Identification Of Wiener Systems Research Articles

Recursive identification of continuous-time Wiener systems

Recursive algorithms to identify both subsystems of a continuous-time Wiener system are presented. The system is driven and disturbed by Gaussian white random signals. The impulse response of the linear dynamic subsystem is recovered with a correlation method. It is shown that the inverse of the non-linear characteristic of the other subsystem is a regression function. Then, to recover the inverse, two estimates are presented. The algorithms converge to the unknown impulse response, and the inverse of the characteristic, respectively. Convergence rates are presented. Moreover, results of simulation examples are given.

Continuous-time Wiener system identification

A continuous-time Wiener system is identified. The system consists of a linear dynamic subsystem and a memoryless nonlinear one connected in a cascade. The input signal is a stationary white Gaussian random process. The system is disturbed by stationary white random Gaussian noise. Both subsystems are identified from input-output observations taken at the input and output of the whole system. The a priori information is very small and, therefore, resulting identification problems are nonparametric. The impulse impulse of the linear part is recovered by a correlation method, while the nonlinear characteristic is estimated with the help of the nonparametric kernel regression method. The authors prove convergence of the proposed identification algorithms and examine their convergence rates.

Modelling and Parameter Identification of Discontinuous Wiener Systems

Abstract The paper deals with the decomposition of block-oriented nonlinear dynamic systems having discontinuous asymmetric nonlinearities and with their identification using the Wiener model. Multiple application of a simple decomposition technique provides a special form of Wiener model with the minimum number of parameters. Putting some parameters of the proposed model to zero, models for the block-oriented nonlinear dynamic systems with pure preload nonlinearities, dead zone or two-segment piecewise-linear asymmetric nonlinearities are obtained. To demonstrate the feasibility of the identification method, more illustrative examples are included.

Linear and Non-Linear System Identification Using Separable Least-Squares

Abstract We demonstrate how the separable least-squares technique of Golub and Pereyra can be exploited in the identification of both linear and non-linear systems based on the prediction error formulation. The model classes to be considered here are the output error model and innovation model in the linear case and the Wiener system in the non-linear case. This technique together with a suitable choice of parameterization allow us to solve, in the linear case, the associated optimization problem using only np parameters instead of the usual n ( m + p ) + mp parameters when canonical forms are used, where n , m and p denote respectively the number of states, inputs and outputs. An example where the Wiener system identification algorithm is applied to real data obtained from a distillation column is given.

Nonparametric approach to Wiener system identification

A Wiener system, i.e., a system consisting of a linear dynamic subsystem followed by a memoryless nonlinear one is identified. The system is driven by a stationary white Gaussian stochastic process and is disturbed by Gaussian noise. The characteristic of the nonlinear part can be of any form. The dynamic subsystem is asymptotically stable. The a priori information about both the impulse response of the dynamic part of the system and the nonlinear characteristics is nonparametric. Both subsystems are identified from observations taken at the input and output of the whole system. The kernel regression estimate is applied to estimate the invertible part of the nonlinearity. An estimate to recover the impulse response of the dynamic part is also given. Pointwise consistency of the first and consistency of the other estimate is shown. The results hold for any nonlinear characteristic, and any asymptotically dynamic subsystem. Convergence rates are also given.

Identification of Wiener-type nonlinear systems in a noisy environment

Wiener systems are widely encountered in engineering and science applications. This paper proposes a straightforward approach to the identification of Wiener systems in a noisy environment. The obtained models are represented in terms of the frequency response for the linear subsystem and the inverse of the static nonlinearity. A variety of input excitation signals, including random binary and periodic, can be used with the proposed method. Simulation studies using a pH neutralization continuous stirred tank reactor show that excellent results are obtained with relatively short data lengths.

Cyclic higher-order statistics: Input/output relations for discrete- and continuous-time MIMO linear almost-periodically time-variant systems

A contribution to the theory of higher-order cyclostationarity very recently introduced to generalize the second-order cyclostationarity theory is given. Input/output relations in terms of cyclic higher-order statistics for multi-input multi-output linear almost-periodically time-variant systems that are excited by cyclostationary inputs are derived. Both continuous- and discrete-time systems are considered. For a single-input single-output linear time-invariant system, the Wiener system identification formula based on second-order cyclic spectra is generalized to higher-order statistics. The problem of reconstructing cyclic higher-order statistics of a continuous-time-series from its samples is addressed and a sufficient condition on the sampling rate to prevent aliasing is stated. Examples of application of the theory are included.

Nonparametric identification of Wiener systems by orthogonal series

A Wiener system, i.e., a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade, is identified. Both the input signal and disturbance are random, white, and Gaussian. The unknown nonlinear characteristic is strictly monotonous and differentiable and, therefore, the problem of its recovering from input-output observations of the whole system is nonparametric. It is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed. The estimates apply the trigonometric, Legendre, and Hermite orthogonal functions. Pointwise consistency of all the algorithms is shown. Under some additional smoothness restrictions, the rates of their convergence are examined and compared. An algorithm to identify the impulse response of the linear subsystem is proposed. >

A new algorithm for the identification of multiple input Wiener systems.

Multiple-input Wiener systems consist of two or more linear dynamic elements, whose outputs are transformed by a multiple-input static non-linearity. Korenberg (1985) demonstrated that the linear elements of these systems can be estimated using either a first order input-output cross-covariance or a slice of the second, or higher, order input-output cross-covariance function. Korenberg's work used a multiple input LNL structure, in which the output of the static nonlinearity was then filtered by a linear dynamic system. In this paper we show that by restricting our study to the slightly simpler Wiener structure, it is possible to improve the linear subsystem estimates obtained from the measured cross-covariance functions. Three algorithms, which taken together can identify any multiple-input Wiener system, have been developed. We present the theory underlying these algorithms and detail their implementation. Simulation results are then presented which demonstrate that the algorithms are robust in the presence of output noise, and provide good estimates of the system dynamics under a wide set of conditions.