Decoupling P-NARX models using filtered CPD

Jan Decuyper, David Westwick, Kiana Karami, Johan Schoukens

Research output: Contribution to journalConference paper

Abstract

Nonlinear Auto-Regressive eXogenous input (NARX) models are a popular class of nonlinear dynamical models. Often a polynomial basis expansion is used to describe the internal multivariate nonlinear mapping (P-NARX). Resorting to fixed basis functions is convenient since it results in a closed form solution of the estimation problem. The drawback, however, is that the predefined basis does not necessarily lead to a sparse representation of the relationship, typically resulting in very large numbers of parameters. So-called decoupling techniques were specifically designed to reduce large multivariate functions. It was found that, often, a more efficient parameterisation can be retrieved by rotating towards a new basis. Characteristic to the decoupled structure is that, expressed in the new basis, the relationship is structured such that only single-input single-output nonlinear functions are required. Classical decoupling techniques are unfit to deal with the case of single-output NARX models. In this work, this limitation is overcome by adopting the filtered CPD decoupling method of Decuyper et al. (2021b). The approach is illustrated on data from the Sliverbox benchmark: measurement data from an electronic circuit implementation of a forced Duffing oscillator.

Original languageEnglish
Pages (from-to)661-666
Number of pages6
JournalIFAC-PapersOnLine
Volume54
Issue number7
DOIs
Publication statusPublished - 1 Jul 2021
Event19th IFAC Symposium on System Identification, SYSID 2021 - Padova, Italy
Duration: 13 Jul 202116 Jul 2021

Keywords

  • Decoupling
  • Filtered CPD
  • Model reduction
  • Nonlinear system identification
  • Polynomial-NARX

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