METHOD OF MATHEMATICAL PROTOTYPING OF ENERGY PROCESSES AS A TOOL FOR SYNTHESIS OF THE MATHEMATICAL KERNEL OF DIGITAL
TWINS OF DIFFERENT PHYSICAL AND CHEMICAL SYSTEMS 

Igor E. Starostin, Doctor of technical sciences, professor, professor of the sub-department of electrical engineering and aviation electrical equipment, Moscow State Technical University of Civil Aviation (20 Kronshtadtskiy boulevard, Moscow, Russia), E-mail: starostinigo@yandex.ru 

Background. A digital twin is essentially a digital copy of an object, which, thanks to the continuous exchange of data with the object, reproduces its current state. This is achieved by using a mathematical model as the mathematical core of the digital twin, based on the real behavior of the object, the parameters of which are updated in accordance with the current information received from the object. To build models of systems of various physical and chemical natures, the authors proposed a method for mathematical prototyping of energy processes, based on the methods of modern nonequilibrium thermodynamics, mechanics, and electrodynamics. Due to this, the mentioned method provides models of the dynamics of processes in a system that do not contradict general physical laws, as well as the peculiarities of the course of processes in a specific physical or chemical system. Then the resulting models are converted to models of systems applicable to solve practical problems, up to constant coefficients determined from experimental data. However, the relevant issue here is the choice of basis in which the transformed model of the system under consideration is built and the choice of training algorithm for the proposed model. This work is devoted to solving the above questions. Matherials and methods. The synthesis of equations for the dynamics of physical and chemical processes is carried out on the basis of the method of mathematical prototyping of energy processes. Transformed models are built by qualitative analysis of the dynamics of the system in various modes of its operation, followed by analysis of the relationships between the parameters of its dynamics and the parameters of input influences with the further construction of an interpolation transformed model. Interpolation methods are selected based on the abovementioned results of qualitative analysis. Results. The proposed concept of constructing system models provides correct models of the system that incorporate its qualitative behavior. This ensures the correctness of the mathematical core of digital twins when operating systems in various operating modes of the system for which the above-mentioned digital twins are built. Conclusions. The proposed concept of the software part of digital twins has a wide range of application due to the breadth of areas of applicability of the method of mathematical prototyping of energy processes. 

method of mathematical prototyping of energy processes, digital twins, interpolation, qualitative analysis 

Starostin I.E. Method of mathematical prototyping of energy processes as a tool for synthesis of the mathematical kernel of digital twins of different physical and chemical systems. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2024;(3):41–50. (In Russ.). doi: 10.21685/2307-4205-2024-3-5