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A second-order stochastic resonance method enhanced by fractional-order derivative for mechanical fault detection

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Abstract

Stochastic resonance (SR), as a noise-enhanced signal processing tool, has been extensively investigated and widely applied to mechanical fault detection. However, mechanical degradation process is continuous where the current value of a mechanical state variable, e.g., vibration, is highly dependent on its previous values, and the widely used SR methods in mechanical fault detection, mainly focusing on integer-order SR, neglect the dependence among the values of the mechanical state variable and are unable to utilize such a dependence to enhance weak fault characteristics embedded in a signal that records the values of the mechanical state variable as time varies. Inspired by fractional-order derivative that characterizes memory-dependent properties and reflects the high dependence between current and previous values of the state variable of a system, a second-order SR method enhanced by fractional-order derivative is developed to enhance weak fault characteristics for mechanical fault detection by using strong background noise, which is able to utilize the dependence among the values of a mechanical state variable to enhance weak fault characteristics embedded in a signal. Numerical analyses show that output signal-to-noise ratio (SNR) versus fractional order in the second-order bistable SR system induced by fractional-order derivative depicts a typical feature of SR. Even the second-order bistable SR system induced by fractional-order derivative is similar to the optimal moving filter by fine-tuning the system parameters and scaling factor. Experimental data including a bearing with slight flaking on the outer race and a gear with scuffing from wind turbine drivetrain are used to validate the feasibility of the proposed method. The experimental results indicate that the proposed method is able to not only suppress multiscale noise embedded in a signal but also enhance the benefits of noise to mechanical fault detection. In addition, the comparison with other advanced signal processing methods demonstrates that the proposed method outperforms the integer-order SR methods, even kurtogram and maximum correlated kurtosis deconvolution in extracting weak fault characteristics of machinery overwhelmed by strong background noise.

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Acknowledgements

This research was supported by the Foundation of the State Key Laboratory of Mechanical Transmission of Chongqing University (SKLMT-MSKFKT-202009), General Scientific Research Project of Educational Committee of Zhejiang Province (Y202043287), Projects in Science and Technique Plans of Ningbo City (2020Z110), the development program in Ningbo University (422008282) and also sponsored by K.C. Wong Magna Fund in Ningbo University. The authors would like to thank editors and anonymous reviewers for their valuable and helpful comments to revise and improve our manuscript. Finally, Zijian Qiao would like to thank his wife Zhe Lin for her encouragement and support all the time.

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Authors and Affiliations

  1. School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, 315211, Zhejiang, China

    Zijian Qiao & Xuedao Shu

  2. The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400044, China

    Zijian Qiao

  3. Zhejiang Provincial Key Laboratory of Part Rolling Technology, Ningbo, 315211, Zhejiang, China

    Zijian Qiao & Xuedao Shu

  4. Department of Civil, Construction, and Environmental Engineering, The University of Alabama at Birmingham, 1075 13th St S, Birmingham, AL, 35205, USA

    Ahmed Elhattab

  5. College of Electrical Engineering and Automation, Anhui University, Hefei, 230601, Anhui, China

    Changbo He

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  1. Zijian Qiao
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Correspondence to Zijian Qiao.

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Qiao, Z., Elhattab, A., Shu, X. et al. A second-order stochastic resonance method enhanced by fractional-order derivative for mechanical fault detection. Nonlinear Dyn 106, 707–723 (2021). https://doi.org/10.1007/s11071-021-06857-7

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