Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models |
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Authors: | Fei He Hua-Liang Wei |
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Affiliation: | Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, United Kingdom |
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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. |
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Keywords: | generalised frequency response functions nonlinear and non-stationary systems system identification time-varying systems wavelet basis functions |
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