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

• Published in: Mechanical systems and signal processing 2017-09, Vol.94, p.279-296
• Main Authors: Kougioumtzoglou, Ioannis A., dos Santos, Ketson R.M., Comerford, Liam
• Format: Article
• Language: English
• Subjects: Fractional calculus; Fractional derivative; Frequency response functions; Harmonic wavelet; Incomplete data; Mathematical models; MISO (control systems); Nonlinear system; Nonlinear systems; Oscillators; Parameter identification; Signal processing; System identification; Wavelet analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.03.004

•A novel multiple-input-single-output system identification technique is developed.•The technique can account for incomplete/missing data via a compressive sampling treatment.•The technique can account for non-stationary data via harmonic wavelets.•The technique can address nonlinear systems with fractional derivative elements. 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.