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

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 bas...

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Bibliographic Details
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
Online Access:Get full text
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Description
Summary: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.
ISSN:1751-9675
1751-9683
1751-9683
DOI:10.1049/iet-spr.2017.0187