Advertisement

Rényi Entropy Based Statistical Complexity Analysis for Gear Fault Prognostics under Variable Load

  • Pavle Boškoski
  • Đani Juričić

Abstract

In this paper we propose an approach for gear fault prognostics in presumably non-stationary and unknown operating conditions. The approach monitors the evolution of the statistical complexity of the generated vibrations envelope vis-à-vis its Rényi entropy. The statistical complexity is obtained through the wavelet coefficients calculated from the generated vibrations. Such an approach allows seamless estimation of the remaining useful life of the monitored drive without any prior information about the operating conditions and no a priori data regarding the physical characteristics of the monitored drive. The effectiveness of the approach was evaluated on experiments monitoring natural gear fault progress under variable load.

Keywords

Statistical Complexity Vibration Signal Wavelet Packet Wavelet Packet Transform Gear Fault 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adami, C.: What is complexity? Bio Essays 24(12), 1085–1094 (2002)Google Scholar
  2. 2.
    Antoni, J.: Cyclostationarity by examples. Mechanical Systems and Signal Processing 23, 987–1036 (2009)CrossRefGoogle Scholar
  3. 3.
    Bartelmus, W., Zimroz, R.: A new feature for monitoring the condition of gearboxes in non–stationary operating conditions. Mechanical Systems and Signal Processing 23(5), 1528–1534 (2009)CrossRefGoogle Scholar
  4. 4.
    Basseville, M.: Divergence measures for statistical data processing. Tech. rep., IRISA (2010)Google Scholar
  5. 5.
    Baydar, N., Ball, A.: Detection of gear deterioration under variying load conditions using the instantaneous power spectrum. Mechanical Systems and Signal Processing 14(6), 907–921 (2000)CrossRefGoogle Scholar
  6. 6.
    Blanco, S., Figliola, A., Quiroga, R.Q., Rosso, O.A., Serrano, E.: Time-frequency analysis of electroencephalogram series. iii. wavelet packets and information cost function. Phys. Rev. E 57(1), 932–940 (1998)CrossRefGoogle Scholar
  7. 7.
    Bole, B.M., Brown, D.W., Pei, H., Goebel, K., Vachtsevanos, L.T.G.: Fault adaptive control of overactuated systems using prognostic estimation. In: Annual Conference of the Prognostics and Health Management Society, Portland OR, USA (2010)Google Scholar
  8. 8.
    Chen, P., Taniguchi, M., Toyota, T., He, Z.: Fault diagnosis method for machinery in unsteady operating condition by instantaneous power spectrum and genetic programming. Mechanical Systems and Signal Processing 19(1), 175–194 (2005)CrossRefGoogle Scholar
  9. 9.
    Gašperin, M., Boškoski, P., Juričić, Đ.: Model-based prognostics under non-stationary operating conditions. In: Annual Conference of the Prognostics and Health Management Society (2011)Google Scholar
  10. 10.
    Hero, A.O., Ma, B., Michel, O., Gorman, J.: Alpha-divergence for classification, indexing and retrieval. Tech. Rep. CSPL-328, Communications and Signal Processing Laboratory. The University of Michigan (2002)Google Scholar
  11. 11.
    Howard, I., Jia, S., Wang, J.: The dynamic modelling of a spur gear in mesh including friction and crack. Mechanical Systems and Signal Processing 15, 831–853 (2001)CrossRefGoogle Scholar
  12. 12.
    Kowalski, A.M., Martin, M.T., Plastino, A., Rosso, O.A., Casas, M.: Distances in probability space and the statistical complexity setup. Entropy 13(6), 1055–1075 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Mallat, S.: A Wavelet Tour of Signal Processing, 3rd edn. Academic Press, Burlington (2008)Google Scholar
  14. 14.
    Martin, M., Plastino, A., Rosso, O.: Generalized statistical complexity measures: Geometrical and analytical properties. Physica A 369(2), 439–462 (2006)CrossRefGoogle Scholar
  15. 15.
    Priestley, M.: Spectral Analyses and Time Series. Academic Press, London (1981)Google Scholar
  16. 16.
    López-Ruiz, R., Mancini, H.L., X.C.: A statistical measure of complexity. Physics Letters A 209, 321–326 (1995)Google Scholar
  17. 17.
    Randall, R.: A new method of modeling gear faults. Journal of Mechanical Design 104, 259–267 (1982)CrossRefGoogle Scholar
  18. 18.
    Randall, R.B.: Vibration-based condition monitoring: industrial, aerospace and automotive applications. John Wiley & Sons, West Sussex (2011)CrossRefGoogle Scholar
  19. 19.
    Rényi, A.: On measures of information and entropy. In: 4th Berkeley Symposium on Mathematics, Statistics and Probability (1960)Google Scholar
  20. 20.
    Rosso, O., Martin, M., Figliola, A., Keller, K., Plastino, A.: EEG analysis using wavelet-based information tools. Journal of Neuroscience Methods 153, 163–182 (2006)CrossRefGoogle Scholar
  21. 21.
    Stander, C., Heyns, P.: Instantaneous angular speed monitoring of gearboxes under non-cyclic stationary load conditions. Mechanical Systems and Signal Processing 19(4), 817–835 (2005)CrossRefGoogle Scholar
  22. 22.
    Wang, X., Makis, V., Yang, M.: A wavelet approach to fault diagnosis of a gearbox under varying load conditions. Journal of Sound and Vibration 329(9), 1570–1585 (2010)CrossRefGoogle Scholar
  23. 23.
    Zhan, Y., Makis, V., Jardine, A.K.: Adaptive state detection of gearboxes under varying load conditions based on parametric modelling. Mechanical Systems and Signal Processing 20(1), 188–221 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Jožef Stefan InstituteLjubljanaSlovenia

Personalised recommendations