A Unified Approach for the Identification of Wiener, Hammerstein, and Wiener–Hammerstein Models by Using WH-EA and Multistep Signals

Abstract

Wiener, Hammerstein, and Wiener-Hammerstein structures are useful for modelling dynamic systems that exhibit a static type nonlinearity. Many methods to identify these systems can be found in the literature; however, choosing a method requires prior knowledge about the location of the static nonlinearity. In addition, existing methods are rigid and exclusive for a single structure.is paper presents a unified approach for the identification of Wiener, Hammerstein, and Wiener-Hammerstein models. is approach is based on the use of multistep excitation signals and WH-EA (an evolutionary algorithm for Wiener-Hammerstein system identification). e use of multistep signals will take advantage of certain properties of the algorithm, allowing it to be used as it is to identify the three types of structures without the need for the user to know a priori the process structure. In addition, since not all processes can be excited with Gaussian signals, the best linear approximation (BLA) will not be required. Performance of the proposed method is analysed using three numerical simulation examples and a real thermal process. Results show that the proposed approach is useful for identifying Wiener, Hammerstein, and Wiener-Hammerstein models, without requiring prior information on the type of structure to be identified.

WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy

“…In line with previous work [28], WH-MOEA uses multi-step signals, which, unlike Gaussian signals, are easy to design, and almost all processes are enabled to be excited by these signals. Even though estimation starts from a completely unknown static non-linearity, multi-step signals will help to highlight the effects of the non-linearity on the signals used for the identification process.…”

“…Thanks to the unified approach proposed in [28], the formulation presented here is also applicable to Wiener and Hammerstein models, which are specific cases of Wiener-Hammerstein structure when one of the two LTI blocks lacks dynamics. In the case of Hammerstein models G w = 1 and ρ w do not exist, while neither do G h = 1 and ρ h in Wiener models.…”

“…Regarding parameter bounds of non-linearity, WH-MOEA takes the approach defined in [28], where a common search space is defined to face the uncertainty of the location of the static non-linearity around the dynamics. The bounds will be vertically defined by the minimum (y min ) and maximum (y max ) values of the output signal, while the horizontal bounds will be given by the minimum (u min ) and maximum (u max ) values of the multi-step input signal.…”

“…From a practical point of view, not all processes are enabled to handle this class of signals. An alternative approach based on a standard linear model and multi-step signals is proposed in [28].…”

“…P op(0) is initialised with N ind P individuals (candidate solutions). First individual is coded from the initial linear model, as indicated in [16] and [28]. Next, this first individual undergoes all mutation operations N ind P −1 times to give rise to the rest of the population.…”