Identification of Hammerstein–Wiener models

Wills, Adrian; Schön, Thomas B.; Ljung, Lennart; Ninness, Brett

doi:10.1016/j.automatica.2012.09.018

Cited by 263 publications

(126 citation statements)

References 40 publications

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“…Most notably, we are able to deal with process noise entering internally to the linear dynamical system, which can be critical in obtaining an accurate model [57]. The inclusion of such process noise in the model significantly complicates the estimation problem, and is therefore often neglected in the existing literature.…”

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confidence: 99%

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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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confidence: 99%

“…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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“…The state of the art in designing, analyzing and implementing identification algorithms for block-oriented nonlinear systems were well summarized in a recent book by Giri and Bai [3]. Depending on the location of the static nonlinear component, block-oriented models can be classified into the Hammerstein model, the Wiener model and the Hammerstein-Wiener model [4][5][6]. The Hammerstein model represents a class of input nonlinear systems, where the nonlinear block is prior to the linear one.…”

Section: Introductionmentioning

confidence: 99%

Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems

Xie

Yang

2017

Algorithms

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Abstract:Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance.

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“…In this paper, we deal with the identification of Hammerstein-Wiener systems, for which many papers have been published in the literature under different conditions and by various methods; for example, an overparametrization method [3], a blind approach [4], iterative methods [5,8,26,31], subspace methods [11,22], an EM-based algorithm [28], an instrumental variable method [21]; moreover in many papers it is assumed that the output nonlinearity is invertible [4,8,11,24,29,31] to get an estimate of the input of the output nonlinearity. Also, the NLN models are used in many applications, including prediction of magneticfield [22] and process controls [30,31], etc.…”

Section: Introductionmentioning

confidence: 99%

Identification of Hammerstein-Wiener Systems using Subspace Method and Separable Least-Squares

Ase¹,

Katayamay²

2017

Stochastic Systems Theory and its Applications (SSS)

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We deal with identification of Hammerstein-Wiener systems, or NLN systems, in which a linear subsystem is sandwiched by two nonlinearities. First we identify an approximate linear state space model of the NLN system by using the ORT (orthogonal projection) subspace method or PO-MOESP method. Then, initialized by the estimated state space model, we optimize the output error (OE) model, which is derived based on the basis functions expansion of nonlinearities, by using a gradient-based optimization method. Numerical results are included to show the applicability of the present approach.

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Identification of Hammerstein–Wiener models

Cited by 263 publications

References 40 publications

Bayesian semiparametric Wiener system identification

Bayesian semiparametric Wiener system identification

Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems

Identification of Hammerstein-Wiener Systems using Subspace Method and Separable Least-Squares

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