BUILDING, BASED ON INTERPOLATION, MODELS OF VARIOUS PHYSICAL AND CHEMICAL SYSTEMS BY METHOD OF MATHEMATICAL PROTOTYPING OF ENERGY PROCESSES

Abstract

Background. Solving practical problems (design and operation of systems) implies the construction of mathematical models of systems. For mathematical modeling of systems of various physical and chemical natures, the authors proposed a method of mathematical prototyping of energy processes, based on modern nonequilibrium thermodynamics, mechanics and electrodynamics. The mentioned method provides adequate models of systems, i.e. that do not contradict general physical laws, as well as the peculiarities of processes in a particular system. However, to determine the controlled parameters of a system from its measured parameters from a system of differential equations obtained by the method of mathematical prototyping, it is necessary to solve the very labor-intensive task of identifying a large number of parameters of these equations. One of the ways to combat the complexity of the mentioned identification problems is the use of interpolation methods, which determines the relevance of the task of developing a methodology for constructing system models by mathematical prototyping of energy processes using interpolation methods. Matherials and methods. To synthesize equations for the dynamics of physical and chemical processes, the method of mathematical prototyping of energy processes is used. In order to simplify the identification of the parameters of equations obtained by the method of mathematical prototyping, special methods for integrating systems of differential equations are used, reducing the integration of differential equations to solving algebraic equations. In order to simplify the solution of the resulting algebraic equations, interpolation methods are used. To determine the constant coefficients of the resulting model from experimental data, methods of identification theory are used. Results. The system model constructed by the methods proposed in this article is correct, i.e. does not contradict general physical laws and incorporates the peculiarities of the processes in a particular system. Also, model training is block-by-block and can be reduced to linear identification, which makes it possible to process experimental data as it arrives. Conclusions. The proposed architecture of transformed system models makes it possible to use the resulting models as part of the mathematical core of digital twins. The architectural features of the proposed models make it possible to passively identify them.

Keywords

• method of mathematical prototyping of energy processes
• digital twins
• interpolation
• linear identification
• machine learning