Informatics, computer technology and management. Рубрика в журнале - Siberian Aerospace Journal
Статья научная
In this paper the approach for external boundary of pole localization region formulation for transfer function with interval-given parameters is proposed. The boundary is formulated as analytic piecewise function of characteristic polynomial parameters of the given transfer function. Analytic formulation of external boundary of poles localization region allows to reduce computations since existing methods require iterative numeric calculations of characteristic equation roots with fixed step size for edges mapping or full interval root locus mapping as well. Formulated boundary allows to clearly describe system behavior and calculate variation ranges of performance indexes. In addition, piecewise function that constrains gives new opportunities for parametric controller synthesis for systems introduced by transfer functions with interval-given parameters. The results can find its practical application in aerospace engineering problems of mathematical analysis and synthesis for highly-precise systems of self-direction missiles. In the research the boundary formulation is performed for third order transfer function. Transfer function order was chosen due to the fact that many physical systems and objects can be described mathematically with the third order transfer function, e.g. model of missile target-seeking head with gyro stabilized drive is described with this model. The research was performed on the basis of the following step sequence: firstly, analytical solving of cubic equation applying Cardano’s formula; secondly, interval root locus edges functions obtaining, next external vertexes set obtaining and, finally, external border formulation and plotting.
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Статья научная
The purpose of the study is to develop a technological process mathematical model of creating permanent joints of dissimilar materials based on electron-beam welding using machine learning algorithms. Each of the connected elements is a responsible unit of the complex device, due to this fact, strict criteria are set for the quality of the welded joint. In essence, the set task is a regression task. There are many algorithms suitable for solving the regression problem. However, often the use of one algorithm does not provide sufficient accuracy of the result. One way to solve this problem is to develop a composition of algorithms to compensate for the prob-lems of each of them. One of the most effective and potent compositional algorithms is the gradient boosting al-gorithm. This algorithm use will improve the quality of the regression model. The proposed model will allow the technologist to set the process parameters and to get an assessment of the final product quality, as well as by setting input and output values. The use of assessment methods and forecasting will reduce the time and labor costs of searching, developing and adjusting the process. A description of the gradient boosting algorithm is given, as well as an analysis of the applicability of this algorithm to the model and a conclusion regarding the areas of its applicability and the reliability of the forecasts obtained by its direct use. In addition, we consider the process of direct model training based on the data obtained as part of search experiments to improve the quality of final product. The results of the applicability analysis allow us to judge the admissibility of using the proposed method for processes that have similar statistical dependencies. The application of the proposed ap-proach will make it possible to support the adoption of technological decisions by specialists in electron-beam welding during the development of the technological process and when new types of products are put into pro-duction.
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Improvement of the construction technique of substitution blocks for symmetric encryption algorithms
Статья научная
As it is known, block symmetric encryption algorithms are widely used to ensure information confidentiality. The resistance of encryption algorithms to the most common types of cryptanalysis is determined the quality of the blocks of substitutions. In the present work, the development of a methodology for constructing substitution blocks is being continued. In the first approach, Boolean functions with given cryptographic properties are used as component functions of substitution blocks. Previously, one of the authors proposed a reasonable methodology for the phased selection of Boolean functions for construction block. In this paper, in addition to such cryptographic properties of Boolean functions, such as: balance, possessing a strict avalanche effect, possessing correlation immunity, for the first time the nonlinearity distances of the first and second orders of Boolean functions are considered simultaneously. A study of the full set of Boolean functions of four variables was conducted. The result of it is the optimal set of Boolean functions for building substitution blocks when encrypted with the GOST 28147-89 algorithm. In the second approach, the substitution block are determined by an irreducible polynomial over the Galois field, such a scheme, used in the Rijndael encryption algorithm, is considered to be strong. The growth of calculating power of the computer necessitates an increase of the cryptographic strength of encryption algorithms. The authors have proposed substitution blocks for each round of the Rijndael scheme, based on different irreducible polynomials. A study of compositions representing a different combination of specially selected irreducible polynomials for ten rounds was carried out and the optimal set of polynomials with the best values of the encryption quality indicators by the Rijndael scheme was obtained.
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Статья научная
Many strategically important sectors of the domestic industry are at the stage of transition to an investment approach to asset management. One of these industries is hydropower, where the current maintenance planning system needs new methods to deliver more efficient results. In general, the planning system for the main equipment (technical impact system) maintenance and repair can be formulated as a scheduling problem. The ant algorithm is of great interest from the point of view of solving the scheduling technical impact problem. Based on the specifics of planning, implementation and factors affecting the maintenance process, a modification of the ant algorithm is proposed. The mathematical description is a methodology for calculating parameters, basic elements of the graph, optimization criteria and constraints. A preparatory stage was also introduced into the solution algorithm, which determines the initial state of the equipment at the vertex K0. The functional model of the technical impact planning process presented in the article can be used to develop a software package within the framework of an innovative approach to asset management for hydropower companies.
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Library of mathematical functions with parallelism at the operational level in the Pythagor language
Статья научная
At present, developed tools and libraries have been designed for imperative and functional programming languages that provide parallelism through processes or threads. There are other alternative approaches to the organization of parallel computing, one of which is implemented in Pythagor – the language of functional-streaming parallel programming, and involves parallelism at the level of operations. The tools of the Pythagor programming language are actively developing, and the repository of predefined functions is expanding. Many mathematical functions have been designed to provide a developer with no less functionality than the math library math.h of the C programming language. A large part of the mathematical functions have been implemented using the Maclaurin’s series. It is both used as an approach of faster and less accurate calculations, in which a predetermined number of elements of the series is calculated without cycles and recursions with the substitution of pre-calculated coefficients in the function code, and as an approach of less rapid and more accurate calculations, in which the elements of the series are calculated dynamically until the desired accuracy is achieved. The development of a library of mathematical functions of a programming language is an applied algorithmic task already implemented in one way or another for a number of existing programming languages. But in many languages, the implementation of algorithms for mathematical functions is hidden from the user, while modern tools of the Pythagor language support an open repository of functions. Additional interest is the possibility of parallelism at the level of operations in the calculation of mathematical formulas in the Pythagor language.
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Managing a group of objects as a task of system analysis
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In this paper, we consider the general statement of the problem of identification and management of a group of objects. A group refers to several objects combined for the manufacture of a product. The main feature is that when managing such systems, it is necessary to change the setting actions for each object. This is due to the fact that today the technological regulations in many cases are wider than they should be for good operating. This is a consequence of the fact that the current production culture (this, in particular, has been shown by the experience of processing data from the technological process for the production of transis-tors at Svetlana) is rather low, which leads to some organizational problems. It is clear that it is necessary to have certain models of objects that naturally differ from each other and can be considered under conditions of both parametric and nonparametric uncertainty. Moreover, there may be cases when an object is considered simultaneously under conditions of both parametric and nonparametric uncertainty over various channels. Now, regarding the delay, due to the fact that the measurement of some variables is carried out in a significantly long-er time interval than the object constant, it is necessary to distinguish the time of measuring technological vari-ables and, in fact, the delay typical to the process itself, taking into account the difference between the channels. This leads to the fact that dynamic processes are essentially forced to be considered as inertialess with delay. Another significant feature is that the components of the output variables are stochastically dependent in ad-vance in an unknown manner. The use of correlation or dispersion relations in this case does not lead to success. A special analysis of T-processes and the ability to simulate such processes are required. In particular, this is one of the tasks of this article. It contains: T-processes, T-models and the corresponding heterogeneous control algorithms. The process of hydrodeparaffinization of diesel fuel is considered according to available data, which can be said a priori that they are incomplete, that is they do not reflect the complex behavior of the pro-cess. From here it follows that these data require replenishment, which today is not carried out for various rea-sons. Thus, the process of hydrodewaxing can be taken to the T-process. Modeling a multidimensional system based on real data has shown that in this problem the presetting effect for different objects should be different. The exception is only the setting actions for the entire complex or group of objects. Modeling was carried out on the basis of T-models considered in the article. It has already been not-ed that these models should not be taken as complete, giving an idea of reality. They will be subject to algorith-mic refinement during further research. The decision is made by the researcher. At this stage that an assessment is given that, under the circumstances, the resulting models and control algorithms can be adopted for use in a production environment. An attempt to use the existing theory of identification and control for the process of hydrodewaxing will inevitably lead to a significant degradation and increase in the cost of a computer system for operating the quality of this process.
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Статья научная
One of the main characteristics of computer appliances for processing real-time information is reliability. The reliability of software is understood as the property of this software to perform specified functions, maintaining its characteristics within the established limits under certain operating conditions. Software reliability is determined by its reliability and recoverability. Reliability of software is a property to maintain its performance when using it for processing information in the information system. The reliability of the software is estimated by the probability of its operation without failures under certain environmental conditions during a given observation period. The development of real-time systems requires a large amount of resources for design and testing. One of the solutions to this problem is mathematical modeling of computer appliances. This allows more flexible design of real-time systems with the specified reliability, taking into account the limitations on price and development time, and also opens the possibility of more flexible optimization of computer appliances for real-time control systems. To develop a mathematical model of the reliability of computer appliance for real-time systems, it is necessary to take into account the provision of a given level of reliability, with reasonable development costs. There are many methods for improving software reliability, but the most promising and effective methods are redundancy, which is achieved using N-version programming. To increase the reliability of the hardware of the computer appliance, it is also necessary to use redundancy and redundancy, which includes multiprocessor and provision of different buses and independent RAM. This paper discusses existing approaches to improving the reliability of hardware and software, proposes a model of reliability of a computer appliance, which is understood as the product of the probability of failure-free operation of hardware and the probability of error-free operation of software. In addition, new formulas are proposed for the steady state probabilities of the hardware states of a multiprocessor computer appliance with heterogeneous processors, which give the same result as the existing ones, but require fewer computations. The paper concludes with a question about the possibility of optimizing the reliability of computer appliances based on the developed model, and indicates optimization methods that can be used to solve this problem.
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Статья научная
Plates, beams and shells with a non-uniform and micro-uniform regular structure are widely used in aviation and rocket and space technology. In calculating the strength of elastic composite structures using the finite element method (FEM) it is important to know the error of the approximate solution for finding where you need to build a sequence of approximate solutions that is connected with the procedure of crushing discrete models. Implementation of the procedure for grinding (within the micro-pass) discrete models of composite structures (bodies) requires large computer resources, especially for discrete models with a microinhomogeneous structure. In this paper, we propose a method of equivalent strength conditions (MESC) for calculating elastic bodies static strength with inhomogeneous and microinhomogeneous regular structures, which is implemented via FEM using multigrid finite elements. The calculation of composite bodies’ strength according to MESC is limited to the calculation of elastic isotropic homogeneous bodies strength using equivalent strength conditions, which are determined based on the strength conditions set for composite bodies. The MESC is based on the following statement. For all composite bodies V0 , which are such a homogeneous isotropic body V b and the number of p , if the safety factor nb of the body Vb satisfies the equivalent conditions of strength 2 pn1(1 ) nb (1 ) pn2 (1 ) , the safety factor n0 of the body V0 meets the defined criteria for strength n1 n0 n2 , where n1 , n2 specified, the safety factor n0 ( nb ) complies with the accurate (approximate) solution of elasticity theory problem is built for body V0 (body Vb ); (n2 n1) / (n2 n1) ; is the upper b error estimation of the maximum equivalent body stress V b , corresponding to approximate solution. When constructing equivalent strength conditions, i. e when finding the equivalence p coefficient, a system of discrete models is used, dimensions of which are smaller than the dimensions of the basic composite bodies models. The implementation of MESC requires small computer resources and does not use procedures for grinding composite discrete models. Strength calculations for bodies with a microinhomogeneous structure using MESC show its high efficiency. The main procedures for implementing the MESC are briefly described.
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Mobile device to collect heat and power parameters of the refrigerator
Статья научная
The article deals with the system used to reduce the amount of time to carry out the refrigeration tests; it was developed to cut the acceptance testing time of each refrigerator up to 6-9 minutes. The main parts of the system , considering each piece of equipment separately and its role in the system as a whole, the way all devices connected to a single unit, communication protocol, cloud storage method to access data from any mobile device are described in the article. The main purpose of the system is to measure the temperature at certain points of the refrigerator capacitor when it is connected to the power grid. The analysis of the thermal energy properties of the refrigerator, combined with the analysis of the cooling speed of the refrigeration chambers (as well as the heating of the capacitor) makes it possible to understand whether each refrigerator corresponds to certain characteristics established by GOST. The article also presents the characteristics of the devices being used (temperature meter-regulator TRM 138, the ME110-224-1M electrical network measurement module).
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Models and algorithms for automatic grouping of objects based on the k-means model
Статья научная
The paper is devoted to the study and development of new algorithms for automatic grouping of objects. The algorithms can improve the accuracy and stability of the result of solving practical problems, such as the problems of identifying homogeneous batches of industrial products. The paper examines the application of the k-means algorithm with the Euclidean, Manhattan, Mahalanobis distance measures for the problem of automatic grouping of objects with a large number of parameters. A new model is presented for solving problems of automatic grouping of industrial products based on the k-means model with the Mahalanobis distance measure. The model uses a training procedure by calculating the averaged estimate of the covariance matrix for the training sample (sample with pre-labeled data). A new algorithm for automatic grouping of objects based on an optimization model of k-means with the Mahalanobis distance measure and a weighted average covariance matrix calculated from a training sample is proposed. The algorithm allows reducing the proportion of errors (increasing the Rand index) when identifying homogeneous production batches of products based on the results of tests. A new approach to the development of genetic algorithms for the k-means problem with the use of a single greedy agglomerative heuristic procedure as the crossover operator and the mutation operator is presented. The computational experiment has shown that the new mutation procedure is fast and efficient in comparison with the original mutation of the genetic algorithm. The high rate of convergence of the objective function is shown. The use of this algorithm allows a statistically significant increase both in the accuracy of the result (improving the achieved value of the objective function within the framework of the chosen mathematical model for solving the problem of automatic grouping), and in its stability, in a fixed time, in comparison with the known algorithms of automatic grouping. The results show that the idea of including a new mutation operator in the genetic algorithm significantly improves the results of the simplest genetic algorithm for the k-means problem.
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Статья научная
The article discusses formalization of the problem of heterogeneous distributed information processing systems (HDIPS) software and hardware configuration management. A formal description of possible optimality criteria for the HDIPS software and hardware configuration is given. The HDIPS model in terms of queuing theory is proposed. The problem of allocating the HDIPS computational resources is formulated as a transport problem according to time criterion with atomic needs. The algorithm for solving this problem is proposed and the boundaries of its applicability to the HDIPS are determined. To meet the selected optimality criterion, the analysis of the HDIPS software and hardware configuration applying its formal model, using the queuing theory methods is presented. HDIPS is presented as a queuing network, where each computing node and route control unit is a mass service system. The problem of computing resource allocation in HDIPS is presented as a transport problem according to the time criterion with atomic needs. The least time algorithm for indivisible needs takes into account the indivisibility condition.
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Multi-grid finite elements in calculations of multilayer oval cylindrical shells
Статья научная
The method of finite elements (FEM) is actively used in calculations of composite shell constructions (rotation shells, circle and oval cylindrical shells), which are widely used in space-rocket and aviation equipment. To calculate multi-layer oval cylindrical shells three-dimensional curvilinear Lagrange multi-grid finite elements (MGFE) are suggested. When building a k-grid finite element (FE), k nested grids are used. The fine grid is generated by the basic split of MGFE that takes into account its complex heterogeneous structure and shape. On k-1 large grids the move functions used for decreasing MGFE dimension are determined. The stress-strain state in MGFE is described by the elasticity theory three-dimensional task equations (without introduction of additional hypotheses) in local Cartesian coordinates systems. The procedure of building shell-type Lagrange MGFE with the use of Lagrange polynomials presented in curvilinear coordinate systems is demonstrated. With the size reduction of discrete models MGFE have constant thickness equal to the thickness of the shell. The Lagrange polynomials nodes coincide in thickness with the MGFE large grid nodes and are located on the shared borders of different module layers. The use of such MGFE generates approximate solutions sequences that uniformly and quickly converge to precise solutions. The main advantages of MGFE are as follows: they form discrete models with the dimension 102–106 times smaller than the basic models dimension and they generate small error solutions. Examples of calculations are given for four- and three-layer oval shells of various thickness and shape under both uniform and local loading with the use of 3-grid FE. Comparative analysis of the obtained solutions with the solutions built with the help of the software package ANSYS shows high efficiency of the suggested MGFE in calculations of multi-grid oval shells.
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Multiversion model of software control systems for space vehicles with range of decision-making
Статья научная
The paper presents a multi-version model with ranking of alternatives in order of preference, taking into account the dependence of the attributes in the design of software for spacecraft control systems of various classes. The applied software with a set of algorithms, based on the general scheme of the method of branches and borders allow determining the exact solution of the optimization problem. To achieve the highest reliability of the software component of spacecraft control systems built with the use of multi-version programming methodology, a large number of versions of software modules are combined into a single structure. While software complexes even without introduction of redundant elements are characterized as complex systems, there is no need to speak about wide use of enumerative methods for their formation. Using the proposed modified method of ordered preference through similarity to an ideal solution, will allow to solve the problem of choosing the best computing system from a number of available systems. This approach is becoming increasingly possible because of the tremendous progress in computing design and manufacturing technology. Even the so-called personal computers provide computational capabilities that some time ago seemed impossible even for computers representing a much more powerful class of computing equipment - supercomputers.
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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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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 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 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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On the location of spacecraft in a given number of orbits
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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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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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