Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements

Ioannis A. Kougioumtzoglou, Ketson R.M. dos Santos, Liam Comerford

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

Various system identification techniques exist in the literature that can handle non-stationary measured time-histories, or cases of incomplete data, or address systems following a fractional calculus modeling. However, there are not many (if any) techniques that can address all three aforementioned challenges simultaneously in a consistent manner. In this paper, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. Several linear and nonlinear time-variant systems with fractional derivative elements are used as numerical examples to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

Original languageEnglish (US)
Pages (from-to)279-296
Number of pages18
JournalMechanical Systems and Signal Processing
Volume94
DOIs
StatePublished - Sep 15 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Ltd

Keywords

  • Fractional derivative
  • Harmonic wavelet
  • Incomplete data
  • Nonlinear system
  • System identification

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