TY - JOUR
T1 - Decoupling P-NARX models using filtered CPD
AU - Decuyper, Jan
AU - Westwick, David
AU - Karami, Kiana
AU - Schoukens, Johan
N1 - Funding Information:
This work was supported by the Flemish fund for scientific research FWO under license number G0068.18N.
Publisher Copyright:
Copyright © 2021 The Authors.
PY - 2021/7/1
Y1 - 2021/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85118185385&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85118185385&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2021.08.436
DO - 10.1016/j.ifacol.2021.08.436
M3 - Conference article
AN - SCOPUS:85118185385
VL - 54
SP - 661
EP - 666
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
SN - 2405-8963
IS - 7
T2 - 19th IFAC Symposium on System Identification, SYSID 2021
Y2 - 13 July 2021 through 16 July 2021
ER -