Skip to main content
SpringerLink
Log in

Caputo–Fabrizio fractional stochastic resonance with graphene potential enhanced by NLOF and its applications in fault diagnosis of rotating machinery

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Stochastic resonance (SR) is an efficient fault feature extraction technique due to its unique noise utilization mechanism. However, both the ignorance of high dependence between the values of mechanical state variables and the output saturation of bistable potential restricts its performance in fault diagnosis. Meanwhile, signals collected from harsh working environments generally contain non-Gaussian noise that aggravates the difficulty of diagnosis. To address the above shortcomings, a Caputo–Fabrizio fractional-order derivative-induced SR with new multi-stable unsaturated potential inspired by graphene band structure is constructed which is enhanced by natural local outlier factor (NLOF) in this paper. First, non-Gaussian noise mingled in the original signal is removed by NLOF in a data cleaning way. Second, aiming at the output saturation problem generated from the bistable potential, a multi-stable potential function originating from the single-layer graphene sheet is established, which can effectively deal with the output saturation. Then, the fractional-order operator is incorporated into the second-order underdamped Duffing oscillator SR model modified by the proposed graphene potential function. Finally, the Caputo–Fabrizio fractional-order derivative is employed to solve the SR model numerically for the response. Weak fault-induced characteristics are supposed to be extracted by the proposed model. The simulation and two diagnosis cases concerning fault bearing and gearbox are applied to demonstrate the effectiveness of the proposed method. Compared with other fault diagnosis methods, the result shows that the proposed method is more effective in revealing the weak fault characteristics and possesses high noise utilization efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33

Similar content being viewed by others

Data availability

The authors do not have permission to share data.

References

  1. Yang, J., Yang, C., Zhuang, X., Liu, H., Wang, Z.: Unknown bearing fault diagnosis under time-varying speed conditions and strong noise background. Nonlinear Dyn. 107, 2177–2193 (2022)

    Google Scholar 

  2. Ma, Y., Cheng, J., Wang, P., Wang, J., Yang, Y.: A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy. Nonlinear Dyn. 111, 16895–16919 (2023)

    Google Scholar 

  3. Mao, W., Chen, J., Liu, J., Liang, X.: Self-supervised deep domain-adversarial regression adaptation for online remaining useful life prediction of rolling bearing under unknown working condition. IEEE Trans. Ind. Inform. 19, 1227–1237 (2022)

    Google Scholar 

  4. He, Y., Fu, Y., Qiao, Z., Kang, Y.: Chaotic resonance in a fractional-order oscillator system with application to mechanical fault diagnosis. Chaos Solitons Fractals 142, 110536 (2021)

    MathSciNet  Google Scholar 

  5. Xu, X., Li, B., Qiao, Z., Shi, P., Shao, H., Li, R.: Caputo–Fabrizio fractional order derivative stochastic resonance enhanced by ADOF and its application in fault diagnosis of wind turbine drivetrain. Renew. Energy 219, 119398 (2023)

    Google Scholar 

  6. Endo, H., Randall, R.B.: Enhancement of autoregressive model based gear tooth fault detection technique by the use of minimum entropy deconvolution filter. Mech. Syst. Signal Process. 21, 906–919 (2007)

    Google Scholar 

  7. Lu, S., He, Q., Kong, F.: Stochastic resonance with woods–saxon potential for rolling element bearing fault diagnosis. Mech. Syst. Signal Process. 45, 488–503 (2014)

    Google Scholar 

  8. Qiao, Z., Shu, X.: Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery. Chaos Solitons Fractals 145, 110813 (2021)

    MathSciNet  Google Scholar 

  9. Moshrefzadeh, A., Fasana, A.: The Autogram: an effective approach for selecting the optimal demodulation band in rolling element bearings diagnosis. Mech. Syst. Signal Process. 105, 294–318 (2018)

    Google Scholar 

  10. Lei, Y., Lin, J., He, Z., Zi, Y.: Application of an improved kurtogram method for fault diagnosis of rolling element bearings. Mech. Syst. Signal Process. 25, 1738–1749 (2011)

    Google Scholar 

  11. Wang, Z., Yang, J., Guo, Y.: Unknown fault feature extraction of rolling bearings under variable speed conditions based on statistical complexity measures. Mech. Syst. Signal Process. 172, 108964 (2022)

    Google Scholar 

  12. Lin, J., Shao, H., Zhou, X., Cai, B., Liu, B.: Generalized MAML for few-shot cross-domain fault diagnosis of bearing driven by heterogeneous signals. Expert Syst. Appl. 230, 120696 (2023)

    Google Scholar 

  13. Liang, P., Xu, L., Shuai, H., Yuan, X., Wang, B., Zhang, L.: Semisupervised subdomain adaptation graph convolutional network for fault transfer diagnosis of rotating machinery under time-varying speeds. IEEE ASME Trans. Mechatron. (2023). https://doi.org/10.1109/TMECH.2023.3292969

    Article  Google Scholar 

  14. Zhao, D., Liu, S., Du, H., Wang, L., Miao, Z.: Deep branch attention network and extreme multi-scale entropy based single vibration signal-driven variable speed fault diagnosis scheme for rolling bearing. Adv. Eng. Inform. 55, 101844 (2023)

    Google Scholar 

  15. Benzi, R., Parisi, G., Sutera, A., Vulpiani, A.: Stochastic resonance in climatic change. Tellus 34, 10–16 (1982)

    Google Scholar 

  16. Lu, S., He, Q., Hu, F., Kong, F.: Sequential multiscale noise tuning stochastic resonance for train bearing fault diagnosis in an embedded system. IEEE Trans. Instrum. Meas. 63, 106–116 (2013)

    Google Scholar 

  17. Qiao, Z., Lei, Y., Lin, J., Jia, F.: An adaptive unsaturated bistable stochastic resonance method and its application in mechanical fault diagnosis. Mech. Syst. Signal Process. 84, 731–746 (2017)

    Google Scholar 

  18. Lu, S., He, Q., Zhang, H., Kong, F.: Enhanced rotating machine fault diagnosis based on time-delayed feedback stochastic resonance. J. Vib. Acoust. 137, 051008 (2015)

    Google Scholar 

  19. He, L., Hu, D., Zhang, G., Lu, S.: Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection. Mod. Phys. Lett. B 33, 1950341 (2019)

    MathSciNet  Google Scholar 

  20. Zhang, G., Wang, H., Zhang, T.Q.: Stochastic resonance of coupled time-delayed system with fluctuation of mass and frequency and its application in bearing fault diagnosis. J. Cent. South Univ. 28, 2931–2946 (2021)

    Google Scholar 

  21. Li, M., Shi, P., Zhang, W., Han, D.: A novel underdamped continuous unsaturation bistable stochastic resonance method and its application. Chaos Solitons Fractals 151, 111228 (2021)

    MathSciNet  Google Scholar 

  22. Shi, P., Xia, H., Han, D., Fu, R., Yuan, D.: Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise. Chaos Solitons Fractals 108, 8–14 (2018)

    MathSciNet  Google Scholar 

  23. Zhang, W., Shi, P., Li, M., Han, D.: A novel stochastic resonance model based on bistable stochastic pooling network and its application. Chaos Solitons Fractals 145, 110800 (2021)

    MathSciNet  Google Scholar 

  24. Zhang, G., Zhang, Y., Zhang, T., Xiao, J.: Stochastic resonance in second-order underdamped system with exponential bistable potential for bearing fault diagnosis. IEEE Access 6, 42431–42444 (2018)

    Google Scholar 

  25. Lu, S., He, Q., Kong, F.: Effects of underdamped step-varying second-order stochastic resonance for weak signal detection, Digit. Signal Process. 36, 93–103 (2015)

    MathSciNet  Google Scholar 

  26. He, C., Niu, P., Yang, R., Wang, C., Li, Z., Li, H.: Incipient rolling element bearing weak fault feature extraction based on adaptive second-order stochastic resonance incorporated by mode decomposition. Measurement 145, 687–701 (2019)

    Google Scholar 

  27. Qiao, Z., Elhattab, A., Shu, X., He, C.: A second-order stochastic resonance method enhanced by fractional-order derivative for mechanical fault detection. Nonlinear Dyn. 106, 707–723 (2021)

    Google Scholar 

  28. Tang, L., Wang, Y., Li, Y., Feng, H., Lu, J., Li, J.: Preparation, structure, and electrochemical properties of reduced graphene sheet films. Adv. Funct. Mater. 19, 2782–2789 (2009)

    Google Scholar 

  29. Geim, A.K.: Graphene: status and prospects. Science 324, 1530–1534 (2009)

    Google Scholar 

  30. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Electricfield effect in atomically thin carbon films. Science 306, 666–669 (2004)

    Google Scholar 

  31. Liu, Y., Ge, X., Li, J.: Graphene lubrication. Appl. Mater. Today 20, 100662 (2020)

    Google Scholar 

  32. Alkahtani, B.S.T., Atangana, A.: Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order. Chaos Solitons Fractals 89, 539–546 (2016)

    MathSciNet  Google Scholar 

  33. Baleanu, D., Ghassabzade, F.A., Nieto, J.J., Jajarmi, A.: On a new and generalized fractional model for a real cholera outbreak. Alex. Eng. J. 61, 9175–9186 (2022)

    Google Scholar 

  34. Caputo, M., Fabrizio, M.: On the singular kernels for fractional derivatives. Some applications to partial differential equations. Progr. Fract. Differ. Appl. 7, 79–82 (2021)

    Google Scholar 

  35. Losada, J., Nieto, J.J.: Fractional integral associated to fractional derivatives with nonsingular kernels. Progr. Fract. Differ. Appl. 7, 137–143 (2022)

    Google Scholar 

  36. Xu, X., Lei, Y., Li, Z.: An incorrect data detection method for big data cleaning of machinery condition monitoring. IEEE Trans. Ind. Electron. 67, 2326–2336 (2019)

    Google Scholar 

  37. Xu, X., Hu, S., Shao, H., Shi, P., Li, R., Li, D.: A spatio-temporal forecasting model using optimally weighted graph convolutional network and gated recurrent unit for wind speed of different sites distributed in an offshore wind farm. Energy 284, 128565 (2023)

    Google Scholar 

  38. Antoni, J.: The infogram: entropic evidence of the signature of repetitive transients. Mech. Syst. Signal Process. 74, 73–94 (2016)

    Google Scholar 

  39. Yang, J.H., Sanjuán, M.A.F., Liu, H.G., Litak, G., Li, X.: Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system. Commun. Nonlinear Sci. Numer. Simul. 41, 104–117 (2016)

    MathSciNet  Google Scholar 

  40. Caponetto, R., Dongola, G., Fortuna, L., Petráš, I.: Fractional Order Systems: Modeling and Control. World Scientific, Singapore (2010)

    Google Scholar 

  41. Chen, M., Shi, J., Deng, W.: High order algorithms for Fokker-Planck equation with Caputo–Fabrizio fractional derivative (2018). arXiv:1809.03263

  42. Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 1, 79–82 (2015)

    Google Scholar 

  43. Wu, C., Yang, J., Huang, D., Liu, H., Hu, E.: Weak signal enhancement by the fractional-order system resonance and its application in bearing fault diagnosis. Meas. Sci. Technol. 30, 035004 (2019)

    Google Scholar 

  44. Petráš, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Higher Education Press, Beijing (2011)

    Google Scholar 

  45. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D., Feliu, V.: Fractional-Order Systems and Controls: Fundamentals and Applications. Springer, London (2010)

    Google Scholar 

  46. Yu, T., Zhang, L., Luo, M.K.: Stochastic resonance in the fractional Langevin equation driven by multiplicative noise and periodically modulated noise. Phys. Scr. 88, 045008 (2013)

    Google Scholar 

  47. Lei, Y.: Intelligent Fault Diagnosis and Remaining Useful Life Prediction of Rotating Machinery. Butterworth-Heinemann, Oxford (2016)

    Google Scholar 

  48. Zhu, Q., Feng, J., Huang, J.: Natural neighbor: a self-adaptive neighborhood method without parameter K. Pattern Recognit. Lett. 80, 30–36 (2016)

    Google Scholar 

  49. Xu, X., Hu, S., Shi, P., Shao, H., Li, R., Li, Z.: Natural phase space reconstruction-based broad learning system for short-term wind speed prediction: case studies of an offshore wind farm. Energy 262, 125342 (2023)

    Google Scholar 

  50. Pukelsheim, F.: The three sigma rule. Am. Stat. 48, 88–91 (1994)

    MathSciNet  Google Scholar 

  51. Yu, K., Lin, T.R., Tan, J., Ma, H.: An adaptive sensitive frequency band selection method for empirical wavelet transform and its application in bearing fault diagnosis. Measurement 134, 375–384 (2019)

    Google Scholar 

  52. CM Benchmarking Vibration Data. <https://pfs.nrel.gov/login.html> (accessed 2017.02.22).

  53. Qin, Y., Xing, J., Mao, Y.: Weak transient fault feature extraction based on an optimized Morlet wavelet and kurtosis. Meas. Sci. Technol. 27, 085003 (2016)

    Google Scholar 

Download references

Funding

This research is supported by Hebei Provincial Natural Science Foundation of China (E2022203093), Open Fund of Key Laboratory of Oil & Gas Equipment, Ministry of Education of Southwest Petroleum University (OGE202302-13) and Cultivation Project for Basic Research and Innovation of Yanshan University (2021LGQN022).

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, Hebei, China

    Xuefang Xu, Bo Li & Peiming Shi

  2. Xi’an Jieda Measurement & Control Co., Ltd., Xi’an, 710199, Shaanxi, China

    Wenyue Zhang

  3. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Ruixiong Li

Authors
  1. Xuefang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenyue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ruixiong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peiming Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuefang Xu.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, X., Li, B., Zhang, W. et al. Caputo–Fabrizio fractional stochastic resonance with graphene potential enhanced by NLOF and its applications in fault diagnosis of rotating machinery. Nonlinear Dyn 112, 2063–2089 (2024). https://doi.org/10.1007/s11071-023-09149-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-09149-4

Keywords

Search

Navigation