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In this paper, the Polynomial NonLinear State Space (PNLSS) approach is applied to model a nonlinear system with a Wiener-Hammerstein structure. To obtain good initial estimates, the best linear approximation of the system under test is first identified. Next, this linear model is extended to a polynomial nonlinear state space model to capture also the system's nonlinear behavior. The identification procedure is applied to measurement data

This paper describes the identification of Wiener-Hammerstein models and two recently suggested algorithms are applied to the SYSID'09 benchmark data. The most difficult step in the identification process of such block-oriented models is to generate good initial values for the linear dynamic blocks so that local minima are avoided. Both of the considered algorithms obtain good initial estimates by using the best linear approximation (BLA) which can easily be estimated from data. Given the BLA, the two algorithms differ in the way the dynamics are separated into two linear parts. The first algorithm simply considers all possible splits of the dynamics. Each of the splits is used to initialize one Wiener-Hammerstein model using linear least-squares and the best performing model is selected. In the second algorithm, both linear blocks are initialized with the entire BLA model using basis function expansions of the poles and zeros of the BLA. This gives over-parameterized linear blocks and their order is decreased in a model reduction step. Both algorithms are explained and their properties are discussed. They both give good, comparable models on the benchmark data.

In this paper, we propose an identification procedure for nonlinear feedback systems by introducing a new type of model structure. The idea is to combine the advantages of two different model structures: the Polynomial NonLinear State Space (PNLSS) model and the block-structured feedback model. By imposing structural information to the existing PNLSS model, we obtain a flexible model with a lower number of parameters compared with the unconstrained structure. The structured-PNLSS model consists of a linear block in the feedforward path and a PNLSS block in the feedback path. The presented identification procedure for the structured-PNLSS model is applied to input/output measurements of a nonlinear device.

In this paper, we focus on the nonlinear modelling of Wiener-Hammerstein structures. The most difficult step in the identification process of such block-oriented models is to generate good initial values for the linear dynamic blocks. Here, good initial estimates are obtained by using the Best Linear Approximation of the system under test, which can easily be extracted from the data. The idea is to write the linear dynamic blocks as a linear combination of basis functions containing the poles and the zeros of the Best Linear Approximation. Next, these initial values are further tuned via a nonlinear optimization procedure. The proposed identification method is applied to real measurement data.