pendulum near the lower equilibrium position. Precisely, the possibility of a pendulum excitation and swing damping parametric control near the lower equilibrium position are discussed. The problem is solved by the method of Lyapunov’s functions of the classical theory of stability.

Two equivalent weightless rods pin-edge fixed at the suspension generic point model the pendulum. Two equal point masses are attached to the ends of each rod. The pendulum allows rotational or oscillatory movements in a vertical plane around the suspension point. Along with these movements in homogenous gravitational field, the pendulum has two equilibrium positions. As is known, the lower position is steady and upper the position is unsteady.

Let us consider the possibility of control realization by implementation of continuous variation of the angle between the two rods. In this case the control law can be set by the function depended on the representative point of motion of the gravity center of pendulum. Natural restriction on the gravity center movement along the bisectrix of angle between the two rods is assumed. Let us consider that the control law has continuous derivative.

In this paper two control laws of processes of excitation and damping pendulum are developed. The corresponding Lyapunov’s functions proving the asymptotic pendulum lower position stability and instability in cases of the pendulum damping and excitation are sel ected. It is shown, that with controlled movements according to the first law the asymptotic oscillations amplitude damping of pendulum occurs for any initial conditions of the movement. When implementing control according to the second law the increase of the amplitude and the transition fr om oscillatory to rotational motions takes place. The theoretical results are confirmed by numerical modeling.

The results of this work may present applied technical interest and be applied while flat pendulum movement of various mechanical systems modeling and control.

Keywords: two-mass pendulum , Lyapunov's function, constrained control, asymptotical stability, the swing principle

Shmyrov A. S., Shmyrov V. A.

Flying near collinear libration points has been implemented since 1978, when the spacecraft ISEE-3 was launched in the vicintyof collinear libration point L1 of Sun-Earth system. Many spacecrafts are widely known, in particular SOHO — solar tracking station. This work considers controlled orbital movement in near unstable collinear libration point L1 of the Sun-Earth system. We use Hill’s equations as a mathematical model. These equations are the non-linear approximation of circular problem of three bodies equations. We also use linearized equations of motion. Libration point is a model concept of circular restricted problem of three bodies, and getting to the libration point is not the purpose of such studies. The important characteristic of the orbital motion of a spacecraft near libration point is the special function of phase variables of «hazard function», which is presented in our article. A spacecraft does not get away quickly from the vicinity of the libration point, when module of the hazard function is small. At zero value of this function the spacecraft stays near libration point wthin the framework of linear approximation. In this paper, we present quadratic functionals, which were built with the help of «hazard function». The instability of the libration point L1 requires solving the problem of spacecraft motion stabilization. The standard methods of modeling of linear-quadratic optimization are often successful for such tasks exploration. For this widely studied model, we proposed the special family of functionals. We applied also sufficient conditions of optimality in view of these functionals, and obtained the stabilizing controls in the explicit analytic form. We simulate controllable orbital motion near collinear libration point with obtained controls. The graphs show that in the course of transition from the model of Hill’s equations to a more adequate model of restricted problem of three bodies, the qualitative nature of controllable motion of a spacecraft on the given period of time integration near L1 does not change.

Keywords: control, stabilization, optimality sufficient condition, restricted problem of three bodies

Хедрих (Стеванович) К. Р.

Статья начинается с описания двух книг Михаила Петровича: ’’Элементы математической феноменологии’’ и ’’Феноменологическое отображение’’. Приводится краткая биография Михаило Петровича (1868-1943) как выдающегося сербского математика, ученика А. Пуанкаре.

Некоторые базовые понятия математической феноменологии связаны с элементами нелинейных преобразований криволинейных координат, таких как базисные векторы касательного пространства в текущем положении фазовой точки, скорости их изменения (как модуля, так и компонент угловой скорости их вращений). Эти элементы представлены в различных криволинейных координатах.

Теория Михаила Петровича содержит два типа аналогий: математическую и качественную. Приводятся примеры аналогий для многих реальных систем, в частности, рассмотрены аналогии в динамике систем с дробными показателями, имеющими одну или несколько степеней свободы, так же как и в multi-body динамике гибридных систем с дробными показателями.

Исследованы математические аналогии между векторными моделями напряженного состояния деформируемого тела в точке, векторными моделями, описывающими малые деформации нагруженного тела в фиксированной точке, векторными понятиями моментов инерции твердого тела в фиксированной точке относительно заданной оси.

Некоторые понятия, касающиеся диссипативных функций для фракционных динамических систем, представлены в соответствующих таблицах.

Показано, что качественные, структурные и математические аналогии при анализе собственных фракционных колебаний имею место при исследовании динамики систем, близких (по своим свойствам) к механическим системам: в электрических и биологических фракционных цепях. Они являются полезным инструментом для упрощения моделей, усиливают эффективность анализа через построение феноменологических отображений между локальными и глобальными моделям.

Keywords: Михаило Петрович, математическая феноменология, фракционная система, производные дробных порядков, обобщеная диссипативная функция для фракционых систем с диссипацией

Хедрих (Стеванович) К. Р.

Михаил Петрович (1868-1943) — выдающийся сербский математик, ученик А. Пуанкаре. Статья начинается с краткого описания двух книг Михаила Петровича: ’’Элементы математической феноменологии’’ и ’’Феноменологическое отображение’’.

Некоторые базовые понятия математической феноменологии, такие как элементы нелинейных преобразований криволинейных координат, описаны в предыдущей статье. Структурные аналогии в системах, состоящих из деформируемых тел, представлены в этой статье.

Описаны феноменологические аппроксимационные отображения нелинейных эффектов в окрестности стационарной точки или стационарного состояния динамической системы. Исследованы линейные и нелинейные аппроксимации, с помощью которых строятся приближенные дифференциальные уравнения и приближенные решения в окрестности сингулярной точки. Показано, что метод локального анализа, использующий феноменологические отображения, позволяет получать информацию о нелинейном поведении динамических систем. Метод локального анализа, основанный на использовании таких отображений, иллюстрируется на ряде примеров.

Keywords: Михаило Петрович, математическая феноменология, феноменологическое аппроксимационное отображение, производные дробных порядков, фракционые собственные колебания, локальное приближение, сингулярная точка, аналогии

Bardin B. S., Panev A. S.

We consider a movement of a solid body carrying sliding single mass point. A body of M mass is situated on a horizontal plane, and a single mass point of m mass is moving relatively to it over circumference of R radius, which center coincides with the centre of mass of the body. Moreover, the angular velocity of the points’ circulatory movement is constant. Frictional forces between the body and horizontal plane are specified by Coulomb friction model. We assume that at the initial instant the body stays at rest, and the moving mass occupies its lowest position.

Thus stated the problem has the two parameters: k — Coulomb friction factor and . With certain values of these parameters, the relative motion of the point can cause motions of the body over the horizontal plane. This work aims at complete qualitative investigation of periodic motions of the body without the horizontal plane liftoff.

The study of the motion of the abovementioned mechanical system presents not only theoretical interest, but also can be applied to the development of mobile devices (vibrating robots) moving due to the displacement of internal mass. Such devices are promising for the modern space industry. In particular, they can be useful for the study of celestial objects: asteroids, planets, solar systems and their satellites.

Based on the analytical and numerical studies made in this work we obtained the following conclusions. The set of values of parameters k and μ wherein the movement of the body is possible is broken down into three areas: I, II and III. The movement of the body in the abovementioned areas bears qualitatively different character. If the values of the parameters belong to region I, then the body performs a periodical reciprocating motion with a period equal to the period of a full turn of the point along the circle. The body moves during equal intervals of time in positive and negative directions. These time intervals of movements interlace with quiescence intervals of the body on horizontal plane. With parameters from area II, the body moves with alternate velocity. With that, during one cycle the body shifts in positive direction, changing twice the direction of its movement. Time intervals of motion in negative direction are separated from those in positive direction by quiescence intervals. But if parameter values belong to region III, there are no quiescence intervals, and body motion in general will not be periodic. The movement is of asymptotic nature, i.e., it approaches a certain limiting periodic mode of movement. In this limiting mode, the body moves in positive direction.

The work is carried out at the Moscow Aviation Institute (National Research University) at the cost of the grant of the Russian Scientific Foundation (project № 14-21-00068).

Keywords: periodic motion, friction, rigid body, mobile robots

Churkin V. M.

The paper considers parachute system with elastic top cords forced vibrations in a vertical plane. While setting the equations of motion the parachute canopy is considered as a symmetrical solid body. The top cords are modeled as two linear weightless springs, and the weight — as a point mass. Disturbing action causing these vibrations is presented as an additional component of the parachute canopy pressure center velocity vector directed horizontally and changed according to harmonic law.

The parachute system with elastic top cords forced vibrations is analyzed with methodology, implemented earlier for studies of forced vibrations of a parachute system model with unchangeable geometry and a model with pivotally suspended weight. The parachute system vibrations are considered in frequency range of the fundamental resonance. It is assumed that the parachute canopy is made of the cloth with low permeability, and, hence, the parachute canopy aerodynamic force normal component is described by highly nonlinear dependence from parachute canopy angle of incidence. While generation of equations of parachute system disturbed motion, harmonic linearization of this non-linear dependence is performed. The equations obtained are separated into two systems: with constant and varying components of desired solutions. We obtain the values of vibrations shift, while the system with varying components is used to obtain amplitude and phase, corresponding to the specified frequency of the desired vibrations. The results obtained allow plotting the amplitude-phase-frequency characteristic of a parachute system.

Keywords: parachute system, elastic straps, forced vibrations, harmonic linearization , parameters of the vibrational modes

### Fluid, gas and plasma mechanics

Kuzenov V. V., Ryzhkov S. V., Skorokhod E. P.

Modern space programs set specialized practical problems to the developers while designing new engines and their upgrading.

Capillary pulse discharge with an evaporating wall of the channel was described in [1].

As a part of the radiating plasma dynamics, taking into consideration the radiation transfer, the problem is set as follows: plasma and gas-dynamic processes in the flame of a capillary discharge with an electrode vaporizing under the assumption that the brightness temperature and the temperature of the outflowing plasma are equal to each other. The results of calculations are given in [1].

Numerical studies of pulsejet, flowing through rather «wide» slice, the channels of more than three millimeters, revealed that the jet formed unsteady vortex structures near the boundaries.

It presents the spatial distribution of temperature and pressure of the jet, formed by three channels, for times: t = 18.5 ms, t = 41.6 ms, t = 94.6 s.

The impact of the magnetic field is considered. For a single channel capillary discharge with an evaporating electrode it demostrates the distributions of temperature in the flame of a capillary discharge when applied to a stream of the external magnetic field B = 1.58 Tl and B = 2.5 Tl, respectively.

The magnetic field affects the high temperature (near the axis) of the plasma jet and a wake vortex (toroidal vortex) in a triple configuration of the shock waves.

If the value of the magnetic pressure pmag= 25 atm, toroidal vortex
does not occur, and the longitudinal size of jet is approximately twice the
size of the jet without a magnetic field presence. Similarly, the maximum value
of the temperature obtained is 1.5–2 times greater than the temperature value obtained
by the calculation without the effect of the external magnetic field.

Keywords: plasma engines, radiation plasma dynamic, capillary discharge plasma jet, the computer system ASTEROID

Aleroev T. S., Khasambiev M. V., Khamzatova Z. U.

In this paper, we study boundary value problems of Sturm-Liouville type the fractional differential equations. Such kind of problems stay in the spotlight of many authors in the first place due to their activities in various physical processes modeling, such as heat and mass transfer within an ambient of fractal structure and memory; random straying point particle, that starts its movement from the origin according to self-similar fractal set; oscillator movement under elastic forces, peculiar to viscoelastic medium, etc.

It is also worth noting that many direct and inverse problems associated with degenerate hyperbolic equations and equations of mixed hyperbolic-parabolic type are easily reduced to Sturm-Liouville problem for second-order equations with fractional derivations in less significant members.

This work consists of two parts. The first part is devoted to the study of boundary value problems for fractional differential equations, and the second — to the study of the of Sturm-Liouville problem for a second order differential equation with fractional derivatives in the less significant members.

In the first part the paper explores non-selfadjoint integral operators, induced by differential equations of fractional order and boundary conditions of Sturm-Liouville type. It should be noted that the spectral structure of these operators is poorly studied. The method, sated in the first part, allows obtaining estimates for eigenfunctions and eigenvalues.

In the second part of the work, we show that the operator generated by the second order differential expression with fractional derivatives (in the sense of Caputo) in the less siginificant members and boundary conditions of the Sturm-Liouville is an operator of Keldysh type. All the eigenfunctions of this operator are written out. We proved by methods of perturbation of linear operators theory that this operator possesses the main oscillation properties, ie all its eigenvalues are simple and of the same sign.

The obtained results show that the second order differential equations with fractional derivative in the less significant term can be applied to study the motion of the oscillator with viscoelastic damping.

Keywords: operator of Keldysh type, perturbation, discrete spectrum, fractional differentiation, eigenvalues, resolution, the core of the integral operator

## Aeronautical and Space-Rocket Engineering

### Aeronautical engineering

Grischenko S. V.

The article is devoted to the actual problem of layered polymer composites considering vozmozhnoyh interlaminar negative effects that lead to delamination — mean the destruction of the composite, which is the worst predicted today. This problem is particularly relevant for areas of variable structure laying laminate composite, in other words — the transition zones. Due to changes in the structure of the load is distributed between the layers, which leads to the entry in the work space of the interlayer shear and tearing.

The question is based on the design strength and is considered mainly in relation to the transitional zone. Solutions are based on the assumption that the interlayer tension in the layered composite material similar to stresses in the adhesive joint. It is also the most logical, since by itself layered composite is a set of layers glued together.

Since the flexural rigidity of its own composite layer is relatively small, and they are rigidly connected to each other with the minimum eccentricity to determine the interlayer stresses as the base model will use a model of Volkersen with more altered boundary conditions.

The concepts of strong and weak layers: a strong layer — a layer that gives the load in the redistribution, weak layer — a layer that takes the pressure off during redistribution.

The highest values of shear and normal stresses occur interlaminar on the free edge of the weak layer, so from the point of view of the load-bearing capacity, we are interested mainly by their highest values. The shear stresses between the layers occur due to the difference of the glued layers. Normal stresses arise due to the occurrence of local points, which causes separation plate.

In practice, before determining the amount of stress between the layers, it is necessary to analyze the structure of the transition zone, highlight the strong and weak layers, define their characteristics of elasticity and thickness.

After identifying the strengths and weaknesses of layers to them, respectively, are assigned to the indices 1 and 2. Then, you must adhere to the following sequence:

1. Determine the hardness of strong and weak layers;

2. If necessary (in case of continuous layers), recalculate the load on a strong layer;

3. To determine the coefficient of mutual stiffness layers;

4. Calculate excessive force;

5. Determine the stresses in the interlayer space.

This technique not only allows speculative and constructive choose the design parameters of the transition zone, but also to evaluate the strength. Also, a technique gives an idea of the physics of structure work of the transition zone under load, provides requirements and recommendations that will effectively reduce the range of possible values of matching options, and generally reduce the complexity of the design. The dependences obtained open additional possibilities for parametric design optimization of constructive transition zones.

Keywords: composite material, mode of deformation, stress-strain state, interlaminar stresses, interlayer shear, adhesive bonding

### Aerodynamics

Maksimov A. K.

An indirect calculation procedure for an angle of attack and an angle of sideslip of any aircraft is considered with using flight parameters measured by aircraft systems. A lift coefficient is calculated from flight dynamics equations which include such parameters as dynamic head, weight and wing area, and normal g-load. Analytical expressions are obtained for the lift coefficient and attack angle relation with an approximation technique using the plots of this relation which are constructed as a result of aircraft model wind-tunnel tests. In addition, the dynamic head is calculated for each dynamic pressure value determined in flight with a pitot tube using the known dynamic head dependence of dynamic pressure. It is shown that an angle of sideslip can be indirectly determined from a side force equation. Probable calculation errors for an angle of attack and an angle of sideslip are considered. These errors are estimated with taking into account the measurement errors for the parameters which are involved into the angle calculation formula. A possibility to estimate the systematic and random components of the measurement error is considered. With a great number of measurements, the random error follows the normal law. With a small number of measurements, the confidence probability and the confidence interval are estimated by using the Student’s distribution.

Calculations are performed to estimate the indirect determination error for a lift coefficient for a typical flight of such airplanes as Yak-52 and M101T «Gzhel». The airplane wind-tunnel tests yield the indirect determination errors for an angle of attack. The accuracy estimation results meet the known measurement accuracy requirements stated in certain publications. Calculations are performed to estimate the indirect determination error for an angle of sideslip for a typical flight for a M101T airplane. The resulted estimates satisfy the accuracy requirements known from publications.

Keywords: angle of attack, angle of sideslip, measurement, accuracy estimation, measurement error, mean square deviation, random error, normal law of distribution, indirect measurement estimation equations

### Aircraft engines and power installations

Sorokin V. A., Kopylov A. V., Tikhomirov М. A., Stirin E. A., Loginov A. N., Fedorov D. Y., Valui P. V.

Based on the analysis of damages arising from heat erosion, thermochemical and oxidative effects of combustion products flow, heat-stressed of rocket and aircraft engines structures made of carbon composite materials we propose thermal protection methods.

The development of a thermal protection system for heat-stressed aircraft engines structures of carbon composite material depending on the temperature level of the firewall, chemical composition of combustion products, pressure, etc. can be performed in several ways:

1. By implementing parts made of carbon-carbon composite material, the ceramic or ceramic like monolayer or multilayer thermal barrier coating, such as silicon carbide SiC with thickness of 100 microns and above, with a refractory metal alloying elements such as molybdenum, tantalum and others.

2. By use of carbon-ceramic composite material without thermal cover, such as carbon-ceramic composite material with silicon carbide of matrix type C/SiC, or a matrix of silicon nitride/Si3N4 obtained by the volumetric saturation of the porous workpiece of carbon-carbon composite material — silicon carbide SiC or silicon nitride Si3N4 of a gas phase. Depending on high temperatures, over 1650°С, and the percentage of oxygen on the surfaces of the parts of carbon-ceramic composite material, the surface layer of the ceramic coating can be applied to prevent the gas permeability of the ceramic matrix, which can cause defects due to the difference of coefficients of thermal expansion at the interface with carbon fiber.

3. It is necessary to generalize and apply the experience of leading material science companies for the protection of carbon composite material with volume and surface saturation ceramic compositions.

4. Based on the operating conditions of heat-stressed rocket and aircraft engines structures of carbon composite material with different parameters of solid fuel combustion products flow (pressure, temperature, equilibrium and non-equilibrium composition of combustion products of solid fuel), together with research organizations it is necessary to develop approaches for experimental study of failure mechanisms of perspective carbon-carbon composite material, carbon-ceramic composite material and thermal barrier coatings and the temperature of the working surface of the carbon-carbon composite material, carbon-ceramic composite material and coatings.

Keywords: solid fuel ramjet rocket engine, heat-stressed structures, carbon-carbon and carbon-ceramic composite materials, heat-shielding coatings, heat erosion and oxidation resistance

### Aircraft engines and power generators

Siluyanova M. V., Shpagin V. P., Yurlova N. Y.

At present the air force faces the challenge of visibility of a flying vehicle in infrared band, caused by hot parts of an engine, turbine blades, afterburner components, nozzle, as well as jet exhaust stream. In principle, the visibility problem can be eliminated by flat nozzle implementation. It becomes possible due to angle of visibility reduction of hot engine parts. However, implementation of flat nozzle only, as a rule, is not enough. To achieve full shielding of hot engine parts bending of nozzle channel is needed. As a rule, bending range is strictly limited, and, thus, one must apply more complicated methods. One of such methods is integration of buffles of special form into nozzle channel. It allows concealing the problematic engine parts behind the smaller curve of a nozzle. The presented study considers the similar case.

We designed the subsonic nozzle blocking entirely the visibility of engine hot parts. We achieved this effect by bending the flow duct of the channel and integrating into it specially curved buffles. We considered linear law of variation on the length of a rectilinear tapering channel cross-sectional area as an initial model. We worked hereafter at the nozzle of the initial version, but with already described engine shielding method. The effect was reached by bending the initial channel and integrating specially bended buffles into it.

In this work, we carried out the analysis of introduction of deflectors into the channel impact on gas-dynamic losses. The calculations were performed with software ANSYS CFX. Three-dimensional viscous turbulent flow of compressible gas modeled using the Reynolds, averaged Navier-—Stokes based equations, closed with the SST Menter turbulence model.

Computational domain of the calculation was a nozzle channel without considering external flow around it. The unstructured mesh consisting of tetrahedrals with a layer of prisms on all surfaces, with the condition of the wall, was used. The calculations were conducted with the following equals for both cases of boundary conditions:

∙— input — the pressure and the temperature;

—∙output — the average static pressure.

The boundary conditions correspond to the turbofan with a bypass ratio degree of m ≈ 4 (engine — analog of the turbofan engine PS-90A).

The calculation reveal that base flat nozzle does not have separation areas, and losses inside the channel are related only to tтhe of the stream wall friction. The value of the velocity coefficient for this option is φ = 0.994.

The curved channel with deflectors does not also have found separation areas, but due to the increased contact area the friction losses increased too. A numerical calculation showed, that in case of the channel with integrated deflectors, the nozzle coefficient of velocity, compared with the original version, decreased by 4.4% and φ = 0.952.

This work results in conclusion about the possibility of profiling non-separable flat unobtrusive nozzle using the proposed method of deflectors integrated into the channel. In this case, the velocity coefficient of the nozzle, selected as a criterion for estimating losses in the output device, in this case fell within 5%, and the pressure field and the output speed remain uniform. The obtained results allow speaking about the possibility of using presented method for designing nozzles with limited sizes.

Keywords: flat nozzle, curved baffle, airflow

### Dynamics, ballistics, flying vehicles movement control

Kulifeev Y. B., Mironova M. M.

This article demonstrates usage of analytical automatic control system (ACS) design by means of the inverse dynamics method within the scope of designing flight-navigation ACS of a UCAV by the example of lateral motion control at the airborne path.

The mathematical simulations of UAV dynamics are based on its aerodynamic, mass-inertia and geometric characteristics and parameters, and also on usage of solid mechanics equations.

Dynamic model equations are used to synthesize UAV motion control procedures both for flight and ground motion. Moreover, the real-time dynamic model provides for UAV motion data not measured with instrumentation that are necessary for the ACS procedures.

UAV flight lateral motion can appear in the case of course change or under such external disturbance as side wind.

For lateral motion control it is necessary to keep the set earth reference value of lateral coordinate .

UAV controlled lateral motion is induced by a sideway force that originates under UAV heel. Therefore, at the first stage of procedure execution, it is necessary to define relevant (required) angle of heel to eliminate existing lateral displacement .

At the second stage of lateral motion control system operation the required UAV heel must be provided by means of aileron movement.

The UAV flight under side wind influence was simulated to check operability of submitted lateral motion control procedures. UAV takeoff, stabilization of horizontal flight at the specified speed and altitude, and landing on a concrete runway were simulated. Simulation results prove satisfactory performance of the lateral control channel procedures.

The established procedure of UAV lateral motion control at the airborne path is sufficiently efficient to eliminate the UAV lateral displacement under flight at the airborne path. Thus, it has been proven that the inverse dynamics method can be used to synthesize the prospective digital control systems for the airplane-type UAVs.

Keywords: drone, flight and navigation system of an unmanned aircraft, lateral motion, angle of heel, aileron movement, airborne path

Starinova O. L., Fain M. K.

The optimal interplanetary trajectories and the trajectories of flights to the Moon pass near the libration point L1 of the Earth-Moon system. Therefore, there is a growing interest in building a space station on the halo orbit near this point. Establishing such a station would require development of a transport system capable of providing the necessary traffic. Implementation of the electric propulsion will greatly improve the mass efficiency of such transport operations and reduce the cost of creation and maintenance of the station.

The exact solution of the problem was established with the use of the Pontryagin’s maximum principle and the numerical integration. In this work we use the Fedorenko successful linearization method that accepts the limitation on composed functions that have Freshe derivatives. The method is based on making the variation optimal control problem the iteration problem of linear programming.

Contrary to the optimal control choice, here the Sun’s perturbation was accounted. According to the above-stated control program the steering angle λ2 could be neglected. The analysis of the optimal solution shows, that the optimal control program for λ1 has three different segments of operation.

The optimal control programs for the Earth-L1 and L1-L2 transfers and corresponding trajectories were obtained. The results are in good agreement with the results obtained by the Pontryagin’s maximum principle.

The applied method demonstrates its effectiveness for the complex optimization of the SC transportation. Findings may be used to calculate the required design-ballistic parameters of the future lunar missions. The optimal interplanetary trajectories and the trajectories of flights to the Moon pass near the libration point L1 of the Earth-Moon system. The usage of the electric propulsion will greatly improve the mass efficiency of such transport operations and reduce the cost of creation and maintenance of the perspective Moon station.

Keywords: spacecraft, low thrust transfer, trajectory optimization, libration point, space tug

### Innovation technologies in aerospace activities

Syrin S. A., Tereshchenko T. S., Shemyakov A. O.

The great attention is paid in Russia to scientific and technological development of space-rocket and industry in the long-term outlook. Particularly, government documents define the directions of its development up to 2030, including the Russian Federation forecast of scientific and technological development for the period up to 2030 (FSTD-2030), forecast of long term social and economic development of the Russian Federation for the period up to 2030, the state and federal programs for scientific and technological orientation.

Based on the results of the existing world experience in the development of scientific and technological forecasts development of the space industry we generated requirements to the contents, structure and characteristics of main forecast elements. Proposals are prepared for the use of industry forecasts on a national level.

Also, the authors formulated the list of the main problems concerning the integration of industry forecasts in the long term FSTD-2030 and variants of its solution:

1. There is no forecast of the space-rocket industry scientific and technological development in the system of state planning.

2. We found rather poor observability of risks, trends, threats and priorities; and absence of the explicit «product — technology — market» chain.

3. It is necessary to define the time interval for analysis and forecast updating.

Mechanisms contributing to the harmonization of scientific and technological development forecast results at the sectoral and national level were analyzed within the framework of this research.

Keywords: sectoral forecasts of scientific and technological development, elements of sectoral forecasts, rocket and space industry, long-term forecast

Kupreev S. A.

To determine the major trends of application of tethered systems performing a wide range of practical tasks in space the effective method of optimum schemes formation of tethered systems operated movement based on the general integrated approach application is offered:

— determination according to preliminary data of the list of tasks which are reasonable to solve, using tethered systems [1–10];

— development of management methods of the relative movement of the connected objects in the course of expansion and functioning of tethered systems;

— determination of the possible modes of the movement of tethered system objects based on research of the sel ected management methods;

— determination of set of modes of tethered system movement by which each of the practical tasks can be solved;

— development of efficiency indicators allowing carrying out a comparative assessment of various modes of the movement of a sheaf for the solution of the considered task, and define a positive effect of the solution of this task with application of tethered system compared to traditionally used technical means;

— selection of such practical tasks where the use of the tethered system solution is reasonable, and to defining the modes of the movement of a sheaf which give the greatest effect fr om application of tethered system.

The realization of this approach is possible due to mathematical models of the operated movement of the connected objects in the form of nonlinear autonomous dynamic systems. For these dynamic systems based on the qualitative theory apparatus of dynamic systems and the theory of bifurcations [11, 12] such methods have been worked out and the studies of the operated movement of tethered systems have been carried out. The results give a general idea of the efficiency of application of tethered systems for the solution of the practical tasks considered in the paper.

Keywords: tethered system, application of technology space tethers, modes of relative motion, placing into orbit

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

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

Doronin D. O., Kuprikov N. M., Ivanov B. V., Rabinsky L. N.

Having its interests in Arctic and Antarctic regions, Russian Federation is seeking maximum economic efficiency while designing and running this infrastructure. Making allowances for infrastructural limitations, proliferation of technologies and geography of exploiting it becomes quite clear that primary measure to provide competitive recovery of Russia in Polar Regions should be monitoring of environmental local objects, ships and aircrafts to support ecological balance and control technogenic impact on the environment.

The implementation of new information technologies, hardware and software, providing a competitive advantage will ensure safe and efficient operation of high-tech marine and aviation equipment. Development of polar transport infrastructure will ensure the growth cargo transportation reduce operational risks, enforce monitoring of local environmental objects and warnings on emergencies. The proposed technique will allow provide real-time operational control over the strategically important waters and borders for Russian Federation.

Intercalibration of monitoring data of polar geophysical and hydro meteorological conditions is necessary in the interest of aircraft operation. Significantly increased incidence of utterly severe weather events (local and deep cyclones, catastrophic floods, storm surges and wind, snow fracture of fast hamice, critical volumes of liquid or solid precipitation, snow , etc.) complicate the development of industry, infrastructure, and navigation on polar routes.

The state of the ice cover, temperature of the surface layer of air and circulation of the atmosphere, in general, are the most significant indicators of rapid changes in Polar climate system. Against the background of the observed current climate changes, resistive pattern of circulation processes in high latitudes also varies. Changes in traditional trajectories of polar cyclones contribute to the appearance of non-specific to the season’s ice conditions along Polar routes.

This is especially critical on the general background of reducing the thickness of multi-year ice and multi-year displacement (pack) ice thinner annuals.

Keywords: Air temperature, Southern ocean, frontal zone, hydro meteorological device, Arctic, competitiveness, modernization, environmental safety

Vavilova N. B., Vasineva I. A., Parusnikov N. A.

Calibration is an important stage of the preparation of a strapdown inertial navigation system (SINS) for operation. The calibration consists in the determination of instrumental errors of inertial sensors by conducting special experiments on a turntable. In the Laboratory of control and navigation at Lomonosov Moscow State University new calibration methods based on the implementqtion of low-grade turntable have been developed. Moreover, these methods have been successfully implemented at some specialized enterprises. This article extends the calibration methods that were developed for SINS calibration procedure on low-grade turntable to the case of high-precision turntable application. One can find characteristics of high-precision turntables e.g. in [4]. SINS consists of three accelerometers, three angular rate sensors and an on-board computer, realizing navigation algorithms. Mathematical models of a calibration algorithm include SINS error equations; models of instrumental errors of inertial sensors: angular rate sensors and accelerometers; model and the equations of supporting measurements. We assumed that instrumental errors of each of the accelerometers include a zero offset error, a scale factor error, non-orthogonality errors and a high-frequency noise component, which is assumed as a white noise.

The calibration procedure comprises three cycles in order to obtain the acceptable accuracy. In these three cycles SINS is consistently set on a turntable platform in three different positions. At each cycle the platform’s rotation is characterized by angular velocity Ω, with the law of Ω behavior close to meander.

There is an opportunity to extend the aiding vector for high-precision turntable due to additional angular data, provided by turntable. After that, the corresponding equations should be written. Finally, the observability analysis for all calibration parameters should be carried out in these three cycles of rotation.

The investigation of SINS calibration was based on covariance analysis. Thus, due to simulation the possibility of obtaining an acceptable accuracy for SINS calibration procedure by means of angular data, provided by turntable was shown. So we can recommend to apply the abovementioned methods.

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

Vavilova N. B., Golovan A. A., Kalchenko A. O.

The errors of the strapdown inertial navigation system (SINS) change with time of system’s operation. The paper investigates the possibilities for these errors estimation while aircraft taxiing and takeoff. These estimated values are used afterwards to correct measurements of inertial sensors during the flight. The position and velocity data provided by GPS are used for the estimation procedure.

The SINS includes three single-component accelerometers, three angular rate sensors and an on-board computer, which implements the navigation algorithms. Mathematical models of the proposed calibration algorithm include SINS error equations, a model of instrument errors of inertial sensors and models of supporting measurements. It is assumed that instrument errors of each of the accelerometers include zero offset, a scale factor error, non-orthogonality errors and a high-frequency noise component, which is assumed as white noise. A similar model is assumed for the instrument errors of the angular rate sensors.

The examination of the SINS calibration is based on the covariance analysis. A priori standard deviations selected for the estimated parameters correspond to standard deviations of SINS operation parameters.

In order to analyze the accuracy of the calibration the autonomous navigation mode has been simulated using the estimated parameters on a trajectory consisting of straight-line segments and turns. The duration of the simulation was 1 hour. The simulation of a flight without calibration results in an error equal to 4.4 km. The usage of the proposed estimations helps to improve the accuracy up to 1.9 km.

Thus, numerical simulation shows that the implementation of SINS calibration while taxiing and takeoff improves the accuracy of further autonomous navigation.

Keywords: strapdown inertial navigation system, calibration, SINS instrumental errors

### Information and measuring and control systems

Bardin V. A., Vasil'ev V. A.

Goals
An object of the research is a control system for ultrasonic piezomotor (USPM) meant for high-speed stage of appliance for precision positioning of multifunction test equipment. The subject of the research is control signal frequency adjustment methods to varying USPM resonant frequency under the influence of external factors. The aim of this work is to develop USPM structure, electric circuit, as well as and USPM control methods with function of self-regulation without the use of external velocity and displacement sensors.

Metods

USPM control of is realized by feeding the piezoelectric elements with control signals shifted by 90°. Frequency adjustment of the control signal during USPM resonance frequency change is performed by measuring control signals amplitude at the USPM piezoelectric elements and keeping it within the working area of relationship amplitude/frequency near the value of the amplitude at the resonant frequency by stepping the output frequency of the controller.

Results

We developed the USPM structure consisting of a stator in the form of a hollow cylinder with four surfaces clipped lengthwise with rigidly attached piezoelectric elements, and a rotor mounted in its hole. The USPM control circuit is also developed. During circuit operation the microcontroller generates and adjusts operating frequency of the control signal; current amplifiers and transformers amplify voltage input signals and form two bipolar signals, isolated from the digital part of the circuit; optocoupler with a resistive output element forms a low-voltage feedback signal, which is fed to the input of the integrated ADC of the microcontroller.

Practical importance We developed high-speed actuator control system for positioning device of multifunctional test equipment, used in combination with precision drive. This provides linear movement of the test sample along one coordinate with a resolution of a fraction of a micrometer with a speed of a several mm/s.

Originality

The developed control system of speed actuator of precision positioning device employs the original design, electric circuit and control method without the use of external feedback sensors to adjust the control signal operating frequency. This technical solution simplifies the design, improves the efficiency and performance reliability.

Keywords: control system, ultrasonic piezomotor, stator, precision positioning

Trofimov D. V., Baev A. B.

The discrete Fourier transform (DFT) is a component of numerous computational techniques in signal processing and scientific computing. The most popular means of computing the DFT is the fast Fourier transform (FFT). FFT is one of the most fundamental numerical algorithms. It computes the DFT of an N-dimensional signal. The algorithm plays a central role in several application areas, including signal processing. However, with the emergence of bulk data volumes problems, when the size of the processed data sets can easily exceed terabytes, the «fast» in FFT is often no longer fast enough. In many applications, however, most of the Fourier coefficients of a signal are small or equal to zero, i.e., the output of the DFT is (approximately) sparse. Since most of video, audio, medical images, spectroscopic measurements (e.g., nuclear magnetic resonance), global positioning system (GPS) signals, seismic data, and many more massive data sets are compressible or are sparse, these results promise a significant practical impact in many big data domains. The sparse Fourier transform (SFT) addresses the big data setting by computing a compressed Fourier transform using only a subset of the input data, in time smaller than the data set size.

The first algorithms of this type were developped for the Hadamard transform. Developed SFT algorithms compute an approximation or compressed version of the DFT in time proportional to the sparsity of the spectrum of the signal (i.e., the number of dominant frequencies), as opposed to the length of the signal. The algorithms run in time proportional to the sparsity or desired compression, considerably faster than in time proportional to the signal length. This is made possible by requiring that the algorithms report only the nonzero or large frequencies and their complex amplitudes, rather than a vector containing this information for all frequencies. We focus on explaining the basic components and techniques used in the aforementioned algorithms and present an empirical analysis of the performance of the algorithms. In this paper, the general principles of the sparse Fourier transform are considered as well as the numerical comparison of several simulation algorithms.

Keywords: sparsity, spectrum, Discrete Fourier transform, sparse Fourier transform, electromagnetic radiation control (monitoring)

Nazarov A. V.

Goal: It is known that the quality of the final stage of matrix large-scale integrated circuits (LSI) design automation (the local routing stage) is determined by the efficiency of forming the large integrated circuits channels netlist generated in the preliminary stage of global tracing. While the problems of local tracing are covered sufficiently by publications, the problems of LSIs global tracing are insufficiently covered. The existing publications on this matter are devoted primarily to multilayered LSIs tracing. The paper proposes LSI global tracing with essentially limited pathways.

Design/Methodology/Approach. The paper presents the algorithm of the first phase of the creating conductors of a matrix LSI — the phase of global conductors tracing. This phase increases the efficiency of the successive stage of the tracing — the layout of interconnections of channels. The proposed algorithm is based on the Bellman-Kalaba method, which had been modified by introducing a system of penalties. This system of penalties allows taking into account the essntially limited resources for conductors tracing of the LSIs in the process of their synthesis.

Conclusions. According to the proposed method computer-based algorithm for LSI conductors tracing was developed. The paper presents the detailed description of the algorithm. Besides, it describes a system of penalties imposed on the new tracks, which take into account the previously created connections. This system of penalties is presented by formulas. The efficiency of the proposed algorithm is illustrated by the concrete example.

Practical implication. The algorithm implementation leads to reduction and balancing of separate channels loads. And, as consequence, tracing resources of the selected type of LSI are employed more efficiently.

Originality/Value. According to studies the suggested algorithm allows reducing the total area occupied by the LSI conductors approximately by 20–25 percent.

Keywords: tracing, global tracing, design automation, gate array, algorithm, penalty function

Khodorovskii A. Z., Nazarov A. V., Azarov A. V., Magomedgadzhiev A. M.

The paper considers the issues of ADC parameters selection based provision of minimum of output data amount condition with specified converted signal recovery error. In contrast to amount of data reduction techniques (such as data compression) realized, as a rule, by digital stream output from the analog-to-digital converters processing, this paper analyses the possibilities of data amounts reduction during primary signal digitizing directly in the process of analog-to-digital conversion. Such an approach in fact supplements the existing techniques, since dataflow optimized by the abovementioned way further can be subjected to processing with traditional techniques.

The scope of the research was strictly defined while problem definition. It is stressed that the case in hand is quasi-reversible signal conversion. Besides, the signals are represented as a regular flow of uniformly quantized samples. Signal recovery is realized by Lagrange interpolating polynoms, and recovery quality is estimated from the output signal uniformity view point. It is demonstrated that the only requirement to input signal is their differentiability. Thus, the results of the study can be successfully applied to a wide class of signals encountered in measuring and telemetric systems.

It is shown that the relative values of the optimal transformation parameters does not depend on the signals dynamics, which is utterly important from the viewpoint of practical use of ADCs. Recommendations are given on the selection of ADCs optimal parameters.

While selecting ADC parameters we studied instrumental errors and system-wide indicators of their effectiveness.

In conclusion, we described the procedure of the ADCs selection and gave an example of practical use of this procedure.

Keywords: minimizing the amount of data, analog-digital converters, the selection of the analog-digital converters, the point of optimum parameters, the search of the transition to the top

Ryazantsev L. B., Likhachev V. P., Shatovkin R. R.

Purpose

The behavior of air targets during an air combat is characterized by performing of complex maneuvers accompanied by large overloads. Maneuvering targets has a strong impact on the quality of support. Late detection of the start of the targets’ maneuver quite often leads to the disruption of auto-tracking due to the emergence of large tracking errors caused by the mismatch of the models to the real behavior of air targets. Recapturing of the target takes an additional time, and this may be the cause of the first attack failure, which is utterly important in conditions of highly maneuverable combat.

To prevent the failure of the automatic tracking, the onboard systems should be supplemented with supporting devices that detect the beginning of the targets’ maneuver providing correction parameters or the structure of servo gauges. The traditional method of determining the start of the maneuver is computing the statistical characteristics of deviations of the actual and estimated parameters of target motion. This requires obtaining measurements over several periods of the on-board radar station observation space. Another way to determine the beginning of the maneuver if a target is to use the information about the acceleration of of air targets and the fighter closing-in. However, the known methods for this purpose are additional sensors, e.g., optical-location system support.

Significant reduction the time spent to determine the start of the maneuver to one contact of the on-board radar antenna with an air target, and elimination of additional sensors is possible by analyzing the changing characteristics of the reflected echo caused by maneuvering.

Design/methodology/approach

The content of this method consists in the following. After each radar contact of the on-board radar station beam pattern with an airborne target, the slope of linear-frequency modulation of a received pack echoed signals, which is proportional to close-in acceleration, is measured. Evaluation of the linear-frequency modulation slope is based on the phase difference method. This method consists in dividing the received echo signal into two parts equal in time, which are multiplied in a complex conjugated way. The position of the obtained correlation function maximum in frequency domain herewith is proportional to close-in acceleration.

Originality/value

The originality of the result is that the adoption of the decision about maneuvering air target coincides with the period of a contacting antenna.

Practical implications

Implementation of the proposed method allows increasing the stability of the tracking gauges on-board radars while tracking maneuvering air targets.

Keywords: airborne radar, linear frequency modulation, phase-difference auto focus method, echo signal, convergence acceleration

Kirsanov A. P., Yampol'skii S. M.

An onboard radar operating in impulse—Doppler mode has the characteristic features of the detection zone. The feature lies in the fact that at every point of the detection zone an airborne object has a sector of directions, where the onboard Doppler radar will not detect it as long as it moves in these directions. This sector is called the sector of invisible motion directions of the flying object. Due to these features, there are hidden trajectories, and objects, flying along such trajectories can not be detected by an onboard Doppler radar such as AWACS radar. The most hidden trajectories are non-linear paths with variable curvature. However, under certain conditions, rectilinear secretive trajectories also exist. They are easier then nonlinear hidden trajectories, and therefore, are of a particular interest.

The article focuses on a rectilinear covert trajectory of the air-borne object within the viewing range of the mobile airborne Doppler radar. Such trajectories are characterized by simplicity of calculation and ease of implementation. The conditions are found under which rectilinear covert paths exist. The formulas for the calculation of the trajectories are derived. All sorts of secretive rectilinear trajectory are found. Schemes of the secretive movement on a straight-line trajectories in the coordinate system associated with a mobile Doppler radar are presented. Classification of rectilinear covert trajectories depending on the parameters of a movement of the air object and Doppler radar is presented.

Keywords: detection zone of an onboard Doppler radar, covert trajectories, rectilinear movement

Bui C. T., Маrin D. V., Rastorguev V. V.

At present, the safety of flight, take-off and landing of light aircrafts in condition of reduced optical visibility is of extreme importance. This paper considers the characteristics of attenuation of electromagnetic waves in the millimeter and infrared wave range contained in hydrometeor and dust with regard to the light aircrafts of, helicopters and drones flight safety systems. The radar of short range, created by a group of specialists of the Department of Radio Receivers at the Moscow Aviation Institute (National Research University), allows create highly detailed radar image (e.g., area of the runway, taxiway) and thus ensure the safety of take-off and landing of aircrafts.

It should be noted that modern small aircraft, depending on the urgency of the tasks perform flight, takeoff and landing in conditions of limited or absence of optical visibility (for example, for helicopter meant for high-rise buildings firefighting systems).

So one of the important tasks in the design phase of the radar for the aircraft is the estimation of electromagnetic waves attenuation in the MM-wave range while their propagation in the atmosphere containing hydrometeors, sand and dust.

Given the proliferation of thermal imagers operating in the infrared range as the possible sensor of vision systems of aircraft and other vehicles, the article compares the characteristics of attenuation of electromagnetic waves in the millimeter and infrared ranges. Thus, a preliminary assessment of the possibility of using the on-board aircraft radar and thermal sensors when operating in conditions of poor optical visibility is given.

The article shows the advantages of the use of electromagnetic millimeter waves for aircraft compared with the infrared range for the vision systems of aircraft at the hydrometeor and dust. Comparing the results of attenuation evaluation of electromagnetic waves in the millimeter wavelength, with the results obtained for the infrared range of electromagnetic waves propagation in the atmosphere with the presence of hydrometeors can be seen that the infrared radiation is attenuated considerably stronger.

Keywords: traffic safety, aircrafts, hydrometeors, dust, attenuation of electromagnetic, radio and infrared wave ranges, radiovision system

### Systems, networks and telecommunication devices

Bogdanov A. S., Shevtsov V. A.

Thus, among the topical issues emerging when developing simulation model of a perspective mobile radio communication system are the issues of system and protocol selection, fundamental for providing high precision positioning of subscribers. Considering the wide use of packet switching networks as a basis for modern networks, the necessity of high precision synchronization, and synchronization algorithm functioning with minimum computational cost, it seems rational to use PTP protocol as a basic synchronization technique for imitation model of positioning and control adaptive algorithm, which provide functioning of the perspective mobile radio communication network.

## Informatics, computation engineering and management

### System analysis, control and data processing

Rodionova D. A.

Nowadays optimal control problems arise in various branches of science. Optimal control synthesis is often applied to modelling manned motion of aerial vehicles in air-space systems. One of possible approaches to solving optimal control problems is the usage of metaheuristic optimal globalization methods. One of these methods is the Luus-Jakola global optimization method (random search with systematic reduction in the size of search region method). This method generates a sequence of iterations, each one sel ected fr om a neighborhood of the current position using a uniform distribution. With each iteration, the neighborhood decreases, and then increases again at the start of next pass. This methods converges with sufficient accuracy for global optimization problems and thus can be used in optimal control problems.

In this paper, the problem of feed-back optimal control for nonlinear deterministic systems was considered and an approach applying iterative dynamic programming is suggested. Iterative dynamic programming method can be applied to high-dimensional optimal control problems, such as the problems of finding optimal paths of aerial vehicles.

An algorithm for finding solution to feed-back optimal control problem using the iterative dynamic programming and Luus-Jakola methods is elaborated. The software environment for the algorithm is developed, which allows to apply the method to a number of typical problems and to analyze how parameters of the algorithms influence the accuracy of the obtained solution. Examples demonstrating method’s efficiency are provided, such as determining the maximum radius orbit transfer of a spacecraft in a given time. It is shown that the developed method is applicable to nonlinear feed-back optimal control problems and allows us to find the solution with sufficient accuracy in a reasonable amount of time.

Keywords: random search, optimal control, continuous systems, iterative dynamic programming

Shmelev V. V., Manuilov Y. S.

The article presents evaluation of the approach to complex technological processes modeling. The approach under evaluation consists in using the graph model of a technological process. Such model is developed based on modified Petri net, and provides the possibility of controlling the trajectory of the developing process. The ramification of the technological process development is provided by indicating, controlling and controlled positions. A distinctive feature of this approach is the possibility of implementing not only temporal control of the processes, but an event-driven technological control as well. With such kind of control the processes are measured by the milestones of meaningful events related to the other processes. In addition, the approach allows parametric control, when the process is measured in the degree of compensation subject to control discrepancies between their current settings and specified (projected) parameters. Thus, the proposed approach compares favorably to the widespread method of modeling processes, when using a process model in a recursive manner.

It seems appropriate to consider the characteristics of this approach using еру concrete technological process of the space industry. As such, it is proposed to use the process of post-flight analysis of telemetry data received during the preparation, launch and flight of the carrier rocket Soyuz-2.

Under consideration are the urgent tasks and advanced features of special software-aided planning and control of technological processes of processing and analysis of measurement information obtained by the results from the telemetry of the carrier rocket at the stages of preparation, launch and flight to the launch site. Critically marked shortcomings of the existing solutions, the cause of which are used as a model of technological processes namely in a recursive model.

The whole process of post-flight sequential analysis of the information is decomposed into the processes of several levels. The article shows straightforwardly the procedure for creating a model of the analysis of only one flight performance, namely, of the propulsion booster based on the proposed approach. We present a modified Petri net, modeling the process under consideration. Modification of classical Petri nets means the introduction of a hierarchy of colored network chips and new network elements: transitions—procedures, predicate transitions, as well as input and output positions of the network.

The proposed approach can be implemented to create the information technology of automated control process of processing and analysis of measurement data of complex technical objects.

Successful practical testing confirms the sufficient adequacy of the processes modeled with this approach to real technological processes in the application domain of analysis of measurement information in space industry.

Keywords: modeling of technological processes, Petri nets, telemetric information, the carrier rocket Soyuz-2

Kargin V. A., Skorokhodov Y. A., Nikolaev D. A., Shovkalyuk A. P.

The subject of this paper is algorithms for information processes probability characteristics estimation. The aim is to organize and present the results of the basic scientific research on the carrier rockets telemetry data on-line processing. This work uses methods of system theory and system analysis theory, decision-making theory, probability theory and mathematical statistics, the theory of ejections of random processes trajectories, pattern recognition theory. Based on the studies of statistical characteristics of telemetry data obtained during the flight test of the carrier rockets such as «Soyuz» and the analysis of the on-board systems technical condition we propose classification of telemetric information «non-homogeneity» by nature of their images. The proposed classification of telemetered parameters structural-parametric non-homogeneity is the first step in the process of developing complex of models and mathematical tool for on-line processing of telemetry information. We suggest a method for nonlinear transformations estimation of information processes based on registration of the number of cross-cups of process realizations with specified levels. Based on analytical equations presented we developed original algorithms for probability characteristics estimation by statistics of «level exceedance». The developed algorithms use zero counters, they are rather simple for realization, and do not require great large computational cost. It all allows implement them for telemetry of rocket carrier at the boost phase automated system and obtain the estimates of telemetered parameters in a mode close to real-time mode.

Keywords: characteristics of the «exceedances above the given levels», ejections of the random processes trajectories, online processing, telemetry information

Smerchinskaya S. O., Yashina N. P.

Problems of multicriteria selection are some of the most widespread problem types arising while decision making. The main difficulty in conventional algorithms implementation is that they are meant for numerical estimates setting by different criteria. Moreover, the criteria scales should be uniform. Furthermore, while decision making account must be taken of the fact, that criteria may be of various importance.

The paper suggests the technique of preference aggregation by criteria and the best alternatives selection that does not require reduction of criteria scales to uniform.

The preference aggregation algorithm presented in this work with an allowance for criteria coefficients of importance is a generalization of the preference aggregation algorithm developed by the authors earlier without allowance for criteria importance. It draws on the total preference majority graph plotting. The advantage of this algorithm is that controversial paths breaking is performed by elimination of arcs of smallest weight, thus preserving and considering all expert estimates.

In the second part of the paper, the authors propose an algorithm for obtaining coefficients of the criteria importance. This technique of obtaining the coefficients is based on plotting straight lines of indifference for each pair of criteria. We plot the straight line of indifference approximating the points of indifference corresponding to vector estimation of equivalent alternatives. We obtain the equivalent alternatives through the dialogue with the decision-makers: change the values of an alternative assessment by one of the criteria, and then set the compensation on the scale of the other criteria.

This article gives examples that demonstrate the algorithm in a dialogue with decision-makers and subsequent preferences aggregation, based on the obtained weighting factors when comparing of criteria importance and the procurement of medium-range passenger aircraft.

Keywords: decision-making, multi-criteria choice, preference relations, ranging, aggregate preference, majority graph, criteria importance coefficients

Bityukov Y. I., Kalinin V. A.

This article focuses on the application of wavelet theory in problems of geometric modeling of aircraft structures. Wavelets are the mathematical tool for layering functions. With their traditional applications in approximation theory, physics and signal processing, wavelets recently found applicaiton in many problems of geometric modeling, mainly in computer graphics. While apparent smoothness of curves and surfaces is enough for the computer graphics, CAD/CAM/CAE-systems require the surfaces belonging to different classes of smoothness. In this article we present the wavelet basiс set built on the interval, based on B-spline of arbitrary order. 2D wavelets are built based on this wavelet basiс set. on the ground of The famous Chaikin’s algorithm used for design of curves and surfaces of arbitrary smoothness class is generalized on the ground of these scheme.

Now, CAD/CAM/CAE/PDM-systems are widely used by the companies engaged in the design and manufacture of complex aircraft systems. This is stipulated by a number of reasons, among which the problems of product quality control are of utter importance, especially while its approach the world market.

Based on the principles of optimization and products parameters control at all stages of the design and manufacture such systems provide a comprehensive design work with sufficient reduction of terms together with simultaneous quality improvement. The main objective here is the steady decline in the cost of production and updating its product range, improved reliability, maintainability, cost, etc.

We can consider the development of methods for modeling curves and surfaces of arbitrary shape technology based on Bezier (Bezier) and NURBS, which has become the international industry standard for the design of complex curved surfaces one of the main achievements of the modern period. That is why the problems of improving current methods of geometrical modeling of 3D objects using mathematical apparatus standard for CAD/CAE/CAM-systems, as well as the adaptation of these methods for specific industrial applications are actual today.

Keywords: wavelet, computer-aided design, spline, geometric modeling, algorithm Chaikin, filter analysis, synthesis filter, the filter unit

### Mathematica modeling, numerical technique and program complexes

Ginzburg I. B.

This paper presents a new method of Web applications operation for the National Geographically Distributed Information System for Remote Sensing Data Receiving, Processing, Archiving and Dissemination (ETRIS DZZ) that extends the possibilities of this system. The proposed method is based on implementation of the software solution called offline-capable fault-tolerant Web application (autonomous web application, AWA) into the client-server system interaction process.

The main feature of the proposed AWA is the ability to preserve all the information (both downloaded from Web server and received from user input) as long as it is needed.

AWA provides a qualitative and quantitative advantages over traditional Web application. Quality advantages are: the possibility to work offline with information downloaded from the Web server and automatic updating of locally stored data; the possibility of an emergency backup of user input and automatic shipping of the stored user input data to the Web server when the connection to the server is restored. Quantitative benefits are: reduction of the network traffic; reduction of Web page loading waiting time.

Software-information AWA complex based on the proposed method, in contrast to its predecessors, is fully compliant to requirements of: cross-platform, fault tolerance and autonomy. This allows end users to consume a variety of terminal devices (including stationary and mobile devices) and data channels (including any local area networks and public wired and wireless Internet connections) for ETRIS DZZ Earth remote sensing data access without risks of losing user input data or having inoperative application in case of connection failures between client and server.

Keywords: geoservice, client applications for Earth remote sensing data access systems, offline-capable web applications

Brekhov O. M., Tin M. A.

The paper considers the problem of database (DB) query processing by associative computing system (ACS). This problem, as an idea, was formulated by T. Kohonen, since ACS implementation can, in principle, significantly increase the speed of query processing.

Due to the necessity of large volumes of DB requests processing and element base upgrading, which is now the main trend of onboard and ground aerospace complexes DBs development, solution of this problem arouses great interest. The additional increase in query speed processing herewith can be achieved by orderly processing of elementary requests forming DB query.

Processing time decrease is possible with concurrent (parallel) processing execution of comparison operation based on associative memory (AM).

On the assumption of abovementioned considerations, we identified problem of determining the structure of the associative computing system.

There are two possible main methods for the request execution: in-depth development (sequential processing of table columns), and with the of in-width development (sequential processing of table rows), as well as the combined method comprising in-depth and in-width development. Based on in-depth development method realization we propose ACS architecture for orderly requests. the paper presents the developed algorithm for orderly requests processing and efficiency evaluation of orderly requests processing.

Keywords: computer system, associative, database, querying, efficiency

Brekhov O. M., Tin M. A.

Interleaved memory is a known means to enhance memory performance. Employing this mechanism for data arrays processing when successive numbers of cells of an array are arranged in successive sections of memory cells (per mod m), found application firstly for high-performance computers, and then became widespread in many classes of computing systems.

The above said circumstances have attracted the attention of many researchers to study the efficiency of interleaved memory via analytical modeling and simulation. Query processing in DBs is associated with processing of data sets. As a result, a great number of address calls streams to interleaved memory sections appear. The calls of target treatments of different streams to gain access to the same sections, which will decrease the interleaved memory effeciency.

In this paper, we studied the interleaved memory efficiency by analytical modeling considering address requests of conflicting streams, and obtained the following results. The absolute and relative average and mean-square deviations of a number of sections in use in cycle of memory access as function of interleaved memory sections number, the number of streams of targeted calls and the number of address requests were determined. Number of sections margin of 1.6 will provide at the average 100% request servicing with any number of streams. Relative average number of sections used in one cycle of memory access depends on the number of streams of targeted calls, but does not depend on the number of address requests in a single stream. With increasing number of streams of targeted calls relative average number of sections used in one cycle of memory access tends to a constant 1 — e—1 = 0.632. Absolute mean-sqaure deviation of the number of sections used in one cycle of memory access decreases with increasing number of targeted calls to flow at a constant absolute value of the average number of sections used. The ratio of the absolute standard deviation to the absolute average number of sections used in one cycle memory access decreases with increasing number of address requests in a stream. The average number of sections used in one cycle of memory access is a significant parameter characterizing the of interleaved memory efficiency.

Keywords: : memory, efficiency, layer, section, querying, database, streams

### Methods and systems of information protection, information security

Korotkova T. I.

The problem of data protection in the aviation systems is considered. The system description of security hazard sources for objects of civil aviation is presented. There are threats of privacy violation, information integrity violation, and malfunction of the system. Hazardous exposures can be accidental and deliberate. All in all the threats are classified as internal and external. The system approach to the description of the information security leads to the problem of information security system synthesis. This problem involves revealing of the protected information, the system of threats and channels of information leakage, assessment of vulnerability and risks, definition of requirements for information security, selection of protection means and security management. To provide the information security system synthesis, a hierarchical system of decision-making is proposed as well as an algorithm based on expert evaluation. Other features of the system are the multicriteriality and the presence of the uncertainties. The decision-making flowchart includes information types, the system of threats, selection of quality indicators, information classification by units of operations, formation of generic quality indicators of protective system. Quality indicators of information protection are arrayed by operation units and threat types. As result the dimension of the problem and the number of possible choices are reduced. The components of the matrix depend on vectors which elements are the uncertain parameters. They are implemented to perform the operation of maximization. The operation of minimization is carried out by the control variables, which define the protection factors. The best option of protection is provided on the principle of the guaranteed result. This option is obtained on the base of the minimax estimation. To obtain optimum solutions the principle of the Pareto cooperative equilibrium is used. Verification is carried out based on computer experiment. A set of procedures of Delphi expert estimation method is applied. The method has three components: intuitive-logical analysis of the problem, decision and delivery of quantitative and qualitative estimates, data processing by a software module and derivation of the final estimate of the degree of information protection. The core modules of the program are Connection module, Administrator module, Users module, Estimates module, Reports module, Authentication module, and Results module.

Keywords: aviation system, algorithm, information protection system, uncertainty condition, hierarchical structure, multicriteriality