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Time Series Modelling of Non-stationary Vibration Signals for Gearbox Fault Diagnosis

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Handbook of Advanced Performability Engineering

Abstract

Gearboxes often operate under variable operating conditions, which lead to non-stationary vibration. Vibration signal analysis is a widely used condition monitoring technique. Time series model-based methods have been developed for the study of non-stationary vibration signals, and subsequently, for fault diagnosis of gearboxes under variable operating conditions. This chapter presented the latest methodologies for gearbox fault diagnosis using time series model-based methods. The main contents include widely used time-variant models, parameter estimation and model structure selection methods, model validation criteria, and fault diagnostic schemes based on either model residual signals or model parameters. Illustrative examples are provided to show the applications of model residual-based fault diagnosis methods on an experimental dataset collected from a laboratory gearbox test rig. Future research topics are pointed out at the end.

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References

  1. Carlin, P. W., Laxson, A. S., & Muljadi, E. B. (2003). The history and state of the art of variable-speed wind turbine technology. Wind Energy., 6(2), 129–159.

    Article  Google Scholar 

  2. McBain, J., & Timusk, M. (2009). Fault detection in variable speed machinery: Statistical parameterization. Journal of Sound and Vibration, 327(3), 623–646.

    Article  Google Scholar 

  3. Chen, Y., Liang, X., & Zuo, M. J. (2019). Sparse time series modeling of the baseline vibration from a gearbox under time-varying speed condition. Mech Syst Signal Process., 1(134), 106342.

    Article  Google Scholar 

  4. Chen, Y., Schmidt, S., Heyns, P. S., & Zuo, M. J. (2020). A time series model-based method for gear tooth crack detection and severity assessment under random speed variation. Mechanical System and Signal Processing, 9, 1–32.

    Google Scholar 

  5. Spiridonakos, M. D., & Fassois, S. D. (2014). Non-stationary random vibration modelling and analysis via functional series time-dependent ARMA (FS-TARMA) models—A critical survey. Mechanical System and Signal Processing, 47(1–2), 175–224.

    Article  Google Scholar 

  6. Wyłomańska, A., Obuchowski, J., Zimroz, R., Hurd, H. (2017). Periodic autoregressive modeling of vibration time series from planetary gearbox used in bucket wheel excavator. In: Chaari, F., Leśkow, J., Napolitano, A., Sanchez-Ramirez, A., (Eds.), Cyclostationarity: Theory and Methods [Internet]. Springer International Publishing; 2014 [cited 2017 Mar 31]. pp. 171–86. (Lecture Notes in Mechanical Engineering). Available from: https://link.springer.com/chapter/10.1007/978-3-319-04187-2_12.

  7. Zhan, Y., & Mechefske, C. K. (2007). Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov-Smirnov test statistic—Part I: Compromised autoregressive modeling with the aid of hypothesis tests and simulation analysis. Mechanical System and Signal Processing, 21(5), 1953–1982.

    Article  Google Scholar 

  8. Shao, Y., & Mechefske, C. K. (2009). Gearbox vibration monitoring using extended Kalman filters and hypothesis tests. Journal of Sound and Vibration, 325(3), 629–648.

    Article  Google Scholar 

  9. Spiridonakos, M.D., Fassois, S.D. (2014). Adaptable functional series TARMA models for non-stationary signal representation and their application to mechanical random vibration modeling. Signal Process, 96, Part A, 63–79.

    Google Scholar 

  10. Spiridonakos, M. D., & Fassois, S. D. (2013). An FS-TAR based method for vibration-response-based fault diagnosis in stochastic time-varying structures: Experimental application to a pick-and-place mechanism. Mechanical Systems and Signal Processing, 38(1), 206–222.

    Article  Google Scholar 

  11. Sakellariou, J.S., Fassois, S.D. (2007). A functional pooling framework for the identification of systems under multiple operating conditions. In: 2007 Mediterranean Conference on Control Automation, pp. 1–6.

    Google Scholar 

  12. Kopsaftopoulos, F., Nardari, R., Li, Y.-H., & Chang, F.-K. (2018). A stochastic global identification framework for aerospace structures operating under varying flight states. Mechanical Systems and Signal Processing, 1(98), 425–447.

    Article  Google Scholar 

  13. Sakellariou, J. S., & Fassois, S. D. (2016). Functionally Pooled models for the global identification of stochastic systems under different pseudo-static operating conditions. Mechanical Systems and Signal Processing, 1(72–73), 785–807.

    Article  Google Scholar 

  14. Kopsaftopoulos, F. P., & Fassois, S. D. (2013). A functional model based statistical time series method for vibration based damage detection, localization, and magnitude estimation. Mechanical Systems and Signal Processing, 39(1), 143–161.

    Article  Google Scholar 

  15. Hastie, T., Tibshirani, R., Friedman, J.H. (2009). The Elements of Statistical Learning: data mining, inference, and prediction. [Internet]. 2nd ed. 2009 [cited 2020 Feb 18]. Available from: https://web.stanford.edu/~hastie/ElemStatLearn/.

  16. Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303.

    Article  Google Scholar 

  17. Heyns, T., Godsill, S. J., de Villiers, J. P., & Heyns, P. S. (2012). Statistical gear health analysis which is robust to fluctuating loads and operating speeds. Mechanical Systems and Signal Processing, 27, 651–666.

    Article  Google Scholar 

  18. Yang, M., & Makis, V. (2010). ARX model-based gearbox fault detection and localization under varying load conditions. Journal of Sound and Vibration, 329(24), 5209–5221.

    Article  Google Scholar 

  19. Li, G., McDonald, G.L., Zhao, Q. (2017). Sinusoidal synthesis based adaptive tracking for rotating machinery fault detection. Mechanical Systems and Signal Processing, 83(Supplement C), 356–370.

    Google Scholar 

  20. Hios, J. D., & Fassois, S. D. (2014). A global statistical model based approach for vibration response-only damage detection under various temperatures: A proof-of-concept study. Mechanical Systems and Signal Processing, 49(1), 77–94.

    Article  Google Scholar 

  21. Aravanis, T.-CI., Sakellariou, J.S., Fassois, S.D. (2019). A stochastic Functional Model based method for random vibration based robust fault detection under variable non–measurable operating conditions with application to railway vehicle suspensions. Journal of Sound and Vibration, 115006.

    Google Scholar 

  22. Schmidt, S., Heyns, P. S., & de Villiers, J. P. (2018a). A novelty detection diagnostic methodology for gearboxes operating under fluctuating operating conditions using probabilistic techniques. Mechanical Systems and Signal Processing, 1(100), 152–166.

    Article  Google Scholar 

  23. Chen, Y., Liang, X., & Zuo, M. J. (2020). An improved singular value decomposition-based method for gear tooth crack detection and severity assessment. Journal of Sound and Vibration, 3(468), 115068.

    Article  Google Scholar 

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Acknowledgements

This research is supported by the Natural Science and Engineering Research Council of Canada, Canada [grant number RGPIN-2015-04897, RGPIN-2019-05361]; Future Energy Systems under Canada First Research Excellent Fund [grant number FES-T11-P01, FES-T14-P02]; University of Manitoba Research Grants Program (URGP); Sadler Graduate Scholarship in Mechanical Engineering, Canada; and China Scholarship Council, China [grant number 201506840098].

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Correspondence to Ming J. Zuo .

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Chen, Y., Liang, X., Zuo, M.J. (2021). Time Series Modelling of Non-stationary Vibration Signals for Gearbox Fault Diagnosis. In: Misra, K.B. (eds) Handbook of Advanced Performability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-55732-4_15

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  • DOI: https://doi.org/10.1007/978-3-030-55732-4_15

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  • Online ISBN: 978-3-030-55732-4

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