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№3

Publication date:

16 September 2019

## Articles of journal № 2 at 2018 year.

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21. A methodical approach to modeling of complex technical system support with spare parts

*[№2 за 2018 год]*

**Authors:**D.Yu. Brezhnev, Dopira R.V., A.A. Sudarikov

**Visitors:**1695

The article considers a methodical approach to constructing a model of a multilevel system for providing spare parts for complex technical systems. The model is designed to justify a quantitative and nomenclature composition of spare parts kits considering the requirements for efficiency of performance restoration of the equipment samples in the system. The key idea is to put the simulated flow of requests to the model input and to investigate the response of a spare parts system by modeling the time for fulfillment of requests from sets of spare parts, tools of various levels, gradually increasing their nomenclature and quantity composition. At the same time, the simulated stream of requests can be different from the simplest one. It allows reasonable distributing applications for spare parts between sets of spare parts, tools of various levels. The model provides for the possibility of using one of three strategies for replenishment of spare parts kits both in the maintenance system of spare parts and in the specific nomenclature of spare parts in particular. The principle of modular representation of spare parts sets allows modeling a system of providing spare parts in different versions of a single-level or multi-level structure depending on application conditions or the principles of constructing complex technical systems. Modeling takes into account the contribution of each spare part cost to the total cost of the spare parts maintenance system with restriction for the required delay time related spare parts delivery. As a result, it is possible to justify the composition of spare parts kits of a complex technical system in an optimal way.

22. Finite element structural design in the mathematical package MathCAD

*[№2 за 2018 год]*

**Author:**Bakushev S.V.

**Visitors:**2037

The paper analyses mathematical package MathCAD potential when solving the problems of strength and deformation calculation of building and machine-building constructions using the finite element method. It is shown that MathCAD potentials are definitely not sufficient to solve such problems. It is due to the necessity to process quite a large amount of information. For illustrative and study tasks, when a rigidity matrix has not big dimension and its components can be introduced manually, it is enough to use MathCAD. It can help to solve a problem. In this case, the rigidity matrix should be formed by manual introduction of its component data that were calculated beforehand in MathCAD. In real calculation tasks, a rigidity matrix has a large order (thousands, tens and hundreds of thousands). Therefore, there are specialized software packages to solve them, such as LIRA, SCAD, ANSYS, etc. The paper considers a specific numerical example of calculating a compound profile plate under plain stress condition using the finite element method. The plate is separated into three finite elements. In this case, a rigidity matrix has the order equal to ten; the problem is solved only with manual introduction of its component data.

23. Application of a tree search algorithm and a annealing simulated method in optimization of heat network configuration and structure

*[№2 за 2018 год]*

**Authors:**V.A. Stennikov, A.A. Chemezov

**Visitors:**2171

The paper considers a mathematically complex problem of heat network configuration and structure optimization. It presents a problem statement and methodological approaches and algorithms to solve it. Traditionally in design practice, comparing 2 or 3 pre-planned alternate schemes solve this problem. Significant complication of the scheme and system scale led to the fact that the obtained solutions are far from optimal ones and often lead to insufficient load of network sections and even their inoperability. The development of mathematical programming and optimization methods gives new possibilities for solving practical problems. At the same time, it requires understanding of energy and mathematical features, as well as corresponding connections between them in order to apply mathematical methods correctly. There is a large arsenal of methods. Choosing effective ones requires special research related to capabilities and limited application. The complexity of scheme-structural optimization problem is in the fact that the objective function in the form of reduced costs is convex in terms of flow rate and concave on the heads. Fixing the heads by transformations, it can be reduced to a concave function. The problem is multiextremal as concave programming problems. An optimal solution will look like a tree. Each possible variant of the tree corresponding to the vertex of a constraint polyhedron will correspond to the local minimum of the objective function. This makes this task difficult to formalize, which does not allow finding an analytical solution. The paper considers a historically applied method of tree search, suggests its modifications, as well as other methods that were not previously used to optimize heat networks. The authors compare the proposed methods and algorithms, and assesse their performance in calculation of networks of different sizes and complexity. The algorithm realizations are universal and might be applied to different types of energy systems with a network structure.

24. A program of modeling wire temperature and power losses based on operation and atmospheric factors

*[№2 за 2018 год]*

**Authors:**Balametov A.B., Khalilov E.D., M.P. Bayramov, K.A. Agakhanova

**Visitors:**2550

In modern conditions, due to the growth of power consumption and noticeable climatic changes, the interest in calculating admissible mechanical and current loads on the aerial wires has been increased. The maximum use of overhead line capacity can be achieved with reliable information on the line state. The accuracy of calculating electric power losses in overhead power transmission lines might be increased by determining active resistance of wires taking into account the operating current flowing along the lines, the ambient air temperature, wind speed and solar radiation heat. In these conditions, it is very important to have software for evaluating and continuously monitoring wire temperature under various weather conditions, to reliably determine the permissible current load and to be able, if unacceptable line overload occurs, including repair modes, to carry out measures for unloading the remaining work of an aerial line. Modern programs for calculating power systems modes do not include thermal balance equations of aerial lines. This leads to the impossibility of taking into account their temperature conditions due to the mismatch of wire active resistance to their temperature. The authors have developed an algorithm and a program for calculating the specific active resistance of aerial lines wires taking into account the air temperature, working current, wind speed and solar radiation. They also carried out a quantitative assessment of the load current influence, ambient temperature, solar radiation and wind speed on the active resistance of aerial wires. There are the results of calculation of limited current loads for aerial wires. Based on the calculations to evaluate the effect of load current, ambient temperature, solar radiation and wind speed on active resistance of aerial wires, it is established that when calculating power losses for wires without considering the resistance temperature dependence, relative errors can reach 26 % or more, which is not permissible. Therefore, it is required to automatically detect the wire temperature in order to improve the accuracy of the calculation of active power and energy losses.

25. Comparison of the adaptive and rigid algorithms of traffic control based on a simulation model in AnyLogic

*[№2 за 2018 год]*

**Authors:**Ya.I. Shamlichky, A.S. Okhota, S.N. Mironenko

**Visitors:**1672

The growth of an automobile park and traffic volume led to increasing traffic intensity. This causes a transport problem in the conditions of cities with historically developed buildings. The problem is especially serious in key points of the street-road network. The problem is related to the increase in transport delays, queues and traffic jams, which in turn causes a reduction in the communication speed, unjustified fuel overexpenditure and increased wear of vehicle units and assemblies. There are two ways to solve the problem: engineering and construction works (widening the carriageway, applying complex road interchanges) and using automated traffic control system (ATCS). The first option is expensive and takes a long time from development to putting the object into use. The second option is less global in terms of changing a road network, but more productive. There are several types of ATCS. A specially trained operator sets up a hard algorithm manually, which is not always convenient and effective. The adaptive algorithm automatically adjusts to the flow, which is more convenient during the so-called “rush hour”. The change in traffic intensity observed during the day requires a corresponding change in a cycle duration and enable signals. The multi-program rigid control is not capable of taking into account short-term random fluctuations in the number of cars approaching an intersection. The use of ATCS based on the adaptive algorithm will solve the problem with increasing traffic in cities. The citywide ATCS should be based on principles that ensure maximum management efficiency and reliability of the system. The improvement and development of ATCS is essential to any major metropolis.

26. A comparative analysis of methods of calculation the number Pi by standard means

*[№2 за 2018 год]*

**Author:**O.A. Bakaeva

**Visitors:**2258

The process of the research on finding the number Pi can be divided into three periods: the ancient period, the classical era and the era of modern computers. Each of them has its own methods and tools. The purpose of this work is to analyze and compare various methods of calculating the number Pi using standard tools: MS Excel spreadsheet and Free Pascal programming environment. Computational methods are based on mathematical expressions, which are a qualitative approximation of the number Pi. They are the series of Gregory-Leibniz, Madhava, Neelakant, Euler's and Wallis's formulas, etc. The comparative analysis of these expressions and algo-rithms created on their basis has revealed the fastest and exact method of finding thhe number Pi. The paper describes computational studies, the result of which is finding the number Pi accurate within the 10th decimal place. The pur-pose of this study was to determine which computing environment is more accurate and effective for finding the number Pi. Based on the study results, there is a comparative analysis of MS Excel and Free Pascal computational capabilities regarding laboriousness, calculation time and Pi number computing accuracy. The originality of the work is in calculation of the sum of a series that converges to Pi for each new place of summands. Thus, the author shows in practice the dynamics of series convergence to the number Pi. For each of these approximate values of Pi, the absolute and relative errors are calculated. The number of summands is chosen based on calculation accuracy, which is considered satisfactory if the relative error is <0.001%.

27. Software tools of a wavelet/fractal correlation method for detecting space debris objects

*[№2 за 2018 год]*

**Authors:**Palyukh B.V., I.I. Zykov

**Visitors:**1561

The problem of space exploration efforts depends on orbiters, which in turn require their safety precautions from the effects of space debris. Each satellite, space probe or manned mission might be a potential source of space debris. The paper presents a method of detecting various objects of space debris. Images of cosmic space from an optoelectronic device placed on a spacecraft are transformed into halftone images. They are further processed by wavelet transforms. The next stage includes binarization and filling operations for the obtained results. At the end of this stage, there is a formation of the minimum rectangular areas covering the supposed objects of space debris. As a result, these areas have formed statistics in the form of the maximum eigenvalues of autocorrelation matrices and fractal dimensions for making a decision on detection space debris according to the Neyman-Pearson criterion. The obtained results show that space debris objects can be successfully detected.

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