and Computational Methods

Rubric: "2.3.1. System analysis, management and information processing (technical sciences)"

doi: 10.18698/2309-3684-2022-1-129140

The article discusses the method of finding optimal solutions in the presence of a model of a complex technical system in the optimal design problem. The method is based on the use of nondominable, lambda optimal solutions and is a generalization of the method of Krasnoshchekov P.S., Morozov V.V., Fedorov V.V. [1]. The method allows in many cases (for lambda monotone objective functions) to reduce the number of calculations and reduce the dimension of the original problem. A numerical method for constructing lambda optimal solutions has been developed. A numerical example is given in which it is shown that the number of lambda optimal solutions consists of a single point, and the set of Pareto–optimal solutions is a curve on which it is necessary to build an ε–network to find the optimal solution.

Киселев В.В. Метод нахождения недоминируемых решений в задачах декомпозиции моделей сложных систем. Математическое моделирование и численные методы, 2022, № 1, с. 129–140.

doi: 10.18698/2309-3684-2021-2-96116

The problems of estimating the similarity index of inhomogeneous scientific publications containing equations and formulas are discussed for the first time. It is shown that the presence of equations and formulas (as well as figures, drawings, and tables) is a complicating factor that significantly complicates the study of such texts. It has been proved that the method for determining the similarity index of publications, based on taking into account individual mathematical symbols and parts of equations and formulas, is ineffective and can lead to erroneous and even completely absurd conclusions. Possibilities of the most popular analytical systems Antiplagiat and iThenticate, currently used in scientific journals, are investigated for detecting plagiarism and self–plagiarism. The results of processing by the iThenticate system of specific examples and specific test problems containing equations and formulas are presented. It has been established that this analytical system, when analyzing heterogeneous texts, is often unable to distinguish self– plagiarism from pseudo-self-plagiarism, seeming real (but false and imaginary) self– plagiarism. A model complex situation is considered, in which the identification of self–plagiarism requires the involvement of highly qualified specialists of a narrow profile. Various ways to improve the work of analytical systems for comparing inhomogeneous texts are proposed. This article will be useful to researchers and university teachers in physics, mathematics, and engineering, programmers dealing with problems in image recognition and research topics of digital image processing, as well as a wide range of readers who are interested in issues of plagiarism and self–plagiarism.

Полянин А.Д., Шингарева И.К. Индекс подобия математических и других научных публикаций с уравнениями и формулами и проблема идентификации самоплагиата. Математическое моделирование и численные методы, 2021, № 2, с. 96–116.

doi: 10.18698/2309-3684-2022-1-109128

Modelling and analysis methods for economic characteristics variation in the innovation process have become a common technique, via employing diffusion equations for a medium with given parameters. The analysis results in this case significantly depend on the measurement accuracy of the industrial environment parameters, which is hard to achieve in practice. It seems, therefore, reasonable to make a transition from the diffusion paradigm to the innovation implementation paradigm, i.e., sequential modelling of the innovation states with variables and characteristics that correspond to the practical measurement and control techniques. Applying the described approach, the economic state dynamics of the innovation development work, manufacturing and implementation can be described by systems of ordinary differential equations, where the initial conditions and coefficients depend on the parameters of the industry’s internal andexternal environments. Two discrete mathematical models developed in this work enable control of the industrial environment parameters, via application of practical measurement methods. The first discrete model is in the form of a functional (mapping), which enables conversion of the actual internal industrial environment parameters in the beginning of the innovation scaling into the coefficients of the differential equations and initial conditions that reflect the results of manufacturing process preparation. The initial data is available from the EPR data base of the industry. The second discrete model is realized as a cellular automaton. An autonomous model of the external industrial environment uses the data that can be measured by the well-developed marketing methods. The results of the computational experiments support the hypothesis of transition from the diffusion model paradigm to the paradigm of the sequential modelling of the innovation economic states.

Белов В.Ф., Гаврюшин С.С., Маркова Ю.Н., Занкин А.И. Моделирование среды предприятия с использованием дискретных вычислительных алгоритмов.Математическое моделирование и численные методы, 2022, № 1, с. 109–128

doi: 10.18698/2309-3684-2022-2-88101

In this paper, optimization of the flight of a low-mass satellite from Earth orbit to the orbit of Venus using ion engines is considered. The first flight to the planet took place in 1961 by the Soviet automatic interplanetary station "Venus-1", which passed 100,000 kilometers from Venus. In addition, in 1962, the American station "Mariner-2" was flown. The most recent spacecraft launched to the planet was the European Space Agency's Venus Express in 2005, which flew to Venus in 153 days. When solving the current problem, the following assumptions were made: an interorbital flight is considered without taking into account the attraction of the planets, and the orbits of the planets are considered circular and lying in the same plane. The angle between the tangential velocity of the spacecraft and the thrust direction was chosen as the control. Optimization of satellite control was carried out using the Pontryagin maximum principle. The resulting boundary value problem for a system of ordinary differential equations was solved by a numerical method — the targeting method. Newton's method was used to solve systems of nonlinear algebraic equations. The calculation program was written using the C++ programming language. As a result of the work, it was possible to minimize the flight time between orbits, thus the operability of the shooting method for solving optimization problems was shown.

Мозжорина Т.Ю., Закуражная Д.А. Моделирование и оптимизация управления полетом космического аппарата с орбиты Земли на орбиту Венеры с помощью ионных двигателей. Математическое моделирование и численные методы, 2022, № 2, с. 90–103

doi: 10.18698/2309-3684-2023-1-112123

The study's aim is to predict main trends and create scenarios for the economic development of BRICS countries (Brazil, India, China, Russia, South Africa) and the USA. Regression autonomous macro models were built, as well as a model of trade between them. The autonomous submodels use Population, Fixed Capital, Gross Domestic Product and Gross Capital Formation as key indicators. Autoregressive equations describe the dynamics of these variables. The resulting system of equations allowed us to describe the historical dynamics of demographic and macroeconomic indicators from 1990 to 2015 and to do a forecast until 2030. In the trade submodel bilateral trade flows link with gross domestic products of the economies. The relationship is described by the power dependence of the export flow on the gross domestic product of both trading partners. Unlike gravity-type models, the regression equation parameters are assumed to be constant for each pair of trading partners over the entire predicted time interval. The calculations showed that the models satisfactorily describe the dynamics of monotonically changing indicators and therefore can be used as a simple tool for forecasting the national and regional economy.

Малинецкий Г.Г., Махов С.А. Динамика макроэкономических показателей и взаимной торговли стран БРИКС и США. Математическое моделирование и численные методы, 2023, No 1, с. 112–123.

doi: 10.18698/2309-3684-2022-3-98123

The purpose of this work is to organize from a unified viewpoint the results of the author's work in the field of the structural theory of complex systems modeling and the practice of their implementing of the last two decades. We propose a formal definition of the complex system computer model, as a species of structure in the sense of N. Bourbaki — the М (System) species of structure, based on the humanitarian analysis of the complex systems key properties, recognized by a number of authoritative researchers and practicians in this field, and the assumption of the possibility of constructing a mathematical computer model of a complex system, — the closure hypothesis. The class of mathematical objects defined by the М species of structure has the following two properties: a complex created by combining a finite number of mathematical objects of the М species of structure, according to the certain rules, is itself a mathematical object of the same М species of structure. The computation organization process is same for all the mathematical objects of the М species of structure and therefore can be implemented by a single universal program for the simulation calculations organization. The presence of these two properties of the М species of structure representatives allows us to build an end-to-end technology for the description, synthesis and software implementation of the complex systems models — Model Synthesis and Model-Oriented Programming. By studying the morphisms of the М species of structure base sets of the model constructed with the model synthesis help, and the invariants limiting such morphisms, we obtain a formal mathematical language for the study of complex open (changing their composition) systems. By conducting a traditional humanitarian discourse, one can always correlate it with the corresponding object of the М species of structure — translating the higher-level language of humanitarian concepts into mathematical language. The proposed theory has a practical application in the field of development, description and implementation of complex software systems. A new programming paradigm is proposed — Model-Oriented Programming, which is a complete implementation of CAD methods in programming. When developing a software system, it is possible to stay within the framework of declarative programming, avoiding imperative, which greatly simplifies both its development and implementation, and subsequent debugging.

Бродский Ю.И. Структурная теория сложных систем. Модельный синтез. Математическое моделирование и численные методы, 2022, № 3, с. 98–123.

doi: 10.18698/2309-3684-2022-2-6377

The paper presents a mathematical statement and presents the results of calculations in the problem of determining the temperature field during deformation of a strip made of aluminum alloy AD0 on a vertical-type casting and forging module of a new modification. The design of the casting and forging module assumes that one of the four walls of the mold is stationary, the second performs a rotational movement on eccentric shafts, the other two move in a vertical plane, ensuring that the deformed billet is fed down. When solving the problem, a proven numerical method is used. For a moving medium, the heat equation is written in finite difference form in a curvilinear orthogonal coordinate system. The solution of the problem is carried out by the iterative method. When calculating the initial temperature field and its further change, the heat removal on the contact surfaces of the metal with the deformation tools is taken into account. The result of the solution is the temperature field in the spatial domain for discrete times corresponding to the steps of the numerical calculation. At each step, the boundary of the liquid and solidified metal is determined

Дмитриев Э.А., Потянихин Д.А., Одиноков В.И., Евстигнеев А.И., Квашин А.Е. Моделирование поля температур при получении металлоизделий на литейно-ковочном модуле с односторонним воздействием бокового бойка и неподвижной плитой. Математическое моделирование и численные методы, 2022, № 2, с. 65–79

doi: 10.18698/2309-3684-2021-4-103120

The article deals with the problem of classifying pixels of the radar image (RI). A locally homogeneous radar image model was used, in which the readings of each small area (local area) were considered to belong to only one class. The classification results of several real radar images by local areas are compared using the statistical criteria for the maximum a posteriori probability, Kolmogorov and Cramer-Mises-Smirnov. At the same time, in the case when the listed criteria made it difficult to classify a local area — when it hit the interface of the underlying surfaces, it was considered to be assigned to a special, boundary class, and its readings were processed using the grid method for separating mixtures of probability distributions. For each criterion, the classification accuracy was evaluated as the proportion of correctly classified pixels within the selected homogeneous areas. It has been established that in the case of significant interclass differences, the best classification accuracy is ensured by the use of the least powerful Kolmogorov criterion among nonparametric criteria. Also, using a real image as an example, it is shown that when the differences in the characteristics of objects of the same class are comparable to interclass differences, the highest classification accuracy is achieved when using the maximum a posteriori probability criterion. Such cases are typical for a wide class of classification problems, including those not related to image processing.

Достовалова А.М. Моделирование локально-однородных радиолокационных изображений при использовании различных статистических критериев. Математическое моделирование и численные методы, 2021, № 4, с. 103–120.

doi: 10.18698/2309-3684-2023-3-125133

With the help of probabilistic methods, a model of the conflict of two interacting systems consisting of numerous structural units is proposed, taking into account the effect of delaying information about the mutual state: about the structure, number and parameters of each other's structural units. A study was made of the influence of insufficient information at a particular point in time on the outcome of the process of conflict development. It is shown that the availability of information about the state of the structural units of the opposite side can significantly increase the probability of successful development of the conflict, and with an increase in the number of units of structural units, the difference in the probability of successful development of the conflict scenario increases significantly

Чуев В.Ю., Дубограй И.В. Моделирование конфликта взаимодействующих систем с учетом эффекта получения информации о взаимном состоянии. Математическое моделирование и численные методы, 2023, № 3, с. 125–133