Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models

Fei He, Hua Liang Wei, Stephen A. Billings

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
115 Downloads (Pure)


This paper introduces a new approach for nonlinear and non-stationary (time-varying) system identification based on time-varying nonlinear autoregressive moving average with exogenous variable (TV-NARMAX) models. The challenging model structure selection and parameter tracking problems are solved by combining a multiwavelet basis function expansion of the time-varying parameters with an orthogonal least squares algorithm. Numerical examples demonstrate that the proposed approach can track rapid time-varying effects in nonlinear systems more accurately than the standard recursive algorithms. Based on the identified time domain model, a new frequency domain analysis approach is introduced based on a time-varying generalised frequency response function (TV-GFRF) concept, which enables the analysis of nonlinear, non-stationary systems in the frequency domain. Features in the TV-GFRFs which depend on the TV-NARMAX model structure and time-varying parameters are investigated. It is shown that the high-dimension...
Original languageEnglish
Pages (from-to)2087-2100
Number of pages14
JournalInternational Journal of Systems Science
Issue number11
Early online date19 Nov 2013
Publication statusPublished - 18 Aug 2015
Externally publishedYes

Bibliographical note

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Systems Science on 19/11/13, available online:


  • generalised frequency response functions
  • nonlinear and non-stationary systems
  • system identification
  • timevarying systems
  • wavelet basis functions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications


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