Identification of system models from potential-stream equations on the basis of deep learning on experimental data

Abstract

The functioning of various systems (in particular technical objects, living cells, the atmosphere and the ocean, etc.) is determined by the course of physical and physico-chemical processes in them. In order to model physicochemical processes in the general case, the authors previously developed a potential-flow method based on an experimental study (on the results of system tests) of the properties of substances and processes. In the general case, from these experimental data, many possible values of these properties are obtained. Knowing these properties of substances and processes, the initial state of the system, external influences on it (or the set of possible values of these quantities), we can analyze the dynamics of physicochemical processes in this system, and from it the dynamics of the characteristics of this system that have practical meaning. Thus, from the system of equations of this method, a relationship is obtained between the unobservable characteristics of these systems with the observed characteristics of the systems and laboratory systems under consideration (in which the properties of substances and processes in the system under study are experimentally studied). As the potential flow equations describing the physicochemical processes are generally quite complicated for analytical transformations, the aforementioned relationship must be obtained by numerical methods. The present work is devoted to the use of deep learning as a universal approximator for obtaining the described connection between the characteristics of arbitrary systems. These models are trained on the dynamics of the characteristics of the systems under consideration, obtained from potential-flow equations of physicochemical processes in them for different values of the parameters that determine the properties of substances and processes in these systems, their initial states, and external influences.

Distributed computing system for creating digital portraits of complex systems

“…Having received these input data, the proposed information and analytical system generates random values of the parameters of the dynamics of processes in the studied system in the specified ranges, then simulates the corresponding dynamics of the observed and controlled parameters for these generated parameter values [9,28], using the acceleration of counting due to parallelization. Then, based on the set of these system controlled and observed parameters obtained dynamics, its model is approximated [10], using symbolic regression methods [29] and neural networks [30].…”

“…The described methods for constructing systems of equations for the dynamics of processes in complex systems (and the dynamics of subsystems of complex systems) allow us to synthesize a system of equations for the dynamics of processes in the system under consideration, for the numerical implementation of which it is necessary to have experimentally studied parameters of the dynamics of processes in the system [1 -8, 10]: constant coefficients of this model of processes, the initial state of the system, unknown external influences. The resulting system of equations must be supplemented with equations for the observed and controlled parameters of the system [9,10].…”

“…In order to use this system of equations to solve practical problems of system development (synthesis of optimal structure and selection of optimal parameters [11 -14]) in accordance with the specified requirements [11,12], as well as the tasks of operating these systems (synthesis of the control system [15], diagnostics and forecasting of the technical condition [12,16], analysis of the system reliability [12,16,17], development of the system maintenance methodology [17]), it is necessary to transform the resulting system of equations of process dynamics in such a way that only the observed and controlled parameters remain in the resulting system of equations [9,10]. As a result of this transformation (in general, by numerical and analytical methods [10,[18][19][20], which consists in calculating the dynamics of the observed and controlled parameters of the system under study for various randomly set parameters of the processes dynamics in this system and further approximating the model of the system under study on a set of the observed and controlled parameters dynamics [10,18,19]), the relationship between the controlled parameters of the system and the observed parameters is obtained with accuracy to the control parameters (obtained from the test results of the considered system and laboratory systems) [10]. The controlled parameters of the system also include the observed parameters values predicted for subsequent time moments [10].…”

“…As a result of this transformation (in general, by numerical and analytical methods [10,[18][19][20], which consists in calculating the dynamics of the observed and controlled parameters of the system under study for various randomly set parameters of the processes dynamics in this system and further approximating the model of the system under study on a set of the observed and controlled parameters dynamics [10,18,19]), the relationship between the controlled parameters of the system and the observed parameters is obtained with accuracy to the control parameters (obtained from the test results of the considered system and laboratory systems) [10]. The controlled parameters of the system also include the observed parameters values predicted for subsequent time moments [10].…”

“…As can be seen from the above, the formation of a system model is quite a time-consuming process [9,10,18,19]. This leads to the need for software implementation of the presented methodology for creating a digital portrait, which includes multiprocessor and multicomputer parallelization [9,19,27].…”