DOI QR코드

DOI QR Code

Bearing fault detection through multiscale wavelet scalogram-based SPC

  • Jung, Uk (Production and Operations Division, School of Business, Dongguk University) ;
  • Koh, Bong-Hwan (Department of Mechanical, Robotics, and Energy Engineering, Dongguk University-Seoul)
  • 투고 : 2013.07.18
  • 심사 : 2014.01.14
  • 발행 : 2014.09.25

초록

Vibration-based fault detection and condition monitoring of rotating machinery, using statistical process control (SPC) combined with statistical pattern recognition methodology, has been widely investigated by many researchers. In particular, the discrete wavelet transform (DWT) is considered as a powerful tool for feature extraction in detecting fault on rotating machinery. Although DWT significantly reduces the dimensionality of the data, the number of retained wavelet features can still be significantly large. Then, the use of standard multivariate SPC techniques is not advised, because the sample covariance matrix is likely to be singular, so that the common multivariate statistics cannot be calculated. Even though many feature-based SPC methods have been introduced to tackle this deficiency, most methods require a parametric distributional assumption that restricts their feasibility to specific problems of process control, and thus limit their application. This study proposes a nonparametric multivariate control chart method, based on multiscale wavelet scalogram (MWS) features, that overcomes the limitation posed by the parametric assumption in existing SPC methods. The presented approach takes advantage of multi-resolution analysis using DWT, and obtains MWS features with significantly low dimensionality. We calculate Hotelling's $T^2$-type monitoring statistic using MWS, which has enough damage-discrimination ability. A bootstrap approach is used to determine the upper control limit of the monitoring statistic, without any distributional assumption. Numerical simulations demonstrate the performance of the proposed control charting method, under various damage-level scenarios for a bearing system.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

  1. Bakir, S. (2006), "Distribution-free quality control charts based on signed rank-like statistics", Commun. Stat. - Theor. M., 35, 743-757. https://doi.org/10.1080/03610920500498907
  2. Bajgier, S.M. (1992), "The use of bootstrapping to construct limits on control charts", Proceedings of the Decision Science Institute, San Diego, CA.
  3. Chakraborti, S., Van der Laan, P. and Bakir, S.T. (2001), "Nonparametric control chart: an overview and some results", J. Quality Technol., 33(3), 304-315.
  4. Chou, Y.M., Mason, R.L. and Young, J.C. (2001), "The control chart for individual observations from a multivariate non-normal distribution", Commun. Stat. - Simul. C., 30(8-9), 1937-1949.
  5. Cong, F., Chen, J., and Dong, G. (2010), "Research on the order selection of the autoregressive modelling for rolling bearing diagnosis", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 224(10), 2289-2297. https://doi.org/10.1243/09544062JMES1958
  6. Dyer, D. and Stewart, R.M., (1978), "Detection of rolling element bearing damage by statistical vibration analysis", J. Vib. Acoust., 100(2), 229-235.
  7. Efron, B. (1979), "Bootstrap method: another look at jackknife", Ann. Stat., 7(1), 1-26. https://doi.org/10.1214/aos/1176344552
  8. Fan, J. (1996), "Test of significance based on wavelet thresholding and Neyman's truncation", J. Am. Stat. Assoc., 91, 674-688. https://doi.org/10.1080/01621459.1996.10476936
  9. Ganesan, R., Das, T.K. and Venkataraman, V. (2004), "Wavelet-based multiscale statistical process monitoring: A literature review", IIE Trans., 36, 787-806. https://doi.org/10.1080/07408170490473060
  10. Goswami, J.C. and Chan, A.K. (1999), Fundamentals of wavelets: theory, algorithms, and applications, Wiley, New York, NY.
  11. Hall, P., Poskitt, D.S. and Presnell, D. (2001), "Functional data-analytic approach to signal discrimination", Technometrics, 43(1), 1-9. https://doi.org/10.1198/00401700152404273
  12. Hotelling, H. (1947), Multivariate quality control, in techniques of statistical analysis, (Eds. Eisenhart, C., Hastay, M.W. and Wills, W.A. ), McGraw-Hill, New York, NY.
  13. Jardine, A.K.S., Lin D. and Banjevic, D. (2006), "A review on machinery diagnostics and prognostics implementing condition-based maintenance", Mech. Syst. Signal Pr., 20(7), 1483-1510. https://doi.org/10.1016/j.ymssp.2005.09.012
  14. Jeong, M.K., Chen, D. and Lu, J.C. (2003), "Thresholoded scalogram and its applications in process fault detection", Appl. Stoch. Model. Bus., 19, 231-244. https://doi.org/10.1002/asmb.495
  15. Jones, L.A. and Woodall, W.H. (1998), "The performance of bootstrap control charts", J. Quality Technol., 30(4), 362-375.
  16. Jung, U., Jeong, M.K. and Lu, J.C. (2006), "A vertical-energy-thresholding procedure for data reduction with multiple complex curves", IEEE T. Syst. Man. Cy. - B, 36(5), 1128-1138. https://doi.org/10.1109/TSMCB.2006.874681
  17. Jung, U. and Koh, B.H. (2009), "Structural damage localization using wavelet-based silhouette statistics", J. Sound Vib., 321, 590-604. https://doi.org/10.1016/j.jsv.2008.10.016
  18. Kim, S.H., Alexopoulos, C., Tsui, K.L. and Wilson, J.R. (2007), "A distribution-free tabular CUSUM chart for autocorrelated data", IIE Trans., 39(3), 317-330. https://doi.org/10.1080/07408170600743946
  19. Koh, B.H., Nagarajaiah, S. and Phan, M.Q. (2008), "Reconstructing structural changes in a dynamic system from experimentally identified state-space models", J. Mech. Sci. Technol., 22(1), 103-112. https://doi.org/10.1007/s12206-007-1012-y
  20. Kresta, J., MacGregor, J.F. and Marlin, T.E. (1991), "Multivariate statistical monitoring of process operating performance", Can J. Chem. En., 69(1), 35-47. https://doi.org/10.1002/cjce.5450690105
  21. Ku, W., Storer, R.H. and Georgakis, C. (1995), "Disturbance detection and isolation by dynamic principal component analysis", Chemomet. Intell. Lab., 30(1), 179-196. https://doi.org/10.1016/0169-7439(95)00076-3
  22. Law, S.S., Li, X.Y., Zhu, X.Q. and Chan, S.L. (2005), "Structural damage detection from wavelet packet sensitivity", Eng. Struct., 27, 1339-1348. https://doi.org/10.1016/j.engstruct.2005.03.014
  23. Lei, Y., He, Z. and Zi, Y. (2011), "EEMD method and WNN for fault diagnosis of locomotive roller bearings", Expert Syst. Appl., 38(6), 7334-7341. https://doi.org/10.1016/j.eswa.2010.12.095
  24. Li, H., Deng, X. and Dai, H. (2007), "Structural damage detection using the combination method of EMD and wavelet analysis", Mech. Syst. Signal Pr., 21, 298-306. https://doi.org/10.1016/j.ymssp.2006.05.001
  25. Li, Z., Xia, S., Wang, J. and Su, X. (2006), "Damage detection of cracked beams based on wavelet transform", Int. J. Impact Eng., 32, 1190-1200. https://doi.org/10.1016/j.ijimpeng.2004.09.012
  26. Lin, J. and Zhang, A. (2005), "Fault feature separation using wavelet-ICA filter", NDT&E Int., 38(6), 421-427. https://doi.org/10.1016/j.ndteint.2004.11.005
  27. Lio, Y.L. and Park, C. (2008), "A bootstrap control chart for Birnbaum-Saunders percentiles", Qual. Reliab. Eng. Int., 24, 585-600. https://doi.org/10.1002/qre.924
  28. Liu, R.Y. and Tang, J. (1996), "Control charts for dependent and independent measurements based on bootstrap methods", J. Am. Stat. Assoc., 91, 1694-1700. https://doi.org/10.1080/01621459.1996.10476740
  29. Liu, R.Y., Singh, K. and Teng, J.H. (2004), "DDMA-charts: nonparametric multivariate moving average control charts based on data depth", Allgemeines Stat. Archiv., 88(2), 235-258. https://doi.org/10.1007/s101820400170
  30. MacGregor, J.F. and Kourti, T. (1995), "Statistical process control of multivariate processes", Control Eng. Pract., 3(3), 403-414. https://doi.org/10.1016/0967-0661(95)00014-L
  31. Mallat, S.G. (1989), A wavelet tour of signal processing, Academic Press, San Diego.
  32. McFadden, P.D. and Smith, J.D. (1984), "Model for the vibration produced by a single point defect in a rolling element bearing", J. Sound Vib., 96(1), 69-82. https://doi.org/10.1016/0022-460X(84)90595-9
  33. Mason, R.L. and Young, J.C. (2002), Multivariate statistical process control with industrial applications, ASA/SIAM: Philadelphia, PA.
  34. Peng, Z., Chu, F. and He, Y. (2002), "Vibration signal analysis and feature extraction based on reassigned wavelet scalogram", J. Sound Vib., 253(5), 1087-1100. https://doi.org/10.1006/jsvi.2001.4085
  35. Phaladiganon, P., Kim, S.B., Chen, V.C.P., Baek, J.G. and Park, S.K. (2011), "Bootstrap-based $T^{2}$ multivariate control charts", Commun. Stat. - Simul. C., 40, 645-662. https://doi.org/10.1080/03610918.2010.549989
  36. Polansky, A.M. (2005), "A general framework for constructing control charts", Qual. Reliab. Eng. Int., 21, 633-653. https://doi.org/10.1002/qre.680
  37. Prabhakar, S., Mohanty, A.R. and Sekhar, A.S. (2002), "Application of discrete wavelet transform for detection of ball bearing race faults", Tribol. Int., 35(12), 793-800. https://doi.org/10.1016/S0301-679X(02)00063-4
  38. Qiu, P. (2008), "Distribution-free multivariate process control based on log-linear modeling", IIE Trans., 40(7), 664-677. https://doi.org/10.1080/07408170701744843
  39. Randall, R.B. and Antoni, J. (2011), "Rolling element bearing diagnostics - a tutorial", Mech. Syst. Signal Pr., 25(2), 485-520. https://doi.org/10.1016/j.ymssp.2010.07.017
  40. Rioul, O. and Vetterli, M. (1991), "Wavelets and signal processing", IEEE Signal Proc. Mag., 14-38.
  41. Royston, J.P. (1983), "Sone techniques for assessing multivariate normality based on the Shapiro-Wilk W", Appl. Stat., 32(2), 121-133. https://doi.org/10.2307/2347291
  42. Scargle, J.D. (1997), Wavelet methods in astronomical time series analysis, Application of Time Series Analysis in Astronomy and Meteorology, Chapman & Hall, New York.
  43. Seber, G.A.F. (1984), Multivariate observations, Wiley, New York.
  44. Seppala, T., Moskowitz, H., Plante, R. and Tang, J. (1995), "Statistical process control via the subgroup bootstrap", J. Qual. Technol., 27, 139-153.
  45. Sohn, H., Czarnecki, J.J. and Farrar, C.R. (2000), "Structural health monitoring using statistical process control", J. Struct. Eng. - ASCE, 126, 1356-1363. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:11(1356)
  46. Stoumbos, Z.G., Reynolds, M.R., Ryan, T.P. and Woodall, W.H. (2000), "The state of statistical process control as we proceed into the 21st century", J. Am. Stat. Assoc., 95, 992-998. https://doi.org/10.1080/01621459.2000.10474292
  47. Sukchotrat, T., Kim, S.B. and Tsung, F. (2010), "One-class classification-based control chart for multivariate process monitoring", IIE Trans., 42, 107-120.
  48. Vidakovic, B. (1999), Statistical modeling by wavelets, John Wiley & Sons.
  49. Wang, W. and Wong A.K. (2002), "Autoregressive model-based gear fault diagnosis", J. Vib. Acoust., 124, 172-179. https://doi.org/10.1115/1.1456905
  50. Woodall, W.H. (2000), "Controversies and contradictions in statistical process control", J. Qual. Technol., 32(4), 341-350.
  51. Woodall, W.H. and Montgomery, D.C. (1999), "Research issues and ideas in statistical process control", J. Qual. Technol., 31(4), 376-386.
  52. Yu, Y., Yu, D. and Junsheng, C. (2006), "A roller bearing fault diagnosis method based on EMD energy entropy and ANN", J. Sound Vib., 294(1-2), 269-277. https://doi.org/10.1016/j.jsv.2005.11.002

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