Decoupling P-NARX models using filtered CPD

TL;DR

This paper introduces a novel decoupling method for P-NARX models using filtered CPD, enabling efficient parameterisation of single-output nonlinear dynamical systems, demonstrated on electronic circuit data.

Contribution

It extends decoupling techniques to single-output NARX models by adopting filtered CPD, improving model sparsity and efficiency.

Findings

Effective decoupling of P-NARX models demonstrated

Reduced parameter complexity achieved

Validated on electronic circuit benchmark

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.