A variable projection approach for efficient estimation of RBF-ARX model

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

103 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Article number6844855
Pages (from-to)476-485
Journal / PublicationIEEE Transactions on Cybernetics
Volume45
Issue number3
Online published26 Jun 2014
Publication statusPublished - Mar 2015

Abstract

The radial basis function network-based autoregressive with exogenous inputs (RBF-ARX) models have much more linear parameters than nonlinear parameters. Taking advantage of this special structure, a variable projection algorithm is proposed to estimate the model parameters more efficiently by eliminating the linear parameters through the orthogonal projection. The proposed method not only substantially reduces the dimension of parameter space of RBF-ARX model but also results in a better-conditioned problem. In this paper, both the full Jacobian matrix of Golub and Pereyra and the Kaufman's simplification are used to test the performance of the algorithm. An example of chaotic time series modeling is presented for the numerical comparison. It clearly demonstrates that the proposed approach is computationally more efficient than the previous structured nonlinear parameter optimization method and the conventional Levenberg-Marquardt algorithm without the parameters separated. Finally, the proposed method is also applied to a simulated nonlinear single-input single-output process, a time-varying nonlinear process and a real multiinput multioutput nonlinear industrial process to illustrate its usefulness.

Research Area(s)

  • Modeling, parameter optimization, separable nonlinear least-squares problems, state-dependent models, system identification, variable projection

Citation Format(s)

A variable projection approach for efficient estimation of RBF-ARX model. / Gan, Min; Li, Han-Xiong; Peng, Hui.
In: IEEE Transactions on Cybernetics, Vol. 45, No. 3, 6844855, 03.2015, p. 476-485.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review