Modeling and parameter learning method for the Hammerstein–Wiener model with disturbance

Feng Li,Shengquan Li,Songlin Wo,Qingfeng Cao,Lianyu Chen

doi:10.1177/0020294020912790

Abstract

In this paper, a novel modeling and parameter learning method for the Hammerstein–Wiener model with disturbance is proposed, and the Hammerstein–Wiener model is implemented to approximate complex nonlinear industrial processes. The proposed Hammerstein–Wiener model has two static nonlinear blocks represented by two independent neuro-fuzzy models that surround a dynamic linear block described by the finite impulse response model. The parameter learning method of the Hammerstein–Wiener model with disturbance can be summarized in the following three steps: First, the designed input signals are implemented to completely separate the parameter learning problem of output nonlinear block, linear block, and input nonlinear block. Meanwhile, the static output nonlinear block parameters can be learned based on input and output data of two sets of separable signals with different sizes. Second is to determine the dynamic linear block parameter using correlation analysis algorithm using one set of separable signal; thus, the process disturbance can be compensated by the calculation of correlation function. The final one is to achieve unbiased estimation of the static input nonlinear block parameters using least squares method according to the input–output data of random signal. Furthermore, with the parameter learning method, the proposed model can achieve less computation complexity and good robustness. The simulation results of two cases are provided to demonstrate the advantage of the proposed modeling and parameter learning method.

Highlights

Almost all practical industrial processes have nonlinear characteristics to some extent.1,2 For decades, many methodologies have been carried out in the field of nonlinear dynamic system modeling and identification, for example, Volterra series,3 block-oriented nonlinear models,4–12 neural networks,13,14 support vector machines,15,16 and Markov jump systems.17 Among these methodologies, block-oriented nonlinear models have received widespread attention due to their simple structure and excellent modeling ability.18The Hammerstein and Wiener models represent the most familiar models of the nonlinear block-oriented models
The extension of the Hammerstein and Wiener models is the Hammerstein–Wiener model, which constituted by one dynamic linear block surrounded by two static nonlinear blocks has a great flexibility for describing practical nonlinear systems, such as electric arc furnace system,19 pH neutralization process,20,21 continuous stirred tank reactor (CSTR),22 and fermentation bioreactor system
Two advantages can be obtained from Theorem 1: first, the parameter learning of static input nonlinear block and the Wiener model are implemented

Summary

Introduction

Almost all practical industrial processes have nonlinear characteristics to some extent.1,2 For decades, many methodologies have been carried out in the field of nonlinear dynamic system modeling and identification, for example, Volterra series,3 block-oriented nonlinear models,4–12 neural networks,13,14 support vector machines,15,16 and Markov jump systems.17 Among these methodologies, block-oriented nonlinear models have received widespread attention due to their simple structure and excellent modeling ability.18The Hammerstein and Wiener models represent the most familiar models of the nonlinear block-oriented models. Keywords Hammerstein–Wiener model, process disturbance, designed input signals, parameter learning To deal with the issues described above, a novel modeling and parameter learning method for the Hammerstein–Wiener model with disturbance is considered, whose two static nonlinearities are represented using two independent four-layer neuro-fuzzy models, while a dynamic linear block is described using the finite impulse response model.

Results

Conclusion