Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the input nonlinearity is allowed to be a memory operator of backlash type and both input and output nonlinearities are polynomial and may be noninvertible. The linear subsystem may be parametric or not, continuousor discrete-time. A two-stage identification method is develop...

We show a result that can be viewed as a generalization of Bussgang’s classic theorem about static nonlinearities with Gaussian inputs. This new result is used to characterize the best linear approximation of a nonlinear finite impulse response (NFIR) system with a Gaussian input. The best linear approximation is here defined as the causal LTI system that minimizes the expected squared predicti...

This paper describes a benchmark for nonlinear system identi cation. A Wiener-Hammerstein system is selected as test object. In such a structure there is no direct access to the static nonlinearity starting from the measured input/output, because it is sandwiched between two unknown dynamic systems. The signal-to-noise ratio of the measurements is quite high, which puts the focus of the benchma...

In this paper, subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented. The proposed algorithms consist basically of two steps. The first one is a standard (linear) subspace algorithm applied to an equivalent linear system whose inputs (respectively outputs) are filtered (by the nonlinear functi...

Abstract. This paper presents the synthesis and analysis of the enhanced predictive fuzzy Hammerstein model of the water tank system. Fuzzy Hammerstein model was compared with three other fuzzy models: the first was synthesized using Mamdani type rule base, the second – Takagi-Sugeno type rule base and the third – composed of Mamdani and Takagi-Sugeno rule bases. The synthesized model is invert...

The identification problem for non-linear Wiener-Hammerstein-type systems is considered. Unlike alternative techniques that are based on deterministic system representations, a stochastic model structure that explicitly accounts for both the input-output and noise dynamics is postulated. The uniqueness properties of this structure are analysed, and appropriate necessary and sufficient condition...

Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, its hyperparameterestimation procedure suffers from numerous covariance-matrix inversions of prohibitively O(N) operations. In this paper, we propose using the quasi-Newton BFGS O(N)-operation formula to update recursively the inverse of covariance matrix at every itera...