Uncertainty in Prognostics and Systems Health Management
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Published
Nov 3, 2020
Shankar Sankararaman
Kai Goebel
Abstract
This paper presents an overview of various aspects of uncertainty quantification and management in prognostics and systems health management. Prognostics deals with predicting possible future failures in different types of engineering systems. It is almost practically impossible to precisely predict future events; therefore, it is necessary to account for the different
sources of uncertainty that affect prognostics, and develop a systematic framework for uncertainty quantification and management in this context. Researchers have developed computational methods for prognostics, both in the context of testing-based health management and condition-based health management. This paper explains that the interpretation
of uncertainty for these two different types of situations is completely different. While both the frequentist (based on the presence of true variability) and Bayesian (based on subjective
assessment) approaches are applicable in the context of testing-based health management, only the Bayesian approach is applicable in the context of condition-based health management. This paper illustrates that the computation of the remaining useful life is more meaningful in the context of condition-based monitoring and needs to be approached
as an uncertainty propagation problem. Further, uncertainty management issues are discussed and possible solutions are explored. Numerical examples are presented to illustrate the various concepts discussed in the paper.
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Keywords
prognostics, sensitivity analysis, uncertainty, remaining useful life prediction
References
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Coppe, A., Haftka, R. T., Kim, N. H., & Yuan, F.-G. (2010). Uncertainty reduction of damage growth properties using structural health monitoring. Journal of Aircraft, 47(6), 2030–2038.
Daigle, M. J., & Goebel, K. (2013). Model-based prognostics with concurrent damage progression processes. Systems, Man, and Cybernetics: Systems, IEEE Transactions on, 43(3), 535–546.
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Farrar, C. R., & Lieven, N. A. (2007). Damage prognosis: the future of structural health monitoring. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365(1851), 623–632.
Glynn, P. W., & Iglehart, D. L. (1989). Importance sampling for stochastic simulations. Management Science, 35(11), 1367–1392.
Goebel, K., Saha, B., & Saxena, A. (2008). A comparison of three data-driven techniques for prognostics. In 62nd meeting of the society for machinery failure prevention technology (mfpt) (pp. 119–131).
Gu, J., Barker, D., & Pecht, M. (2007). Uncertainty assessment of prognostics of electronics subject to random vibration. In AAAI fall symposium on artificial intelligence for prognostics (pp. 50–57).
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Hastings, D. and McManus, H. (2004). A framework for understanding uncertainty and its mitigation and exploitation in complex systems. In Engineering Systems Symposium MIT (p. 19). Cambridge MA..
Hohenbichler, M., & Rackwitz, R. (1983). First-order concepts in system reliability. Structural safety, 1(3), 177–188.
Kiureghian, A. D. (1989). Measures of structural safety under imperfect states of knowledge. Journal of Structural Engineering, 115(5), 1119–1140.
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Sankararaman, S., & Goebel, K. (2013b). Remaining useful life estimation in prognosis: An uncertainty propagation problem. In 2013 aiaa infotech@ aerospace conference.
Sankararaman, S., & Goebel, K. (2013c). Why is the remaining useful life prediction uncertain? In Annual conference of the prognostics and health management society.
Sankararaman, S., & Goebel, K. (2014). Uncertainty in prognostics: Computational methods and practical challenges. In Aerospace Conference, 2014 IEEE (pp. 1–9).
Sankararaman, S., Ling, Y., & Mahadevan, S. (2011). Uncertainty quantification and model validation of fatigue crack growth prediction. Engineering Fracture Mechanics, 78(7), 1487–1504.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2011). Uncertainty quantification in fatigue crack growth prognosis. International Journal of Prognostics and Health Management, 2(1), 15 pages.
Sankararaman, S., & Mahadevan, S. (2011). Likelihoodbased representation of epistemic uncertainty due to sparse point data and/or interval data. Reliability Engineering & System Safety, 96(7), 814–824.
Sankararaman, S., & Mahadevan, S. (2013a). Distribution type uncertainty due to sparse and imprecise data. Mechanical Systems and Signal Processing, 37(1), 182–198.
Sankararaman, S., & Mahadevan, S. (2013b). Separating the contributions of variability and parameter uncertainty in probability distributions. Reliability Engineering & System Safety, 112, 187–199.
Sankararaman, S., Saxena, A., & Goebel, K. (2014). Are current prognostic performance evaluation practices sufficient and meaningful? In Proceedings of the 2014 annual conference of the prognostics and health management society.
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine runto- failure simulation. In Prognostics and health management, 2008. phm 2008. international conference on (pp. 1–9).
Saxena, A., Sankararaman, S., & Goebel, K. (2014). Performance evaluation for fleet-based and unit-based prognostic methods. In Second European conference of the Prognostics and Health Management society.
Swanson, D. C. (2001). A general prognostic tracking algorithm for predictive maintenance. In Aerospace conference, 2001, ieee proceedings. (Vol. 6, pp. 2971–2977).
Tang, L., Kacprzynski, G., Goebel, K., & Vachtsevanos, G. (2009, march). Methodologies for uncertainty management in prognostics. In Aerospace conference, 2009 IEEE (p. 1 -12).
Van Zandt, J. R. (2001). A more robust unscented transform. In International symposium on optical science and technology (pp. 371–380).
Zio, E., & Peloni, G. (2011). Particle filtering prognostic estimation of the remaining useful life of nonlinear components. Reliability Engineering & System Safety, 96(3), 403–409.
Bucher, C. G. (1988). Adaptive samplingan iterative fast monte carlo procedure. Structural Safety, 5(2), 119–126.
Caflisch, R. E. (1998). Monte carlo and quasi-monte carlo methods. Acta numerica, 1998, 1–49.
Celaya, J., Saxena, A., & Goebel, K. (2012). Uncertainty representation and interpretation in model-based prognostics algorithms based on kalman filter estimation. In Proceedings of the Annual Conference of the PHM Society (pp. 23–27).
Coppe, A., Haftka, R. T., Kim, N. H., & Yuan, F.-G. (2010). Uncertainty reduction of damage growth properties using structural health monitoring. Journal of Aircraft, 47(6), 2030–2038.
Daigle, M. J., & Goebel, K. (2013). Model-based prognostics with concurrent damage progression processes. Systems, Man, and Cybernetics: Systems, IEEE Transactions on, 43(3), 535–546.
Der Kiureghian, A., Lin, H.-Z., & Hwang, S.-J. (1987). Second-order reliability approximations. Journal of Engineering Mechanics, 113(8), 1208–1225.
Dolinski, K. (1983). First-order second-moment approximation in reliability of structural systems: critical review and alternative approach. Structural Safety, 1(3), 211–231.
Farrar, C. R., & Lieven, N. A. (2007). Damage prognosis: the future of structural health monitoring. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365(1851), 623–632.
Glynn, P. W., & Iglehart, D. L. (1989). Importance sampling for stochastic simulations. Management Science, 35(11), 1367–1392.
Goebel, K., Saha, B., & Saxena, A. (2008). A comparison of three data-driven techniques for prognostics. In 62nd meeting of the society for machinery failure prevention technology (mfpt) (pp. 119–131).
Gu, J., Barker, D., & Pecht, M. (2007). Uncertainty assessment of prognostics of electronics subject to random vibration. In AAAI fall symposium on artificial intelligence for prognostics (pp. 50–57).
Haldar, A., & Mahadevan, S. (2000). Probability, reliability, and statistical methods in engineering design. John Wiley & Sons, Incorporated.
Hastings, D. and McManus, H. (2004). A framework for understanding uncertainty and its mitigation and exploitation in complex systems. In Engineering Systems Symposium MIT (p. 19). Cambridge MA..
Hohenbichler, M., & Rackwitz, R. (1983). First-order concepts in system reliability. Structural safety, 1(3), 177–188.
Kiureghian, A. D. (1989). Measures of structural safety under imperfect states of knowledge. Journal of Structural Engineering, 115(5), 1119–1140.
Kulkarni, C. S., Celaya, J. R., Goebel, K., & Biswas, G. (2013). Physics based electrolytic capacitor degradation models for prognostic studies under thermal overstress. International Journal of Prognostics and Health Management, 4(5).
Liao, H., Zhao, W., & Guo, H. (2006). Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model. In Reliability and Maintainability Symposium, 2006. RAMS’06. Annual (pp. 127–132).
Loh, W.-L. (1996). On latin hypercube sampling. The annals of statistics, 24(5), 2058–2080.
Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vachtsevanos, G. (2008, oct.). Advances in uncertainty representation and management for particle filtering applied to prognostics. In Prognostics and Health Management, 2008. PHM 2008. International Conference on (p. 1 -6). doi: 10.1109/PHM.2008.4711433
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., . . . Tarantola, S. (2008). Global sensitivity analysis: the primer. John Wiley & Sons.
Sankararaman, S. (2015). Significance, interpretation, and quantification of uncertainty in prognostics and remaining useful life prediction. Mechanical Systems and Signal Processing, 52, 228–247.
Sankararaman, S., Daigle, M., & Goebel, K. (2014, June). Uncertainty quantification in remaining useful life prediction using first-order reliability methods. Reliability, IEEE Transactions on, 63(2), 603-619. doi: 10.1109/TR.2014.2313801
Sankararaman, S., & Goebel, K. (2013a). A novel computational methodology for uncertainty quantification in prognostics using the most probable point concept. In Annual conference of the prognostics and health management society.
Sankararaman, S., & Goebel, K. (2013b). Remaining useful life estimation in prognosis: An uncertainty propagation problem. In 2013 aiaa infotech@ aerospace conference.
Sankararaman, S., & Goebel, K. (2013c). Why is the remaining useful life prediction uncertain? In Annual conference of the prognostics and health management society.
Sankararaman, S., & Goebel, K. (2014). Uncertainty in prognostics: Computational methods and practical challenges. In Aerospace Conference, 2014 IEEE (pp. 1–9).
Sankararaman, S., Ling, Y., & Mahadevan, S. (2011). Uncertainty quantification and model validation of fatigue crack growth prediction. Engineering Fracture Mechanics, 78(7), 1487–1504.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2011). Uncertainty quantification in fatigue crack growth prognosis. International Journal of Prognostics and Health Management, 2(1), 15 pages.
Sankararaman, S., & Mahadevan, S. (2011). Likelihoodbased representation of epistemic uncertainty due to sparse point data and/or interval data. Reliability Engineering & System Safety, 96(7), 814–824.
Sankararaman, S., & Mahadevan, S. (2013a). Distribution type uncertainty due to sparse and imprecise data. Mechanical Systems and Signal Processing, 37(1), 182–198.
Sankararaman, S., & Mahadevan, S. (2013b). Separating the contributions of variability and parameter uncertainty in probability distributions. Reliability Engineering & System Safety, 112, 187–199.
Sankararaman, S., Saxena, A., & Goebel, K. (2014). Are current prognostic performance evaluation practices sufficient and meaningful? In Proceedings of the 2014 annual conference of the prognostics and health management society.
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine runto- failure simulation. In Prognostics and health management, 2008. phm 2008. international conference on (pp. 1–9).
Saxena, A., Sankararaman, S., & Goebel, K. (2014). Performance evaluation for fleet-based and unit-based prognostic methods. In Second European conference of the Prognostics and Health Management society.
Swanson, D. C. (2001). A general prognostic tracking algorithm for predictive maintenance. In Aerospace conference, 2001, ieee proceedings. (Vol. 6, pp. 2971–2977).
Tang, L., Kacprzynski, G., Goebel, K., & Vachtsevanos, G. (2009, march). Methodologies for uncertainty management in prognostics. In Aerospace conference, 2009 IEEE (p. 1 -12).
Van Zandt, J. R. (2001). A more robust unscented transform. In International symposium on optical science and technology (pp. 371–380).
Zio, E., & Peloni, G. (2011). Particle filtering prognostic estimation of the remaining useful life of nonlinear components. Reliability Engineering & System Safety, 96(3), 403–409.
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Technical Papers