Integrating Survival-Based Aging Models with Data-Driven RUL Prognostics
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Juan Carlos Andresen Sepideh Pashami
Anders Holst
Abstract
Predictive maintenance requires reliable remaining useful life (RUL) estimation. Existing methods mainly follow two paradigms: wear-based aging models that capture cumulative degradation and sensor-driven data models that reflect instantaneous health conditions, each providing only partial information. In this work, we propose a probabilistic fusion framework that integrates wear-based and sensor-based prognostic components through failure probability distributions. Based on explicit structural assumptions linking wear, latent health, sensor observations, and failure, we derive a principled combination rule that enables uncertainty-aware integration with adaptive weighting of the components. Experimentally, we assess this combination rule by learning the wear-based component using a parametric survival model and the sensor-based component using a 1D convolutional neural network (1D-CNN) with a post-hoc uncertainty model. Evaluation on multiple N-CMAPSS datasets demonstrates that the fused model improves point accuracy, preserves the C-index, and produces narrower yet well-calibrated prediction intervals compared to either component alone. The results highlight the complementary roles of wear-based survival model and sensor-based deep learning model, and show that their probabilistic integration provides a structured pathway toward more robust and consistent prognostics over the life-time.
How to Cite
##plugins.themes.bootstrap3.article.details##
Remaining Useful Life Prediction, Probabilistic Fusion, Uncertainty Quantification, Weibull Survival Model, 1D Convolutional Neural Networks
Bechhoefer, E., Bernhard, A., & He, D. (2008). Use of Paris law for prediction of component remaining life. In 2008 IEEE Aerospace Conference (pp. 1–9).
Cao, H., Xiao, W., Sun, J., Gan, M.-G., & Wang, G. (2024). A hybrid data- and model-driven learning framework for remaining useful life prognostics. Engineering Applications of Artificial Intelligence, 135, 108557.
Chao, M. A., Kulkarni, C., Goebel, K., & Fink, O. (2022). Fusing physics-based and deep learning models for prognostics. Reliability Engineering & System Safety, 217, 107961.
Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187–202.
Cygu, S., Seow, H., Dushoff, J., & Bolker, B. M. (2023). Comparing machine learning approaches to incorporate time-varying covariates in predicting cancer survival time. Scientific Reports, 13(1), 1370.
Deng, Y., Barros, A., & Grall, A. (2015). Degradation modeling based on a time-dependent Ornstein–Uhlenbeck process and residual useful lifetime estimation. IEEE Transactions on Reliability, 65(1), 126–140.
Fink, O., Wang, Q., Svensen, M., Dersin, P., Lee, W.-J., & Ducoffe, M. (2020). Potential, challenges and future directions for deep learning in prognostics and health management applications. Engineering Applications of Artificial Intelligence, 92, 103678.
Ishwaran, H., Kogalur, U. B., Blackstone, E. H., & Lauer, M. S. (2008). Random survival forests.
Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.
Katzman, J. L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., & Kluger, Y. (2018). DeepSurv: Personalized treatment recommender system using a Cox proportional hazards deep neural network. BMC Medical Research Methodology, 18(1), 24.
Klein, J. P., & Moeschberger, M. L. (2003). Survival analysis: Techniques for censored and truncated data (Vol. 1230). Springer.
Liao, L., & Köttig, F. (2016). A hybrid framework combining data-driven and model-based methods for system remaining useful life prediction. Applied Soft Computing, 44, 191–199.
Murtaza, A. A., Saher, A., Zafar, M. H., Moosavi, S. K. R., Aftab, M. F., & Sanfilippo, F. (2024). Paradigm shift for predictive maintenance and condition monitoring from Industry 4.0 to Industry 5.0: A systematic review, challenges and case study. Results in Engineering, 24, 102935.
Nemani, V. P., Lu, H., Thelen, A., Hu, C., & Zimmerman, A. T. (2022). Ensembles of probabilistic LSTM predictors and correctors for bearing prognostics using industrial standards. Neurocomputing, 491, 575–596.
Nieves Avendano, D., Vandermoortele, N., Soete, C., Moens, P., Ompusunggu, A. P., Deschrijver, D., & Van Hoecke, S. (2022). A semi-supervised approach with monotonic constraints for improved remaining useful life estimation. Sensors, 22(4), 1590.
Rahat, M., & Kharazian, Z. (2024). SurvLoss: A new survival loss function for neural networks to process censored data. In PHM Society European Conference (Vol. 8, pp. 7–7).
Rahat, M., Kharazian, Z., Mashhadi, P. S., Rögnvaldsson, T., & Choudhury, S. (2023). Bridging the gap: A comparative analysis of regressive remaining useful life prediction and survival analysis methods for predictive maintenance. In PHM Society Asia-Pacific Conference (Vol. 4).
Yang, Z., Kanniainen, J., Krogerus, T., & Emmert-Streib, F. (2022). Prognostic modeling of predictive maintenance with survival analysis for mobile work equipment. Scientific Reports, 12(1), 8529.
Zezhou, W., Jian, H., Jiantai, Z., Liyuan, W., & Zhongyi, C. (2024). Stochastic degradation modeling and remaining useful lifetime prediction based on long short-term memory network. Measurement, 234, 114803.
Zhang, B., Li, N., Huang, J., Arakawa, T., Ishii, K., & Yashima, R. (2025). Remaining useful life prediction for tools based on monitoring data and stochastic degradation model. Journal of Advanced Computational Intelligence and Intelligent Informatics, 29(3), 668–676. doi: 10.20965/jaciii.2025.p0668
Zhang, S., Zhai, Q., & Li, Y. (2023). Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts. Reliability Engineering & System Safety, 231, 109021.
Zheng, S., Ristovski, K., Farahat, A., & Gupta, C. (2017). Long short-term memory network for remaining useful life estimation. In 2017 IEEE International Conference on Prognostics and Health Management (ICPHM) (pp. 88–95).

This work is licensed under a Creative Commons Attribution 3.0 Unported License.
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
https://orcid.org/0000-0003-4178-5257