Integrating Survival-Based Aging Models with Data-Driven RUL Prognostics

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Published Jul 3, 2026
Abishek Srinivasan
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

Srinivasan, A., Andresen, J. C., Pashami, S., & Holst, A. (2026). Integrating Survival-Based Aging Models with Data-Driven RUL Prognostics. PHM Society European Conference, 9(1), 1–12. https://doi.org/10.36001/phme.2026.v9i1.4939
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Keywords

Remaining Useful Life Prediction, Probabilistic Fusion, Uncertainty Quantification, Weibull Survival Model, 1D Convolutional Neural Networks

References
Arias Chao, M., Kulkarni, C., Goebel, K., & Fink, O. (2021). Aircraft engine run-to-failure dataset under real flight conditions for prognostics and diagnostics. Data, 6(1), 5.

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).
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Technical Papers