Sains Malaysiana 50(11)(2021): 3405-3420

http://doi.org/10.17576/jsm-2021-5011-24

Wavelet Characterizations for Investigating Nonlinear Oscillators

(Pencirian Gelombang Kecil untuk Mengakaji Pengayun Tak Linear)

MOHD AFTAR ABU BAKAR¹, NORATIQAH MOHD ARIFF¹*, ANDREW V. METCALFE² & DAVID A. GREEN²

¹Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

²School of Mathematical Sciences, Faculty of Engineering, Computer and Mathematical Sciences, University of Adelaide, 5005, South Australia, Australia

Received: 27 August 2020/Accepted: 3 March 2021

ABSTRACT

This study investigates the wavelet-based system identification capabilities on determining the system nonlinearity based on the system impulse response function. Wavelet estimates of the instantaneous envelopes and instantaneous frequency are used to plot the system backbone curve. This wavelet estimate is then used to estimate the values of the parameter for the system. Two weakly nonlinear oscillators, which are the Duffing and the Van der Pol oscillators, have been analyzed using this wavelet approach. A case study based on a model of an oscillating flap wave energy converter (OFWEC) was also discussed in this study. Based on the results, it was shown that this technique is recommended for nonlinear system identification provided the impulse response of the system can be captured. This technique is also suitable when the system's form is unknown and for estimating the instantaneous frequency even when the impulse responses were polluted with noise.

Keywords: Nonlinear oscillator; system identification; wavelet; wave energy converter

ABSTRAK

Penyelidikan ini telah mengkaji kemampuan pengecaman sistem berasaskan gelombang kecil untuk menentukan ketaklinearan sesuatu sistem berdasarkan fungsi sambutan dedenyut sistem tersebut. Anggaran sampul seketika dan frekuensi seketika oleh penganggar gelombang kecil digunakan untuk memplot lengkung tulang belakang sistem tersebut. Penganggar gelombang kecil ini digunakan untuk menganggarkan nilai parameter bagi sistem tersebut. Dua jenis pengayun tak linear, iaitu pengayun Duffing dan Van der Pol, telah dianalisis menggunakan kaedah ini. Satu kajian kes berdasarkan model penukar tenaga ombak jenis pengayun berkibas (OFWEC) turut dibincangkan dalam kajian ini. Berdasarkan keputusan yang diperoleh, didapati bahawa teknik ini sesuai digunakan untuk pengecaman sistem tak linear apabila sambutan dedenyut sistem tersebut boleh diperoleh. Teknik ini juga sesuai digunakan apabila bentuk sesuatu sistem itu tidak diketahui dan juga untuk menganggarkan frekuensi serta-merta walaupun dedenyut sistem dicemari dengan hingar.

Kata kunci: Gelombang kecil; pengayun tak linear; pengecaman sistem; penukar tenaga ombak

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*Corresponding author; email: tqah@ukm.edu.my