Multi-stage kernel method based identification of Wiener-Hammerstein system with cyclostationary input signal

Abstract

This paper proposes a new algorithm for identifying a Wiener-Hammerstein type sandwich system. The asymptotic consistency of the estimators is proven, and technical modifications are made to improve the accuracy of the method with a limited number of measurements. The considered approach is distinguished by the fact that the identification of both linear dynamic blocks and a nonlinear element is based on one and the same input process. The typical and highly restrictive assumption of Gaussianity and whiteness of excitation is not required in the proposed algorithm. The approach is combined, parametric-nonparametric, i.e. the local linear least squares procedure or correlation analysis is supported by multi-dimensional kernel selection. Cyclostationary excitation, widely found in telecommunications applications, manufacturing systems, and mechanical systems, was used. The aim is to identify a system in a passive experiment under operational conditions when measured signals have a repetitive yet stochastic nature. The proposed strategy makes it possible to determine many scaled models of the system based on different operating points, and aggregate them to alleviate the problem of the “curse of dimensionality”. The results of the theoretical analysis are illustrated by a series of experimental studies.