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

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  • Fei He
  • Hua-Liang Wei
  • Stephen A. Billings

Abstract

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-dimensional frequency features can be visualised in a low-dimensional time–frequency space.

Suggested Citation

  • Fei He & Hua-Liang Wei & Stephen A. Billings, 2015. "Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 2087-2100, August.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:11:p:2087-2100
    DOI: 10.1080/00207721.2013.860202
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