A Sequential Bayesian Semi Markov Framework for Mission Based Prognostics
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Abstract
Prognostics focuses on predicting the Remaining Useful Life (RUL) of engineering systems, which is a key enabler for informed decision-making in Predictive Maintenance (PdM) and operational planning. While substantial research has addressed maintenance strategies, the impact of operational decisions on system degradation and RUL remains relatively underexplored. In mission-based operations, systems may be subjected to different operating profiles, each influencing degradation dynamics. Understanding how operational choices affect RUL is therefore crucial for reliable mission planning.
This paper proposes a sequential Bayesian semi-Markov (SBSM) framework for prognostics that explicitly accounts for operational variability. System degradation is modelled using a hidden semi-Markov model (HSMM), a data-driven and unsupervised approach. Inference is performed via a particle filter (PF), enabling online estimation of hidden degradation states and RUL prediction under varying profiles.
The proposed framework is validated using simulated degradation data. During training, multiple operational profiles are available, with each run‑to‑failure trajectory conducted under a single, fixed operating profile. In contrast, the testing phase considers degradation histories in which the operating profile changes during system operation. Results demonstrate that the proposed SBSM approach can effectively track degradation and provide meaningful RUL estimates under varying operational profiles, highlighting its potential for mission‑based prognostics.
How to Cite
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prognostics, mission-based, remaining useful life, bayesian filters
Review of Post-Prognostics Decision-Making in Prognostics
and Health Management. International Journal
of Prognostics and Health Management, 11(15),
31. Retrieved from https://hal.science/hal
-03107810
Chang, L., Lin, Y.-H., & Zio, E. (2022). Remaining useful
life prediction for complex systems considering varying
future operational conditions. Quality and Reliability
Engineering International, 38(1), 516-531. Retrieved
from https://onlinelibrary.wiley
.com/doi/abs/10.1002/qre.2997 doi:
https://doi.org/10.1002/qre.2997
Flory, J. A., Kharoufeh, J. P., & Gebraeel, N. Z. (2014).
A switching diffusion model for lifetime estimation
in randomly varying environments. IIE Transactions,
46(11), 1227–1241. Retrieved from https://doi
.org/10.1080/0740817X.2014.893400 doi:
10.1080/0740817X.2014.893400
Gal, Y., & Ghahramani, Z. (2016). Dropout as a bayesian approximation:
Representing model uncertainty in deep
learning. In international conference on machine
learning (pp. 1050–1059).
Goebel, K., Daigle, M., Saxena, A., Sankararaman, S.,
Roychoudhury, I., & Celaya, J. (2017). Prognostics:
The science of making predictions. CreateSpace
Independent Publishing Platform. Retrieved
from https://books.google.nl/
books?id=M0AztAEACAAJ
Jain, A. K., & Lad, B. K. (2020). Prognosticating ruls
while exploiting the future characteristics of operating
profiles. Reliability Engineering & System Safety,
202, 107031. doi: https://doi.org/10.1016/j.ress.2020
.107031
Jouin, M., Gouriveau, R., Hissel, D., P´era, M.-C., & Zerhouni,
N. (2016). Particle filter-based prognostics:
Review, discussion and perspectives. Mechanical Systems
and Signal Processing, 72-73, 2-31. doi: https://
doi.org/10.1016/j.ymssp.2015.11.008
Keizers, L., Loendersloot, R., & Tinga, T. (2021). Unscented
kalman filtering for prognostics under varying
operational and environmental conditions. International
Journal of Prognostics and Health Management,
12(2).
Kontogiannis, T., Salinas-Camus, M., & Eleftheroglou, N.
(2026). Himap: Hidden markov for advanced prognostics.
Journal of Open Source Software, 11(121), 9491.
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, 88-100. doi: https://doi.org/10.1016/j.ress
.2019.02.017
Liu, X., Lunde, E., Diehl, F., Zhang, A., Vatn, J., & Yin, S.
(2024). Degradation modeling under time-varying operating
conditions: Inference and prognosis with particle
filter. Reliability Engineering & System Safety,
245, 109965. doi: https://doi.org/10.1016/j.ress.2024
.109965
Pham, H. (2022). Distribution functions and its applications.
In Statistical reliability engineering: Methods, models
and applications (pp. 67–134). Cham: Springer International
Publishing. Retrieved from https://doi
.org/10.1007/978-3-030-76904-8 2 doi:
10.1007/978-3-030-76904-8 2
Salinas-Camus, M., Goebel, K., & Eleftheroglou, N. (2025).
A comprehensive review and evaluation framework for
data-driven prognostics: Uncertainty, robustness, interpretability,
and feasibility. Mechanical Systems and
Signal Processing, 237, 113015. doi: 10.1016/j.ymssp
.2025.113015
Salinas-Camus, M., Kulkarni, C. S., & Orchard, M. E.
(2023). Battery state-of-health aware path planning for
a mars rover. In 15th annual conference of prognostics
and health management.
Tamssaouet, F., Nguyen, K., & Medjaher, K. (2019). System
remaining useful imaximization through mission
profile optimization. In Asia-pacific conference of the
prognostics and health management society.
Tang, L., Hettler, E., Zhang, B., & DeCastro, J. (2011). A
testbed for real-time autonomous vehicle phm and contingency
management applications. In Annual conference
of the phm society (Vol. 3).
Teubert, C., Jarvis, K., Corbetta, M., Kulkarni, C., & Daigle,
M. (2023). Progpy: Python packages for prognostics
and health management of engineering systems.
Journal of Open Source Software, 8(87), 5099.
Retrieved from https://doi.org/10.21105/
joss.05099 doi: 10.21105/joss.05099
Wesendrup, K., & Hellingrath, B. (2020). A process-based
review of post-prognostics decision-making. In Phm
society european conference (Vol. 5, pp. 12–12).
Xiao, Q., Fang, Y., Liu, Q., & Zhou, S. (2018). Online
machine health prognostics based on modified
duration-dependent hidden semi-markov model and
high-order particle filtering. The International Journal
of Advanced Manufacturing Technology, 94(1),
1283–1297. Retrieved from https://doi.org/
10.1007/s00170-017-0916-7 doi: 10.1007/
s00170-017-0916-7
Xue, B., Yu, Y., Fu, H., Zhu, J., & Xu, Z. (2025). Advanced
prognostics techniques for machinery under
time-varying operating conditions: a review. Applied
Intelligence, 55(16), 1066.
Yang, J., Zhou, J., Chai, Y., Chen, D., & Qin, Y.
(2025). Benchmark transformation neural network
for health indicator construction under timevarying
speed and its application in machinery
prognostics. Reliability Engineering & System
Safety, 257, 110823. Retrieved from https://
www.sciencedirect.com/science/
article/pii/S0951832025000262 doi:
https://doi.org/10.1016/j.ress.2025.110823
Yu, S.-Z. (2010). Hidden semi-markov models. Artificial
Intelligence, 174(2), 215-243. (Special Review Issue)
doi: 10.1016/j.artint.2009.11.011
Zhang, B., Tang, L., DeCastro, J., Roemer, M., & Goebel,
K. (2014). Autonomous vehicle battery state-of-charge
prognostics enhanced mission planning. International
Journal of Prognostics and Health Management, 5(2).
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