Auxiliary Particle Filter for Prognostics and Health Management
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Published
Dec 18, 2023
Hang Xiao
Jamie Coble
J Wesley Hines
https://orcid.org/0000-0002-8245-1141
Jamie Coble
J Wesley Hines
Abstract
Accurately predicting the remaining useful life (RUL) of a system is a crucial factor in prognostics and health management (PHM). This paper introduces an auxiliary particle filter (APF) model, which has the advantages of dynamically updating the model parameters and being optimized in computational speed for prognosis applications in real engineering problems. The development of particle filter (PF) in the recent decade focused on increasing the PF model’s complexity to solve more difficult problems. However, the added complexity negatively impacts the computational speed. The number of particles is commonly reduced to compensate for this increased computational burden, but this significantly reduces the accuracy of PF’s posterior distribution. The developed APF model can estimate unknown states and model parameters at the same time with a large number of particles. This algorithm was demonstrated with a dataset from an electric motor accelerated aging experiment. The results show that this model can quickly and accurately predict the RUL and is robust to measurement noise.
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Keywords
particle filter, maintenance-dependent, data-driven prognostics
References
Alamaniotis, M., Grelle, A., & Tsoukalas, L. H. (2014). Regression to fuzziness method for estimation of remaining useful life in power plant components. Mechanical Systems and Signal Processing, 48(1–2), 188–198.
An, D., Choi, J. H., & Kim, N. H. (2012). A comparison study of methods for parameter estimation in the physics-based prognostics. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012, 1–11.
Andrieu, C., Doucet, A., & Holenstein, R. (2010). Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 72(3), 269–342.
Andrieu, C., Doucet, A., & Punskaya, E. (2001). Sequential Monte Carlo Methods for Optimal Filtering. In A. Doucet, N. de Freitas, & N. Gordon (Eds.), Sequential Monte Carlo Methods in Practice (pp. 79–95). Springer New York
Bain, A., & Crisan, D. (2009). Fundamentals of Stochastic Filtering.
Baraldi, P., Mangili, F., & Zio, E. (2015). A prognostics approach to nuclear component degradation modeling based on Gaussian Process Regression. Progress in Nuclear Energy, 78, 141–154.
Barbieri, F., Hines, J. W., Sharp, M., & Venturini, M. (2015). Sensor-based degradation prediction and prognostics for remaining useful life estimation: Validation on experimental data of electric motors. International Journal of Prognostics and Health Management, 6(SP3), 1–20.
Cappé, Olivier. (2005). Inference in hidden Markov models (Eric. Moulines & Tobias. Ryden, Eds.). Springer. Chen, T., Morris, J., & Martin, E. (2005). Particle filters for state and parameter estimation in batch processes. Journal of Process Control, 15(6), 665–673.
Coble, J. B. (2010). Merging data sources to predict remaining useful life--an automated method to identify prognostic parameters. Ph.D dissertation. The University of Tennessee.
Coble, J., & Wesley Hines, J. (2009). Identifying optimal prognostic parameters from data: A genetic algorithms approach. Annual Conference of the Prognostics and Health Management Society, PHM 2009, 1–11.
Daroogheh, N., Baniamerian, A., Meskin, N., Member, S., & Khorasani, K. (2017). Prognosis and Health Monitoring of Nonlinear Systems Using a Hybrid Scheme Through Integration of PFs and Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 1990–2004.
Djeddi, M., Granjon, P., & Leprettre, B. (2007). Bearing fault diagnosis in induction machine based on current analysis using high-resolution technique. 2007 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, SDEMPED, 23–28.
Dong, H., Jin, X., Lou, Y., & Wang, C. (2014). Lithium-ion battery state of health monitoring and remaining useful life prediction based on support vector regression-particle filter. Journal of Power Sources, 271, 114–123.
Doucet, A., Godsill, S., & Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 197–208.
Elvira, V., Miguez, J., & Djurie, P. M. (2017). Adapting the Number of Particles in Sequential Monte Carlo Methods Through an Online Scheme for Convergence Assessment. IEEE Transactions on Signal Processing, 65(7), 1781–1794.
Gnanaprakasam, C. N., & Chitra, K. (2014). Prognostic of electrical motor vibration signals: A hybrid technique. Journal of Theoretical and Applied Information Technology, 63(2), 543–559.
Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to nonlinear/non-gaussian Bayesian state estimation. IEEE Proceedings, Part F: Radar and Signal Processing, 140(2), 107–113.
Hol, J. D., Schön, T., & Gustafsson, F. (2006). On Resampling Algorithms for Particle Filters. 2006 IEEE Nonlinear Statistical Signal Processing Workshop, 79–82.
Hu, Y., Baraldi, P., Di Maio, F., & Zio, E. (2015). A particle filtering and kernel smoothing-based approach for new design component prognostics. Reliability Engineering and System Safety, 134, 19–31.
Huynh, K. T., Castro, I. T., Barros, A., & Bérenguer, C. (2012). Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks. European Journal of Operational Research, 218(1), 140–151.
IEEE Standard Test Procedure for Evaluation of Systems of Insulating Materials for Random-Wound AC Electric Machinery. (1974). In ANSI C50.32-1976 and IEEE Std 117-1974 (Reaffirmed 1984) (Revision of IEEE Std 117-1956) (pp. 1–24).
Jardine, A. K. S., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 20(7), 1483–1510.
Jouin, M., Gouriveau, R., Hissel, D., Péra, M. C., & Zerhouni, N. (2016). Particle filter-based prognostics: Review, discussion and perspectives. Mechanical Systems and Signal Processing, 72–73, 2–31.
Kim, G., Kim, H., Zio, E., & Heo, G. (2018). Application of particle filtering for prognostics with measurement uncertainty in nuclear power plants. Nuclear Engineering and Technology, 50(8), 1314–1323.
Kim, H., Robert, C. P., & Casella, G. (2000). Monte Carlo Statistical Methods. In Technometrics (Vol. 42, Issue 4).
Kitagawa, G. (1996). Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models. Journal of Computational and Graphical Statistics, 5(1), 1–25.
Kong, A., & Liu, J. S. (1994). Sequential imputations and Bayesian missing data problems. Journal of the American Statistical Association, 89(425), 278–288.
Li, X., Ding, Q., & Sun, J. Q. (2018). Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability Engineering and System Safety, 172(December 2017), 1–11.
Liu, J. S., & Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association, 93(443), 1032–1044.
Liu, J., & West, M. (2001). Combined Parameter and State Estimation in Simulation-Based Filtering. Sequential Monte Carlo Methods in Practice, 197–223.
Orchard, M., & Vachtsevanos, G. J. (2009). A particle-filtering approach for on-line fault diagnosis and failure prognosis. Transactions of the Institute of Measurement and Control, vol. 31, no. 3-4, pp. 221-246.
Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vachtsevanos, G. (2008). Advances in uncertainty representation and management for particle filtering applied to prognostics. 2008 International Conference on Prognostics and Health Management, 1–6.
Orchard, M., Tang, L., Saha, B., Goebel, K., & Vachtsevanos, G. (2010). Risk-Sensitive Particle-Filtering-based Prognosis Framework for Estimation of Remaining Useful Life in Energy Storage Devices. Studies in Informatics and Control, 19, 209–218.
Park, J. I., & Bae, S. J. (2010). Direct Prediction Methods on Lifetime Distribution of Organic Light-Emitting Diodes From Accelerated Degradation Tests. IEEE Transactions on Reliability, 59(1), 74–90.
Pecht, M. (1991). Prognostics and Health Management of Electronics. In New York: John Wiley (pp. 1–13).
Pitt, M. K., & Shephard, N. (1999). Filtering via Simulation: Auxiliary Particle Filters. Journal of the American Statistical Association, 94(446), 590–599.
Rabiei, E., Droguett, E. L., & Modarres, M. (2018). Fully adaptive particle filtering algorithm for damage diagnosis and prognosis. Entropy, 20(2).
Savitzky, Abraham., & Golay, M. J. E. (1964). Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36(8), 1627–1639.
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2010). Metrics for offline evaluation of prognostic performance. International Journal of Prognostics and Health Management, 1(1).
Sharp, M. E. (2012). Prognostic Approaches Using Transient Monitoring Methods. Ph.D Dissertation, The University of Tennessee.
Si, X. S., Wang, W., Hu, C. H., & Zhou, D. H. (2011). Remaining useful life estimation - A review on the statistical data driven approaches. European Journal of Operational Research, 213(1), 1–14.
Storvik, G. (2002). Particle filters for state-space models with the presence of unknown static parameters. IEEE Transactions on Signal Processing, 50(2), 281–289.
Tseng, S. T., & Peng, C. Y. (2004). Optimal burn-in policy by using an integrated Wiener process. IIE Transactions (Institute of Industrial Engineers), 36(12), 1161–1170.
Upadhyaya, B. R., Erbay, A. S., & McClanahan, J. P. (1997). Accelerated Aging Studies of Induction Motors and Fault Diagnostics. Maintenance and Reliability Center, The University of Tennessee, Knoxville.
Wang, X., & Xu, D. (2010). An inverse gaussian process model for degradation data. Technometrics, 52(2), 188–197.
Wicker, N., Muller, J., Kalathur, R. K. R., & Poch, O. (2008). A maximum likelihood approximation method for Dirichlet’s parameter estimation. Computational Statistics & Data Analysis, 52(3), 1315–1322.
Yu, J. (2017). Aircraft engine health prognostics based on logistic regression with penalization regularization and state-space-based degradation framework. Aerospace Science and Technology, 68, 345–361.
Zhang, Q., Tse, P. W. T., Wan, X., & Xu, G. (2015). Remaining useful life estimation for mechanical systems based on similarity of phase space trajectory. Expert Systems with Applications, 42(5), 2353–2360.
Zhang, Z., Si, X., Hu, C., & Lei, Y. (2018). Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods. European Journal of Operational Research, 271(3), 775–796.
Zhao, Z., Huang, B., & Liu, F. (2013). Parameter estimation in batch process using EM algorithm with particle filter. Computers & Chemical Engineering, 57, 159–172.
Zio, E., & Peloni, G. (2011). Particle filtering prognostic estimation of the remaining useful life of nonlinear components. Reliability Engineering and System Safety, 96(3), 403–409.
An, D., Choi, J. H., & Kim, N. H. (2012). A comparison study of methods for parameter estimation in the physics-based prognostics. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012, 1–11.
Andrieu, C., Doucet, A., & Holenstein, R. (2010). Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 72(3), 269–342.
Andrieu, C., Doucet, A., & Punskaya, E. (2001). Sequential Monte Carlo Methods for Optimal Filtering. In A. Doucet, N. de Freitas, & N. Gordon (Eds.), Sequential Monte Carlo Methods in Practice (pp. 79–95). Springer New York
Bain, A., & Crisan, D. (2009). Fundamentals of Stochastic Filtering.
Baraldi, P., Mangili, F., & Zio, E. (2015). A prognostics approach to nuclear component degradation modeling based on Gaussian Process Regression. Progress in Nuclear Energy, 78, 141–154.
Barbieri, F., Hines, J. W., Sharp, M., & Venturini, M. (2015). Sensor-based degradation prediction and prognostics for remaining useful life estimation: Validation on experimental data of electric motors. International Journal of Prognostics and Health Management, 6(SP3), 1–20.
Cappé, Olivier. (2005). Inference in hidden Markov models (Eric. Moulines & Tobias. Ryden, Eds.). Springer. Chen, T., Morris, J., & Martin, E. (2005). Particle filters for state and parameter estimation in batch processes. Journal of Process Control, 15(6), 665–673.
Coble, J. B. (2010). Merging data sources to predict remaining useful life--an automated method to identify prognostic parameters. Ph.D dissertation. The University of Tennessee.
Coble, J., & Wesley Hines, J. (2009). Identifying optimal prognostic parameters from data: A genetic algorithms approach. Annual Conference of the Prognostics and Health Management Society, PHM 2009, 1–11.
Daroogheh, N., Baniamerian, A., Meskin, N., Member, S., & Khorasani, K. (2017). Prognosis and Health Monitoring of Nonlinear Systems Using a Hybrid Scheme Through Integration of PFs and Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 1990–2004.
Djeddi, M., Granjon, P., & Leprettre, B. (2007). Bearing fault diagnosis in induction machine based on current analysis using high-resolution technique. 2007 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, SDEMPED, 23–28.
Dong, H., Jin, X., Lou, Y., & Wang, C. (2014). Lithium-ion battery state of health monitoring and remaining useful life prediction based on support vector regression-particle filter. Journal of Power Sources, 271, 114–123.
Doucet, A., Godsill, S., & Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 197–208.
Elvira, V., Miguez, J., & Djurie, P. M. (2017). Adapting the Number of Particles in Sequential Monte Carlo Methods Through an Online Scheme for Convergence Assessment. IEEE Transactions on Signal Processing, 65(7), 1781–1794.
Gnanaprakasam, C. N., & Chitra, K. (2014). Prognostic of electrical motor vibration signals: A hybrid technique. Journal of Theoretical and Applied Information Technology, 63(2), 543–559.
Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to nonlinear/non-gaussian Bayesian state estimation. IEEE Proceedings, Part F: Radar and Signal Processing, 140(2), 107–113.
Hol, J. D., Schön, T., & Gustafsson, F. (2006). On Resampling Algorithms for Particle Filters. 2006 IEEE Nonlinear Statistical Signal Processing Workshop, 79–82.
Hu, Y., Baraldi, P., Di Maio, F., & Zio, E. (2015). A particle filtering and kernel smoothing-based approach for new design component prognostics. Reliability Engineering and System Safety, 134, 19–31.
Huynh, K. T., Castro, I. T., Barros, A., & Bérenguer, C. (2012). Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks. European Journal of Operational Research, 218(1), 140–151.
IEEE Standard Test Procedure for Evaluation of Systems of Insulating Materials for Random-Wound AC Electric Machinery. (1974). In ANSI C50.32-1976 and IEEE Std 117-1974 (Reaffirmed 1984) (Revision of IEEE Std 117-1956) (pp. 1–24).
Jardine, A. K. S., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 20(7), 1483–1510.
Jouin, M., Gouriveau, R., Hissel, D., Péra, M. C., & Zerhouni, N. (2016). Particle filter-based prognostics: Review, discussion and perspectives. Mechanical Systems and Signal Processing, 72–73, 2–31.
Kim, G., Kim, H., Zio, E., & Heo, G. (2018). Application of particle filtering for prognostics with measurement uncertainty in nuclear power plants. Nuclear Engineering and Technology, 50(8), 1314–1323.
Kim, H., Robert, C. P., & Casella, G. (2000). Monte Carlo Statistical Methods. In Technometrics (Vol. 42, Issue 4).
Kitagawa, G. (1996). Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models. Journal of Computational and Graphical Statistics, 5(1), 1–25.
Kong, A., & Liu, J. S. (1994). Sequential imputations and Bayesian missing data problems. Journal of the American Statistical Association, 89(425), 278–288.
Li, X., Ding, Q., & Sun, J. Q. (2018). Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability Engineering and System Safety, 172(December 2017), 1–11.
Liu, J. S., & Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association, 93(443), 1032–1044.
Liu, J., & West, M. (2001). Combined Parameter and State Estimation in Simulation-Based Filtering. Sequential Monte Carlo Methods in Practice, 197–223.
Orchard, M., & Vachtsevanos, G. J. (2009). A particle-filtering approach for on-line fault diagnosis and failure prognosis. Transactions of the Institute of Measurement and Control, vol. 31, no. 3-4, pp. 221-246.
Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vachtsevanos, G. (2008). Advances in uncertainty representation and management for particle filtering applied to prognostics. 2008 International Conference on Prognostics and Health Management, 1–6.
Orchard, M., Tang, L., Saha, B., Goebel, K., & Vachtsevanos, G. (2010). Risk-Sensitive Particle-Filtering-based Prognosis Framework for Estimation of Remaining Useful Life in Energy Storage Devices. Studies in Informatics and Control, 19, 209–218.
Park, J. I., & Bae, S. J. (2010). Direct Prediction Methods on Lifetime Distribution of Organic Light-Emitting Diodes From Accelerated Degradation Tests. IEEE Transactions on Reliability, 59(1), 74–90.
Pecht, M. (1991). Prognostics and Health Management of Electronics. In New York: John Wiley (pp. 1–13).
Pitt, M. K., & Shephard, N. (1999). Filtering via Simulation: Auxiliary Particle Filters. Journal of the American Statistical Association, 94(446), 590–599.
Rabiei, E., Droguett, E. L., & Modarres, M. (2018). Fully adaptive particle filtering algorithm for damage diagnosis and prognosis. Entropy, 20(2).
Savitzky, Abraham., & Golay, M. J. E. (1964). Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36(8), 1627–1639.
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2010). Metrics for offline evaluation of prognostic performance. International Journal of Prognostics and Health Management, 1(1).
Sharp, M. E. (2012). Prognostic Approaches Using Transient Monitoring Methods. Ph.D Dissertation, The University of Tennessee.
Si, X. S., Wang, W., Hu, C. H., & Zhou, D. H. (2011). Remaining useful life estimation - A review on the statistical data driven approaches. European Journal of Operational Research, 213(1), 1–14.
Storvik, G. (2002). Particle filters for state-space models with the presence of unknown static parameters. IEEE Transactions on Signal Processing, 50(2), 281–289.
Tseng, S. T., & Peng, C. Y. (2004). Optimal burn-in policy by using an integrated Wiener process. IIE Transactions (Institute of Industrial Engineers), 36(12), 1161–1170.
Upadhyaya, B. R., Erbay, A. S., & McClanahan, J. P. (1997). Accelerated Aging Studies of Induction Motors and Fault Diagnostics. Maintenance and Reliability Center, The University of Tennessee, Knoxville.
Wang, X., & Xu, D. (2010). An inverse gaussian process model for degradation data. Technometrics, 52(2), 188–197.
Wicker, N., Muller, J., Kalathur, R. K. R., & Poch, O. (2008). A maximum likelihood approximation method for Dirichlet’s parameter estimation. Computational Statistics & Data Analysis, 52(3), 1315–1322.
Yu, J. (2017). Aircraft engine health prognostics based on logistic regression with penalization regularization and state-space-based degradation framework. Aerospace Science and Technology, 68, 345–361.
Zhang, Q., Tse, P. W. T., Wan, X., & Xu, G. (2015). Remaining useful life estimation for mechanical systems based on similarity of phase space trajectory. Expert Systems with Applications, 42(5), 2353–2360.
Zhang, Z., Si, X., Hu, C., & Lei, Y. (2018). Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods. European Journal of Operational Research, 271(3), 775–796.
Zhao, Z., Huang, B., & Liu, F. (2013). Parameter estimation in batch process using EM algorithm with particle filter. Computers & Chemical Engineering, 57, 159–172.
Zio, E., & Peloni, G. (2011). Particle filtering prognostic estimation of the remaining useful life of nonlinear components. Reliability Engineering and System Safety, 96(3), 403–409.
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Technical Papers