Generation of initial estimates for Wiener-Hammerstein models via basis function expansions

Tiels, Koen; Schoukens, Maarten; Schoukens, Johan

doi:10.3182/20140824-6-za-1003.02292

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…LS‐CPDs appear in a wide range of applications (see, e.g., other works), but the CPD structure is often not recognized or not fully exploited. In this paper, the applicability of LS‐CPDs is illustrated in three different domains: classification, multilinear algebra, and signal processing.…”

Section: Introductionmentioning

confidence: 99%

Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications

Bousse

Vervliet

Domanov

et al. 2018

Numerical Linear Algebra App

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Summary Real‐life data often exhibit some structure and/or sparsity, allowing one to use parsimonious models for compact representation and approximation. When considering matrix and tensor data, low‐rank models such as the (multilinear) singular value decomposition, canonical polyadic decomposition (CPD), tensor train, and hierarchical Tucker model are very common. The solution of (large‐scale) linear systems is often structured in a similar way, allowing one to use compact matrix and tensor models as well. In this paper, we focus on linear systems with a CPD‐constrained solution (LS‐CPD). Our main contribution is the development of optimization‐based and algebraic methods to solve LS‐CPDs. Furthermore, we propose a condition that guarantees generic uniqueness of the obtained solution. We also show that LS‐CPDs provide a broad framework for the analysis of multilinear systems of equations. The latter are a higher‐order generalization of linear systems, similar to tensor decompositions being a generalization of matrix decompositions. The wide applicability of LS‐CPDs in domains such as classification, multilinear algebra, and signal processing is illustrated.

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Section: Introductionmentioning

confidence: 99%

Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications

Bousse

Vervliet

Domanov

et al. 2018

Numerical Linear Algebra App

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“…Ding et al presented a hierarchical multi‐innovation gradient estimator for SISO Hammerstein ARMAX models. Furthermore, for Hammerstein‐Wiener and Wiener‐Hammerstein models, various works have been developed and published in the literature dealing with the formulation of problems related to parametric estimation methods . In , a hierarchical least squares algorithm is proposed for the Hammerstein‐Wiener system by based on the auxiliary model identification idea.…”

Section: Introductionmentioning

confidence: 99%

“…The Wiener‐Hammerstein model can describe the dynamic of a nonlinear system with three blocks where a static nonlinear part is sandwiched between two dynamic linear ones. Thus, the research work of Tiels et al discussed three system identification methods for Wiener‐Hammerstein models based on the best linear approximation (BLA), the generalized orthonormal basis and the bilinear optimization of the model parameters. Furthermore, Giordano et al presented a new fractional approach for initializing Wiener‐Hammerstein models via the best linear approximation method.…”

Section: Introductionmentioning

confidence: 99%

A recursive hierarchical parametric estimation algorithm for nonlinear systems described by Wiener‐Hammerstein models

Ghanmi

Elloumi

Salhi

et al. 2019

Asian Journal of Control

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In this paper, a recursive hierarchical parametric estimation (RHPE) algorithm is proposed for stochastic nonlinear systems which can be described by Wiener-Hammerstein (W-H) mathematical models. The formulation of parameters estimation problem is based on the prediction error approach and the gradient techniques. The convergence analysis of the developed RHPE algorithm is derived using stochastic gradient-based theory. Wiener-Hammerstein hydraulic process is treated to prove the efficiency of the proposed approach.

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Identification of block-oriented nonlinear systems starting from linear approximations: A survey

2017

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Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the -approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.

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Generation of initial estimates for Wiener-Hammerstein models via basis function expansions

Cited by 5 publications

References 13 publications

Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications

Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications

A recursive hierarchical parametric estimation algorithm for nonlinear systems described by Wiener‐Hammerstein models

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

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