Идентификация динамических процессов в виде дифференциальных уравнений и их систем с помощью эволюционных подходов

Abstract

The paper considers approaches based on the evolutionary algorithms to identify the dynamic processes. The first approach lies in obtaining a model in the form of a differential equation from the numerical data that describe the system behavior. The second approach makes it possible to describe processes with several output actions in the form of a differential equations system. The proposed approaches are searching for a model in the symbolic form, which is convenient in the further system analysis. A modified genetic programming algorithm was introduced in search for the structure, and the equations numerical parameters were selected using the differential evolution algorithm. Evolutionary algorithm self-tuning procedures were applied. The proposed approaches were tested on the problems described by differential equations of various orders and types. Testing included a study of the approaches effectiveness in the presence of noise in the initial data and of the model accuracy dependence on the sample size. Practical identification problems were solved. The first practical task was connected to monitoring the state of hydraulic systems and contained 14 input and 1 output variables. The second practical task was connected to the air composition monitoring and contained 8 input and 2 output variables. For the first task, the obtained results were compared with the model obtained by the nonparametric identification method