Research on Multi-signal Based Neuro-fuzzy Hammerstein-Wiener Model

Separation identification approach for the Hammerstein‐Wiener nonlinear systems with process noise using correlation analysis

“…In the research, set designed linear PI controller parameters $$$ {K}_c=0.7 $$$ and $$$ {\tau}_I=18 $$$. To verify the effectiveness of the designed controller, the nonlinear PI controller $$$ u(t)=u\left(t-1\right)+{K}_c^{\prime}\left(e(t)-e\left(t-1\right)+\frac{e(t)}{\tau_i^{\prime }}\right) $$$ with $$$ {K_c}^{\prime }=2 $$$ and $$$ {\tau}_I^{\prime }=10 $$$, and TSLM‐NF‐HW 34 are also presented to control CSTR process. The performance results of different set points are shown in Figures 12 and 13.…”

“…A Hammerstein‐Wiener system contains simultaneously Hammerstein system (static nonlinear is followed by linear dynamic block) and Wiener system (linear dynamic block is followed by static nonlinear block), thus its application is widespread and growing, and which has been often implemented to describe the nonlinear dynamics of continuous stirred tank reactor, 3 fermentation bioreactor system, 30 power system 31 and pH neutralization process 32 . Two predominant algorithms have been reported on the Hammerstein‐Wiener systems identification, that is, synchronous identification algorithms 30,33 and separation identification algorithms 3,34,35 . The synchronous identification algorithms include parameters product term of the static nonlinear block and the linear dynamic block, which leads to many redundant parameters.…”

“…32 Two predominant algorithms have been reported on the Hammerstein-Wiener systems identification, that is, synchronous identification algorithms 30,33 and separation identification algorithms. 3,34,35 The synchronous identification algorithms include parameters product term of the static nonlinear block and the linear dynamic block, which leads to many redundant parameters. By contrast, the separation identification methods aim at decomposing the Hammerstein-Wiener system into three blocks and identifying each block parameters, thereby the computational cost is reduced.…”

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

“…1. In our previous work, 39 the input signals that consist of binary signal and random multistep signal are used to identify the Hammerstein-Wiener model. In contrast, in this work, the first part of the special input signal is extended to include more general independent separable signals, such as binary signal, sine signal, and Gaussian signal.…”

“…1. In our previous work, 39 The modeling and parameter learning problem of the Hammerstein-Wiener model is briefly presented in section ''The neuro-fuzzy Hammerstein-Wiener model.'' The three-stage parameter learning algorithms of the neuro-fuzzy Hammerstein-Wiener model with disturbance are discussed carefully in section ''Parameter learning of the neuro-fuzzy Hammerstein-Wiener model.''…”