Статьи журнала - Siberian Aerospace Journal
Все статьи: 387
Статья научная
The paper discusses new classes of models of multidimensional inertia-free systems with a delay in the condi-tions of a lack of a priori information. The subject is multidimensional discrete-continuous processes, the com-ponents of the vector of output variables of which are stochastically dependent in an unknown way. There are also processes, through some channels of which aprior information corresponds simultaneously to both the par-ametric and nonparametric type of source data about the studied process. The mathematical description of such processes leads to a system of implicit nonlinear equations, some of which will be unknown, while others will be known with accuracy to the parameter vector. The main purpose of a model of an object having stochastic de-pendencies of output variables is to find a forecast of output variables with known input variables. To find the predicted values of the output variables from known inputs, it is necessary to solve a system of im-plicit nonlinear equations. The problem is to solve a system that is actually unknown, when only equations for some channels of a multidimensional system are known. Thus, a rather nontrivial situation arises when solving a system of implicit nonlinear equations under conditions when, in one channel of a multidimensional system, the equations themselves are not in the usual sense, and in others they are known accurate to parameters. Therefore, an object model cannot be constructed using the methods of the existing identification theory because of a lack of aprior information. The purpose of this work is the solution of the identification problem in the presence of a partially-parameterized discrete-continuous process, and despite the fact that the parameterization stage cannot be overcome without additional priori information about the process under study. The control algorithm for multidimensional processes with dependencies of output variables is a sequential multi-step algorithmic chain that allows finding the control action and bring the object to the desired state. Computational experiments to study the proposed models and to control multidimensional discrete-continuous processes have shown quite satisfactory results. The article presents the results of computational experiments illustrating the effectiveness of the proposed technology for predicting the values of output varia-bles from known input variables, as well as for managing these processes.
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Nonparametric identification of dynamic systems under normal operation
Статья научная
The research gives nonparametric identification algorithms under the conditions of incomplete a priory information. The identification case differs from the previously known ones due to the fact that, besides the control action, an uncontrollable variable, but a measurable one, impacts on the object input. In contrast to parametric identification, the research considers the situation when the equations describing dynamic objects are not given with accuracy to the parameters. In this case, there are some features to study while getting the recovery characteristics of various object channels. The main characteristic is that the transition response of a channel is taken when the other channel is in a stable position. Moreover, the identification problem is analyzed under normal object operation, opposite to the previously known nonparametric approach based on Heaviside function input to the object and further Duhamel integral application. An arbitrary signal is input to the object during normal operation as a result we have a corresponding response of the object output. It should be noted that the measurements of the input and output variables are carried out with random noise. 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 discrete 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 with the Duhamel integral, we obtain a nonparametric model of a linear dynamical system of unknown order. The article also describes the case of constructing nonparametric model when a delta-shaped function is input to the object. It is interesting to find out how delta-shaped function might differ from the delta function. The weight function is determined in the class of nonparametric Nadaraya-Watson estimates. Previously proposed nonparametric algorithms consider the case when Heaviside function is applied to the object; this narrows the scope of nonparametric identification practical use. It is important to construct nonparametric model of the dynamic object under conditions of normal operation.
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Статья научная
Testing the hypothesis of independence of random variables is one of the main stages of sys-tem analysis of statistical data. Based on its results, the synthesis of effective decision-making algorithms is carried out. The traditional method of testing the hypothesis of independence of random variables is based on the use of the Pearson criterion, which contains a difficult to formalize stage of dividing the range of the values of random variables into multidimensional intervals. A method for testing the hypothesis of independence of random variables is proposed, which uses a nonparametric pattern recognition algorithm corresponding to the maximum likelihood criterion. Its application makes it possible to circumvent the problem of decomposing the range of the values of random variables into intervals. The idea of the approach is to form a training sample based on the initial statistical data to solve a two-alternative pattern recognition problem. Each class is defined under the assumption of independence or dependence of random variables, which is manifested in the difference in their distribution laws in the classes. Under these conditions, it becomes possible to replace the initial hypothesis with the task of checking the reliability of the difference in the probabilities of pattern recognition errors in classes. Using the apparatus of graph theory, the proposed method is developed in the formation of sets of independent random variables. The obtained results are generalized when testing the hypothesis of independence of random variables for large volumes of statistical data based on compression of the original information. This allows increasing the computational efficiency of the problem being solved. The article substantiates the method for testing the hypothesis of independence of random variables, based on the use of a nonparametric pattern recognition algorithm in conditions of large volumes of statistical data. The results of comparing the technique with the generally recognized Pearson consensus criterion in the study of ambiguous dependences between random variables of varying complexity are presented. The effectiveness of the proposed method is confirmed by the results of its application in processing remote sensing information from anthropogenic territories in the vicinity of the city of Krasnoyarsk.
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Numerical analysis of the influence of defects a on the durability of turbomachines working blades
Статья научная
The aim of the study is to numerically analyze the effect of damages and defects of various types and levels on the fatigue life of blades and impellers of axial and radial turbomachines. In the field of turbine technology, it is of particular importance to increase the durability and reliability of turbine blades, especially in conditions of defects and parameter adjustments. Defects such as cracks, corrosion, material irregularities, etc., can significantly reduce the service life of components, causing the risk of accidents and increasing operating costs. The article presents a numerical analysis of the effect of parameter adjustments related to turbine blade defects on their durability. The research includes the development of mathematical models based on the finite element method (FEM) to assess the impact of damage on the strength characteristics of the working blades of pipe machines. The research methodology is based on the use of FEM using modern software systems, as well as machine learning algorithms. The analysis results showed that impeller fatigue life varies significantly depending on the location and orientation of cracks and damage. These findings can be used to develop diagnostic and service life prediction methods for turbomachines, as well as to optimize their design to improve operational reliability. The study demonstrates the possibility of increasing the durability of the blades by purposefully changing their geometric parameters.
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Object tracking with deep learning
Статья научная
Tracking objects is a key task of video analytics and computer vision, which has many applications in various fields. A lot of tracking systems include two stages: detecting objects and tracking changes in the position of objects. At the first stage, objects of interest are detected in each frame of the video sequence, and at the second, the correspondence of the detected objects in neighboring frames is assessed. Nevertheless, in difficult conditions of video surveillance, this task has a number of difficulties associated with changing the illumination of the frame, changing the shape of objects, for example, when a person is walking, and the task is also complicated in the case of camera movement. The aim of the work is to develop a method for tracking objects on the basis of deep learning, which allows to track several objects in the frame, including those in the rough conditions of video surveillance. The paper provides an overview of modern methods for solving objects tracking tasks, among which the most promising one is deep learning neural networks application. The main approach used in this paper is neural networks for detecting regions (R-CNN), which has proven to be an effective method for solving problems of detection and recognition of objects in images. The proposed algorithm uses an ensemble containing two deep neural networks to detect objects and to refine the results of classification and highlight the boundaries of the object. The article evaluates the effectiveness of the developed system using the classical in the field MOT(Multi-Object tracking) metric for objects tracking based on the known databases available in open sources. The effectiveness of the proposed system is compared to other well-known works.
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On an alternative method for testing the dynamic strength of a small spacecraft structure
Статья научная
This article presents an analysis of the possibility of applying an alternative approach to testing the mechanical effects of the design of a small spacecraft for remote sensing of the Earth, which has an analog product that has passed a full cycle of ground experimental testing. However, despite the similar power scheme and the maximum borrowing of onboard equipment with minimal modifications, the spacecraft planned for testing has a number of significant differences. The application of the main alternative strategies in foreign and domestic practice in the ground-based experimental development of space technology is considered, their advantages and disadvantages are described. Some criteria for decision-making on the rejection of the use of traditional methods of ground-based experimental testing of space technology for mechanical effects are given. The analysis of the normative and technical documentation adopted in the domestic industry in terms of clarifying the list of development tests of spacecraft, the assumptions of applying the computational and experimental method to the development of dynamic (vibration) strength and the analysis of the design of the spacecraft planned for testing in comparison with an analog product showed that the most preferred method of testing dynamic (vibration) strength is the strategy “protocol qualifications”. In accordance with the chosen strategy, a list of tasks was defined that will clarify the nomenclature of the development tests of the research object.
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On incorrect representation of the shock process on shock polars in a viscous heat-conducting gas
Статья научная
The shock gas-dynamic processes that have found wide application in rocket and space technology in the design and optimization of devices and power plants are considered. The analysis of known exact and asymptotic relations/conditions on a shock wave, in particular, generalized differential relations (GDRs) on a curvilinear oblique shock wave (SW) (COSW) for a model of a viscous heat-conducting gas at high Reynolds numbers is made. The advantages of using the discrete-analytical approach are shown, for exam-ple: 1) the ability to make maximal use of the smoothness of the shock gas-dynamic formation (shock wave) in the tangential direction; 2) to build efficient computational algorithms devoid of the negative effect of approximation/artificial viscosity on the schematized discontinuity. In parallel, a very common graphical method for mapping the results of gas-dynamic calculations on the plane of shock polars, proposed by Busemann, and a volumetric (3D) polaroid, proposed by V. N. Uskov, are considered. The mathematical apparatus of shock polars itself is based on exact relations of the Rankine-Hugoniot type and has proven itself well even in modeling the flows of a viscous heat-conducting gas. However, in numerous literature sources there are results (shock solutions) of both physical and computational experiments, which are not mapped strictly on shock polars. In this paper, we show that in rare cases this very common way of such mapping may be incorrect. It has been proven that the main causes of such a defect are the combined ac-tion of three main factors: the nonuniform flow in front of the shock formation, the edge/boudary effect be-hind it, the action of the external factor of viscosity and the heat conduction mechanism.
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On remote sensing of the Earth by spacecraft
Статья научная
Remote sensing is a process which implies collecting information about an object. Due to their properties, satellite images are widely used in both practical and scientific fields. Satellite imagery is used in research aimed at the comprehensive study of natural resources, the dynamics of natural phenomena, and in the tasks of environmental protection. Special attention is paid to the use of space information for daily operational monitoring of the state of the environment in the implementation of geo-ecological monitoring of regions. In particular, this poses the problem to find the regions of the earth's surface with the characteristics determined by the considered parameters using the values of established parameters at certain points of the earth's surface. In this paper, we consider the special case of this problem when the given four points of the earth's surface determine the regions of the earth's surface (the so-called kernels of generalized squares) that have a specified configuration (square).
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On the application of the Bayesian search method for detecting underwater objects
Статья научная
Underwater archaeology and, in particular, the study of shipwrecked vessels, is one of the most advanced fields in the discipline, covering a range of theoretical and applied problems. In the practice of searching for sunken ships, it is quite rare to find a ship on the basis of previously (a priori) known data. In this regard, as well as in connection with the use of definitions from the field of probability theory and mathematical statistics, Bayesian statistics, namely, a search method that has found application in a number of well-known international search projects, has become the natural direction for the development of search systems. The Bayesian search method for determining the location of sunken ships, as well as their identification, has been almost never used in domestic underwater archeology practice. However, there is a need for its use, as it was demonstrated by the 2024 expedition to search for the transport ship Tbilisi, sunk during the Great Patriotic War in the Yenisei Gulf: despite the relatively small area of the search zone, determining the ship’s location became a very labor-intensive process. At the same time, the use of Bayesian search could significantly simplify this task. In this regard, the paper examines the methodology of using Bayesian search to detect sunken ships (an example of constructing a probability distribution in the search zone of the ship Tbilisi is given). In addition, the author considered the issue of using the Bayesian method for identifying objects (a database model is proposed with the inclusion of various search parameters). As a real example, the results of the 2024 expedition are presented with a description of the historical object, search conditions, and problems that arose during this work.
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On the choice of orbits for spacecrafts
Статья научная
The problem of distribution of a given number of spacecrafts over a certain structured set of orbits consisting of k np orbits is considered. The solution to this problem is given under the condition that the set of possible orbits for spacecraft coincides with the number of spacecrafts. In addition, it is assumed that the given set is divided into disjoint subsets of orbits, and the number of orbits in the indicated subset is the same. In the situation under consideration, it is equal to some prime number p. Currently, several orbits are used to place satellites on them, depending on the tasks they solve. Geostationary orbit is used for live TV broadcasting. Low satellite orbits are used for communication between satellite phones. Their own orbits exist for satellites of navigation systems GPS, Navstar, GLONASS, military satellites, satellites for various scientific research. Naturally, under these conditions, the problem of structuring a set of orbits with some restrictions on the location of the spacecraft in given orbits, depending on the purpose of the spacecraft arises. The problem of the complexity of calculating the number of orbits under these constraints is considered.
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On the construction of stress discontinuity lines for a two-dimensional plastic region
Статья научная
The paper considers the plasticity equations in case of two dimensions and the construction of stress discontinuity lines. The construction of stress discontinuity lines is based on the fact that they are located at the intersection point of lines of the same family (characteristics) and are directed along the bisector of the angle formed by these characteristics. Therefore, to find these lines, we constructed characteristics. Such a problem is easier to solve in case of plastic torsion, then there is only one characteristic, it is directed along the normal to the outer contour, and finding the sliding lines and their intersection points is quite simple. Consequently, most of the works devoted to the construction of stress discontinuity lines solve the problem of plastic torsion for isotropic and anisotropic media. For problems of plane strain of plastic ma-terial, this method is not sufficiently developed. This is due to the complexity of constructing sliding lines for such problems and the presence of two families of sliding lines. In this paper, we construct a homotopy of two known exact solutions: that of Prandtl and of Nadai, that is, a continuous transformation of one solution into another. In this case, one can observe the evolution of characteristics that depend on the group parameter a: for a = 1, the characteristics of the Prandtl solution are obtained; at a = 0, the characteristics of the Nadai solution, at a = 0.5, the characteristics of one fami-ly begin to intersect and lines of stress discontinuity appear. These lines are constructed in this paper.
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On the function of time distribution of a complex computing system uptime
Статья научная
Any space computing complex is a complicated system. A complicated system is understood as a set of functionally related heterogeneous devices designed to perform certain functions and solve problems facing the system. One of the important characteristics of a system is its uptime. This characteristic is often considered to be a random variable. However, such a mathematical model is quite limited, since the uptime depends on many characteristics (parameters) that describe a system. Therefore, the uptime can be assumed to be a continuous random field (that is, a random function of many variables). It is this approach that is used in this work. If there are certain restrictions on the uptime of a computing system, upper estimates are found for the distributions of a random number of system failures. Therefore, the problem of estimating Gaussian field distribution in Hilbert space arises. Two theorems that allow calculating the probability of a Gaussian vector falling into a sphere of a given radius are proved in the paper. The paper is devoted to the reliability of a computing system. The random number of a computing system failures v(r) is a characteristic of its reliability. The v(r) distribution is the distribution of the sum of a computing system random uptime. It is impossible to write down the distribution v (r) explicitly. Therefore, one has to look for an estimate of these distributions from above. Assuming that the uptime of a computing system is the sum of many variables, the authors of the paper obtained the following results: it is shown that the problem of estimating the distributions of a random number of system failures can be considered as the problem of estimating the convergence rate in the central limit theorem in Banach spaces; if there are certain restrictions on the uptime of a computing system, upper estimates are found for the distributions of a random number of system failures. The estimates obtained can be used for further research in the theory of computing systems reliability. Knowing these upper estimates, it is possible to predict the level of average costs for computer systems restoration, as well as for the development of special mathematical and algorithmic support for analysis systems, for management, decision-making and information processing tasks.
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Статья научная
The results of the study of the damping capacity of manganese-copper alloys based on the Mn – 40 % Cu alloy with additives (0.5 – 1.5) % zirconium in the field of amplitude-independent damping are present-ed. Mn – Cu alloys with high damping capacity can be effectively used to reduce vibration and noise. Stud-ies on the influence of a number of alloying elements on the magnitude and stability of the damping capaci-ty of Mn – Cu double alloys in the field of small deformations of relative shear are not enough. In the pa-per, the influence of one of these elements, zirconium, was elucidated. Mn – Cu alloys were smelted in an induction furnace. From the ingots cast into cast iron molds, samples for studies with dimensions (11 × 15 × 117) ± 1 mm were obtained by mechanical cutting. The samples were subjected to aging at a temperature of 643 K for 0.5–40 hours. The damping capacity of Mn – Cu alloys (the logarithmic decrement of attenua-tion of oscillations) was studied for longitudinal oscillations of samples in the frequency range 14–17 kHz and the amplitudes of the relative shift (1 ... 3) × 10–6. It has been established that alloying the Mn – 40 % Cu alloy with zirconium from 0.5 % to 1.5 % does not increase its damping capacity in the cast state, as well as in the cast and aged at a temperature of 643 K for 40 hours. It was found that the minimum values of the frequencies of resonant vibrations of samples of Mn – Cu alloys correspond to the maximum levels of the damping capacity of these alloys. Itʼs shown that the high damping capacity of cast and aged alloys at 643 K for 40 hours Mn – 40 % Cu, Mn – 38.5–39.5 % Cu – 0.5–1.5 % Zr after natural aging at 293 K for 7 months decreases by 2.0–2.6 times.
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On the issue of hydrodynamic braking efficiency dur-ing high-velocity tests on a rocket-rail track
Статья научная
At present, the creation of high-velocity aircraft is a promising direction in the development of aircraft and armament both in Russia and abroad. The increase in velocity characteristics of newly developed sam-ples imposes new requirements on test bench equipment, including rocket-rail tracks. The requirements are growing both for the acceleration and braking means, which ensure the tested materiel safety. The proposed work deals with a hydrodynamic braking method used in high-velocity dynamic tests on a rocket-rail track at the Federal State Enterprise “State Governmental Scientific-Testing Area of Aircraft Systems named after L.K. Safronov". The paper gives the description of the braking devices, presents the dependencies determining the calculated values of the braking force developed by them, and describes the braking intensity control methods, which increase the efficiency and safety of braking as well as expand the permissible speed range of the hydrodynamic braking device application. The method of increasing the efficiency of the braking devices functioning by using a special form of its working part profile is presented. The corresponding examples of the braking modes are given for a comparative assessment of the braking efficiency parameters when using braking devices with special and triangular profiles. The working part profile of the hydrodynamic braking device calculated according to the proposed method provides more efficient and safe braking compared with the previously used triangular profile, by maintaining a constant stopping force in a wide velocity range.
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On the location of spacecraft in a given number of orbits
Статья научная
Space vehicles are an expensive product. For example, just putting such a device into orbit costs at least one hundred million dollars plus the cost of the satellite itself and scientific equipment it carries. However, the cur-rent state of human civilization does not allow us to do without the presence of satellites in orbit. There were 2,062 active satellites in the international database as of March 2019. Compared to 2018, the number of new devices increased by 15 %. Experts warn that in the coming years, the world is expecting a «satellite boom» with a projected increase in the number of devices of about 15–30 % annually. All these satellites are rather different. Currently, several orbits are used for placing satellites on them, depending on the tasks they solve. A geostationary orbit is used for live television broadcasting. Low satellite orbits are used for communication between satellite phones. There are some orbits for navigation systems (GPS, Navstar, GLONASS). Naturally, under these conditions, there is a prob-lem of placing spacecraft over a given number of orbits, with some restrictions on the location of the spacecraft in certain orbits, depending on the purpose of the spacecraft. The solution to this problem is considered on the condition that the number of spacecraft coincides with the number of possible orbits in which they can be placed with some additional re-strictions on the possibility of their placement in orbit. Several solutions to this problem are obtained that allow us to calculate the number of possible combinations for such placement of spacecraft over a given number of orbits.
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On the possibility of flight of a single-stage rocket to the planets of the Solar system
Статья научная
A new concept for building a small-sized rocket engine containing a special gas ionizer in the combus-tion chamber to increase its conductivity to an optimal value with a corresponding improvement in the fuel combustion process is proposed. A simplified calculation for the relative velocity of gases in a conical noz-zle is given when heating the supersonic flow of gases by plasma in a conical nozzle by means of a power-ful, electromagnetic, high-frequency field, and the influence of some technical parameters on the efficiency of the rocket's flight is also considered. A comparison of the flight altitude of a rocket with plasma heating of the gas flow in a conical nozzle with a scale model corresponding to the well-known single-stage Zenit rocket with the same weight and geometry, taking into account air resistance for the cargo version of the rocket with one small-sized engine, is made. The result is a significant reduction in fuel consumption and an increase in the maximum flight altitude by 2 times with an increase in specific impulse by 2.7 times, other things being equal. It is estab-lished that under certain conceptual parameters, it is possible to rapidly accelerate and fly a single-stage cargo rocket with a launch weight of 17.25-20.00 tons to the planets of the solar system directly from the Earth's surface using a bunch of engines of the same type. The use of many of the same type of small-sized engines allows you to abandon the Laval nozzle in favor of a simple conical nozzle, which reduces the size of the rocket as a whole. This is determined by the need to reduce the diameter of the conical nozzle in order to achieve a greater specific heating power of the plasma compared to the specific power of the fuel burned in the combustion chamber. It is also proposed a complete rejection of the steering engines, the function of which will be performed by part of the engines located closer to the diameter of the rocket. As electric generators, it is proposed to use promising prototypes of electric generators MEG-6NS, MEG-15NS and others, the company "NaukaSoft", with good weight indicators that allow in the future producing such a liquid propellant rocket engine (LPE) of small dimensions. The redistribution of part of the fuel used to produce electricity is compensated by a significant increase in the specific impulse of the LPE to increase the speed and overall efficiency of the flight with an optimal ratio of the amount of fuel to the weight of the rocket before refueling.
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One class of solutions to the equations of ideal plasticity
Статья научная
Much attention is given to the study and solution of nonlinear differential equations in the modern mathematical literature. Despite this, there are not many methods for researching and solving such equations. These are point and contact transformations of equations, various methods of separating variables, the method of differential connections, the search for various symmetries and their use to construct solutions, as well as conservation laws. The paper considers a nonlinear differential equation describing the plastic flow of a prismatic rod. A group of point symmetries is found for this equation. The optimal system of onedimensional subalgebras is calculated. Conservation laws corresponding to Noetherian symmetries are given, and it is also shown that there are infinitely many non-Noetherian conservation laws. Several new invariant solutions of rank one, i. e. depending on one independent variable, are constructed. It is shown how classes of new solutions can be constructed from two exact solutions, passing to a linear equation. Thus, in this short article, almost all methods of modern research of nonlinear differential equations are involved.
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Статья научная
One of the promising types of spacecrafts are large-size transformable reflectors. Such apparatuses are delivered to a target orbit folded, and then deployed to a working condition. The large aperture allows sig-nificantly expanding the capabilities of the antenna. In this case, the tasks arise of a smooth and reliable deployment, adjusting the shape of a radio-reflecting net, and adjusting the orbital position. Due to the fact that the deployment process takes a long time, accounting for disturbing influences is an important prob-lem. The presence of radiation, large temperature differences, solar wind affect the entire system and main-ly on the directional diagram. It is also necessary to smoothly deploy the structural elements, since with an increase in the diameter of the radio-reflecting surface, the moments of inertia of the antenna increase, which leads to prolonged oscillations. In this paper, the process of deployment of the reflector spokes in the presence of disturbances and measurement errors is considered. The solution to the problem is presented using the separation theorem. To estimate the parameters of the system in the presence of measurement noise, the Kalman filter is applied. Its performance is shown at various values of the noise intensity. A ran-dom process such as white noise was selected as external disturbances and measurement noises. The con-trol problem is solved using the optimal control algorithm according to the hierarchy of target criteria. The possibility of minimizing energy costs by means of interval switching on of measuring sensors is shown. The results of numerical simulation are presented.
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Статья научная
Currently, the development of large-sized space structures and, in particular, transformable reflectors is actively developing. A feature of these devices is a small volume during transportation and large dimensions in the expanded working condition. Therefore, it is important to carry out a reliable and smooth deployment, adjust the shape of the active radio-reflecting surface with a given accuracy, and adjust the orbital position. In outer space, the system is constantly exposed to radiation, there is a large temperature difference in near-Earth orbit, there is a solar wind, which mainly affects the radiation pattern. In this paper, the process of deployment of the reflector spokes in the presence of disturbances and measurement errors is considered. The solution to the problem is presented using the separation theorem. To estimate the parameters of the system in the presence of measurement noise, the Kalman filter is applied. Its performance is shown at various values of the noise intensity. A random process such as white noise was selected as external disturbances and measurement noises. The control problem is solved using the optimal control algorithm according to the hierarchy of target criteria. The possibility of minimizing energy costs by means of interval switching on of measuring sensors is shown. The results of numerical simulation are presented.
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Optimization control actions for the electrolytic method of aluminium production
Статья научная
The most common indicator of the aluminium production process managing efficiency is the cost of the metal production, but this concept includes a lot of components. First, this is the cost of raw materials and electricity in this region, as well as the labour cost per ton of products, consumption coefficients of raw materials and energy, capital costs for construction and repairs, waste disposal cost, environmental payments, etc. At the same time, there is no single functional of the process quality, depending on technological parameters, that is, the problem of complete and relatively strict mathematical process optimization as a whole is currently not solvable, not only because of its volume, but because of the lack of a complete efficiency model. In this study, particular efficiency criteria are considered, the improvement of which is aimed at the optimization model of control actions developed by the authors, which are selected based on the possible levers of the current automated process control system (APCS) for aluminium electrolysis. All tests were carried out on Virtual cell software without transfer to a real control object.
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