Informatics, computer technology and management. Рубрика в журнале - Siberian Aerospace Journal
6-aperiodic words over the three-letter alphabet
Статья научная
The work is devoted to the study of sets of aperiodic words over a finite alphabet. A set of such words can be considered as some kind of finite formal language. W. Burnside raised the issue of local finiteness of periodic groups. The negative answer was given only sixty years later by E. S. Golod. Soon S. V. Aleshin, R. I. Hryhorczuk, V. I. Sushchanskii constructed more examples confirming the negative answer to Burnside's question. Finiteness of the free Burnside group of period n was established for periods two and three (W. Burnside), for period four (W. Burnside, I. N. Sanov), for period six (M. Hall). The infinity of such a group, for odd indicators exceeding 4381, is established in the work of P. S. Novikov and S. I. Adyan (1967), and for odd indicators exceeding 664 in the book by S. I. Adian (1975). A more intuitive version of the proof for odd n > 1010 was proposed by A. Yu. Olshansky (1989). In this article, we consider the set of 6-aperiodic words. In the monograph by S. I. Adyan (1975) it was shown the proof of S. E. Arshon (1937) theory that there are infinitely many three-aperiodic words of any length in the two-letter alphabet. In the book of A. Y. Olshansky (1989), a proof of the infinity of the set of six-aperiodic words is given and an estimate of the number of such words of any given length is obtained. Here we try to estimate the function of the number of six-aperiodic words of any given length in a three-letter alphabet. The results obtained can be useful for encoding information in space communication sessions.
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A routing algorithm for the Cayley graphs generated by permutation groups
Статья научная
The purpose of this work is to create an effective routing algorithm on the Cayley graphs of permutation groups, superior in its characteristics to an algorithm using an automatic group structure. In the first section of the article we describe the auxiliary algorithm A–1 which allows numbering elements of a given permutation group. In the second section we present the algorithm A–2 for calculating the routing table on the Cayley graph and algorithm A–3 for determination the optimal route between two arbitrary vertices of the graph. Estimates of time and space complexity are also obtained for these algorithms. In the third section we describe the algorithm A–4 for calculation the minimal word of a group element. It is proved that the computational complexity of the algorithm will be proportional to the length of the input word. The fourth section presents the results of computer experiments for some groups of permutation groups, which compare the time for calculating the minimum words using algorithm A – 4 and an algorithm based on the construction of an automatic group structure. It is shown that A – 4 is much faster than its competitor.
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About non-parametric identification of partial-parametred discrete-continuous process
Статья научная
The paper considers a new class of models under conditions of incomplete information. We are talking about multidimensional discrete-continuous processes for the case where the components of the vector of output variables are stochastically dependent. The nature of this dependence is a priori unknown, but for some channels the a priori information corresponds to both nonparametric and parametric type of the initial data in the process under study. Such a situation leads to a system of nonlinear equations, some of which will be unknown, while others are known accurate to the vector of parameters. The main purpose of the model is to determine the forecast of output variables with known input, and for implicit nonlinear equations it is only known that one or another component of the output depends on other variables that determine the state of the object. Thus, a rather nontrivial situation arises when solving a system of implicit nonlinear equations under conditions where in one channel of a multidimensional system equations themselves are not in the usual sense, while in others they are known up to parameters. Therefore, an object model cannot be constructed using the methods of the existing identification theory as a result of a lack of a priori information. If it was possible to parameterize the system of nonlinear equations, then with a known input this system should be solved, since it is known and the parameterization stage is over. However, in this case it is still necessary to evaluate parameters. The main content of this article is the solution of the identification problem in the presence of a partially-parameterized discrete-continuous process, despite the fact that the parameterization stage cannot be overcome without additional a priori information on the process under study. In this regard, the scheme for solving the system of nonlinear equations can be represented as a certain sequential algorithmic chain. First, on the basis of the available training sample, including all components of the input and output variables observation, a residual vector is formed. After that, an estimate of the object output with known values of the input variables is constructed based on the estimates of Nadarai-Watson. Thus, for given values of the input variables of such a process, it is proposed to carry out a procedure for evaluating the forecast of output variables in accordance with the developed algorithmic chain. Numerous computational experiments, studying the proposed models of partially-parameterized discrete-continuous processes have shown their rather high efficiency. The article presents the results of computational experiments illustrating the effectiveness of the proposed technology for predicting values of output variables from known input variables.
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Algorithm for correcting camera pan and tilt on aircraft based on recorded video
Статья научная
Due to the difficulties that arise when using satellite navigation systems at airfields at present, and the insufficient accuracy of inertial navigation systems, optical measuring systems have again begun to be used to carry out trajectory measurements. However, existing measuring systems have a number of disadvantages. The purpose of this work is to describe a method for increasing the accuracy of trajectory measurements obtained by the goniometric method. The article reviews the main algorithms currently used in trajectory measurements and their shortcomings. An algorithm for frame-by-frame post-flight processing of recorded video from cameras of an optical-electronic measuring complex is proposed. A description of the implementation of this algorithm is given, taking into account the specifics of graphical software interfaces for processing user of the algorithm’s input. The proposed algorithm allows, after carrying out trajectory measurements, without time restrictions, to correct pan and tilt of the platform at each moment in time. The proposed algorithm makes it possible to increase the accuracy of trajectory measurements when testing aircraft, both already carried out and future ones. The proposed algorithm can also be used to obtain would-be pan and tilt of the camera when implementing a goniometric direction-finding complex using fixed wide-angle optical cameras. For example, when measuring the radiation patterns of an aircraft's onboard antennas using a quadcopter-meter to determine its position in space at each moment in time. The article also presents the main advantages and disadvantages of the algorithm, makes proposals for its improvement, and suggests possible areas of its application.
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Algorithmic and software of the system profiling the actions of users of the information system
Статья научная
The paper describes the software of the system for profiling the actions of users of the information system. This profiling system is aimed at solving the problem of trust in users of information systems. The system should regulate access to protected resources by analyzing user behavior. The algorithmic component of the system is represented by a user behavior model and a general system operation algorithm. The user behavior model is based on the apparatus of Markov chains Software implementation allows in practice to obtain the foundations of the proposed approach to work. At the development stages, the choice of software architecture is carried out. The client-server architecture was chosen as a reasonable decision. The software component of the user activity profiling system consists of five separate software modules. At the end of development, a brief testing of the components is carried out. The novelty of this work lies in the proposal of an approach that uses the profiling of user actions as an additional determining factor in managing access to objects, as a way to strengthen the basic measures “Controlling access of subjects to access objects” in the order system of FSTEC of Russia.
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An algorithm for fast multiplication of elements in 2-groups based on the Zhegalkin polynomials
Статья научная
Network design for a multiprocessor computing system or data center is an important problem where the search for graph models that have attractive topological properties and allow the use of efficient routing algorithms is carried out. Cayley graphs have the indicated properties, in particular such as high symmetry, hierarchical structure, recursive design, high connectivity and fault tolerance. The definition of the Cayley graph implies that the vertices of the graph are elements of some algebraic group. Selecting a group and its generating elements allows us to obtain a graph that meets the necessary requirements for diameter, degree of vertices, number of nodes, etc. A large number of scientific articles and monographs are devoted to solving this problem. The goal of this work is to create an algorithm for fast multiplication of elements in finite 2-groups whose exponent is 2n. The first section of the article provides a theoretical justification for the algorithm for fast multiplication in finite 2-groups. It is shown that elements of these groups can be represented in the form of bit strings, and their multiplication is carried out based on the Zhegalkin polynomials. The second section presents the pseudocode of the algorithm on the basis of which the Zhegalkin polynomials are calculated. The third section demonstrates an example of obtaining the Zhegalkin polynomials for a two-generated group of exponent 4. In conclusion, the prospects for using the algorithm on the real hardware are discussed.
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Analysis of corporate network cyber threats based on parallel processing of Netflow data
Статья научная
Public services of various organizations are subject to constant cyber attacks, which increases information security risks. Network traffic analysis is an important task to ensure the safe operation of network infrastructure, including corporate networks. This paper provides an overview of the main approaches for analyzing network traffic, it provides the related work and points out the shortcomings of the existing work. Here is a method is to analyze network traffic data using the Netflow protocol, which allows traffic data to be stored at the L3 layer of the OSI model. A feature of the study is the use of long observation periods. When storing data over long time intervals, the logs become large, which requires parallelization for primary data processing. The authors developed a cross-platform software package for distributed processing of network activity logs, which was used to analyze the network activity of the corporate network of the Krasnoyarsk Scientific Center for 2021–2022. A diagram of the software package is shown, its capabilities and operating features are described. Data sources for analysis and processing methods are provided. In this paper the authors formulated and formalized heuristic criteria for the anomaly of network traffic, which identify the presence of possible network attacks, and extracted datasets on the network activity of various application-level protocols. For the obtained data sets, statistical indicators were calculated, information about anomalous network activity was obtained for two years. In this research, we tested the previously proposed method for comparing the cyber threats risks for different time intervals, which showed a significant increase in risks for 50% of indicators in 2022. Comparisons of monthly intervals over different years showed similar increases in risk. Therefore, the method has shown its efficiency and can be used in other areas in which there are groups of criteria for independent indicators. The authors have proposed plans for further development of methods for analyzing network activity.
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Статья научная
The subject of research of this paper is anomalies in the final products of the International GNSS Service (IGS), namely in the orbits and clock drifts of navigation satellites (NSs). The purpose of research is to de-termine the influence of such anomalies on the accuracy of solving the precise point positioning (PPP) problem. The method of approximation by polynomials of high degrees previously proposed by the authors is used as a method for detecting and distinguishing anomalies in the orbits of navigation satellites. The methodology recommended by the IGS is used in solving the PPP problem. The proposed method for de-tecting and distinguishing anomalies in orbits is applied to the analysis of anomalies in the orbits of GPS navigation satellites. The examples of anomalies that can be detected using the proposed method are dem-onstrated. The brief statistical analysis and comparison of the frequencies of anomalies occurrence in the orbits of GPS navigation satellites published by various IGS analytical centers from 2010 to 2018 are pre-sented. It is shown that orbital anomalies occurring at the boundaries of daily intervals are, as a rule, cor-related with anomalies in clock drifts and have a partially mutually compensating effect on the solution of navigation problems. Experiments showed that when solving the PPP problem, anomalies significantly in-crease the root-mean-square deviation (RMSD) of the solution residual. Two options for solving the prob-lem with anomalous orbits are considered: the exclusion of satellites with anomalous boundaries of daily intervals from the solution and the "correction" of the anomaly in the orbit. The most natural method of correcting orbits (changing the orbit in order to remove large anomalies) at the boundaries of the daily segments of the published final orbits was tested. The exclusion of satellites with anomalies in the orbit turned out to be the most effective from the point of view of PPP problems, since attempts to "correct" the orbit more often led not to a decrease in the RMSD of the pseudorange residuals, but to its increase, which is associated with correlated anomalies in the navigation satellite clock drift. According to the research results, we can conclude: before solving the PPP problems, it is necessary to study the orbits and the navi-gation satellites clocks drifts for the presence of anomalies by the proposed methods and, if possible, to exclude such satellites from the data used to solve the PPP problem. Our proposed methods for detecting and accounting for anomalies in the orbits and clocks of navigation satellites, in addition to obvious appli-cations to solving ground navigation problems, are also applicable to monitoring the quality of the space and ground segments of the GLONASS and GPS systems.
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Статья научная
In this article authors are considering information security data integrity problem relevant for electronic archive management. In high-tech industry large electronic photo archives arise as a part of quality management. Photofixation applied for responsible operations control, documenting technological process, fixing the components state on input and output control, incongruities registration. An image substitution or reuse possibility makes necessary electronic archive proto document integrity control. These illegal actions can be both the result of an operator’s mistake and motivated by intentional defect concealment. As a solution authors suggest an electronic archive organizing method for storing photo documents. The method based on a digital watermark labeling of full-color images with orthogonal Zernike moments calculated for certain image points (and their neighborhoods). Suggested method can prevent watermark destruction by geometric image transformation (rotation, compressing, reflection etc.). Digital watermark contains both information about technological process on current image and information about other images – this fact allows talking about integrity of the whole photo documents set. One of the most important method characteristic is image format invariability and making additional metadata files unnecessary which allows user to apply standard software for a further work with photo document.
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Статья научная
To analyze the stress-strain state of homogeneous and composite bodies (CB), the method of multigrid finite elements (MMFE) is effectively applied, which uses multigrid finite elements (MgFE). MMFE gener-ates multigrid discrete models of small dimension, in which the inhomogeneous structure of bodies is taken into account within the framework of a micro-approach using MgFE. Basic discrete models (BM), taking into account the heterogeneous structure of bodies, have a high dimension. To reduce the dimensionality of discrete models of bodies, MMFE is used. However, there are BM CB (for example, BM bodies with a mi-cro-inhomogeneous structure), which have such a high dimension that the implementation of MMFE for such BM, due to limited computer resources, is difficult. In addition, for multigrid discrete models of high dimension, the MMFE generates numerically unstable solutions, which is associated with the error of com-puter calculations. To solve these problems, it is proposed here to use fictitious discrete models in calcula-tions, the peculiarity of which is that their dimensions are smaller than the dimensions of BM CB. In this paper, we propose a method of fictitious discrete models (MFDM) for calculating the static strength of elastic composite bodies with an inhomogeneous, micro-inhomogeneous regular structure. MFDM is implemented using MMFE with adjusted strength conditions application which takes into ac-count the error of approximate solutions. The MFDM is based on the position that the solutions that meet the BM CB differ little from the exact ones, i. e. we consider these solutions to be accurate. The calculation of CB by MFDM is reduced to the construction and calculation of the strength of ficti-tious discrete models (FM), which have the following properties. FM reflecst: the shape, characteristic dimensions, fastening, loading and type of inhomogeneous structure of the CB, and the distribution of elas-tic modulus corresponding to BM CB. The dimensions of FM are smaller than the dimensions of BM CB. The sequence consisting of FM converges to BM, i. e. the limiting FM coincides with BM. Calculations show that the convergence of such a sequence ensures uniform convergence of the maximum equivalent stresses of the FM to the maximum equivalent stress of the BM CB, which allows the application of such FM in the calculations of elastic bodies for strength. Two types of FM are considered. The first type is scaled FM; the second type is FM with variable char-acteristic sizes. In this paper, the FM of the second type is considered in detail. Calculations show that the implementation of MMFE for FM with one, two or three variable characteristic sizes leads to a large sav-ing of computer resources, which allows the use of MFDM for bodies with a micro-inhomogeneous regular structure. Calculations for the strength of CB according to MFDM require several times less computer memory than a similar calculation using BM CB, and does not contain a procedure for grinding BM. The given example of calculating the strength of a three-dimensional composite beam according to MFDM us-ing FM with three variable characteristic dimensions shows its high efficiency.
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Статья научная
Trends in the development of the spacecraft (SC) industry pose increasingly complex problems for mechatronic systems. Due to the complexity of the assembly processes of large-sized transformable struc-tures (LTC) and solar panels, the current methods of structures deployment are becoming less reliable and relevant. In addition, the development of orbital stations leads to the emergence of a whole range of new problems. Using mechatronic manipulators is one of the promising approaches. However, the functionality of their application is severely limited by the algorithms for moving the effector and manipulating objects predetermined during development. In this regard, there is a need to develop new approaches to finding and determining the shape of the target object, for further calculation of the algorithm for its interaction with the mechatronic manipulator gripper. The paper presents a method for reconstructing the three-dimensional shape of objects, based on using a computer vision system. A stereo camera is used to obtain the spatial characteristics of the scene. Based on the data obtained, the scene is divided into several independent geometric surfaces, followed by stage-by-stage processing by neural network algorithms. The required parameters of the target objects are ex-tracted at each stage of the algorithm. YOLACT EDGE is used as a neural network architecture, which performs semantic segmentation and classification of objects. The correlation of the spatial characteristics of the target objects and the replacing three-dimensional model can be considered as a separate problem. To ensure this correlation, the neural network architecture was supplemented with the branch "Keypoints mask", which provides a prediction of the positions of the keypoints of objects that unambiguously deter-mine the spatial characteristics of the target object. As a result, the system obtained is able to provide the construction of a three-dimensional map of the swept area in real time. In addition, based on the received telemetric information, it is possible to calculate the trajectory of the manipulator's effector and its interaction with objects.
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Статья научная
Internal network security is an important aspect of a successful enterprise. There are various means to prevent cyber threats and analyze visited Internet resources, but their speed and the possibility of applica-tion strongly depend on the volume of input data. This article discusses the existing methods for determin-ing network threats by analyzing proxy server logs, and proposes a method for clustering Internet re-sources aimed at reducing the volume of input data by excluding groups of secure Internet resources or selecting only suspicious Internet resources. The proposed method consists of 3 stages: data preprocessing, data analysis and interpretation of the results obtained. The initial data for the method are the proxy server log entries. At the first stage, data useful for analysis is selected from the source data, after which the con-tinuous data stream is divided into small sessions using the nuclear density estimation method. At the sec-ond stage, soft clustering of visited Internet resources is performed by applying the thematic modeling method. The result of the second stage are unmarked groups of Internet resources. At the third stage, with the help of an expert, the results are interpreted by analyzing the most popular Internet resources in each group. The method has many settings at each stage, which allows to configure it for any format and specif-ics of the input data. The scope of the method is not limited in any way. The resulting method can be used as an additional preprocessing step in order to reduce the amount of input data.
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Applied classification problems using ridge regression
Статья научная
The rapid development of technical devices and technology allows monitoring the properties of different physical nature objects with very small discreteness of the data. As a result, one can accumulate large amounts of data that can be used with advantage to manage an object, a multiply connected system, and a technological enterprise. However, regardless of the field of activity, the tasks associated with small amounts of data remains. In this case the dynamics of data accumulation depends on the objective limitations of the external world and the environment. The conducted research concerns high-dimensional data with small sample sizes. In this connection, the task of selecting informative features arises, which will allow both to improve the quality of problem solving by eliminating “junk” features, and to increase the speed of decision making, since algorithms are usually dependent on the dimension of the feature space, and simplify the data collection procedure (do not collect uninformative data). As the number of features can be large, it is impossible to use a complete search of all features spaces. Instead of it, for the selection of informative features, we propose a two-step random search algorithm based on the genetic algorithm uses: at the first stage, the search with limiting the number of features in the subset to reduce the feature space by eliminating “junk” features, at the second stage - without limitation, but on a reduced set features. The original problem formulation is the task of supervised classification when the object class is determined by an expert. The object attributes values vary depending on its state, which makes it belong to one or another class, that is, statistics has an offset in class. Without breaking the generality, for carrying out simulation modeling, a two-alternative formulation of the supervised classification task was used. Data from the field of medical diagnostics of the disease severity were used to generate training samples.
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Applying software-mathematical models of onboard equipment to develop onboard software
Статья научная
This paper deals with the testing of the functioning logic of spacecraft subsystems at the stage of developing system onboard software. The increasing complexity of the structure and operation logic of spacecraft due to the increased requirements in terms of providing consumers with information services (navigation, satellite monitoring of transport, geodesy, communications etc.) demands maintaining the reliability of uninterrupted operation, the implementation of automated parrying of emergency situations during the operation of spacecraft onboard equipment. In order to meet these requirements, it is necessary to test the interaction of onboard equipment and onboard integrated computing complex software that implements the target-oriented operation of spacecraft onboard systems. In such a case, meeting the requirements for reliability increase of onboard software should not lead to the increase of the manufacturing period of spacecraft. In this work we propose the approach for testing information and logical interaction between onboard equipment and software of a spacecraft onboard integrated computing complex with the use of a laboratory testing sample unit and a software-mathematical model. We described the basic concepts of conducting two-stage testing of onboard software, involving autonomous and system testing on the ground testing complex. The proposed approach is applied as part of the onboard software development cycle in accordance with the standards of the JSC “Academician M.F. Reshetnev “Information Satellite Systems”. The approach proposed in this work helps reduce the number of errors during onboard software development and testing of information and logical interaction between onboard equipment and a spacecraft as a whole in every operation mode.
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Asymptotic behavior of the average recovery cost in models of recovery processes
Статья научная
Failures can occur during the operation of rocket and space technology, electronic computing systems, power supply systems, heat supply systems, transport systems and many others; there are threats of attacks, security threats and many other impacts that are random in nature and have got a negative role in their operation. Such impacts lead to recovery processes where the operating time of the recovered elements before their failure, the number of failures, the time and cost of recoveries are random variables. In the theory of probability and in the mathematical theory of reliability, when studying recovery processes, the recovery function (the average value of the number of random failures) plays a special role. We especially note its importance in optimization problems when choosing a strategy for carrying out recovery processes. So one of the most important optimality criteria is the average number of failures, the average cost of recovery, cost intensity, availability factor. We also outline the problem of the need and timing of preventive recoveries. Within the framework of the mathematical theory of reliability, models of recovery processes are considered taking into account the cost of recoveries with varying distribution functions of the time to failure of the recovered elements and the costs of recoveries. For the models under consideration, a formula for the cost function (average recovery cost) through the recovery functions of two general recovery processes is obtained, which allows to prove theorems on the asymptotic behavior of the cost function, well known for the asymptotic behavior of the recovery function of the general recovery process, where the recovery time is not taken into consideration. The obtained asymptotic theorems for the average cost of recoveries are generalized to the introduced alternating (when the random time of recoveries is also considered) recovery process, taking into account the cost of recoveries with changing distribution functions of the time to failure of the recovered elements and the costs of their recoveries.
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Attribute features application in specification of regression model of apartments cost
Статья научная
In the study of statistical data with a pronounced endogenous variable, it is necessary to identify factors (explanatory variables) that have a strong impact on the result. In this, factors can be both quantitative and attributive. To assess influence of numerical features, regression analysis methods can be used. Influence of attributive features is not taken into account. However, often these are they who make the decisive contribution to variation of the result. It is necessary to develop methods for analyzing influence of attributive features and accounting for these features in regression models. On the example of sets of apartments proposed for sale in the city of Krasnoyarsk, a new method is used to assess influence of attributive features on the quantitative using ranking them in accordance with their influence on the endogenous variable. Method of fictitious variables is used to analyze the attribute features. Each attribute with m values is assigned (m-1) dummy variables and a regression model is constructed. Influence of exogenous variables can be expressed using standardized regression coefficients. In this case, influence of attributes can be estimated by cumulative correlation coefficient calculated on the basis of a regression model with fictitious variables. For further research, set is proposed to rank, assigning each element a "rank" – value of a standardized coefficient which reflects closeness of the relationship with the endogenous variable. Thus, all features have a numerical value. A standardized regression model is constructed. Proposed approach can be used in the analysis of statistical aggregates, units of which are characterized by quantitative and attributive features.
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Статья научная
For successful technological process in automated control systems it is necessary to maintain technological parameters constantly at the required level, which is ensured by the use of automated process control systems (APCS). The classical solution of this problem is the application of control devices of various types, the choice of which directly depends on the system under consideration and the requirements to it. The leading position among the automatic control system regulators for the last decades belongs to the proportional-integral-differentiating (PID) regulator, which efficiency of application in the technological process is defined by the speed and accuracy of its work. These qualities directly depend on the correct setting of the regulator parameters. The synthesis of regulators requires using of modern computer-aided design systems. The article presents the method of automatic setting of PID-regulator of the dynamic system of high order with negative feedback on the example of automatic room temperature control system. The modern Russian environment of dynamic simulation of technical systems SimInTech applied at a number of nuclear, oil refining and aerospace enterprises is used as the environment for system model development, as well as the process of its analysis and optimization. The main components of the system and transfer functions of its elements are presented. The stepby- step description of the process of project construction from standard software blocks and submodels, interacting through a single database with the use of built-in programming language, is described. The use of the built-in block of SimInTech visual simulation environment optimization for automated search of PID-regulator parameters is described in details and illustrated. The advantages and disadvantages of this adjustment method revealed during the project implementation are listed.
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Automated system for detecting anomalies of periodic electrical signals
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The aim of the work is to develop an automated system for detecting anomalies of periodic electrical signals with improved characteristics of the speed and efficiency of search. To solve this goal, the analysis of the problem of detecting anomalies of periodic electrical signals measured from electronic equipment was carried out and its relevance was substantiated. A hardware and software system for detecting anoma-lies of periodic electrical signals has been developed, which makes it possible to automate the testing pro-cess and increase the efficiency of detecting malfunctions of electronic equipment for various purposes. The improvement of the aforementioned characteristics was achieved due to a new test method underlying the implementation of the proposed system and protected by the patent of the Russian Federation for an inven-tion, as well as due to the high-quality implementation of software and hardware. When solving the set tasks, the methods of algebra-logic, mathematical statistics and object-oriented programming were used. The results of developing hardware, software and test algorithms are presented. A program for an electronic computer that implements control of the proposed hardware-software system is described.
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Technologies and production widely use composite materials now. “Mechanics of deformable solids” was formed as a science based on the study of materials used in the 19th and 20th centuries. Modern composite materials require new theoretical and experimental studies. Determining the stresses and deformations that occur at the points of contact of the matrix with the fibers is a special problem. Composites with a plastic matrix play an important role in modern technology. These materials successfully cope with cracking and significantly slow down the growth of cracks. In this article, the problem of the stress state of a composite beam with an elastic-plastic matrix and elastic fibers located along the axis of the beam is solved. It is assumed that in the zone of contact of the matrix with the fibers, according to the model of Yu. N. Rabotnov, a constant tangential stress is realized, less than the yield strength of the fiber. One end of the beam is fixed, and a constant force applied to the center of gravity coinciding with the origin of coordinates acts on the second. It is assumed that at the free boundary of the beam and at the points of contact of the beam with the fibers, the stresses reach the plasticity limit. The problem is solved with the help of conservation laws. This makes it possible to find the stress state at an arbitrary point of the section as a calculation of integrals along the outer boundary of the beam and the boundaries of the matrix and fibers.
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The article presents a computational and experimental study of the dynamic characteristics of a spacecraft telescope frame mock-up. The main attention is paid to the methodology of vibrodynamic tests using a three-component laser vibrometer and the creation of a finite element model of the mock-up under study. To analyze the dynamics of the structure, the main criteria such as modal parameters, model validation and harmonic analysis are defined. Particular attention is paid to the effect of experimental data transformation on the accuracy of calculating the modal assurance criterion. The research investigates telescope frame mock-up, which is a truss structure fixed on springs. The tests were carried out by applying a random impact of the “white noise” type. The dynamic characteristics of the structure were obtained, including the natural frequency of oscillations, which was 93.7 Hz. The experimental data were compared with the results of finite element modeling, which showed a significant discrepancy between them, especially in the area of natural frequencies. This indicates the need to adjust the finite element model. Various criteria for assessing the compliance of calculated and experimental models are considered, such as the coordinate modal assurance criterion (COMAC), the modal assurance criterion (MAC), the cross signature assurance criterion (CSAC) and the cross signature scale factor (CSF). These criteria help to assess the degree of coincidence of vibration modes and frequency characteristics. An analysis of the effect of transforming experimental data into different units of measurement on the results of calculating these criteria is carried out. It is concluded that the current calculation model requires revision and clarification of parameters to achieve better compliance with reality.
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