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Chaotic resonance in a fractional-order oscillator system with application to mechanical fault diagnosis

Author

Listed:
  • He, Yuzhu
  • Fu, Yuxuan
  • Qiao, Zijian
  • Kang, Yanmei

Abstract

This paper is to generalize the research on chaotic resonance (CR) towards fractional-order chaotic systems and then develop a new technique for detecting weak signals embedded in strong background noise. For illustration, a fractional-order Duffing oscillator system is evaluated by means of bifurcation analysis, revealing the phenomenon of chaotic resonance, with the optimal driving amplitude falling within a chaotic interval. It is found that the weak signal can be amplified by the intrinsic fluctuations in the chaotic system instead of stochastic noise. Based on this investigation, a novel weak signal detection method is developed and successfully applied to mechanical fault diagnosis without the need of signal preprocessing. Extensive numerical results show that the signal-to-noise ratio of the incipient fault signal of machinery can be greatly improved.

Suggested Citation

  • He, Yuzhu & Fu, Yuxuan & Qiao, Zijian & Kang, Yanmei, 2021. "Chaotic resonance in a fractional-order oscillator system with application to mechanical fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920309280
    DOI: 10.1016/j.chaos.2020.110536
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    References listed on IDEAS

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    1. Liu, Xuanliang & Han, Maoan, 2005. "Poincaré bifurcation of a three-dimensional system," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1385-1398.
    2. Li Lai & Yuan-Dong Ji & Su-Chuan Zhong & Lu Zhang, 2017. "Sequential Parameter Identification of Fractional-Order Duffing System Based on Differential Evolution Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-13, September.
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    Citations

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    Cited by:

    1. Qiao, Zijian & He, Yuanbiao & Liao, Changrong & Zhu, Ronghua, 2023. "Noise-boosted weak signal detection in fractional nonlinear systems enhanced by increasing potential-well width and its application to mechanical fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Claudia A. Pérez-Pinacho & Cristina Verde, 2022. "A Note on an Integral Transformation for the Equivalence between a Fractional and Integer Order Diffusion Model," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
    3. Baysal, Veli & Solmaz, Ramazan & Ma, Jun, 2023. "Investigation of chaotic resonance in Type-I and Type-II Morris-Lecar neurons," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Huang, Pengfei & Chai, Yi & Chen, Xiaolong, 2022. "Multiple dynamics analysis of Lorenz-family systems and the application in signal detection," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. Ahmad Taher Azar & Farah Ayad Abdul-Majeed & Hasan Sh. Majdi & Ibrahim A. Hameed & Nashwa Ahmad Kamal & Anwar Jaafar Mohamad Jawad & Ali Hashim Abbas & Wameedh Riyadh Abdul-Adheem & Ibraheem Kasim Ibr, 2022. "Parameterization of a Novel Nonlinear Estimator for Uncertain SISO Systems with Noise Scenario," Mathematics, MDPI, vol. 10(13), pages 1-17, June.
    6. Livija Cveticanin & Nicolae Herisanu & Ivona Ninkov & Mladen Jovanovic, 2022. "New Closed-Form Solution for Quadratic Damped and Forced Nonlinear Oscillator with Position-Dependent Mass: Application in Grafted Skin Modeling," Mathematics, MDPI, vol. 10(15), pages 1-15, July.

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