A novel parameter learning scheme using multi-signal processing is developed that aims at estimating parameters of the Hammerstein nonlinear model with output disturbance in this paper. The Hammerstein nonlinear model consists of a static nonlinear block and a dynamic linear block, and the multi-signals are devised to estimate separately the nonlinear block parameters and the linear block parameters; the parameter estimation procedure is greatly simplified. Firstly, in view of the input-output data of separable signals, the linear block parameters are computed through correlation analysis method, thereby the influence of output noise is effectively handled. In addition, model error probability density function technology is employed to estimate the nonlinear block parameters with the help of measurable input-output data of random signals, which not only controls the space state distribution of model error but also makes error distribution tends to normal distribution. The simulation results demonstrate that the developed approach obtains high learning accuracy and small modeling error, which verifies the effectiveness of the developed approach.

This article develops a novel separation identification approach for the Hammerstein‐Wiener nonlinear systems with process noise using correlation analysis technique. The Hammerstein‐Wiener nonlinear systems have three parts, namely, an input nonlinear block, a linear block, and an output nonlinear block. The designed hybrid signals that consist of separable signal and random signal are devoted to achieving parameters separation identification of the Hammerstein‐Wiener nonlinear system, that is, the three blocks are identified independently. First, the characteristics of separable signals under the action of static nonlinear block are analyzed, and two groups of separable signals with amplitude relation are utilized to estimate parameters of output nonlinear block. Moreover, the linear block parameters are identified by using correlation analysis approach, which deals with effectively immeasurable problem of internal variable information. Finally, the data filtering technique is implemented to weaken the influence of noises, and filtering‐based recursive extended least squares algorithm is developed for figuring out the parameters of nonlinear block and colored noise model. The validity and accuracy of the proposed scheme are verified by two simulations, and simulation results exhibit that the proposed method can obtain higher identification precision and better robustness than the existing identification algorithms.

This study investigates a two-stage parameter identification algorithm for the Hammerstein nonlinear system based on special test signals. The studied Hammerstein nonlinear system has a static nonlinear subsystem represented by polynomial basis function and a dynamic linear subsystem described by canonical observable state space model, and special test signals composed of binary signals and random signals are applied to parameter identification separation of the nonlinear subsystem and linear subsystem. The detailed identification procedures consist of two main steps. Firstly, using the characteristics that binary signals do not excite the static nonlinear subsystem, the dynamic linear subsystem parameters are identified through recursive least squares algorithm based on input-output data of binary signals. Secondly, unmeasurable state variables of the identified system are replaced with estimated values, thus the nonlinear subsystem parameters are obtained using recursive least squares algorithm with the help of input-output data of random signals. The efficiency and accuracy of proposed identification scheme are confirmed on experiment results of a numerical simulation and a practical nonlinear process, and experimental simulation results show that the developed two-stage identification algorithm has excellent predictive performance for identifying the Hammerstein nonlinear state space systems.

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To address the strong nonlinearity and unknown disturbance in practical nonlinear process, an identification scheme of neural fuzzy network (NFN)–based Hammerstein nonlinear system using multi-signals is developed in this paper. The proposed Hammerstein system has a static nonlinear subsystem approximated by NFN and a dynamic linear subsystem described by autoregressive exogenous system (ARX). First, the nonlinear subsystem and the linear subsystem are separated and identified by the designed multi-signals, and then parameters of the linear subsystem and noise model are identified simultaneously by making use of recursive extended least squares approach, which is effective for compensating the error caused by output noise. Furthermore, in order to cope with unmeasurable variable issue of the identified system, auxiliary model technology is developed, and the nonlinear subsystem parameters are estimated by applying derived auxiliary model recursive extended least squares approach. Experimental results of three typical nonlinear processes verify the effectiveness and accuracy of the proposed method, and the simulation results show that the proposed method can obtain higher identification accuracy than other optimization algorithms.