A Hybrid Particle Filter-Weibull Approach for Probabilistic End-of-life Prediction of Industrial Machines Using Vibration Data
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Published
Sep 11, 2026
Nagesh Dewangan
Amiya Ranjan Mohanty
Abstract
Accurate degradation modeling is essential for ensuring the reliability of industrial machinery operating under uncertain conditions. This paper presents a hybrid prognostic framework that integrates Particle Filters (PF) with a Weibull Failure Rate Function (WFRF) for probabilistic End-of-Life (EOL) prediction using vibration data. The PF is employed to estimate hidden degradation states and update model parameters sequentially, while the WFRF provides a statistical representation of failure behavior. The proposed framework enables joint degradation tracking and uncertainty quantification. The method is validated using vibration datasets from a mining dumper operating under real conditions and from an induction motor operating under controlled laboratory conditions. Results demonstrate that the hybrid PF-WFRF approach achieves accurate EOL prediction with small deviation from actual failure thresholds (within ~120 seconds) and provides meaningful uncertainty bounds through probability density functions. Unlike existing hybrid approaches that rely on machine learning, the proposed framework provides a computationally efficient, interpretable probabilistic solution. The framework is robust to both smooth and noisy degradation signals, making it suitable for real-world prognostics applications.
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Keywords
End-of-life estimation, Vibration analysis, Particle filter, Weibull failure rate function, Probabilistic analysis
References
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Rathore MS, Harsha SP. Prognostic analysis of high-speed cylindrical roller bearing using Weibull distribution and k-nearest neighbor. J Nondestruct Eval Diagnostics Progn Eng Syst 2022;5:1–12. https://doi.org/10.1115/1.4051314.
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Kundu P, Darpe AK, Kulkarni MS. Weibull accelerated failure time regression model for remaining useful life prediction of bearing working under multiple operating conditions. Mech Syst Signal Process 2019;134:106302. https://doi.org/10.1016/j.ymssp.2019.106302.
Cameron ZA, Krantz TL. Statistical distribution of gear surface fatigue lives at high reliability. Int J Fatigue 2023;167:107350. https://doi.org/10.1016/j.ijfatigue.2022.107350.
de Souza LGP, de Castro Cesário M, Ribeiro RRC, Ferreira JR, de Paiva AP. A simulation-based method for cutting tool reliability estimation without experimental replications. Int J Adv Manuf Technol 2025:1749–64. https://doi.org/10.1007/s00170-025-17181-4.
Guo J, Li Z, Li M. A review on prognostics methods for engineering systems. IEEE Trans Reliab 2020;69:1110–29. https://doi.org/10.1109/TR.2019.2957965.
Khan S, Yairi T, Tsutsumi S, Nakasuka S. A review of physics-based learning for system health management. Annu Rev Control 2024;57. https://doi.org/10.1016/j.arcontrol.2024.100932.
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Salinas-Camus M, Goebel K, Eleftheroglou N. A comprehensive review and evaluation framework for data-driven prognostics: Uncertainty, robustness, interpretability, and feasibility. Mech Syst Signal Process 2025;237:113015. https://doi.org/10.1016/j.ymssp.2025.113015.
Cheng Z. A hybrid prognostics approach to estimate the residual useful life of a planetary gearbox with a local defect. J Vibroengineering 2015;17:682–94.
Ahmad W, Ali Khan S, Kim JM. A hybrid prognostics technique for rolling element bearings using adaptive predictive models. IEEE Trans Ind Electron 2017;65:1577–84. https://doi.org/10.1109/TIE.2017.2733487.
Li S, Fang H, Shi B. Remaining useful life estimation of lithium-ion battery based on interacting multiple model particle filter and support vector regression. Reliab Eng Syst Saf 2021;210:107542. https://doi.org/10.1016/j.ress.2021.107542.
Kang Z, Catal C, Tekinerdogan B. Remaining useful life (RUL) prediction of equipment in production lines using artificial neural networks. Sensors (Switzerland) 2021;21:1–20. https://doi.org/10.3390/s21030932.
Skordilis E, Moghaddass R. A double hybrid state-space model for real-time sensor-driven monitoring of deteriorating systems. IEEE Trans Autom Sci Eng 2020;17:72–87. https://doi.org/10.1109/TASE.2019.2921285.
Li X, Ding Q, Sun JQ. Remaining useful life estimation in prognostics using deep convolution neural networks. Reliab Eng Syst Saf 2018;172:1–11. https://doi.org/10.1016/j.ress.2017.11.021.
Fricke K, Nascimento RG, Corbetta M, Kulkarni CS, Viana FAC. Prognosis of Li-ion batteries under large load variations using hybrid physics-informed neural networks. Proc. Annu. Conf. Progn. Heal. Manag. Soc. PHM, vol. 15, 2023, p. 1–12. https://doi.org/10.36001/phmconf.2023.v15i1.3463.
Labbe Jr RR, Mei H, Yang H, Zhang K. Kalman and Bayesian filters in Python. vol. 27. 2020.
Dewangan N, Mohanty AR, Kumar R. Dump truck activity recognition using vibration signal and convolutional neural network. Autom Constr 2024;165:105495. https://doi.org/10.1016/j.autcon.2024.105495.
Santana CM. Correlation between vibration level, lubricating oil viscosity and total number base of an internal combustion engine operated with gasoline and ethanol. SAE Tech Pap 2022:1–8. https://doi.org/10.4271/2022-01-0620.
Siddiqui MAH, Pal SK, Dewangan N, Chattopadhyaya S, Sharma S, Nekoonam S, et al. Sludge formation analysis in hydraulic oil of load haul dumper 811MK V machine running at elevated temperatures for bioenergy applications. Int J Chem Eng 2021;2021:1–14. https://doi.org/10.1155/2021/4331809.
Rai VK, Mohanty AR. Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert-Huang transform. Mech Syst Signal Process 2007;21:2607–15. https://doi.org/10.1016/j.ymssp.2006.12.004.
Dewangan N, Agrawal AK, Siddiqui MAH, Chattopadhyaya S. Degradation analysis of gear oil SAE 90 used in load haul dumper machine. IOP Conf. Ser. Mater. Sci. Eng., vol. 624, Chennai: 2019. https://doi.org/10.1088/1757-899X/624/1/012011.
Santana CM, Mautone J, Almeida H. Analysis of the increase level of vibration in an internal combustion engine due to the degradation of the lubricating oil. SAE Tech Pap 2019;2019-April. https://doi.org/10.4271/2019-01-0780.
Gupta N, Tandon N, Pandey RK, Vidyasagar KEC, Kalyanasundaram D. Tribological and vibration studies of textured spur gear pairs under fully flooded and starved lubrication conditions. Tribol Trans 2020;63:1103–20. https://doi.org/10.1080/10402004.2020.1794093.
Pradhan PK. Condition monitoring of submersible pump using motor current signature analysis. Indian Institute of Technology Kharagpur, India, n.d.
Nectoux P, Gouriveau R, Medjaher K, Ramasso E, Chebel-Morello B, Zerhouni N, et al. PRONOSTIA: An experimental platform for bearings accelerated degradation tests. IEEE Int Conf Progn Heal Manag PHM’12 2012:1–8.
Qiu H, Lee J, Lin J, Yu G. Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics. J Sound Vib 2006;289:1066–90. https://doi.org/10.1016/j.jsv.2005.03.007.
Zhu R, Peng W, Wang D, Huang CG. Bayesian transfer learning with active querying for intelligent cross-machine fault prognosis under limited data. Mech Syst Signal Process 2022;183:109628. https://doi.org/10.1016/j.ymssp.2022.109628.
Pal RSC, Dewangan N, Mohanty AR. Fault diagnosis of induction motors: an architecture for real-time assessment as a cyber-physical system. Eng Trans 2023;71:1–20. https://doi.org/10.24423/EngTrans.2243.20230112.
Mohanty AR, Pradhan PK, Mahalik NP, Dastidar SG. Fault detection in a centrifugal pump using vibration and motor current signature analysis. Int J Autom Control 2012;6:261–76. https://doi.org/10.1504/IJAAC.2012.051884.
Hachem H, Vu HC, Fouladirad M. Different methods for RUL prediction considering sensor degradation. Reliab Eng Syst Saf 2024;243:109897. https://doi.org/10.1016/j.ress.2023.109897.
Chen T, Guestrin C. XGBoost: A scalable tree boosting system. Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., vol. August 201, 2016, p. 785–94. https://doi.org/10.1145/2939672.2939785.
Jin Z, Li X, Qiu Z, Li F, Kong E, Li B. A data-driven framework for lithium-ion battery RUL using LSTM and XGBoost with feature selection via Binary Firefly Algorithm. Energy 2025;314. https://doi.org/10.1016/j.energy.2024.134229.
Rezamand M, Kordestani M, Carriveau R, Ting DSK, Saif M. An Integrated Feature-Based Failure Prognosis Method for Wind Turbine Bearings. IEEE/ASME Trans Mechatronics 2020;25:1468–78. https://doi.org/10.1109/TMECH.2020.2978136.
Cuesta J, Leturiondo U, Vidal Y, Pozo F. A review of prognostics and health management techniques in wind energy. Reliab Eng Syst Saf 2025;260. https://doi.org/10.1016/j.ress.2025.111004.
Wang Y, He L, Jiang S, Chow TWS. Failure Prediction of Hard Disk Drives Based on Adaptive Rao-Blackwellized Particle Filter Error Tracking Method. IEEE Trans Ind Informatics 2021;17:913–21. https://doi.org/10.1109/TII.2020.3016121.
Wang Y, Peng Y, Chow TWS. Adaptive Particle Filter-Based Approach for RUL Prediction under Uncertain Varying Stresses with Application to HDD. IEEE Trans Ind Informatics 2021;17:6272–81. https://doi.org/10.1109/TII.2021.3051285.
Rathore MS, Harsha SP. Prognostic analysis of high-speed cylindrical roller bearing using Weibull distribution and k-nearest neighbor. J Nondestruct Eval Diagnostics Progn Eng Syst 2022;5:1–12. https://doi.org/10.1115/1.4051314.
Jafari S, Byun YC. XGBoost-Based Remaining Useful Life Estimation Model with Extended Kalman Particle Filter for Lithium-Ion Batteries. Sensors 2022;22:1–18. https://doi.org/10.3390/s22239522.
Kundu P, Darpe AK, Kulkarni MS. Weibull accelerated failure time regression model for remaining useful life prediction of bearing working under multiple operating conditions. Mech Syst Signal Process 2019;134:106302. https://doi.org/10.1016/j.ymssp.2019.106302.
Cameron ZA, Krantz TL. Statistical distribution of gear surface fatigue lives at high reliability. Int J Fatigue 2023;167:107350. https://doi.org/10.1016/j.ijfatigue.2022.107350.
de Souza LGP, de Castro Cesário M, Ribeiro RRC, Ferreira JR, de Paiva AP. A simulation-based method for cutting tool reliability estimation without experimental replications. Int J Adv Manuf Technol 2025:1749–64. https://doi.org/10.1007/s00170-025-17181-4.
Guo J, Li Z, Li M. A review on prognostics methods for engineering systems. IEEE Trans Reliab 2020;69:1110–29. https://doi.org/10.1109/TR.2019.2957965.
Khan S, Yairi T, Tsutsumi S, Nakasuka S. A review of physics-based learning for system health management. Annu Rev Control 2024;57. https://doi.org/10.1016/j.arcontrol.2024.100932.
Khine MHH, Kim CG, Aunsri N. A review of Bayesian-filtering-based techniques in RUL prediction for Lithium-Ion batteries. J Energy Storage 2025;111. https://doi.org/10.1016/j.est.2025.115371.
Salinas-Camus M, Goebel K, Eleftheroglou N. A comprehensive review and evaluation framework for data-driven prognostics: Uncertainty, robustness, interpretability, and feasibility. Mech Syst Signal Process 2025;237:113015. https://doi.org/10.1016/j.ymssp.2025.113015.
Cheng Z. A hybrid prognostics approach to estimate the residual useful life of a planetary gearbox with a local defect. J Vibroengineering 2015;17:682–94.
Ahmad W, Ali Khan S, Kim JM. A hybrid prognostics technique for rolling element bearings using adaptive predictive models. IEEE Trans Ind Electron 2017;65:1577–84. https://doi.org/10.1109/TIE.2017.2733487.
Li S, Fang H, Shi B. Remaining useful life estimation of lithium-ion battery based on interacting multiple model particle filter and support vector regression. Reliab Eng Syst Saf 2021;210:107542. https://doi.org/10.1016/j.ress.2021.107542.
Kang Z, Catal C, Tekinerdogan B. Remaining useful life (RUL) prediction of equipment in production lines using artificial neural networks. Sensors (Switzerland) 2021;21:1–20. https://doi.org/10.3390/s21030932.
Skordilis E, Moghaddass R. A double hybrid state-space model for real-time sensor-driven monitoring of deteriorating systems. IEEE Trans Autom Sci Eng 2020;17:72–87. https://doi.org/10.1109/TASE.2019.2921285.
Li X, Ding Q, Sun JQ. Remaining useful life estimation in prognostics using deep convolution neural networks. Reliab Eng Syst Saf 2018;172:1–11. https://doi.org/10.1016/j.ress.2017.11.021.
Fricke K, Nascimento RG, Corbetta M, Kulkarni CS, Viana FAC. Prognosis of Li-ion batteries under large load variations using hybrid physics-informed neural networks. Proc. Annu. Conf. Progn. Heal. Manag. Soc. PHM, vol. 15, 2023, p. 1–12. https://doi.org/10.36001/phmconf.2023.v15i1.3463.
Labbe Jr RR, Mei H, Yang H, Zhang K. Kalman and Bayesian filters in Python. vol. 27. 2020.
Dewangan N, Mohanty AR, Kumar R. Dump truck activity recognition using vibration signal and convolutional neural network. Autom Constr 2024;165:105495. https://doi.org/10.1016/j.autcon.2024.105495.
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Technical Papers