Vol 19, No 3 (2018)

Complexity and dimensionality of real-world optimization problems are rapidly increasing year by year. A lot of real-world optimization problems are complex, thus researchers consider these problems as ‘black box’ models due to the fact that the analysis of the problem is complicated or completely impossible, and partial information about the problem is rarely useful. Heuristic search algorithms have become an effective tool for solving such ‘black box’ optimi- zation problems. In recent decades, many researchers have designed a lot of heuristic algorithms for solving large- scale global optimization (LSGO) problems. In this paper, we proposed an innovative approach, which is called DECC-RAG. The approach is based on an original method of grouping variables (random adaptive grouping (RAG)) for cooperative cooperation framework. The RAG method uses the following idea: after a specified number of fitness evaluation in the cooperative coevolution with the SaNSDE algorithm, we choose a half of subcomponents with the worst fitness values and randomly mix indices of variables in these subcomponents. We have evaluated the DECC-RAG algorithm with 20 LSGO benchmark problems from the IEEE CEC’2010 and on 15 LSGO benchmark problems from the IEEE CEC’2013 competitions. The dimensionality of benchmark problems was equal to 1000. The experimental results have shown that the proposed method of optimization (DECC-RAG) outper- forms some well-known algorithms on the large-scale global optimization problems from LSGO CEC’2010 and LSGO CEC’2013.

The problem of nonparametric identification of linear dynamic objects is being investigated. In contrast with para- metric identification, the case is analyzed when equations describing a dynamic object are not specified according to the parameters. Moreover, the identification problem is analyzed under normal object operation, opposite to the previ- ously known nonparametric approach based on Heaviside function input to the object and further Duhamel integral application. An arbitrary signal is inputted to the object during normal operation and weight function realizations are represented by observations of input-output object variables measured with random interferences. As a result, we have a sample of input-output variables. As linear dynamical system can be described by the Duhamel integral, with known input and output object variables, corresponding values of the weight function can be found. This is achieved by dis- crete representation of the latter. Having such realization, nonparametric estimate of the weight function in the form of the nonparametric Nadaraya-Watson estimate is used later. Substituting this into the Duhamel integral, we obtain a nonparametric model of a linear dynamical system of unknown order. The article also describes the case of nonparametric model constructing when a delta-shaped function is inputted to the object. It was interesting to find out how delta-shaped function might differ from the delta function. The weight function was determined in the class of nonparametric Nadaraya-Watson estimates. Nonparametric models were investigated by means of statistical modeling. In general, nonparametric models have shown sufficient efficiency in terms of accuracy prediction by nonparametric model in relation to the actually measured output of the object. Evi- dentally, the accuracy of nonparametric models reduces with the growing influence of interference from the meas- urement of input-output variables or the discreteness of their measurement. Previously proposed nonparametric al- gorithms consider the case when Heaviside function was applied to the object, which narrows the scope of nonpara- metric identification practical use. It is important to construct nonparametric model of a dynamic object in condi- tions of normal operation.

The increased requirements for strength calculations of space-rocket and aviation technology designs cause the need for the development and improvement of approximate solutions for elasticity theory tasks with small error algo- rithms. The article considers the numerical method of calculating elastic layered conical shells (LCS) of various thickness under static loading which are widely used in space-rocket technology. The suggested method uses three-dimensional curvilinear Lagrange multigrid finite elements (MGFE). A system of nested grids is used for MGFE constructing. The fine grid is generated by the basic partition that takes into account MGFE heterogeneous structure. The basic partition dimensionality is reduced with the help of large grids which leads to the system of linear algebraic equations of the small dimension finite elements method. Three-dimensional elasticity theory equations use allows to apply MGFE for calculating LCS of any thickness. Displacements in MGFE are approximated by Lagrange polynomials which, in con- trast to power polynomials, gives the opportunity to design big size three-dimensional thin shell elements. Lagrange polynomials nodes coincide in shell thickness with the nodes of MGFE large grids which lie on the shared borders of multi-module layers. The efficiency of the presented method is that the suggested MGFE generate small dimension discrete models that require 103-107 times less electronic computing machine (ECM) memory than basic models. The suggested law of dis- crete models grinding generates uniform and fast convergence of numerical solutions which allows to make solutions with the specified (small) error. Examples of LCS calculating (whole ones as well as with holes) under axisymmetric and local loading are given. Comparative analysis of solutions obtained with the help of MGFE, single-grid finite elements and the program com- plex ANSYS has been conducted.

In this paper we study equations describing a slow plastic flow of material. In this case the material is in the flat state of stress. The paper presents the equations that can be used to simulate slow plastic material flows compressed between rigid plates, converging with constant acceleration. In the above equations we neglect convective terms, which greatly simplifies all calculations. The Lie algebra of point symmetries admitted by these equations is calculated for reduced equations. It has dimension eight. The optimal system of one-dimensional subalgebras is constructed for this algebra. It allows to give a view of all the different invariant solutions of rank two. That means such solutions depend only on two independent variables. To demonstrate this we offer a table of switches of all basis operators, as well as a table of all internal automorphisms functioning. One of the solutions, which simulates the slow plastic flow of the mate- rial compressed between rigid plates, converging with constant acceleration, built in. Among the most popular solu- tions in the flat theory of ideal plasticity is the Prandtl’s solution, which describes the compression of a plastic layer between rigid plates. In this case, the plates approach at a constant speed. The popularity of the solution is explained by its simplicity, as well as the fact that it can be used to describe various technological processes. The analogue of such a solution for the plane stress state cannot be constructed. In general, there are big problems with finding analytical solu- tions for the plane state of stress. It is caused by the fact that the equations describing this state are quite complex, even in spite of their linearization. In one of the previous works, one of the authors of the present article managed to find a solution that describes compression of a plastic layer between rigid plates which converge with constant acceleration. In this work the analogue of such a solution is found for the plane stress state. The authors hope that the suggested so- lution can also be used for the analysis of real technological processes.

This article is devoted to the construction of a new class of models under incomplete information. In this article we will discuss multidimensional inertial-free objects, where the output vector components are stochastically dependent, but the nature of this dependence is not known to us. Constructing a model of a multidimensional inertial-free object, when the input and output vectors are not linear, leads to the necessity to solve the problems of systems of implicit func- tions. It should also be noted that the form of these functions is unknown up to parameters. So there is a need to use T-processes, when predicting output variables is carried out by known input. Thus there is a system of nonlinear im- plicit equations which form is unknown at the initial stage of the statement of the identification problem, but it is only known that this or that component of the output depends on other variables that determines the state of the object. Proceeding from the above, a nontrivial situation arises that solves a system of implicit nonlinear equations under the conditions when the equations themselves are not in the usual sense. Consequently, the model of the object can not be constructed using the existing theory of identification because of the lack of a priori information. Therefore, the solu- tion of this system can be represented in the form of some successive algorithmic chain of the T-model. The main goal of this paper is to solve the identification problem for multidimensional inertia-free objects with de- lay, in the presence of T-processes, i.e. construction of T-models under conditions of nonparametric uncertainty. In this case, to predict the output variables by the known input, it becomes necessary to use a step-by-step solution of the prob- lem under consideration. In the article some calculations of the T-process simulation will be presented, which showed the high efficiency of the proposed technology of forecasting the values of the output variables by the known input.

One of the most difficult tasks in the development of a liquid rocket engine is to ensure its reliable and stable igni- tion. During this period of engine operation, in the process of its development, abnormal and emergency situations very often appear. It typically happens due to a large range of the mass flow of components entering the gas generator and combustion chamber. For these moments of entering and the mass flow value, the processes of filling of free volumes and mixing heads of the gas generator and the combustion chamber have a significant effect. The mix ratio of the com- ponents coming into them depends on the evolution of the working processes and, in particular, the temperature of the generator gas. Its efficiency depends on the working opportunity of the nozzle apparatus and turbine blades. It is very important, in the process of starting the engine, not to allow large temperature to spike in the gas generator, especially for engines with an oxidative scheme of gas generation, as in an oxidizing environment, the ignition of elements of the gas path is possible at relatively low gas temperatures. The article shows the problem of filling the mixing heads of the gas generator and the effect of this process on the dynamics of the launch of a liquid rocket engine which does not use special starter devices. The analysis of the designs of gas generators and their mixing heads is carried out; the features of the organization of the working process in the volumes of the gas generator are considered. For a theoretical analysis of the problem a nonlinear mathematical model of a liquid rocket engine is used. With its help, the study of the launch of a liquid rocket engine with and without taking into account the injection of gas into the mixing head of the gas generator was made. The injection of gas is one of the methods for metering the mass flow of the fuel component, which essentially enhances the spray of the component entering the combustion zone. When examining the start-up process of a gas generator without injection of gas, various forms of the functions of the outflow of fuel from the mixing head have been studied. It is shown that the shape of the functions of the outflow has a significant effect on the presence and amplitude of the temperature burst in the gas generator. In order for the results of mathematical simulation of the launch of a liquid rocket engine to be adequate for full- scale testing of engines, it is necessary to conduct special experiments to fill the mixing heads on normal-boiling and cryogenic components of the fuel.

Over the past several years the concept of the so-called “all electric propulsion spacecraft” has gained popularity among both customers and developers of geostationary (GEO) spacecraft; this issue is being actively discussed. The main advantages of the concept are the following: decreasing the mass of spacecraft and increasing its economic effi- ciency by means of pair orbital injection. There are some illustrative cases of implementation of this concept by Ameri- can, European and Russian companies. However, specialists interpret the content of the concept in different ways. That causes the problems connected to the development of the conceptual design of spacecraft. It is therefore very important to consider the concept in more detail, to compare various points of view in order to form understanding reflecting its essence the most accurately. At the same time, on the basis of the available examples, it would be feasible to analyze the advantages and disadvantages of this concept in comparison with other approaches to the construction of propulsion system of spacecraft. In the article we offer to interpret the concept as “ All electric propulsion spacecraft ” . This inter- pretation allows to understand its content unambiguously by the specialists of both Russian and Western Technical Schools. We offer to define “ All electric propulsion spacecraft ” as an apparatus that does not have in its composition an apogee engine unit that is chemically fuelled. It has to execute manoeuvres on geostationary orbit raising, orbit correc- tion and momentum wheel unloading by electrical propulsion only. We have shown that with the existing level of excel- lence of the equipment this concept does not have any advantages over the concept of separate propulsion subsystems for the correction and orientation by total mass as well as by the level of reliability.

The paper is devoted to cross-section geometrical parameters optimization of thin-walled spokes of large-size, um- brella-type deployable satellite parabolic antennas with radial spokes. The spokes in the structures mentioned above must have maximal bending stiffness and minimal mass. Spokes with uniform thickness of walls both in the section and along their lengths are not optimal to achieve the maximal stiffness while keeping predetermined mass, because they have the same bending stiffness in any direction. In the given paper the authors suggest changing the shape of the spoke cross-section by using sections of different thicknesses. This would allow increasing the bending stiffness of each spoke in the perpendicular to the antenna surface direction while preserving the same mass of the complete structure. The thickness will be increased stepwise in the cross-sectional areas of the maximum distance from each other in the bend plane; in the remaining part of the section it will be reduced. The main objective of this paper is to obtain analytical dependences for assessment of the bending stiffness of the cross section of the umbrella-type antenna spoke with a stepwise change in its thickness. Formulas were obtained within the framework of the beam theory of bending. The obtained analytical dependencies were verified by numerical simulation in the finite element software Ansys. Verification of the obtained results by numerical simulation showed good convergence with theoretical conclusions. The formulas obtained in the paper make it possible to give practical recommendations for design of large deploy- able space antennas with improved parameters, namely maximum stiffness with minimum mass of the structure.

The article is devoted to the peculiarities of the flight trajectories design to the centre of the Solar system for two perspective Russian spacecrafts. A scientific goal of the project is to study the near-solar space from close distances (60-80 solar radii) and non-ecliptic inclinations. As part of the draft project, management decided to create two space- crafts (SC), where an option with a “chemical” propulsion system based on low-thrust engines is offered as a march. In connection with a significant increase in the initial mass of the spacecraft, it is necessary to use means of deducing a heavier class. Therefore, now options are being considered for launching at “Angara-A5” and “Soyuz-5” (“Sumkar”) with “DM” and “Fregat-SBU” upper stages from the Vostochny and Baikonur launch sites. The active life of the SC should exceed seven years, for which an inclination of more than 25 ° must be achieved. The article describes the additional version of the propulsion system with the use of two-component engines, pro- duced by NIIMash (Nizhnyaya Salda), and the main characteristics of the flight schemes for two spacecrafts are indi- cated. The developed scheme of the first spacecraft flight assumes the launch in August 2026. Convergence with the Sun at a minimum distance of 61.5 solar radii occurs 6 years after the start. After the last, the eighth, gravitational maneu- ver, 8.3 years after launching the spacecraft reaches heliocentric latitude of 33.1°. The trajectory of the second space- craft assumes the launch in April 2028. Six years after the start it also approaches the Sun to approximately the same distance 63.0 solar radii. The spacecraft reaches the heliocentric latitude of 29.1° with the help of subsequent gravity- assists at Venus. The presented design appearance of the ‘chemical’ propulsion system with the use of low-thrust engines makes it possible to achieve the specified parameters of the Sun orbit and to execute the scientific program within the given period of active existence of two spacecrafts.

In JSC “ ISS ” the task of evaluating the efficiency of using the previously developed unified platforms for the creation of a new spacecraft was solved in a more empirical way, by generalizing the reserve for existing developments and as- sessing opportunity and expediency of applying the existing reserve in the future (continuity of development). However, the methodological basis for solving this kind of problem has not been developed to this day. From this follows the con- clusion about the urgency of developing a methodology for assessing the range of effective application of the unified space platform and the need for its implementation. In this article, the methodical approach to problems of expediency of use of existing unified space platforms for creation of new space vehicles on their basis is considered. The sources of uncertainties arising in the design of space vehicles and the stages of choosing the optimal project under conditions of uncertainty are determined. This article describes such a design approach of space vehicles as a rational design. The main task of this approach is indicated. Also in the article the design parameters that determine the structural stability of the spacecraft are listed. A mathe- matical model of a spacecraft based on a unified space platform has been developed, which determines the dependence of design parameters on the characteristics of the payload. The criterion of a space vehicle optimal design based on a unified space platform, defined as the ratio of the effi- ciency index to the cost index for the creation of a spacecraft, is formed. A methodology for assessing the range of effec- tive application of unified space platforms has been developed. Approbation of the developed technique was carried out based on existing geostationary space communication apparatuses on the basis of a unified space platform ”Express-1000NT”, developed by JSC “ ISS ” . Calculated data and graphical representations of effective application ranges of the unified space platform “Express-1000NT” are presented. Based on the results of approbation, it can be concluded that the developed methodology allows to asses properly the range of effective application of unified space platforms for communication satellites in the geostationary orbit.

For crystals grown from a liquid melt by the Czochralski method, when monitoring and controlling the current crystal area, based on the contact method of measurement, the basic requirements for ensuring the accuracy of measuring the area of the crystal on the cylindrical part of the growing are determined. In the control system with respect to the coordinates of the movement of the crystal and the crucible, it is necessary to use photo-reading optical rulers, with a sampling resolution of 0.1 µm, to determine the amount of movement during the control signal evaluation cycle. To eliminate the error due to the accuracy of stabilization of the melt level in the crucible, the following algorithm for the operation of the crystal growing apparatus is proposed. During the evaluation of the control signal on the cylindrical part of the growing crystal, the sampling time of the predetermined number of pulses of the crucible movement is adopted. Calculation of the evaluation time of the control signal begins at the moment of closure of the melt sensor and ends when the melt sensor closes, provided that a predetermined number of pulses of the crucible transfer is sampled. The evaluation time of the control signal in the previous control cycle is used in the current cycle to calculate the closure pause as part of the calculated evaluation cycle time. In the control system, at the moment of closing the contact sensor, a pause of the closed sensor is maintained, followed by a similar pause of the open state of the level sensor. During the moments of pauses, the state of the contact sensor by the control system is not analyzed and the control of the crucible lift occurs with a slowed and accelerated rate of the crucible lift during the moments of the “conditionally” closed and “conditionally” open states of the level sensor. All this ensures in this control system the accuracy of measuring the current area of the crystal, on the cylindrical part, by a value not worse than 1 %.