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Remaining useful life estimation based on Wiener degradation processes with random failure threshold

  • Mechanical Engineering, Control Science and Information Engineering
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Abstract

Remaining useful life (RUL) estimation based on condition monitoring data is central to condition based maintenance (CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold (RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization (EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.

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References

  1. VAIDYA P, RAUSAND M. Remaining useful life, technical health, and life extension [J]. Proceedings of the Institution of Mechanical Engineers Part O: Journal of Risk and Reliability, 2011, 225(2): 219–231.

    Google Scholar 

  2. LORTON A, FOULADIRAD M, GRALL A. Computation of remaining useful life on a physic-based model and impact of a prognosis on the maintenance process [J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2013, 227(4): 434–449.

    MATH  Google Scholar 

  3. BO S, SHENGKUI Z, RUI K, PECHT M G. Benefits and challenges of system prognostics [J]. IEEE Transactions on Reliability, 2012, 61(2): 323–335.

    Article  Google Scholar 

  4. SI X, WANG W, HU C, ZHOU D. Remaining useful life estimation–A review on the statistical data driven approaches [J]. European Journal of Operational Research, 2011, 213(1): 1–14.

    Article  MathSciNet  Google Scholar 

  5. CARR M J, WANG W. An approximate algorithm for prognostic modelling using condition monitoring information [J]. European Journal of Operational Research, 2011, 211(1): 90–96.

    Article  MATH  Google Scholar 

  6. WANG H, JIANG Y. Performance reliability prediction of complex system based on the condition monitoring information [J]. Mathematical Problems in Engineering, 2013, 2013: 1–7.

    MathSciNet  Google Scholar 

  7. WANG X L, JIANG P, GUO B, CHENG Z J. Real-time reliability evaluation based on damaged measurement degradation data [J]. Journal of Central South University, 2012, 19(11): 3162–3169.

    Article  Google Scholar 

  8. SI X, WANG W, HU C H, ZHOU D H, PECHT M G. Remaining useful life estimation based on a nonlinear diffusion degradation process [J]. IEEE Transactions on Reliability, 2012, 61(1): 50–67.

    Article  Google Scholar 

  9. PENG C, TSENG S. Mis-specification analysis of linear degradation models [J]. IEEE Transactions on Reliability, 2009, 58(3): 444–455.

    Article  Google Scholar 

  10. WANG X. Wiener processes with random effects for degradation data [J]. Journal of Multivariate Analysis, 2010, 101(2): 340–351.

    Article  MathSciNet  MATH  Google Scholar 

  11. TANG S, GUO X, YU C, XUE H, ZHOU Z. Accelerated degradation tests modeling based on the nonlinear Wiener process with random effects [J]. Mathematical Problems in Engineering, 2014, 2014: 1–11.

    Google Scholar 

  12. WANG W, CARR M, XU W, KOBBACY K. A model for residual life prediction based on Brownian motion with an adaptive drift [J]. Microelectronics Reliability, 2011, 51(2): 285–293.

    Article  Google Scholar 

  13. YE Z, TSUI K L, WANG Y, PECHT M G. Degradation data analysis using wiener processes with measurement errors [J]. IEEE Transactions on Reliability, 2013, 62(4): 772–780.

    Article  Google Scholar 

  14. TANG S, YU C, WANG X, GUO X, SI X. Remaining useful life prediction of Lithium-ion batteries based on the Wiener process with measurement error [J]. Energies, 2014, 7(2): 520–547.

    Article  Google Scholar 

  15. TANG S, GUO X, ZHOU Z. Mis-specification analysis of linear Wiener process–based degradation models for the remaining useful life estimation [J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2014, 228(5): 478–487.

    Google Scholar 

  16. YE Z, SHEN Y, XIE M. Degradation-based burn-in with preventive maintenance [J]. European Journal of Operational Research, 2012, 221(2): 360–367.

    Article  MathSciNet  MATH  Google Scholar 

  17. GEBRAEEL N Z, LAWLEY M A, LI R, RYAN J K. Residual-life distributions from component degradation signals: A Bayesian approach [J]. IIE Transactions, 2005, 37(6): 543–557.

    Article  Google Scholar 

  18. YE Z, CHEN N, TSUI K L. A Bayesian approach to condition monitoring with imperfect inspections [J]. Quality and Reliability Engineering International, 2015, 31(3): 513–522.

    Article  Google Scholar 

  19. WANG X, GUO B, CHENG Z. Residual life estimation based on bivariate Wiener degradation process with time-scale transformations [J]. Journal of Statistical Computation and Simulation, 2012, 84(3): 1–19.

    MathSciNet  Google Scholar 

  20. SI X, WANG W, HU C, ZHOU D. Remaining useful life estimation–A review on the statistical data driven approaches [J]. European Journal of Operational Research, 2011, 213(1): 1–14.

    Article  MathSciNet  Google Scholar 

  21. WANG X, JIANG P, GUO B, CHENG Z. Real-time reliability evaluation with a general wiener process-based degradation model [J]. Quality and Reliability Engineering International, 2014, 30(2): 205–220.

    Article  Google Scholar 

  22. TANG S, GUO X, YU C, ZHOU Z, ZHOU Z, ZHANG B. Real time remaining useful life prediction based on nonlinear Wiener based degradation processes with measurement errors [J]. Journal of Central South University, 2014, 21(12): 4590–4517.

    Google Scholar 

  23. WANG X, BALAKRISHNAN N, GUO B. Residual life estimation based on a generalized Wiener degradation process [J]. Reliability Engineering & System Safety, 2014, 124: 13–23.

    Article  Google Scholar 

  24. XU Z, JI Y, ZHOU D. Real-time reliability prediction for a dynamic system based on the hidden degradation process identification [J]. IEEE Transactions on Reliability, 2008, 57(2): 230–242.

    Article  Google Scholar 

  25. FENG L, WANG H, SI X, ZOU H. A State-space-based prognostic model for hidden and age-dependent nonlinear degradation process [J]. IEEE Transactions on Automation Science and Engineering, 2013, (10)4: 1072–1086.

    Article  Google Scholar 

  26. WANG X, GUO B, CHENG Z, JIANG P. Residual life estimation based on bivariate Wiener degradation process with measurement errors [J]. Journal of Central South University, 2013, 20(7): 1844–1851.

    Article  Google Scholar 

  27. WANG P, COIT D W. Reliability and degradation modeling with random or uncertain failure threshold [C]// Proceedings of the Reliability and Maintainability Symposium, 2007 RAMS '07 Annual. Orlando, FL: IEEE, 2007: 392–397.

    Chapter  Google Scholar 

  28. WANG W. A two-stage prognosis model in condition based maintenance [J]. European Journal of Operational Research, 2007, 182(3): 1177–1187.

    Article  MATH  Google Scholar 

  29. WEI M, CHEN M, ZHOU D. Multi-sensor information based remaining useful life prediction with anticipated performance [J]. IEEE Transactions on Reliability, 2013, 62(1): 183–198.

    Article  Google Scholar 

  30. ZIO E, COMPARE M. Evaluating maintenance policies by quantitative modeling and analysis [J]. Reliability Engineering & System Safety, 2013, 109: 53–65.

    Article  Google Scholar 

  31. USYNIN A, HINES J W, URMANOV A. Uncertain failure thresholds in cumulative damage models [C]// Proceedings of the Reliability and Maintainability Symposium, 2008 RAMS 2008 Annual. Las Vegas: IEEE, 2008: 334–340.

    Chapter  Google Scholar 

  32. JIANG R, JARDINE A K S. Health state evaluation of an item: A general framework and graphical representation [J]. Reliability Engineering & System Safety, 2008, 93(1): 89–99.

    Article  Google Scholar 

  33. JIANG R. A multivariate CBM model with a random and time-dependent failure threshold [J]. Reliability Engineering & System Safety, 2013, 119: 178–185.

    Article  Google Scholar 

  34. GREENE W H. Econometric analysis [M]. 5th Ed, Upper Saddle River. New Jersey: Prentice Hall, 2003: 756–760.

    Google Scholar 

  35. FOLKS J L, CHHIKARA R S. The inverse gaussian distribution and its statistical application-A review [J]. Journal of the Royal Statistical Society Series B: Methodological, 1978, 40(3): 263–289.

    MathSciNet  MATH  Google Scholar 

  36. SI X, WANG W, CHEN M, HU C, ZHOU D. A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution [J]. European Journal of Operational Research, 2013, 226(1): 53–66.

    Article  MathSciNet  MATH  Google Scholar 

  37. SI X, WANG W, HU C, CHEN M, ZHOU D. A Wiener-processbased degradation model with a recursive filter algorithm for remaining useful life estimation [J]. Mechanical Systems and Signal Processing, 2013, 35(1/2): 219–237.

    Article  Google Scholar 

  38. ZHOU Z, HU C, YANG J, XU D, ZHOU D. Online updating belief-rule-base using the RIMER approach [J]. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 2011, 41(6): 1225–1243.

    Article  Google Scholar 

  39. YOU M, LIU F, WANG W, MENG G. Statistically planned and individually improved predictive maintenance management for continuously monitored degrading systems [J]. IEEE Transactions on Reliability, 2010, 59(4): 744–753.

    Article  Google Scholar 

  40. CADINI F, ZIO E, AVRAM D. Model-based Monte Carlo state estimation for condition-based component replacement [J]. Reliability Engineering & System Safety, 2009, 94(3): 752–758.

    Article  Google Scholar 

  41. CURCURÙ G, GALANTE G, LOMBARDO A. A predictive maintenance policy with imperfect monitoring [J]. Reliability Engineering & System Safety, 2010, 95(9): 989–997.

    Article  Google Scholar 

  42. DEMPSTER A P, LAIRD N M, RUBIN D B. Maximum likelihood from incomplete data via the EM algorithm [J]. Journal of the Royal Statistical Society Series B: Methodological, 1977, 39(1): 1–38.

    MathSciNet  MATH  Google Scholar 

  43. YE Z, NG H K T. On analysis of incomplete field failure data [J]. The Annals of Applied Statistics, 2014, 8(3): 1713–1727.

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Correspondence to Chuan-qiang Yu  (于传强).

Additional information

Foundation item: Projects(51475462, 61174030, 61473094, 61374126) supported by the National Natural Science Foundation of China

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Tang, Sj., Yu, Cq., Feng, Yb. et al. Remaining useful life estimation based on Wiener degradation processes with random failure threshold. J. Cent. South Univ. 23, 2230–2241 (2016). https://doi.org/10.1007/s11771-016-3281-z

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  • DOI: https://doi.org/10.1007/s11771-016-3281-z

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