Informatics, computer technology and management. Рубрика в журнале - Siberian Aerospace Journal
Optimizing the readability of tests generated by symbolic execution
Статья научная
Taking up about half of the development time, testing remains the most common method of software quality control and its disadvantage can lead to financial losses. With a systematic approach, the test suite is considered to be complete if it provides a certain amount of code coverage. At the moment there are a large number of systematic test generators aimed at finding standard errors. Such tools generate a huge number of difficult-to-read tests that require human verification which is very expensive. The method presented in this paper allows improving the readability of tests that are automatically generated using symbolic execution, providing a qualitative reduction in the cost of verification. Experimental studies of the test generator, including this method as the final phase of the work, were conducted on 12 string functions from the Linux repository. The assessment of the readability of the lines contained in the optimized tests is comparable to the case of using words of a natural language, which has a positive effect on the process of verification of test results by humans.
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The article proposes an approach to developing the architecture of a service-oriented information processing system, modeling and process control. The system, which is being developed, is a tool for identifying, predicting and controlling discrete-continuous processes. Its mathematical apparatus is based on nonparametric algorithms of identification and control. The software architecture includes the following main modules: the module for processing data, modeling and forecasting output process variables and the process control module. The first module includes data preprocessing algorithms: normalization, centering and analysis of outliers and omissions. The modeling module is an algorithm for research and recovery dependencies between process variables, process identification using nonparametric estimation of the regression function from observations. The last module is an implementation of nonparametric dual control algorithms. Control devices built on the basis of these algorithms perform functions of both object control and its study. The article discusses the application of architectural solutions based on two proven approaches in the field of software development: the composite approach and the service- oriented approach.. The main principles of composite architecture as a set of software systems with many characteristics that perform a specific task and service-oriented architecture as a modular approach to software development are described. The advantages of the applied composite service-oriented architecture over other variants of software architecture for control systems are shown, in particular, monolithic software architecture is compared with composite service-oriented architecture. This means that a researcher can use a single operation, which is a logically isolated, repeated task related to the production process of the enterprise. At the same time, it is necessary to ensure positive results when integrating with existing software products of enterprises which greatly complicates and requires the development of new components, as well as support for the "inherited" parts of the system.
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Piecewise approximation based on nonparametric modeling algorithms
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In this research the issue of inertialess processes modeling is under study. The main modeling algorithm is the non-parametric recovery algorithm of the regression function. The algorithm allows to build a process model under conditions of low a priori information. This feature may be particularly important in modeling processes of large dimensions prevailing in the space industry. One important feature of the algorithm for nonparametric estimation of the regression function is that the accuracy of modeling using this algorithm highly depends on the quality of the observations sample. Due to the fact that in processes with large dimensions of input and output variable vectors observation sampling elements are in most cases unevenly distributed, the development of modifications to improve the quality of mod-eling is relevant. The modification of the nonparametric dual algorithm based on piecewise approximations has been devel-oped. According to the proposed modification, the process area is divided into sub-areas and a non-parametric esti-mate of the regression function for each of these sub-areas is recovered. The proposed modification reduces the impact of some observation sampling features, such as sparseness or voids in observation samples on the quality of the built model. The computational experiments were carried out, during which a comparison was made between the classical algorithm of non-parametric estimation of regression function and the developed modification. As the computa-tional experiments have shown, with uniform distribution of the sample elements of observations, the developed modification does not lead to the improvement of the quality of modeling. With a substantial uneven distribution of the observations sample elements, the developed modification resulted in a 2-fold improvement in the quality of the simulation. The results suggest that the proposed modification can be used to model complex technologi-cal processes, including those in the space industry.
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Статья научная
Inspection of underwater objects, such as underwater archaeological sites, sunken technical objects, and un-der water located technical structures, requires the use of specially trained divers, manned or unmanned, re-motely operated or autonomous underwater vehicles. A relatively rarely used design for such underwater vehicles is a design in the form of a quadrotor with posi-tive buoyancy. This article discusses the design and the control system of the remotely operated underwater vehicle in the form of a quadrotor. The aim of the work is the selection and justification of the shape of the vehicle, the selection of the optimal structure of the control system with the expectation of the subsequent use of the vehicle as an au-tonomous one. The potential advantages of the selected design in the form of a quadcopter with a cylindrical body are de-scribed, in particular, the large volume of the sealed space of the vehicle, the possibility of installing capacious power sources, the potential for stabilizing the vehicle in a given position if there is a current at the place of work. The sealed case of the device is designed to place control electronics, power electronics and battery power of the device. The selection and justification of the shape of the sealed enclosure were made using a hydrostatic modeling apparatus and theoretical mechanics. A solid cylinder made of polycarbonate was selected as a form of the sealed housing of the vehicle. The advantage of the selected form in comparison with the parallelepiped-shaped case is shown under the condition of the same material parameters. The control system of the device includes software and hardware components. The choice of hardware com-ponents is justified, their key characteristics are described. As the control device of the top level, a single board computer (SBC, Single Board Computer) Orange Pi PC was selected, the direct control of the motor of the vehi-cle is performed using the Cortex-M3 microcontroller. The software architecture of the device is described. The choice of architecture is determined by the requirements of poorly connected components (which makes it easy to replace particular software elements without the need to modify the other elements), the simplicity of the potential replacement of the top-level control modules (which potentially allows switching from a remote control model to an autonomous control model). Some software components are described. The control system is implemented with the high-level lan-guage Python version 3.7, the basis of the control mechanism is message passing, the MQTT protocol maintained by the Mosquitto server is selected as a messaging mechanism. Testing of the vehicle was carried out in pools with standing water and with a simulated current. Testing showed the need to gain experience to control the underwater vehicle. The study will allow us to further develop a new version of the underwater vehicle, taking into account the wishes and identified problems.
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Today, there are many approaches to developing parallel programs. It is considered that it is more efficient to write such programs for a particular computing system. The article proposes to ignore the features of a particular computing system and outline plans for the development of a certain automated system that allows trying to improve code efficiency by developing programs with unlimited parallelism, as well as explore the possibility of developing more efficient programs using the restrictions imposed on maximum parallelism. This approach was demonstrated on the example of the analysis of various matrix multiplication algorithms. As a mathematical apparatus, the study considered various approaches to the description of algorithms to increase their implementation, including an approach based on unlimited parallelism and, also, an approach based on various restrictions on parallelism is proposed. In the course of the work, sequential and parallel methods of matrix multiplication were studied in detail, including tape and block algorithms. As a result of the study, various matrix multiplication methods (sequential, with left and right recursion, parallel methods) were studied and more effective ones were found in terms of the resources used and the restrictions imposed on parallelism. A sequential method and a cascade summation scheme were analyzed and proposed as possible ways of convolving the results of solving the problem obtained after the decomposition stage. Also, a number of programs with different levels of parallelism were developed and implemented in the functional-stream parallel programming language. In the future, such transformations can be carried out formally, relying on a knowledge base and a language that allows equivalent transformations of the original program in accordance with the axioms and algebra of transformations laid down in it, as well as replacing functions that are equivalent in results and have different levels of parallelization. These studies can be used to increase the efficiency of developed programs in terms of resource use in many branches of science, including in the field of software development for the needs of astronomy and rocket science.
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Semi-analytical method for calculating elastic-hydrodynamic contact
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A semi-analytical method for calculating elastic-hydrodynamic contact based on the partial use of Computer Aided Design / Computer Aided Engineering (CAD / CAE) packages and solutions of the integral equation of functional relationship between pressure and deformation have been described. The pressure in the lubricating layer is described by solving the modernized Reynolds equation taking into account the factors such as elastic deformation of surfaces in the contact zone, cavitation effect in the low-pressure region, and variable viscosity of the lubricant layer, which depends on thermodynamic parameters. Based on the stationary solution, a tensor damping coefficient has been obtained, with the help of which calculations of transient non-stationary modes that occur in cases of a sharp change in the external load have been further performed. A comparison of the results of modeling a plain bearing obtained by using the proposed semi-analytical method has been made and the full calculation performed using CAD / CAE programs such as ANSYS and COMSOL Multiphysics. The comparison showed good convergence of all numerical methods. At the same time, the “hybrid” method showed a number of advantages over direct calculations in CAD / CAE packages, such as: faster calculation speed, low requirements for computing resources and accounting for the cavitation effect. The described semi-analytical method allows to create digital twins of bearing units, centrifugal pumps and hydraulic supports used in satellite cooling systems and in rotary mechanisms of ground-based satellite dishes.
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Simulation computer model for virtual research of optoelectronic measuring systems
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The paper considers a simulation computer model of an optoelectronic system for measuring the point objects coordinates. The model allows optimal coordination of the system links parameters in order to minimize the measurement error. The method of multiple statistical tests which allows accumulating the results of single computational experiments for each specific measurement event with a unique random distribution of links parameters and characteristics, and then carrying out statistical processing of the accumulated results is the main method of computer simulation. As a result of multiple analyses, multi-parameter functional dependencies that provide optimal coordination of parameters controlled by the designer or operator according to the criterion of the resulting measurement error minimizing are realized. The article presents the results of evaluating modeling parameters that reduce the measurement error. It is relevant to apply this method when using the same measuring system in different operating conditions, for different measured objects and when performing various functional tasks since it allows adapting the system for a specific application. The model presented in the article can be concretized for the purpose of evaluating and multi-parameter optimization of particular object parameters, as well as for developing a virtual measuring stand on the basis of the model and its modifications.
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Статья научная
Obtaining electricity from renewable energy sources is primarily due to the exhaustion of traditional natural energy sources, such as coal, oil, gas. Today it is a promising area of development. The adverse impact on the environment of the use of traditional energy technologies is well known and scientifically proven. The use of traditional technologies inevitably leads to climate change, so the topic of the transition from traditional to alternative energy sources is undoubtedly relevant. Using of solar power plants with photovoltaic modules recently has gained relevance. However, the efficiency of such installations depends largely on their correct orientation to the Sun: the more precisely the system is installed, the more energy it will be able to convert. This article presents the results of the development of a simulation model of the solar panel orientation control system. To maximize the production of solar energy, the control system with tracking the Sun is built using fuzzy logic: fuzzy rules are formulated to control the positions of the object relative to the vertical and horizontal planes. The use of fuzzy logic is based on the product model of knowledge, which implies the use of linguistic variables to avoid the limitations inherent in classical product rules. The use of fuzzy control allows to correct the movement of the panel in the shortest time in the autonomous mode, thus reducing the arising power losses. Russian SimInTech dynamic simulation environment for technical systems is used as the system development environment. Simulation model is represented by several subprojects, united in a single database. The system model is implemented using standard blocks and a set of submodels, as well as a programming unit. The result of the work can be tracked in the 3D module of the built-in visual editor, which allows you to display the interaction of three-dimensional models objectively. In order to simplify and more finely implement the work of the project, a system of loading data, sunrise and sunset points, from an external Excel file was used.
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Software system for mathematical simulation of the electronic beam welding process
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Within the framework of this study, a software system for modeling the distribution of the temperature field in the steady-state mode of the electron-beam welding process for thin-walled aerospace structures is proposed. The purpose of creating such a software system is to improve the quality of control of the electron-beam welding process and, accordingly, to reduce the number of defects in welded joints of thin-walled structures. The software system has a model structure and implements the energy distribution models proposed earlier by the authors. The MySQL database management system and the Embarcadero RAD Studio programming system were chosen as the means of implementing the program. The central link of the system is a database that allows you to store and process information both on mathematical modeling and on the results of simulation and field experiments. The article describes the structure of the developed software system, and also presents algorithms for the operation of its constituent modules. The system provides the user with the opportunity not only to carry out simulation according to the specified technological parameters (welding speed, accelerating voltage, beam current, boundary conditions, simulation time, product material), but also to visualize the results and save them in a single database. The use of the proposed system allows not only to minimize the costs of the enterprise for the development of technological parameters of the steady state for the electron-beam welding process, but also to create a flexible information base for collecting experimental information with the aim of further automating and intellectualizing the technological process of creating permanent joints in the framework of Industry 4.0.
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Статья научная
The plane problem for elasticity equations is well studied. It can be explained by its importance for applications and by the fact that the equations can be reduced to the Cauchy-Riemann system. In spite of this importance, exact solutions that would describe the stress-strain state of bodies of finite dimensions are not numerous. Conservation laws for differential equations have been appeared more than a hundred years ago, but, as a rule, they were not used to solve specific problems, but were of purely academic interest. The situation changed with the development of the technique of construction of conservation laws for arbitrary systems of differential equations, and then with the use of conservation laws to solve boundary value problems of the theory of plasticity and elastic-plasticity. In this article, new conservation laws are constructed for the equations of the plane theory of elasticity in the stationary case. These laws form an infinite series, which is closely related to the elasticity equations solving. This fact made possible to reduce solving of boundary value problems, in terms of displacements, to the calculation of contour integrals along the boundary of a domain bounded by the studying elastic body. As it follows from the proposed technique, the studied area can be multiply connected, and the considered boundary can be piecewise-smooth.
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The article presents the problem of optimizing the structure of information processing computer appli-ances for real-time control systems used, among other things, in the rocket and space industry. In addition, the features of this problem that affect the choice of optimization methods are studied. It’s concluded that this problem can be effectively solved using evolutionary optimization methods. Existing performance models allow you to determine the minimum hardware configuration of a multi-processor computing system. The approach proposed in this article allows us to find configurations that have hardware redundancy (compared to the minimum configuration), but, due to this, have a greater probability of being in states that provide performance sufficient to achieve the goals of functioning of the designed real-time control system. The described approach is more flexible than simply duplicating all hardware components of the minimum configuration, which can be used to reduce the cost of creating and operating the designed control system. The proposed model can be used to optimize the performance of multiprocessor hardware and software complexes of real-time control systems. At the same time, it should be taken into account that the resources allocated for the creation and operation of the hardware and software complex are always limited. There-fore, it is advisable to consider the problem of performance optimization as a multi-criterion: one criterion will be performance, and the other-the cost of creating a hardware and software complex.
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The S-box is the most important component of modern cryptographic algorithms which largely determines the quality of cryptographic transformation. The modern method of estimating the S-boxes quality employs their representation as component Boolean functions to which cryptographic quality criteria are applied. Such criteria include: nonlinearity, correlation immunity, an error propagation criterion, and a strict avalanche criterion. Nevertheless, it is obvious that a cryptanalyst is not constrained in the ways of representing the cipher components, in particular, using the functions of many-valued logic. The design features of modern cryptographic algorithms allow their representation in the form of 4-logic functions, which determines the need to research cryptographic properties of the S-boxes represented as component 4-functions. In the literature today there are methods for measuring the nonlinearity of 4-functions; nevertheless, there are no similar methods for researching the differential properties of 4-functions, in particular, involving their compliance with the strict avalanche criterion. In this paper the strict avalanche criterion is generalized to the case of 4-functions and the compliance of the S-boxes component 4-functions of the “Magma” cryptoalgorithm to the strict avalanche criterion has been researched. All balanced 4-functions of length N = 16 satisfying the strict avalanche criterion were synthesized using the restricted brute-force method. The basic properties of the constructed class of 4-functions are determined, and bijective S-boxes based on them are constructed. It has been established that S-boxes of length N = 16 satisfying the strict avalanche criterion, both in terms of component Boolean functions and in terms of 4-functions, also possess optimal nonlinear properties. This circumstance allows us to recommend S-boxes satisfying the strict avalanche criterion of component 4-functions for use in modern cryptographic algorithms.
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Structure, network protocols of the internet of things for quality production control
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The subject of research is the model and structure of the Internet of things (IoT) network for product quality control in industry and agriculture. The purpose of the article is to analyze communication protocols and structures of IoT networks. The method of analysis and structural design of IoT networks is applied. The field of application is automation of monitoring products of enterprises of the aerospace industry. The article provides an overview and analysis of existing IoT technology; it considers the protocols and composition of IoT networks, and provides variations in the structures of building such networks. 4 levels of IoT architecture are described, as well as the communication protocols are used. The directions of building the Internet of things network for product quality control are defined. A multi-agent model of such system is presented, for the implementation of which the structure of the IoT network is given. The structure of a multi-agent system (MAS) for monitoring product quality in industry and agriculture includes many agents, such as product quality agents, communication agents, database agents, agents for analyzing information received from sensor agents, and decision-making agents. This MAS implements functions to ensure the required class of product quality and it is based on building a local network of the Internet of things. The research proposes an algorithm for processing information in such an IoT network. Analyzers (sensors) product qualities will be periodically polled and their values will be recorded in the server database. The decision-making subsystem sends data on product quality compliance to the enterprise administrator on a mobile device. The server structure is implemented using cloud IoT platforms, for which a brief overview is provided. The one IoT network implementation is developed using LTE NBIoT technology. This approach can be used in the aerospace industry for product quality control within automation 4.0.
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System analysis of dynamic problems of anisotropic plasticity theory
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Dynamic problems are the least studied area of plasticity theory. These problems arise in various fields of engineering and science, but the complexity of the original differential equations do not allow to develop accurate solutions and correctly solve numerical boundary value problems. This is even more typical of dynamic equations of anisotropic plasticity. Anisotropy reduces the group of symmetries allowed by the equations, and therefore narrows the number of invariant solutions. One-dimensional dynamic plasticity problems are well studied, but two-dimensional problems cause insurmountable mathematical difficulties due to the nonlinearity of the basic equations, even in the isotropic case. The study of the symmetries of the plasticity equations allowed us to find some exact solutions. The most known solution was found by B. D. Annin, who described the unsteady compression of a plastic layer made of isotropic material by rigid plates. Annin's solution is linear in two spatial variables, however, it includes arbitrary functions of time. Symmetries are also used in the proposed work. Point symmetries are first calculated for dynamic plasticity equations in the anisotropic case and are presented in the paper. The Lie algebra generated by the found symmetries appeared to be infinite-dimensional. This circumstance made it possible to apply the method of constructing new classes of nonstationary solutions. Symmetry can transform the exact solution of stationary dynamic equations in non-stationary solutions. The framed solutions include arbitrary functions and arbitrary constants. The outline of the article is as follows: according to the method of Lie group of point symmetries allowed by the equations of anisotropic plasticity is calculated. Two classes of new stationary invariant solutions are framed. These stationary solutions, by means of transformations generated by point symmetries, are transformed into new non-stationary solutions. In conclusion, a new selfsimilar solution of unsteady equations of anisotropic plasticity is framed; Annin's solution is generalized for the anisotropic case. The framed solutions can be used to describe the compression of plastic material between rigid plates, as well as to test programs, designed to solve anisotropic plastic problems.
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In practice problems, which consist in the search of the best (optimal) solution according to the different irredundant and contradictory (conflicting) criteria, called multi-objective problems, are of frequent occurrence. One of the most commonly used methods for solving this kind of problems consists in combination of all criteria into the single one by using some linear relation. However, despite the simplicity of this method, solving problems with its help may cause other problems related to the determination of the mentioned linear combination, namely related to the determination of the weight coefficients for each criterion. The incorrect selection of these coefficients may lead to non-optimal solutions (according to the Pareto theory). In this regard, recently various population-based algorithms have been proposed for solving the described problems, which are the modifications of these population-based algorithms for solving singleobjective optimization problems. This article describes the developed modifications of the Differential Evolution algorithm (DE) for solving multi-objective unconstrained optimization problems based on the well-known NSGA (Nondominated Sorting Genetic Algorithm) and MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition) schemes, which use the Pareto theory. The investigation into the efficiency of the Differential Evolution algorithm for solving multi-objective optimization problems in relation to the chosen mutation operator of the original DE algorithm and to the multi-objective scheme was conducted. The developed modifications were tested by using some well-known multi-objective real-valued optimization problems with 30 variables, such as ZDT1, ZDT2, ZDT3, etc. The practical problem of spacecraft control contour variant choice was solved as well. The experimental results show that better results were achieved by the Differential Evolution algorithm with the simplest mutation operators combined with the NSGA scheme. Thus, the applicability of the described modification for solving practical multi-objective optimization problems was demonstrated.
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Plates, beams and shells with non-uniform and micro-inhomogeneities regular structure are widely used in aviation and rocket and space technology. At the preliminary design stage, it is initially important to know whether the design safety factor meets the specified strength conditions. To determine the margin factor, it is necessary to solve the elasticity problem for the designed structure by the finite element method (FEM), taking into account its inhomogeneous structure, which requires large computer resources. In this paper, we propose a method of equivalent strength conditions (MESC) for calculating the static strength of elastic structures with a inhomogeneous regular structure. The proposed method is reduced to the calculation of the strength of isotropic homogeneous bodies using equivalent strength conditions. The MESC is based on the following statement. For any composite body V0 , there exists such an isotropic homogeneous body Vb and such a number p (equivalence coefficient) that if the body Vb stock coefficient satisfies 0 nb the equivalent strength conditions 0 pn1 nb pn2 , then the body V0 stock coefficient satisfies n0 the given strength conditions n1 n0 n2 , and Vice versa, n1 , n2 – given, the coefficients 0 nb , n0 , meet the exact solutions of elasticity problems constructed for bodies V0 , Vb . The method under consideration is reduced to FEM strength calculation of isotropic homogeneous bodies, which is the easiest to implement and requires less computer memory than a similar calculation of composite bodies taking into account their inhomogeneous structure. The procedure for determining the equivalence coefficients for a number of composite plates, beams and shells of rotation is described. High-precision multigrid finite elements generating discrete models of small dimension and solutions with small error are used in the construction of elastic solutions according to FEM for isotropic homogeneous bodies. The adjusted equivalent strength conditions are of the form pn1(11) nb pn2 (12 ) , where nb is the body Vb reserve coefficient and the values 1 , 2 correspond to the approximate solution constructed for the body Vb . Implementation of FEM for multigrid discrete models requires several 103-106 times less computer memory than for basic models. The calculation of the strength of a beam with a micro-homogeneous regular structure with the help of MESC is given.
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Статья научная
When the strength of elastic composite structures (plates, beams, shells) widely used in aviation, rocket and space technology is calculated with the finite element method (FEM), it is important to know the solu-tion error. To analyze the solution error, it is necessary to use a sequence of approximate solutions con-structed according to the FEM using the grinding procedure for basic discrete models (BMs), which take into account an inhomogeneous microheterogeneous structure of bodies within the microapproach. Dis-crete models obtained by grinding BMs have a high dimension, which makes it difficult to use the FEM for them. In addition, there are BMs of composite solids (CSs), for example, BMs of bodies with a microhet-erogeneous structure, which have such a high dimension that the implementation of the FEM for such BMs is practically impossible due to limited computer resources. To solve these problems, it is proposed to use fictitious discrete models in the calculations of CSs according to the FEM. In this paper we propose a method of fictitious discrete models (MFDM) for calculating the strength of elastic bodies with an inhomogeneous microheterogeneous regular structure. The MFDM is implemented with the help of the FEM using corrected strength conditions, which take into account the error of ap-proximate solutions. The method is based on the following provision. We believe that BMs of CSs generate solutions that slightly differ from the exact ones. Such BMs always exist for CSs due to the convergence of the FEM. The calculation of CSs according to the MFDM is reduced to the construction and calculation of the strength of fictitious discrete models (FMs), the dimensions of which are smaller than the dimension of the BMs. FMs reflect: the shape, characteristic dimensions, fastening, loading and the type of the inhomogeneous structure of CSs and the distribution of the elastic moduli corresponding to the BM of the CS. The sequence consisting of the FM converges to the BM, i.e., the limiting FM coincides with the BM. The convergence of such a sequence ensures uniform convergence of the FM stresses to the corresponding BM stresses. The implementation of the FEM for FMs with the use of multigrid finite elements leads to a large saving of computer resources, which makes it possible to use the MFDM for strength calculations of bodies with a microheterogeneous regular structure. Calculation of the CS strength according to the MFDM requires times less computer memory volume than a similar calculation using the BM of the CS, and does not contain the procedure for grinding the BM. The given example of calculating the strength of a beam with an inhomogeneous regular fibrous structure according to the MFDM shows its high efficiency. Applying the adjusted strength conditions allows using approximate solutions with larger errors in CS strength calculations, which leads to improving the efficiency of the MFDM.
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The use of the inverse transformation method for time series analysis
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In modern conditions of technology development, signs of systemacity are manifested to one degree or another in all areas, so the use of system analysis is an urgent task. In this case, the main factors in this situation are data processing and prediction of the state of a system. Mathematical modeling is used as a prediction method for a given subject area. A mathematical model is a universal tool for describing complex systems representing the approximate description of the class of phenomena of the external world expressed by mathematical concepts and language. The mathematical model can be represented as a set of systematic components and a random component. In this article, the object of prediction is the irregular random component of a model, which reflects the impact of numerous random factors. The origin, nature and laws of variation of the random variable are known, therefore, to simulate its behavior or predict its future value, one needs high degree of certainty to establish the form of continuous distribution function of the random variable. The empirical distribution function is calculated using the sample of random variable values. This empirical function is close to the values of the desired unknown function of distribution. The resulting empirical function is discrete, therefore it is necessary to apply piecewise linear interpolation to obtain a continuous distribution function. The predicted random component of time series has been included in the initial regression model. In order to compare augmented and initial regression models, several values were excluded from the time series and new prediction was built. The value of the average approximation error for assessing the quality of the model is calculated. The augmented regression model proved to be more effective than the original one.
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To the task of controlling a group of objects on the basis of information technologies
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To participate the TPP with cross-section communications in the general primary frequency control, it is necessary to have a working main regulator. The main regulator is designed to maintain the steam pressure in the major steam line of the TPP at a given level, which is a difficult task. At the TPP with cross-connections, the steam produced by the boilers enters the major steam line. To maintain the pressure in the major steam line, it is necessary to control the heat load of the working boilers. Traditional solutions to construct the main regulator found no use, as have a number of disadvantages, not allowing exploiting a system of automatic control. Looking at the steam pressure control system in the major steam line from the bottom to up, it is possible to identify disadvantages that prevent the effective operation of the main regulator at each level. At the lower level of the main regulator, there are controllers of heat load of boilers, built according to the scheme task-heat. Heat load controllers are designed to maintain heat release in the boiler furnace at the required level. The heat signal is the sum of the signals for the steam flow of the boiler and the rate of change in the steam pressure in the boiler drum. Such a structure does not allow maintaining the invariance of the heat signal under external disturbances effectively, as sharp changes of the steam pressure in the major steam line lead to a "false" operation of the controllers. At the upper level there is the main regulator itself, which maintains the steam pressure in the major steam line at a given level and corrects the tasks to the controllers of the heat load of the boilers. The simultaneous identical effect on the heat load of the boilers cannot be optimal from the point of view of the criteria for assessing the quality of regulation, since the dynamic properties of the boilers, such as the gain, the transition time constant and the transport delay are individual for each boiler. However, in 2006–2008, the attempt to build an updated main regulator that takes into account the shortcomings of the traditional scheme was made. The basis of the structure of the main regulator is still parametric and, as a result of ten-years’ experience, shortcomings in the operation of the updated main regulator were identified. The shortcomings, in most cases, consist in need of frequent corrections of adjusting coefficients of system because of the change of dynamic properties of an object during the operation. In fact, the same problems related to the parametric structure of the regulator remain. Up-to-date information technologies made it possible to introduce adaptive process control systems that allow to count an extended number of signals entering the system and to form control actions, based on both current and historical data of the technological process. The use of the latest information technologies and modern hardware in the control of complex multi-connected units that solve not only the problems of process control, but also the problem of improving the economic and environmental performance of enterprises, should become a new step in the development of automatic control systems.
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Torsion of prismatic orthotropic elastoplastic rods
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Conservation laws were introduced into the theory of differential equations by E. Noether more than 100 years ago and are gradually becoming an important tool for the study of differential equations systems. Not only do they allow you to qualitatively investigate the equation, but, as the authors of this article show, they also enable you to find exact solutions to the boundary value problems. For the equations of the iso-tropic theory of elasticity, the conservation laws were first calculated by P. Olver. For the equations of the theory of plasticity in the two-dimensional case, the conservation laws were found by one of the authors of this article and used to solve the main boundary value problems of the plasticity equations. Later it turned out that the conservation laws can also be used to find the boundaries between elastic and plastic zones in twisted rods, bent beams, and deformable plates. The proposed work found conservation laws for equations describing the orthotropic elastic state of the twisted straight-line rod. It is assumed that the remaining current depends linearly on the voltage tensor component. In the workit was also found an endless series of laws of preservation, which allows you to find an elastic-plastic boundary, which arises when twisting the orthotropic rod.
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