Skip to main content
SpringerLink
Log in

New degradation feature extraction method of planetary gearbox based on alpha stable distribution

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The planetary transmission system has been widely used in industry because of its various advantages. And the study on degradation feature extraction method of planetary gearbox is of major significance for mechanical system prognostics and health management (PHM). In this paper, the alpha stable distribution characteristics of planetary gearbox vibration signals in performance degradation process are verified. By observing the change of alpha stable distribution for planetary gearbox degradation experiment data, a new degradation feature extraction method based on alpha stable distribution is proposed, which is called the height of probability distribution (HPD). Through comparative analysis, it is determined that HPD has better linearity and less fluctuation compared with conventional degradation features in planetary gearbox accelerated degradation stage. Moreover, in the accelerated degradation stage, the degradation trend prediction result based on HPD is closer to the actual data than conventional degradation features no matter using Wiener-based or LSSVM-based prediction method. These conclusions indicate that the newly proposed HPD works well and gives accurate estimates for condition monitoring and degradation trend prediction of planetary gearbox.

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

Similar content being viewed by others

Abbreviations

α :

Characteristic parameter of alpha stable distribution

β :

Symmetry parameter of alpha stable distribution

γ :

Scale parameter of alpha stable distribution

δ :

Location parameter of alpha stable distribution

RMS:

Root mean square

Amp:

Vibration amplitude

f pdf(x):

Probability of vibration amplitude x

HPD:

Height of probability distribution

t r :

Prediction time

Δt :

Time span

Y(t i):

Degradation feature value at time ti

W(t):

Cumulative degradation amount at t

μ :

Drift coefficient of Wiener process

σ :

Diffusion coefficient of Wiener process

B(τ(t, ξ)):

Non-linear Brownian motion

References

  1. Y. Lei, J. Lin, M. Zuo and Z. He, Condition monitoring and fault diagnosis of planetary gearboxes: a review, Measurement, 48 (2014) 292–305.

    Article  Google Scholar 

  2. X. Chen and Z. Feng, Application of reassigned wavelet scalogram in wind turbine planetary gearbox fault diagnosis under nonstationary conditions, Shock and Vibration (2016) 1–12.

  3. Y. Lei et al., Health condition identification of multi-stage planetary gearboxes using a mRVM-based method, Mechanical Systems and Signal Processing, 60–61 (2015) 289–300.

  4. J. Yu et al., Fault diagnosis of planetary gearbox with incomplete information using assignment reduction and flexible naive Bayesian classifier, Journal of Mechanical Science and Technology, 32(1) (2018) 37–47.

    Article  Google Scholar 

  5. F. Chaari, T. Fakhfakh and M. Haddar, Dynamic analysis of a planetary gear failure caused by tooth pitting and cracking, Journal of Failure Analysis and Prevention, 6(2) (2006) 73–78.

    Article  Google Scholar 

  6. F. Chaari, T. Fakhfakh, R. Hbaieb, J. Louati and M. Haddar, Influence of manufacturing errors on the dynamic behavior of planetary gears, The International Journal of Advanced Manufacturing Technology, 27 (2006) 738–746.

    Article  Google Scholar 

  7. Z. Feng and M. Zuo, Vibration signal models for fault diagnosis of planetary gearboxes, Journal of Sound and Vibration, 331(22) (2012) 4919–4939.

    Article  Google Scholar 

  8. X. Chen and Z. Feng, Iterative generalized time-frequency reassignment for planetary gearbox fault diagnosis under non-stationary conditions, Mechanical Systems and Signal Processing, 80 (2016) 429–444.

    Article  Google Scholar 

  9. Y. Lei, D. Kong, J. Lin and M. Zuo, Fault detection of planetary gearboxes using new diagnostic parameters, Measurement Science and Technology, 23(5) (2012) 55605–55614.

    Article  Google Scholar 

  10. W. Bartelmus and R. Zimroz, Vibration condition monitoring of planetary gearbox under varying external load, Mechanical Systems and Signal Processing, 23 (2009) 246–257.

    Article  Google Scholar 

  11. W. Bartelmus and R. Zimroz, A new feature for monitoring the condition of gearboxes in non-stationary operation conditions, Mechanical Systems and Signal Processing, 23 (2009) 1528–1534.

    Article  Google Scholar 

  12. Y. Lei, N. Li, J. Lin and Z. He, Two new features for condition monitoring and fault diagnosis of planetary gearboxes, Journal of Vibration and Control, 21(4) (2015) 755–764.

    Article  Google Scholar 

  13. E. O. Marcos and J. V. George, A particle-filtering approach for on-line fault diagnosis and failure prognosis, Transactions of the Institute of Measurement and Control, 31(3) (2009) 221–246.

    Google Scholar 

  14. Z. Cheng, N. Q. Hu, F. S. Gu and G. J. Qin, Pitting damage level for planetary gear sets based on model simulation and grey relational analysis, Transactions of the Canadian Society for Mechanical Engineering, 35(3) (2011) 403–417.

    Article  Google Scholar 

  15. Z. Cheng and N. Q. Hu, Quantitative damage detection for planetary gear sets based on physical models, Chinese Journal of Mechanical Engineering, 25(1) (2012) 190–196.

    Article  MathSciNet  Google Scholar 

  16. X. Ni et al., Planetary gearbox remaining useful life estimation based on state space model, International Conference Vibroengineering, Nanjing (2015) 253–258.

  17. X. Ni et al., An adaptive state-space model for predicting remaining useful life of planetary gearbox, Prognostics & System Health Management Conference, Chengdu (2016).

  18. W. Jia, E. E. Kuruoglu and T. Zhou, Alpha-stable channel capacity, IEEE Communication Letters, 15(10) (2011) 1107–1109.

    Article  Google Scholar 

  19. A. Banerjee, P. Burlina and R. Chellappa, Adaptive target detection in foliage-penetrating SAR images using alpha-stable models, IEEE Transactions on Image Processing, 8(12) (1999) 1823–1831.

    Article  Google Scholar 

  20. A. S. Carassso, The APEX method in image sharpening and the use of low exponent Levy stable laws, Journal of Applied Mathematics, 63 (2002) 593–618.

    Google Scholar 

  21. G. Yang et al., Communication signal pre-processing in impulsive noise: a bandpass myriad filtering-based method, IEEE Communications Letters, 99 (2018) 1–4.

    Article  Google Scholar 

  22. G. Yu, C. Li and J. Zhang, A new statistical modeling and detection method for rolling element bearing faults based on alpha-stable distribution, Mechanical Systems and Signal Processing, 41 (2013) 155–175.

    Article  Google Scholar 

  23. Z. Grzegorz, J. Obuchowski, W. Agnieszka and R. Zimroz, Application of ARMA modeling and alpha-stable distribution for local damage detection in bearings, Diagnostyka, 15(3) (2014) 3–10.

    Google Scholar 

  24. Z. Grzegorz, J. Obuchowski, W. Agnieszka and R. Zimroz, Application of alpha-stable distribution approach for local damage detection in rotating machines, Journal of Vibroengineering, 17(6) (2015) 2987–3002.

    Google Scholar 

  25. X. Zhang, J. Kang, L. Xiao and J. Zhao, Alpha stable distribution based morphological filter for bearing and gear fault diagnosis in nuclear power plant, Science and Technology of Nuclear Installations (2015) 1–15.

  26. Y. Li et al., A novel fault diagnosis model for bearing of railway vehicles using vibration signals based on symmetric alpha-stable distribution feature extraction, Shock and Vibration, 2016 (2016) 1–13.

    Google Scholar 

  27. W. Agnieszka et al., Application of tempered stable distribution for selection of optimal frequency band in gearbox local damage detection, Applied Acoustics, 128(15) (2017) 14–22.

    Google Scholar 

  28. Y. Liang and W. Chen, A survey on computing Lévy stable distributions and a new Matlab toolbox, Signal Processing, 93 (2013) 242–251.

    Article  Google Scholar 

  29. L. Liao, Discovering prognostic features using genetic programming in remaining useful life prediction, IEEE Transactions on Industrial Electronics, 61(5) (2014) 2464–2472.

    Article  Google Scholar 

  30. X. Ni et al., A new improved kurtogram and its application to planetary gearbox degradation feature analysis, Journal of Vibroengineering, 19(5) (2017) 3413–3428.

    Article  Google Scholar 

  31. J. P. Nolan, Maximum likelihood estimation and diagnostics for stable distributions Lévy processes: theory and applications, Levy Processes, New York (2001) 379–400.

  32. E. F. Fama and R. Roll, Parameter estimates for symmetric stable distributions, Journal of the American Statistical Association, 66(334) (1971) 331–338.

    Article  Google Scholar 

  33. I. A. Koutrouvelis, Regression-type estimation of the parameters of stable laws, Journal of the American Statistical Association, 75(372) (1980) 918–928.

    Article  MathSciNet  Google Scholar 

  34. I. A. Koutrouvelis, An iterative procedure for the estimation of the parameters of stable laws, Communications in Statistics-Simulation and Computation, B10(1) (1981) 17–20.

    Article  MathSciNet  Google Scholar 

  35. M. Shao and C. L. Nikias, Signal processing with fractional lower order moments: stable processes and their applications, Proceedings of the IEEE, 81(7) (1993) 986–1010.

    Article  Google Scholar 

  36. A. Wyłomanska, Application of tempered stable distribution for selection of optimal frequency band in gearbox local damage detection, Applied Acoustics, 128 (2016) 14–22.

    Article  Google Scholar 

  37. G. Yu and N. Shi, Gear fault signal modeling and detection based on alpha stable distribution, International Symposium on Instrumentation & Measurement, Sensor Network and Automation (IMSNA) (2012) 471–474.

  38. S. Alaswad and Y. Xiang, A review on condition-based maintenance optimization models for stochastically deteriorating system, Reliability Engineering and System Safety, 157 (2017) 54–63.

    Article  Google Scholar 

  39. S. T. Kandukuri et al., A review of diagnostics and prognostics of low-speed machinery towards wind turbine farm-level health management, Renewable and Sustainable Energy Reviews, 53 (2016) 697–708.

    Article  Google Scholar 

  40. X. S. Si, W. Wang, C. H. Hu and D. H. Zhou, Remaining useful life estimation-a review on the statistical data driven approaches, European Journal of Operational Research, 213 (2011) 1–14.

    Article  MathSciNet  Google Scholar 

  41. Z. Pan et al., Bivariate degradation analysis of products based on Wiener processes and copulas, Journal of Statistical Computation and Simulation (2012) 1–14.

  42. I. Ntzoufras, Bayesian Modeling Using WinBUGS, John Wiley & Sons, Hoboken (2011).

    MATH  Google Scholar 

  43. C. Lu et al., Degradation trend estimation of slewing bearing based on LSSVM model, Mechanical Systems and Signal Processing, 76–77 (2016) 353–366.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shijiazhuang Campus of Army Engineering University, Shijiazhuang, 050003, China

    Wenxin Qiao

  2. Luoyang Electronic Equipment Test Center of China, Luoyang, 471003, China

    Xianglong Ni, Lei Wang, Xin Lv, Liwei Chen & Fucheng Sun

Authors
  1. Wenxin Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianglong Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xin Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liwei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Fucheng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianglong Ni.

Additional information

Wenxin Qiao is now a Ph.D. student studying at Army Engineering University, Shijiazhuang, China. Her research interests include system prognostics and health management (PHM).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiao, W., Ni, X., Wang, L. et al. New degradation feature extraction method of planetary gearbox based on alpha stable distribution. J Mech Sci Technol 35, 1–19 (2021). https://doi.org/10.1007/s12206-020-1201-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-1201-5

Keywords

Search

Navigation