Browsing by Author "Kapitsa, Mykhailo I."

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    Defining the Limits of Application and the Values of Integration Variables for the Equations of Train Movement
    (National Technical University «Dnipro Polytechnic», 2019) Bodnar, Borys Ye.; Kapitsa, Mykhailo I.; Bobyr, Dmytro V.; Kyslyi, Dmytro M.
    ENG: Railway transportation is an integral part in the transport infrastructure of our country. They cover passenger and cargo transportations by Ukrzaliznytsia, industrial enterprises, including transportation of the mining sector, which is characterized by heavy loads on the traction rolling stock due to large gradients of the track profile. Railway transport management is always preceded by traction calculations, the center of which is to solve the equation of train movement.Purpose.To determine the rational values of the variables in solving the equation of train movement, as well as relevant limits in their applicability.Methodology. To achieve the purpose, methods of system analysis, nonlinear programming, numerical methods for solving differential equations, namely the classical, Runge-Kutta-Feelberg, and Rosenbrock methods, are used. Computational accuracy was verified using simulation methods and compared with experimental data. Findings. The results of the research involve increasing the calculating speed when solving the equation of train movement without loss of accuracy, which allowed using the proposed method in on-board systems of locomotives. Originality. During the research, new scientifically grounded results were obtained that solve the scientific task in improving the energy efficiency of train operation, and are of great importance for railway transport. The obtained results constitute the originality, which consists in determining the rational limits of applicability and the value in a step of integration variables for the equations of the train movement. Practical value. The research results allow reducing the cost of energy consumed by hauling operations due to the promt recalculation of rational control modes when changing the train situation.
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    Devising an Analytical Method for Solving the Eighth-Order Kolmogorov Equations for an Asymmetric Markov Chain
    (РС ТЕСHNOLOGY СЕNTЕR, Kharkiv, 2024) Kravets, Victor; Kapitsa, Mykhailo I.; Domanskyi, Illia; Kravets, Volodymyr; Hryshechkina, Tatiana S.; Zakurday, Svitlana
    ENG: The object of research is a complex system of three subsystems, which function independently of each other and are in a working or failed state. There is a need to analytically model and manage the Markov random process in the system, varying the intensity of their development-restoration and degradation-destruction flows. In the study, an analytical method for solving Kolmogorov equations of the eighth order for an asymmetric Markov chain was devised. The corresponding Kolmogorov equations of the eighth order have an ordered transition probability matrix. The distribution of the eight roots of this equation in the complex plane has central symmetry. The results are analytical solutions for the probabilities of the eight states of the Markov chain in time in the form of ordered determinants with respect to the indices of the eight roots and the indices of the eight states, including the column vector of the initial conditions. Symmetry has been established in the distribution on the complex plane of eight real, negative roots of the characteristic Kolmogorov equation centered at the point defined as Re ϑ = –a7/8, where a7 is the coefficient of the characteristic equation of the eighth degree at the seventh power. Formulas expressing eight roots of the characteristic Kolmogorov equation have been heuristically derived, one of which is zero, due to the intensities of failures and recovery of three subsystems, the eight states of which in general make up an asymmetric Markov chain. For structures consisting of three independently functioning processes, the random process of the transition of the structure through eight possible states with a known initial state is determined in time. An analytical solution to Kolmogorov differential equations of the eighth order for an asymmetric state graph is proposed in harmonic form for the purpose of analysis and synthesis of a random Markov process in a triple system.