IDENTIFICATION FOR WIENER SYSTEMS WITH INTERNAL NOISE*

In this paper, we study the identification problem for the Wiener systems with internal noises. If the internal noise is iid Gaussian, then the Wiener system can be transformed to the one without internal noise by the Weierstrass transform. The linear subsystems for both the original and transformed systems are the same. Recursive algorithms are proposed to identify the transformed Wiener system. The strong consistency of the estimates is proved under reasonable conditions. Nonparametric estimate for the nonlinear block of the original Wiener system is given trough the inverse Weierstrass transform of the nonlinear function of the transformed Wiener system, and it is proved that the estimate is consistent if the nonlinearity of the original Wiener system is a polynomial. A numerical example is presented showing that the simulation result is consistent with theoretical analysis.

This paper addresses the problem of recursive identification of Wiener nonlinear systems whose linear subsystems are observable state-space models. The maximum likelihood principle and the recursive identification technique are employed to develop a recursive maximum likelihood identification algorithm which estimates the unknown parameters and the system states interactively. In comparison with the developed recursive maximum likelihood algorithm, a recursive generalized least squares algorithm is also proposed for identification of such Wiener systems. The performance of the developed algorithms is validated by two illustrative examples.

Mechatronic systems identification using an impulse response recursive algorithm

In this work, the problem of identifying nonlinear systems is proposed. This latter is structured by Wiener systems. This latter (Wiener models) consist of linear dynamic subsystem followed by a nonlinearity function. The nonlinear systems identification is an active research area. Presently, the linear subsystem is allowed to be nonparametric and of structure entirely unknown. The proposed nonlinearity is of hard type. These nonlinear systems have been confirmed by several practical applications.

The recursive algorithms are given for identifying the single‐input single‐output Wiener system which consists of a moving average type linear subsystem followed by a static nonparametric nonlinearity. The input is defined to be a sequence of mutually independent Gaussian random variables. The estimates for coefficients of the linear subsystem as well as for f(v) at any v are proved to converge to the true values with probability one. A numerical example is given, justifying the theoretical analysis. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Wiener systems consist of a linear dynamic block in cascade with static nonlinearity. One of the challenging issues in the identification of a process noise disturbed Wiener system is that the influence of noise is difficult to eliminate. For Wiener systems with process noise, traditional algorithms will result in biased estimates. To solve this problem, a novel recursive Bayesian algorithm based on variable knot spline approximation is proposed in this paper. First, a spline function is taken to approximate the inverse function of the nonlinear part, which can achieve excellent extrapolation and eliminate oscillatory behaviors. A knot selection method is then presented to achieve accurate estimates. Furthermore, a knot variation strategy to improve the accuracy of the spline approximation is described. Finally, the proposed algorithm is validated through a numerical simulation.

Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity

This paper considers the recursive identification for multi-channel Hammerstein systems with internal noises and observation noise, where the linear parts are ARX systems. With the help of the correlations of system inputs and output, the recursive algorithms are proposed for estimating unknown coefficients of the linear subsystem, while the system nonlin-earity is recursively estimated by using the kernel functions. Strong consistency of the estimates is proved under reasonable conditions, and a simulation example is provided.

Frequency identification of Wiener systems with backlash nonlinearity

Identification of an Induction Motor by a Microcomputer based Structure

This brief deals with the possibilities of using the modified Kolmogorov's neural network for the identification of non-linear dynamic systems, among them the Wiener and Hammerstein systems. The algorithm of training the network is simple, well convergent and with a small error of approximation. The modified neural network is characterized by a simple computer algorithm; it also omits complicated techniques of back propagation. The simulation results are shown to illustrate the modified Kolmogorov theorem.

Study of the LTI relations between the outputs of two coupled Wiener systems and its application to the generation of initial estimates for Wiener–Hammerstein systems

Parameter estimation for Non-uniformly Sampled Wiener Systems with Dead-zone Nonlinearities

Results on experiment design for the identification of nonlinear systems are extremely scarce. This paper examines the identification and optimal input design for a very simple nonlinear system: a Wiener system composed of a Finite Impulse Response (FIR) system followed by a power nonlinearity: (.)n. We first show that an expanding power (n > 1) increases the information about the estimated parameters, while a compressing power (0 < n < 1) decreases the information. We then formulate a simple optimal input design problem for the considered class of Wiener systems and show that solutions can be computed by restricting the class of considered input signals. We provide a solution which offers some intuitive insights for the case of a FIR(2) system with a square nonlinearity and where the inputs are restricted to be Gaussian.

Identification of a Wiener System via Semidefinite Programming