Non-linear system modelling based on NARX model expansion on Laguerre orthonormal bases

• Published in: IET signal processing Vol. 12; no. 2; pp. 228 - 241
• Main Authors: Benabdelwahed, Imen, Mbarek, Abdelkader, Bouzrara, Kais, Garna, Tarek
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.04.2018
• Subjects: autoregressive processes; autoregressive product; benchmark continuous stirred tank reactor; crossed product; discrete nonlinear autoregressive with exogenous inputs model; discrete time systems; exogenous product; genetic algorithm; genetic algorithms; Laguerre orthonormal bases; mean square error methods; minimisation; NARX model expansion; NARX‐Laguerre poles; nonlinear discrete time system; nonlinear system modelling; nonlinear systems; normalised mean square error minimisation; numerical simulations; optimisation algorithm; parameter number reduction; poles and zeros; Research Article; autoregressive product; numerical simulations; NARX model expansion; discrete time systems; NARX-Laguerre poles; nonlinear discrete time system; Laguerre orthonormal bases; autoregressive processes; genetic algorithms; parameter number reduction; poles and zeros; discrete nonlinear autoregressive with exogenous inputs model; genetic algorithm; benchmark continuous stirred tank reactor; nonlinear systems; nonlinear system modelling; crossed product; optimisation algorithm; minimisation; mean square error methods; exogenous product; normalised mean square error minimisation
• ISSN: 1751-9675; 1751-9683; 1751-9683
• DOI: 10.1049/iet-spr.2017.0187

This study proposes a new representation of discrete Non-linear AutoRegressive with eXogenous inputs (NARX) model by developing its coefficients associated to the input, the output, the crossed product, the exogenous product and the autoregressive product on five independent Laguerre orthonormal bases. The resulting model, entitled NARX-Laguerre, ensures a significant parameter number reduction with respect to the NARX model. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the five Laguerre bases. Therefore, the authors propose to use the genetic algorithm to optimise the NARX-Laguerre poles, based on the minimisation of the normalised mean square error. The performances of the resulting NARX-Laguerre model and the proposed optimisation algorithm are validated by numerical simulations and tested on the benchmark Continuous Stirred Tank Reactor.