Identification of Wiener-type nonlinear systems in a noisy environment

Kalafatis, A.; Wang, Liuping; Cluett, William R.

doi:10.1080/002071797224469

Cited by 130 publications

(79 citation statements)

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“…More recently, generalisations based on feedback variants have been studied, such as the work [37,21]. The literature on how to estimate the HammersteinWiener model (and the Hammerstein or Wiener only special cases) is extensive indeed, as evidenced by the selection [18,33,4,40,42,23,7] and their bibliographies. In relation to this, it is important to emphasise that the work here is distinguished from these and other previous contributions in the following ways.…”

Section: Introductionmentioning

confidence: 99%

Identification of Hammerstein–Wiener models

Wills¹,

Schön²,

Ljung³

et al. 2013

Automatica

257

108

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This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and coloured stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

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Section: Introductionmentioning

confidence: 99%

Identification of Hammerstein–Wiener models

Wills¹,

Schön²,

Ljung³

et al. 2013

Automatica

257

108

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show abstract

“…See e.g. [57,17,35,19,39,18,24,51] and the references therein. However, the approach presented here differs from the existing literature on several accounts.…”

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confidence: 99%

Bayesian semiparametric Wiener system identification

2013

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We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturbances, entering both as measurement noise and as process noise, are handled in a systematic manner. The nonparametric nature of the Gaussian process allows us to handle a wide range of nonlinearities without making problem-specific parameterizations. We also consider sparsity-promoting priors, based on generalized hyperbolic distributions, to automatically infer the order of the underlying dynamical system. We derive an inference algorithm based on an efficient particle Markov chain Monte Carlo method, referred to as particle Gibbs with ancestor sampling. The method is profiled on two challenging identification problems with good results. Blind Wiener system identification is handled as a special case.

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“…The Wiener system has been applied as a model for some industrial/biological systems [1], [2], [3], [4], [5], [6]. It comprises a linear dynamical model followed a nonlinear static functional transformation.…”

Section: Introductionmentioning

confidence: 99%

“…Fundamental to the identification and control of the Wiener system is the characterization/representation of the unknown nonlinear static function. Various approaches have been researched including the nonparametric method [7], subspace model identification methods [8], [6], fuzzy modelling [9] and the parametric method [10], [3], [4], [2]. For the parametric method, the unknown nonlinear function is restricted by some parametric representation with a finite number of parameters, and the system identification includes the estimation of the unknown parameters using nonlinear optimization algorithms based on input/output observational data Based on the approximation theory, the polynomial functions are appropriate in approximating the unknown nonlinear static functions.…”

Section: Introductionmentioning

confidence: 99%

Wiener system identification using B-spline functions with De Boor recursion

Hong

Mitchell

Chen

2011

Sensor Signal Processing for Defence (SSPD 2011)

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Abstract-A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

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Identification of Wiener-type nonlinear systems in a noisy environment

Cited by 130 publications

References 0 publications

Identification of Hammerstein–Wiener models

Identification of Hammerstein–Wiener models

Bayesian semiparametric Wiener system identification

Wiener system identification using B-spline functions with De Boor recursion

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