Initial estimates for Wiener-Hammerstein models using phase-coupled multisines

TL;DR

This paper introduces a novel method using phase-coupled multisines and modified frequency domain estimation to generate initial estimates for Wiener-Hammerstein models, facilitating easier system identification.

Contribution

It proposes a new excitation and estimation approach that effectively separates input and output dynamics in Wiener-Hammerstein models, improving initialization accuracy.

Findings

Successful application to experimental benchmark data

Effective separation of input and output dynamics

Enhanced initial estimate accuracy for Wiener-Hammerstein models

Abstract

Block-oriented models are often used to model nonlinear systems. These models consist of linear dynamic (L) and nonlinear static (N) sub-blocks. This paper addresses the generation of initial estimates for a Wiener-Hammerstein model (LNL cascade). While it is easy to measure the product of the two linear blocks using a Gaussian excitation and linear identification methods, it is difficult to split the global dynamics over the individual blocks. This paper first proposes a well-designed multisine excitation with pairwise coupled random phases. Next, a modified best linear approximation is estimated on a shifted frequency grid. It is shown that this procedure creates a shift of the input dynamics with a known frequency offset, while the output dynamics do not shift. The resulting transfer function, which has complex coefficients due to the frequency shift, is estimated with a modified frequency domain estimation method. The identified poles and zeros can be assigned to either the input or output dynamics. Once this is done, it is shown in the literature that the remaining initialization problem can be solved much easier than the original one. The method is illustrated on experimental data obtained from the Wiener-Hammerstein benchmark system.