A. Th. Tlibekov (Bauman Moscow State Technical University) :
Articles:
Tlibekov A. T. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2025-1-116133
An algorithm for identifying the parameters of a mathematical model using experimental data in the form of a matrix of independent variables and a vector of the studied experimental responses is considered. The mathematical model is nonlinear, and the algorithm for solving it is unstable. The conditions under consideration are typical for inverse problems of mathematical physics. The need to solve similar problems is caused by the results of field experiments or information stored in the databases of the characteristics of the production processes of a machine-building plant, which is used for optimal design of a new or modernization of existing production. The mathematical model approximating the independent variables and the studied responses is represented by a modified fractional power series of several variables. An algorithm for searching for coefficients and degrees of a fractional power series has been developed. An iterative method containing blocks of random search, global optimization based on the Lipschitz condition and solving a system of linear algebraic equations is used. The algorithm has been tested. The effectiveness was assessed by the maximum relative error in calculating the studied responses and by the time of calculations.
Тлибеков А.Х. Алгоритм решения некорректной обратной задачи проектирования машиностроительного производства. Математическое моделирование и численные методы, 2025, № 1, с. 116–133.
Tlibekov A. T. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-112125
The comparison of existing and developed new methods of converting optimality criteria into a scalar function of the goal is performed. New converting methods are used in the problems of interpolation of experimental data by a modified fractional-power Newton–Puiseux series. Coefficients and degrees of a fractional-power series are calculated by evolutionary or infinite-step optimization methods, where the modules of the difference between experimental data and the values obtained by calculating the interpolation polynomial are used as optimality criteria. Under such conditions, the optimization task becomes multi-criteria, for which, during the search process, part of the optimality criteria increases, the rest decrease and reduce the scalar goal function and creating the illusion that the search is effective. For new converting methods, all optimality criteria in the search process are reduced. The errors obtained by interpolating the time of laser cutting of steel sheet and forecasting the production program of parts are shown. The use of modified fractional power series and new methods of converting optimality criteria for the implementation of the neural network learning function is proposed.
Тлибеков А.Х. Сравнительный анализ методов свертывания критериев оптимальности в задачах многокритериальной оптимизации. Математическое моделирование и численные методы, 2024, № 2, с. 112-125.