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

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.

Process Modeling, Identification Methods, and Control Schemes for Nonlinear Physical Systems – A Comprehensive Review

“…This involves the requirement of a measured input‐output data set from a physical system, i.e., data acquisition, model identification, and parameter estimation techniques, and the correct validation procedure. Furthermore, iterations are carried out till a process model which mimics that the actual nonlinear model is arrived 7, 56. Some of the constructive and versatile techniques of parameter estimation that effectively estimate the model parameters are presented in this section.…”

Decomposition‐based over‐parameterization forgetting factor stochastic gradient algorithm for Hammerstein‐Wiener nonlinear systems with non‐uniform sampling

“…6 In the literature, Li et al proposed a modeling and parameter learning method for the Hammerstein-Wiener model with disturbance and used the Hammerstein-Wiener model to approximate the complex nonlinear industrial processes. 7 Since the non-uniformly sampled-data (NUSD) systems widely exist in practical control systems, especially in modern large-scale industrial systems, they have drawn a great deal of attention of many researchers in NUSD system identification. 8,9 The recursive identification plays an important role in the field of system identification because it can realize the online identification of the system parameters.…”

An Improved Method for Stochastic Nonlinear System’s Identification Using Fuzzy-Type Output-Error Autoregressive Hammerstein–Wiener Model Based on Gradient Algorithm, Multi-Innovation, and Data Filtering Techniques

“…A neuro-fuzzy-type H-W system was presented in [59] using two-stage input signal. For the same form of system, Jia et al and Li et al [60,61] combined special input signal and correlation technique to identify separately and nonrecursively system parameters. However, most of the above-cited algorithms are based on some restrictive conditions, especially the prior knowledge of some parameters and the output nonlinearity's invertibility assumption to obtain intermediate variable's estimate, which is not always the case.…”