Prognostics of Rolling Element Bearings based on Cyclostationarity-based Indicators and Kalman filter under Varying Load and Speed

##plugins.themes.bootstrap3.article.main##

##plugins.themes.bootstrap3.article.sidebar##

Published Oct 26, 2025
Zhen Li Panagiotis Mantas Toby Verwimp Alexandre Mauricio Konstantinos Gryllias

Abstract

Rolling element bearings (REBs) are key components of rotating machines but the estimation of their remaining useful life (RUL) is still very challenging. First fault detection should be achieved as early as possible and then the RUL should be estimated as accurately as possible. Both steps require dedicated Health Indicators (HIs) which might not be the same when looking towards detection or prognostics. A key property of REB signals is cyclostationarity, as the statistical properties of their vibration behavior vary periodically over time. This characteristic has been effectively exploited to construct HIs for anomaly detection, and fault diagnosis in the field of condition monitoring (CM) achieving high performance. Although a plethora of methodologies have been proposed for RUL estimation, they usually are restricted in cases where the load conditions are assumed steady, reducing significantly their applicability and implementation in industry. Therefore there is a need for methodologies that are able to estimate the RUL of REBs operating under variable and/or varying load and speed conditions. The goal of this paper is the exploration of the performance of different vibration based HIs for fault detection, diagnosis and prognosis, including both time-domain and-order domain features. A dedicated bearing prognostics test rig was used to perform accelerated life tests of a self-aligned bearing, operating under varying load and speed conditions. The speed ranges from 0 to 3000 rpm and the load varies from 0 to 12 kN. The measurements lasted for around 400 hours and the bearing has an outer race fault in the loading zone. Different signals have been acquired during the tests, including accelerations, temperature and strain signals. The results indicate that the cyclic spectral coherence-based indicator is more sensitive to the change of states (healthy or damaged) and thus better for fault detection, while the correlation-based indicator is more sensitive to fault development, and therefore more suitable for the RUL estimation of REBs. Finally, to estimate RUL, different estimators, i.e., the Extended Kalman filter (EKF) and the Adaptive Kernal Kalman filter (AKKF), are used for RUL estimation.

How to Cite

Li, Z., Mantas, P., Verwimp, T., Mauricio, A., & Gryllias, K. (2025). Prognostics of Rolling Element Bearings based on Cyclostationarity-based Indicators and Kalman filter under Varying Load and Speed. Annual Conference of the PHM Society, 17(1). https://doi.org/10.36001/phmconf.2025.v17i1.4405
Abstract 2 | PDF Downloads 0

##plugins.themes.bootstrap3.article.details##

Keywords

Rolling element bearings, Prognostics, Cyclostationarity-based Indicators, Kalman filter, Varying loading condition

References
Antoni, J., Xin, G., & Hamzaoui, N. (2017). Fast computation of the spectral correlation. Mechanical Systems and Signal Processing, 92, 248-277. doi: https://doi.org/10.1016/j.ymssp.2017.01.011

Cui, L., Wang, X., Xu, Y., Jiang, H., & Zhou, J. (2019). A novel switching unscented kalman filter method for remaining useful life prediction of rolling bearing. Measurement, 135, 678-684. doi: https://doi.org/10.1016/j.measurement.2018.12.028

Gabrielli, A., Battarra, M., Mucchi, E., & Dalpiaz, G. (2024). Physics-based prognostics of rolling-element bearings: The equivalent damaged volume algorithm. Mechanical Systems and Signal Processing, 215, 111435. doi: https://doi.org/10.1016/j.ymssp.2024.111435

Li, Y., Huang, X., Ding, P., & Zhao, C. (2021). Wiener-based remaining useful life prediction of rolling bearings using improved kalman filtering and adaptive modification. Measurement, 182, 109706. doi: https://doi.org/10.1016/j.measurement.2021.109706

Li, Z., Zhu, R., Verwimp, T., Wen, H., & Gryllias, K. (2025). Estimation of remaining useful life of rolling element bearings based on the adaptive kernel kalman filter. Mechanical Systems and Signal Processing, 229, 112493. doi: https://doi.org/10.1016/j.ymssp.2025.112493

Lim, C. K. R., & Mba, D. (2015). Switching kalman filter for failure prognostic. Mechanical Systems and Signal Processing, 52-53, 426-435. doi: https://doi.org/10.1016/j.ymssp.2014.08.006

Liu, C., Pluymers, B., Desmet, W., & Gryllias, K. (2022). A digital twin-assisted deep learning model for rolling element bearing prognostics. In Proceedings of 2022 international conference on noise and vibration engineering (isma 2022).

Ma, X., Yan, B., Wang, H., & Liao, H. (2023). A hybrid prognostic method for rotating machinery under time-varying operating conditions by fusing direct and indirect degradation characteristics. Measurement, 214, 112831. doi: https://doi.org/10.1016/j.measurement.2023.112831

Mauricio, A., & Gryllias, K. (2021). Cyclostationary-based multiband envelope spectra extraction for bearing diagnostics: The combined improved envelope spectrum. Mechanical Systems and Signal Processing, 149, 107150. doi: https://doi.org/10.1016/j.ymssp.2020.107150

Mauricio, A., Smith, W. A., Randall, R. B., Antoni, J., & Gryllias, K. (2020). Improved envelope spectrum via feature optimisation-gram (iesfogram): A novel tool for rolling element bearing diagnostics under non-stationary operating conditions. Mechanical Systems and Signal Processing, 144, 106891. doi: https://doi.org/10.1016/j.ymssp.2020.106891

Qi, J., Zhu, R., Liu, C., Mauricio, A., & Gryllias, K. (2024). Anomaly detection and multi-step estimation based remaining useful life prediction for rolling element bearings. Mechanical Systems and Signal Processing, 206, 110910. doi: https://doi.org/10.1016/j.ymssp.2023.110910

Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2010). Damage propagation modeling for aircraft engine run-to-failure simulation. International Journal of Prognostics and Health Management, 1(1), 1–17.

Singleton, R. K., Strangas, E. G., & Aviyente, S. (2015). Extended kalman filtering for remaining-useful-life estimation of bearings. IEEE Transactions on Industrial Electronics, 62(3), 1781-1790. doi: 10.1109/TIE.2014.2336616

SKF Evolution Team. (2024). Condition monitoring with ai at your elbow. (Accessed: 2025-07-07)

Soave, E., D’Elia, G., & Dalpiaz, G. (2023). Prognostics of rotating machines through generalized gaussian hidden markov models. Mechanical Systems and Signal Processing, 185, 109767. doi: https://doi.org/10.1016/j.ymssp.2022.109767

Vencl, A., Gašić, V., & Stojanović, B. (2017, feb). Fault tree analysis of most common rolling bearing tribological failures. IOP Conference Series: Materials Science and Engineering, 174(1), 012048. doi: 10.1088/1757-899X/174/1/012048

Wang, D., Zhao, X., Kou, L.-L., Qin, Y., Zhao, Y., & Tsui, K.-L. (2019). A simple and fast guideline for generating enhanced/squared envelope spectra from spectral coherence for bearing fault diagnosis. Mechanical Systems and Signal Processing, 122, 754-768. doi: https://doi.org/10.1016/j.ymssp.2018.12.055

Wen, Y., Fashiar Rahman, M., Xu, H., & Tseng, T.-L. B. (2022). Recent advances and trends of predictive maintenance from data-driven machine prognostics perspective. Measurement, 187, 110276. doi: https://doi.org/10.1016/j.measurement.2021.110276

Zhang, L., Sidoti, D., Bienkowski, A., Pattipati, K. R., Bar-Shalom, Y., & Kleinman, D. L. (2020). On the identification of noise covariances and adaptive kalman filtering: A new look at a 50 year-old problem. IEEE Access, 8, 59362-59388. doi: 10.1109/ACCESS.2020.2982407
Section
Technical Research Papers

Most read articles by the same author(s)