Алгоритмы непараметрической идентификации сложных технических систем

Abstract

In a practice, it often happens that complex engineering systems consist of several interconnected different-type simpler subsystems. An adequate model formulation for every subsystem is impractical due to the complexity of physical processes proceeding in the subsystem. In such cases, a non-detailed black-box model is commonly used. For stationary linear systems (or subsystems), the connection between an input and an output of the black-box is defined by the Volterra integral equation of the first kind with an undetermined difference kernel also known as an impulse response in the automatic control theory. It is necessary to evaluate the unknown impulse response to use the black-box model .This statement is a non-parametric identification problem. For complex systems, the problem needs to be solved both for a whole system and for every isolated subsystem that makes identification substantially complex. Formally, impulse response evaluation is a solution of the integral equation of the first kind for its kernel over registered noise-contaminated discrete input and output values. This problem is ill-posed because of possible solution instability regarding measurement noises in initial data. To find a unique stable solution regularizing algorithms are used, but specific input and output signals in impulse response identification experiments do not allow applying computational methods of these algorithms (system of linear equations or discrete Fourier transformation). In this paper, the authors propose two specific-considering identification algorithms for complex engineering systems. In these algorithms, smoothing cubic splines are used for stable calculation of first derivatives of identified system signals. The results of the complex “Heater-Blower-Room” system identification prove the efficiency of algorithms proposed.