A Comparison Study of Methods for Parameter Estimation in the Physics-based Prognostics
Prediction of remaining useful life of a system is important for safety and maintenance scheduling. In the physics-based prognostics, the accuracy of predicted remaining useful life is directly related to that of estimated model parameters. It, however, is not a simple task to estimate the model parameters because most real systems have multivariate model parameters, which are often correlated each other. This paper mainly discusses the difference in estimating model parameters among different prognostics methods: the particle filter method, the overall Bayesian method, and the incremental Bayesian method. These methods are based on the same theoretical foundation, Bayesian inference, but they are different from each other in the sampling scheme and/or uncertainty analysis process. A simple analytical example and the Paris model for crack growth are used to demonstrate the difference among the three methods in terms of prognostics metrics. The numerical results show that particle filter and overall Bayesian methods outperform the incremental Bayesian method. Even though the particle filter shows slightly better results in terms of prognostics metrics, the overall Bayesian method is efficient when batch data exist.
How to Cite
particle filter, Markov chain Monte Carlo, Bayesian inference, parameter estimation, physics based prognostics, remaining useful life
An, D., Choi, J. H., Schmitz, T. L., & Kim, N. H., (2011). In-Situ Monitoring and Prediction of Progressive Joint Wear using Bayesian Statistics, Wear, vol. 270(11-12), pp. 828-838.
An, D., Choi, J. H., & Kim, N. H., (2012). Identification of Correlated Damage Parameters under Noise and Bias Using Bayesian Inference. Structural Health Monitoring, vol. 11(3), pp. 292-302.
Andrieu, C., Freitas, de N., Doucet, A., & Jordan, M., (2003). An Introduction to MCMC for Machine Learning. Machine Learning, vol. 50(1), pp. 5-43.
Bayes, T., (1763). An Essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, vol. 53, pp. 370-418. Campillo, F., & Rossi, V., (2009). Convolution Particle Filter for Parameter Estimation in General State-Space Models. IEEE Transactions on Aerospace and Electronic Systems, vol. 45, pp. 1063-1072.
Daigle, M., & Goebel, K., (2011). Multiple Damage Progression Paths in Model-based Prognostics. Aerospace Conference, 2011 IEEE.
DeCastro, J. A., Tang, L., Loparo, K. A., Goebel, K., and Vachtsevanos, G., (2009). Exact Nonlinear Filtering and Prediction in Process Model-based Prognostics. Annual Conference of the Prognostics and Health Management Society.
Gašperin, M., Juričić, Ð., Boškoski, P., & Vižintin, J., (2011). Model-based Prognostics of Gear Health using Stochastic Dynamical Models. Mechanical Systems and Signal Processing, vol. 25, pp. 537-548.
Giurgiutiu, V., (2008). Structural Health Monitoring: with Piezoelectric Wafer Active Sensors, Academic Press (an Imprint of Elsevier). Burlington, MA.
Glynn, P. W., & Iglehart, D. L., (1989). Importance Sampling for Stochastic Simulations. Management Science, vol. 35(11), pp. 1367-1392.
Haldar, A., & Mahadevan, S., (2000). Probability, reliability, and statistical methods in engineering design. New York: John Wiley & Sons, Inc.
Julier, S. J., & Uhlmann, J. K., (1997). A New Extension of the Kalman Filter to Nonlinear Systems. In Proc. of AeroSense: The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls.
Kalman, R. E., (1960). A New Approach to Linear Filtering and Prediction Problems. Transaction of the ASMEJournal of Basic Engineering, vol. 82(1), pp. 35-45.
Li, P., Goodall, R., & Kadirkamanathan, V., (2003).Parameter Estimation of Railway Vehicle Dynamic Model using Rao-Blackwellised Particle Filter. In Proceedings of the European Control Conference. Cambridge, UK.
Luo, J., Pattipati, K.R., Qiao, L., & Chigusa, S., (2008).Model-based Prognostic Techniques Applied to a Suspension System. IEEE Transactions on System, Man and Cybernetics, vol. 38(5), pp. 1156-1168.
Orchard, M. E., & Vachtsevanos, G. J., (2007). A Particle Filtering Approach for On-Line Failure Prognosis in a Planetary Carrier Plate. International Journal of Fuzzy Logic and Intelligent Systems, vol. 7(4), pp. 221-227.
Paris, P. C., & Erdogan, F., (1963). A Critical Analysis of Crack Propagation Laws. ASME Journal of Basic Engineering, vol. 85, pp. 528–534.
Park, B. J., Zhang, Y., Lord, D., (2010). Bayesian Mixture Modeling Approach to Account for Heterogeneity in Speed Data. Transportation Research Part Bmethodological, vol. 44(5), pp. 662-673.
Payne, S. J., (2005). A Bayesian Approach for the Estimation of Model Parameters from Noisy Data Sets. IEEE Signal Processing Letters, vol. 12(8), pp. 553-556.
Rago, C., Prasanth,R., Mehra, R. K., & Fortenbaugh, R., (1998). Failure Detection and Identification and Fault Tolerant Control using the IMM-KF with applications to the Eagle-Eye UAV. Proceedings of the 37th IEEE, Conference on Decision & Control. Tampa, Florida, USA, December.
Ristic, B., Arulampalam, S., & Gordon, N., (2004). Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House.
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K., (2009). On Applying the Prognostic Performance Metrics. Annual Conference of the Prognostics and Health Management Society.
Schwabacher, M. A., (2005). A survey of data-driven prognostics. in AIAA Infotech@Aerospace Conference.
Reston,VA. Storvik, G., (2001). Particle Filters in State Space Models with the Presence of Unknown Static Parameters. IEEE Transactions on, Signal Processing, vol. 50(2), pp. 281289. Wang, W., Liao, S., & Xing, T., (2009). Particle Filter for State and Parameter Estimation in Passive Ranging. Intelligent Computing and Intelligent Systems (ICIS), 2009 IEEE International Conference on. Yan, J. & Lee, J., (2007). A Hybrid Method for On-line Performance Assessment and Life Prediction in Drilling Operations. in IEEE International Conference on Automation and Logistics.
Zio, E., & Peloni, G., (2011). Particle Filtering Prognostic Estimation of the Remaining Useful Life of Nonlinear Components. Reliability Engineering and System Safety, vol. 96(3), pp. 403-409.
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