Title: Over parameterisation and optimisation approaches for identification of nonlinear stochastic systems described by Hammerstein-Wiener models

Authors: Saif Eddine Abouda; Mourad Elloumi; Yassine Koubaa; Abdessattar Chaari

Addresses: Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), LR11ES50, National School of Engineering of Sfax, University of Sfax, Postal Box 1173, 3038 Sfax, Tunisia; National Engineering School of Tunis (ENIT), University of Tunis El Manar, BP 37, 1002 Le Belvedere, Tunisia ' Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), LR11ES50, National School of Engineering of Sfax, University of Sfax, Postal Box 1173, 3038 Sfax, Tunisia ' Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), LR11ES50, National School of Engineering of Sfax, University of Sfax, Postal Box 1173, 3038 Sfax, Tunisia ' Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), LR11ES50, National School of Engineering of Sfax, University of Sfax, Postal Box 1173, 3038 Sfax, Tunisia

Abstract: This paper proposes two iterative procedures based on over-parameterisation and optimisation approaches for the identification of nonlinear systems which can be described by Hammerstein-Wiener stochastic models. In this case, the dynamic linear part of the considered system is described by ARMAX mathematical model. The static nonlinear block is approximated by polynomial functions. The first procedure is based on a combination of the prediction error method by using the recursive approximated maximum likelihood estimator (RAML), the singular value decomposition (SVD) approach and the fuzzy techniques in order to estimate the parameters of the considered process. As for the second procedure, it includes an appropriate representation named as generalised orthonormal basis filters (GOBF) in order to reduce the complexity of the considered system. The parametric estimation problem is formulated using the recursive extended least squares (RELS) algorithm incorporated with the singular value decomposition (SVD) and fuzzy techniques in order to segregate the coupled parameters and improve the estimation quality. The validity of the developed approaches is proved by considering a nonlinear hydraulic process simulation.

Keywords: nonlinear stochastic systems; Hammerstein-Wiener models; ARMAX model; GOBF representation; parametric estimation; prediction error method; SVD approach; fuzzy technique; hydraulic process simulation.

DOI: 10.1504/IJMIC.2019.103975

International Journal of Modelling, Identification and Control, 2019 Vol.33 No.1, pp.61 - 75

Received: 30 Jun 2018
Accepted: 01 Mar 2019
Published online: 04 Dec 2019 *

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