Initialization of nonlinear state-space models applied to the Wiener–Hammerstein benchmark

Abstract

In this work a new initialization scheme for nonlinear state-space models is applied to the problem of identifying a Wiener-Hammerstein system on the basis of a set of real data. The proposed approach combines ideas from the statistical learning community with classic system identification methods. The results on the benchmark data are discussed and compared to the ones obtained by other related methods.

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

“…The PNLSS identification problem is to find the terms A , B , and E in Eqs. 3–4 when the only available information is process input/output data . For the case when all states are available as measured outputs (full state feedback), an optimization problem can be used to find these terms that involves the following two steps: A linear state‐space model is obtained using a frequency domain subspace identification algorithm. The linear model is used as an initial guess for a nonlinear optimization problem to identify a nonlinear model that captures the nonlinear behavior of the system. …”

“…The need for a general nonlinear system identification technique that can represent many classes of nonlinear systems led to the development of state‐space nonlinear system identification techniques based on input/output data. The polynomial nonlinear state‐space (PNLSS) approach is a system identification method for MIMO systems that leads to a model of a multivariable nonlinear system based purely on input/output data . PNLSS is a promising all‐purpose nonlinear system identification method that can be used for many different types of systems, including those that are described by bilinear models, Wiener‐Hammerstein models, and models with nonlinearities appearing in the states or inputs, or appearing in both …”

“…In the PNLSS approach, a linear state‐space model is first obtained and it is then extended to a nonlinear model for the system using polynomial nonlinear terms with coefficients identified through an optimization problem . The linear part can be obtained using the best linear fit or least‐squares, or using subspace system identification . The linear model is determined first so that the nonlinear model subsequently identified will achieve a performance at least as good as that of the linear model in a small neighborhood of the measured process states used in the identification process .…”

A subspace-based identification of Wiener–Hammerstein benchmark model

“…But, the benchmark session at SYSID 2009 (Schoukens, Suykens, & Ljung, 2008) has stimulated the interest in identification of Wiener-Hammerstein systems; see the Special Section in Control Engineering Practice (CEP) with nine papers (Wills & Ninness, 2012;Piroddi, Farina, & Lovera, 2012;Sjöberg, Lauwers, & Schoukens, 2012;Marconato, Sjöberg, & Schoukens, 2012;Paduart, Lauwers, Pintelon, & Schoukens, 2012;Tan, Wong, & Godfrey, 2012;Han & de Callafon, 2012;Lopes dos Santos, Ramos, & de Carvalho, 2012;Falck et al, 2012). Among others, in , Tan et al (2012), the transfer function of the best linear approximation of the Wiener-Hammerstein system is first obtained by least-squares or frequency domain methods.…”

Identification of Nonlinear Systems Structured by Wiener-Hammerstein Model

“…iterative nonlinear optimization procedures e.g. [2]- [3]; stochastic methods e.g. [4]- [5]; frequency methods [6]- [9].…”