Block-oriented models are often used to model a nonlinear system. This paper presents an identification method for parallel Wiener-Hammerstein systems, where the obtained model has a decoupled static nonlinear block. This decoupled nature makes the interpretation of the obtained model more easy. First a coupled parallel Wiener-Hammerstein model is estimated. Next, the static nonlinearity is dec...

Two existing Hammerstein-Wiener identification algorithms and a third novel Hammerstein-Wiener identification algorithm are considered for application to the magnetospheric system. A modified subspace algorithm that allows missing data points is described and used for identifying periodically switching Hammerstein-Wiener models, to capture the periodically time-varying nature of the system. The...

An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identif...

In this paper, non iterative algorithms for the identification of (multivariable) Hammerstein and Wiener systems are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. For the Hammerstein model, the algorithm provides consistent estimates even in the presence of coloured output noise, under weak assu...

In the previous work our research group introduced an exact solution to the Hammerstein system and is known as H-BEST (Hammerstein BlockOriented Exact Solution Technique). It was later expanded to multiple input, multiple output (MIMO) Hammerstein and Wiener (W-BEST) systems. This work is extends this approach to more complicated block-oriented systems, namely a Hammerstein-Wiener process. By e...

A recursive algorithm is proposed in this paper to identify Hammerstein–Wiener systems with heteroscedastic measurement noise. Based on the parameterization model of Hammerstein–Wiener systems, the algorithm is derived by minimizing the expectation of the sum of squared parameter estimation errors. By replacing the immeasurable internal variables with their estimations, the need for the commonl...

The problem of the identification of Hammerstein and Wiener models is considered in this paper. The suggested approach in this paper utilizes the spectral magnitude matching method that minimizes the sum squared error between the spectral magnitudes evaluated for a number of short-time frames of the measured output signal of the nonlinear system and the output signal of the nonlinear model. The...

It is suggested that the differences between the Hammerstein and Wiener models be interpreted and understood in terms of the system eigenvalues. In particular, it is shown that the Wiener representation should be preferred when the system dynamics vary with the operating point. Conversely, when only the system gain varies with the operating point, Hammerstein models generally outperform the Wie...