Надежность и качество сложных систем (Jun 2023)

# ANALYTICAL APPROXIMATION OF SOLUTIONS OF EQUATIONS OF THE METHOD OF MATHEMATICAL PROTOTYPING OF ENERGY PROCESSES BY QUALITATIVE ANALYSIS OF THESE EQUATIONS

• I.E. Starostin,
• A.A. Druzhinin

DOI
https://doi.org/10.21685/2307-4205-2023-2-3
Journal volume & issue
no. 2

## Abstract

Background. Solving the problem of choosing the optimal parameters, as well as diagnosing and predicting the technical condition of aircraft equipment components, necessitates the construction of a model of this components. At the input of the models, the measured characteristics are fed, and the controlled characteristics are obtained at the output. The authors proposed a method of mathematical prototyping of energy processes, allowing to build adequate mathematical models (which do not contradict the general physical laws) of the dynamics of physical and chemical processes of various nature. Then these equations are converted to models that are directly used to solve the mentioned practical problems. To simplify calculations, it is necessary to correctly set the analytical approximation of solutions to differential equations of the method of mathematical prototyping of energy processes. This determines the urgency of the mentioned problem. Matherials and methods. In the case of using special methods for solving a system of differential equations, it is necessary to specify an approximate analytical expression for the solution (general or particular) of the system being solved, the coefficients of which are determined from the system of equations being solved. The analytical approximation of the solution of systems of differential equations of the method of mathematical prototyping of energy processes is based on the concept of the system tending to some stationary state, which changes as a result of feedback. Results. The proposed method for setting the analytical approximation of solutions to the equations of the method of mathematical prototyping of energy processes makes it possible to set a class of correct mathematical models (which do not contradict the general physical laws, as well as the features of the flow of physical and chemical processes in a particular system under consideration) of various components of aviation equipment. In such a class, models are built (methods of identification theory, machine learning, etc.) with the lowest computational costs. Conclusions. Qualitative analysis of the equations of the method of mathematical prototyping of energy processes makes it possible to specify the most narrowed class of mathematical models, in which an adequate mathematical model of the required accuracy of an arbitrary system is built with the lowest computational costs.