Unscented Kalman Filtering for Prognostics Under Varying Operational and Environmental Conditions
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Published
Nov 10, 2021
Luc Keizers
Richard Loendersloot
Tiedo Tinga
https://orcid.org/0000-0002-3406-9263
Richard Loendersloot
Tiedo Tinga
Abstract
Prognostics gained a lot of research attention over the last decade, not the least due to the rise of data-driven prediction models. Also hybrid approaches are being developed that combine physics-based and data-driven models for better performance. However, limited attention is given to prognostics for varying operational and environmental conditions. In fact, varying operational and environmental conditions can significantly influence the remaining useful life of assets. A powerful hybrid tool for prognostics is Bayesian filtering, where a physical degradation model is updated based on realtime data. Although these types of filters are widely studied for prognostics, application for assets in varying conditions is rarely considered in literature. In this paper, it is proposed to apply an unscented Kalman filter for prognostics under varying operational conditions. Four scenarios are described in which a distinction is made between the level in which real-time and future loads are known and between short-term and long-term prognostics. The method is demonstrated on an artificial crack growth case study with frequently changing stress ranges in two different stress profiles. After this specific case, the generic application of the method is discussed. A positioning diagram is presented, indicating in which situations the proposed filter is useful and feasible. It is demonstrated that incorporation of physical knowledge can lead to highly accurate prognostics due to a degradation model in which uncertainty in model parameters is reduced. It is also demonstrated that in case of limited physical knowledge, data can compensate for missing physics to yield reasonable predictions.
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Keywords
Predictive maintenance, Varying operating conditions, Hybrid prognostics, Unscented Kalman Filter, Crack growth
References
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Baraldi, P., Compare, M., Sauco, S., & Zio, E. (2013). Ensemble neural network-based particle filtering for prognostics. Mechanical Systems and Signal Processing, 41(1), 288 - 300.
Chadha, H. S. (2018). The unscented kalman filter: Anything ekf can do i can do it better! https://towardsdatascience.com/the-unscented-kalman-filter-anything-ekf-can-do-i-can-do-it-better-ce7c773cf88d. (Retrieved on 26-02-2021)
Chao, M. A., Kulkarni, C., Goebel, K., & Fink, O. (2020). Fusing physics-based and deep learning models for prognostics. , arXiv:2003.00732, 1-18. (Unpublished)
Chen, Z. (2003). Bayesian filtering: From kalman filters to particle filters, and beyond. Statistics, 182(1), 1-69.
Cubillo, A., Perinpanayagam, S., & Esperon-Miguez, M. (2016). A review of physics-based models in prognostics: Application to gears and bearings of rotating machinery. Advances in Mechanical Engineering, 8(8), 1-21.
Dourado, A., & Viana, F. (2020). Physics-informed neural networks for bias compensation in corrosion-fatigue. In Aiaa scitech 2020 forum (p. 1-13). doi: https://doi.org/10.2514/6.2020-1149
Elattar, H., Elminir, H. K., & Riad, A. (2016). Prognostics: a literature review. Complex & Intelligent Systems, 2(2), 125-154.
Elfring, J., Torta, E., & van de Molengraft, R. (2021). Particle filters: A hands-on tutorial. Sensors, 21(2), 1-28.
Frederick, D., DeCastro, J., & Litt, J. (2007). User’s guide for the commercial modular aero-propulsion system simulation (c-mapss). NASA Technical Manuscript, 2007–215026, 1-38.
Goebel, K., Eklund, N., & Bonanni, P. (2006). Fusing competing prediction algorithms for prognostics. In 2006 IEEE aerospace conference (p. 1-10). doi: 10.1109/AERO.2006.1656116
Gordon, N., & Salmondand, D. (1993). Novel approach to nonlinear/non-gaussian bayesian state estimation. IEEE Proceedings-F (Radar and Signal Processing), 140(2), 107-113.
Guo, J., Li, Z., & Li, M. (2020). A review on prognostics methods for engineering systems. IEEE Transactions on Reliability, 69(3), 1110-1129.
Jain, A. K., & Lad, B. K. (2020). Prognosticating ruls while exploiting the future characteristics of operating profiles. Reliability Engineering System Safety, 202(C), 1-13.
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(5), 2-31.
Julier, S. J. (1998). Skewed approach to filtering. In Signal and data processing of small targets 1998 (Vol. 3373, p. 271 - 282).
Kalman, R. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
Kumar, S., Torres, M., Chan, Y. C., & Pecht, M. (2008). A hybrid prognostics methodology for electronic products. In 2008 IEEE international joint conference on neural networks (IEEE world congress on computational intelligence) (p. 3479-3485). doi: 10.1109/IJCNN.2008.4634294
Labbe, R. R. (2015). Kalman and bayesian filters in python. https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python. (Retrieved on 12-03-2021)
LaViola, J. J. (2003). A comparison of unscented and extended kalman filtering for estimating quaternion motion. In Proceedings of the 2003 american control conference, 2003. (Vol. 3, p. 2435-2440).
Lee, J., Wu, F., Zhao, W., Ghaffari, M., Liao, L., & Siegel, D. (2014). Prognostics and health management design for rotary machinery systems—reviews, methodology and applications. Mechanical Systems and Signal Processing, 42(1), 314-334.
Li, N., Gebraeel, N., Lei, Y., Bian, L., & Si, X. (2019). Remaining useful life prediction of machinery under timevarying operating conditions based on a two-factor state-space model. Reliability Engineering System Safety, 186(2), 88-100.
Liao, L., & K¨ottig, F. (2014). Review of hybrid prognostics approaches for remaining useful life prediction of engineered systems, and an application to battery life prediction. IEEE Transactions on Reliability, 63(1), 191-207.
Liao, L., & K¨ottig, F. (2016). A hybrid framework combining data-driven and model-based methods for system remaining useful life prediction. Applied Soft Computing, 44(7), 191 - 199.
Montero Jimenez, J. J., Schwartz, S., Vingerhoeds, R., Grabot, B., & Sala¨un, M. (2020). Towards multimodel approaches to predictive maintenance: A systematic literature survey on diagnostics and prognostics. Journal of Manufacturing Systems, 56(7), 539-557.
Paris, P., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Fluids Engineering, Transactions of the ASME, 85(4), 528-533.
Pillai, P., Kaushik, A., Bhavikatti, S., Roy, A., & Kumar, V. (2016). A hybrid approach for fusing physics and data for failure prediction. International Journal of Prognostics and Health Management, 7(4), 2153-2648.
Rai, R., & Sahu, C. (2020). Driven by data or derived through physics? a review of hybrid physics guided machine learning techniques with cyber-physical system (cps) focus. IEEE Access, 8(4), 71050-71073.
Raju, M., & Anandh, A. (2018). A study on common ship structural failures. International Journal of Mechanical Engineering and Technology, 9(7), 746-754.
Rezamand, M., Kordestani, M., Orchard, M. E., Carriveau, R., Ting, D. S.-K., & Saif, M. (2021). Improved remaining useful life estimation of wind turbine drivetrain bearings under varying operating conditions. IEEE Transactions on Industrial Informatics, 17(3), 1742-1752.
Saho, K., & Masugi, M. (2015). Automatic parameter setting method for an accurate kalman filter tracker using an analytical steady-state performance index. IEEE Access, 3(10), 1919-1930.
Taheri, E., Kolmanovsky, I. V., & Gusikhin, O. (2019). Survey of prognostics methods for condition-based maintenance in engineering systems. ArXiv, abs/1912.02708, 1-74. (Unpublished)
Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics (intelligent robotics and autonomous agents). The MIT Press.
Tiddens, W. (2018). Setting sail towards predictive maintenance: developing tools to conquer difficulties in the implementation of maintenance analytics (Unpublished doctoral dissertation). University of Twente.
Tiddens, W., Braaksma, A., & Tinga, T. (2018). Selecting suitable candidates for predictive maintenance. International Journal of Prognostics and Health Management, 9(1), 1-14.
Tiddens, W., Braaksma, J., & Tinga, T. (2020). Exploring predictive maintenance applications in industry. Journal of quality in maintenance engineering, 1-18. (ahead-of-print) doi: https://doi.org/10.1108/JQME-05-2020-0029
Tinga, T. (2013). Principles of loads and failure mechanisms. Applications in maintenance, reliability and design. Springer.
Tinga, T., Wubben, F., Tiddens, W. W., Wortmann, H., & Gaalman, G. (2021). Dynamic maintenance based on functional usage profiles. Journal of Quality in Maintenance Engineering, 27(1), 21-42.
Tsui, K.-L., Chen, N., Zhou, Q., Hai, Y., & Wang, W. (2015). Prognostics and health management: A review on data driven approaches. Mathematical Problems in Engineering, 2015(5), 1-17.
Van Der Merwe, R. (2004). Sigma-point kalman filters for probabilistic inference in dynamic state-space models (Unpublished doctoral dissertation). OGI School of Science & Engineering, Oregon Health Science University.
Wan, E., & Van Der Merwe, R. (2000). The unscented kalman filter for nonlinear estimation. In Proceedings of the IEEE 2000 adaptive systems for signal processing, communications, and control symposium (Vol. Cat. No.00EX373, p. 153-158).
Wang, J., Liang, Y., Zheng, Y., Gao, R. X., & Zhang, F. (2020). An integrated fault diagnosis and prognosis approach for predictive maintenance of wind turbine bearing with limited samples. Renewable Energy, 145(1), 642-650.
Wang, Y., Gogu, C., Binaud, N., Bes, C., & Fu, J. (2019). A model-based prognostics method for fatigue crack growth in fuselage panels. Chinese Journal of Aeronautics, 32(2), 396-408.
Wang, Y., Peng, Y., & Chow, T. W. S. (2021). Adaptive particle filter-based approach for rul prediction under uncertain varying stresses with application to hdd. IEEE Transactions on Industrial Informatics, 17(9), 6272-6281.
Wheatley, G., Niefanger, R., Estrin, Y., & Hu, X. (1998). Fatigue crack growth in 316l stainless steel. Key Engineering Materials, 145-14(2), 631-636.
Yang, Z., Eddy, D., Krishnamurty, S., Grosse, I., Denno, P., Lu, Y., & Witherell, P. (2017). Investigating grey-box modeling for predictive analytics in smart manufacturing. In Asme 2017 international design engineering technical conferences and computers and information in engineering conference (Vol. 2B, p. 1-10).
Yucesan, Y., & Viana, F. (2020). A physics-informed neural network for wind turbine main bearing fatigue. International Journal of Prognostics and Health Management, 11(1), 1-17.
Zendehboudi, S., Rezaei, N., & Lohi, A. (2018). Applications of hybrid models in chemical, petroleum, and energy systems: A systematic review. Applied Energy, 228(10), 2539 - 2566.
Zhao, F., Tian, Z., Bechhoefer, E., & Zeng, Y. (2015). An integrated prognostics method under time-varying operating conditions. IEEE Transactions on Reliability, 64(2), 673-686.
Zhao, F., Tian, Z., & Zeng, Y. (2013). Uncertainty quantification in gear remaining useful life prediction through an integrated prognostics method. IEEE Transactions on Reliability, 62(1), 146-159.
Baraldi, P., Compare, M., Sauco, S., & Zio, E. (2013). Ensemble neural network-based particle filtering for prognostics. Mechanical Systems and Signal Processing, 41(1), 288 - 300.
Chadha, H. S. (2018). The unscented kalman filter: Anything ekf can do i can do it better! https://towardsdatascience.com/the-unscented-kalman-filter-anything-ekf-can-do-i-can-do-it-better-ce7c773cf88d. (Retrieved on 26-02-2021)
Chao, M. A., Kulkarni, C., Goebel, K., & Fink, O. (2020). Fusing physics-based and deep learning models for prognostics. , arXiv:2003.00732, 1-18. (Unpublished)
Chen, Z. (2003). Bayesian filtering: From kalman filters to particle filters, and beyond. Statistics, 182(1), 1-69.
Cubillo, A., Perinpanayagam, S., & Esperon-Miguez, M. (2016). A review of physics-based models in prognostics: Application to gears and bearings of rotating machinery. Advances in Mechanical Engineering, 8(8), 1-21.
Dourado, A., & Viana, F. (2020). Physics-informed neural networks for bias compensation in corrosion-fatigue. In Aiaa scitech 2020 forum (p. 1-13). doi: https://doi.org/10.2514/6.2020-1149
Elattar, H., Elminir, H. K., & Riad, A. (2016). Prognostics: a literature review. Complex & Intelligent Systems, 2(2), 125-154.
Elfring, J., Torta, E., & van de Molengraft, R. (2021). Particle filters: A hands-on tutorial. Sensors, 21(2), 1-28.
Frederick, D., DeCastro, J., & Litt, J. (2007). User’s guide for the commercial modular aero-propulsion system simulation (c-mapss). NASA Technical Manuscript, 2007–215026, 1-38.
Goebel, K., Eklund, N., & Bonanni, P. (2006). Fusing competing prediction algorithms for prognostics. In 2006 IEEE aerospace conference (p. 1-10). doi: 10.1109/AERO.2006.1656116
Gordon, N., & Salmondand, D. (1993). Novel approach to nonlinear/non-gaussian bayesian state estimation. IEEE Proceedings-F (Radar and Signal Processing), 140(2), 107-113.
Guo, J., Li, Z., & Li, M. (2020). A review on prognostics methods for engineering systems. IEEE Transactions on Reliability, 69(3), 1110-1129.
Jain, A. K., & Lad, B. K. (2020). Prognosticating ruls while exploiting the future characteristics of operating profiles. Reliability Engineering System Safety, 202(C), 1-13.
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(5), 2-31.
Julier, S. J. (1998). Skewed approach to filtering. In Signal and data processing of small targets 1998 (Vol. 3373, p. 271 - 282).
Kalman, R. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
Kumar, S., Torres, M., Chan, Y. C., & Pecht, M. (2008). A hybrid prognostics methodology for electronic products. In 2008 IEEE international joint conference on neural networks (IEEE world congress on computational intelligence) (p. 3479-3485). doi: 10.1109/IJCNN.2008.4634294
Labbe, R. R. (2015). Kalman and bayesian filters in python. https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python. (Retrieved on 12-03-2021)
LaViola, J. J. (2003). A comparison of unscented and extended kalman filtering for estimating quaternion motion. In Proceedings of the 2003 american control conference, 2003. (Vol. 3, p. 2435-2440).
Lee, J., Wu, F., Zhao, W., Ghaffari, M., Liao, L., & Siegel, D. (2014). Prognostics and health management design for rotary machinery systems—reviews, methodology and applications. Mechanical Systems and Signal Processing, 42(1), 314-334.
Li, N., Gebraeel, N., Lei, Y., Bian, L., & Si, X. (2019). Remaining useful life prediction of machinery under timevarying operating conditions based on a two-factor state-space model. Reliability Engineering System Safety, 186(2), 88-100.
Liao, L., & K¨ottig, F. (2014). Review of hybrid prognostics approaches for remaining useful life prediction of engineered systems, and an application to battery life prediction. IEEE Transactions on Reliability, 63(1), 191-207.
Liao, L., & K¨ottig, F. (2016). A hybrid framework combining data-driven and model-based methods for system remaining useful life prediction. Applied Soft Computing, 44(7), 191 - 199.
Montero Jimenez, J. J., Schwartz, S., Vingerhoeds, R., Grabot, B., & Sala¨un, M. (2020). Towards multimodel approaches to predictive maintenance: A systematic literature survey on diagnostics and prognostics. Journal of Manufacturing Systems, 56(7), 539-557.
Paris, P., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Fluids Engineering, Transactions of the ASME, 85(4), 528-533.
Pillai, P., Kaushik, A., Bhavikatti, S., Roy, A., & Kumar, V. (2016). A hybrid approach for fusing physics and data for failure prediction. International Journal of Prognostics and Health Management, 7(4), 2153-2648.
Rai, R., & Sahu, C. (2020). Driven by data or derived through physics? a review of hybrid physics guided machine learning techniques with cyber-physical system (cps) focus. IEEE Access, 8(4), 71050-71073.
Raju, M., & Anandh, A. (2018). A study on common ship structural failures. International Journal of Mechanical Engineering and Technology, 9(7), 746-754.
Rezamand, M., Kordestani, M., Orchard, M. E., Carriveau, R., Ting, D. S.-K., & Saif, M. (2021). Improved remaining useful life estimation of wind turbine drivetrain bearings under varying operating conditions. IEEE Transactions on Industrial Informatics, 17(3), 1742-1752.
Saho, K., & Masugi, M. (2015). Automatic parameter setting method for an accurate kalman filter tracker using an analytical steady-state performance index. IEEE Access, 3(10), 1919-1930.
Taheri, E., Kolmanovsky, I. V., & Gusikhin, O. (2019). Survey of prognostics methods for condition-based maintenance in engineering systems. ArXiv, abs/1912.02708, 1-74. (Unpublished)
Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics (intelligent robotics and autonomous agents). The MIT Press.
Tiddens, W. (2018). Setting sail towards predictive maintenance: developing tools to conquer difficulties in the implementation of maintenance analytics (Unpublished doctoral dissertation). University of Twente.
Tiddens, W., Braaksma, A., & Tinga, T. (2018). Selecting suitable candidates for predictive maintenance. International Journal of Prognostics and Health Management, 9(1), 1-14.
Tiddens, W., Braaksma, J., & Tinga, T. (2020). Exploring predictive maintenance applications in industry. Journal of quality in maintenance engineering, 1-18. (ahead-of-print) doi: https://doi.org/10.1108/JQME-05-2020-0029
Tinga, T. (2013). Principles of loads and failure mechanisms. Applications in maintenance, reliability and design. Springer.
Tinga, T., Wubben, F., Tiddens, W. W., Wortmann, H., & Gaalman, G. (2021). Dynamic maintenance based on functional usage profiles. Journal of Quality in Maintenance Engineering, 27(1), 21-42.
Tsui, K.-L., Chen, N., Zhou, Q., Hai, Y., & Wang, W. (2015). Prognostics and health management: A review on data driven approaches. Mathematical Problems in Engineering, 2015(5), 1-17.
Van Der Merwe, R. (2004). Sigma-point kalman filters for probabilistic inference in dynamic state-space models (Unpublished doctoral dissertation). OGI School of Science & Engineering, Oregon Health Science University.
Wan, E., & Van Der Merwe, R. (2000). The unscented kalman filter for nonlinear estimation. In Proceedings of the IEEE 2000 adaptive systems for signal processing, communications, and control symposium (Vol. Cat. No.00EX373, p. 153-158).
Wang, J., Liang, Y., Zheng, Y., Gao, R. X., & Zhang, F. (2020). An integrated fault diagnosis and prognosis approach for predictive maintenance of wind turbine bearing with limited samples. Renewable Energy, 145(1), 642-650.
Wang, Y., Gogu, C., Binaud, N., Bes, C., & Fu, J. (2019). A model-based prognostics method for fatigue crack growth in fuselage panels. Chinese Journal of Aeronautics, 32(2), 396-408.
Wang, Y., Peng, Y., & Chow, T. W. S. (2021). Adaptive particle filter-based approach for rul prediction under uncertain varying stresses with application to hdd. IEEE Transactions on Industrial Informatics, 17(9), 6272-6281.
Wheatley, G., Niefanger, R., Estrin, Y., & Hu, X. (1998). Fatigue crack growth in 316l stainless steel. Key Engineering Materials, 145-14(2), 631-636.
Yang, Z., Eddy, D., Krishnamurty, S., Grosse, I., Denno, P., Lu, Y., & Witherell, P. (2017). Investigating grey-box modeling for predictive analytics in smart manufacturing. In Asme 2017 international design engineering technical conferences and computers and information in engineering conference (Vol. 2B, p. 1-10).
Yucesan, Y., & Viana, F. (2020). A physics-informed neural network for wind turbine main bearing fatigue. International Journal of Prognostics and Health Management, 11(1), 1-17.
Zendehboudi, S., Rezaei, N., & Lohi, A. (2018). Applications of hybrid models in chemical, petroleum, and energy systems: A systematic review. Applied Energy, 228(10), 2539 - 2566.
Zhao, F., Tian, Z., Bechhoefer, E., & Zeng, Y. (2015). An integrated prognostics method under time-varying operating conditions. IEEE Transactions on Reliability, 64(2), 673-686.
Zhao, F., Tian, Z., & Zeng, Y. (2013). Uncertainty quantification in gear remaining useful life prediction through an integrated prognostics method. IEEE Transactions on Reliability, 62(1), 146-159.
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Technical Papers