Title: Identification of non-linear stochastic systems using a new Hammerstein-Wiener neural network: a simulation study through a non-linear hydraulic process

Authors: Saif Eddine Abouda; Donia Ben Halima Abid; Mourad Elloumi; Yassine Koubaa; Abdessattar Chaari

Addresses: Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), National School of Engineering of Sfax, University of Sfax, Sfax, Tunisia; National Engineering School of Tunis (ENIT), University of Tunis El Manar, Tunis, Tunisia ' Control and Energy Management Laboratory, National Engineering School of Sfax, University of Sfax, Sfax, Tunisia ' Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), National School of Engineering of Sfax, University of Sfax, Sfax, Tunisia ' Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), National School of Engineering of Sfax, University of Sfax, Sfax, Tunisia ' Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), National School of Engineering of Sfax, University of Sfax, Sfax, Tunisia

Abstract: Hammerstein-Wiener models have been proved to be suitable in modelling a class of typical non-linear dynamic systems. This paper aims at developing a Hammerstein-Wiener Neural Network (HWNN) which formulates a Hammerstein-Wiener mathematical model, in order to identify a nonlinear dynamic system operating in a stochastic environment. A central aspect is that a general situation has been considered including non-invertible non-linearity output and correlation of stochastic disturbances after the dynamic linear block. Different from the existing parameter identification methods, the model is developed to handle two types of learning algorithms that can directly obtain the parameters of the unknown time-varying nonlinear system. Firstly, all neural network weights in HWNN are adapted using a Back Propagation-based Gradient algorithm (BPG). The second method, namely Recursive Least Square Back Propagation based Gradient (RLSBPG) is derived from the BPG algorithm to achieve the parametric estimation of the Hammerstein scheme where the remaining parameters are estimated by the least-squares approach based on fuzzy technique to ameliorate the estimation quality. The convergence analysis of the algorithms is presented, and their performances are tested through a simulation study of a nonlinear hydraulic process.

Keywords: non-linear stochastic systems; Hammerstein-Wiener mathematical model; Hammerstein-Wiener neural network; BPG learning algorithm; RLSBPG learning algorithm; fuzzy technique; convergence analysis; hydraulic process.

DOI: 10.1504/IJCAT.2020.109340

International Journal of Computer Applications in Technology, 2020 Vol.63 No.3, pp.241 - 256

Received: 27 Dec 2018
Accepted: 20 Jan 2020
Published online: 03 Sep 2020 *

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