Bifurcated Remaining Useful Life Prediction: A Hybrid Approach for Realistic Uncertainty Characterization
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
https://orcid.org/0000-0001-7616-5643
Antonio Nappa
Arkaitz Artetxe
Basilio Sierra
Abstract
This study presents a novel hybrid prognostic framework for uncertainty-aware Remaining Useful Life (RUL) estimation in turbofan engines using the NASA C-MAPSS dataset. The framework employs a state-aware strategy that bifurcates the engine's operational lifespan into `healthy' and `degraded' regimes. An LSTM-based autoencoder, trained strictly on nominal data (RUL > 150 cycles), monitors reconstruction error to act as a robust state classifier. For the healthy regime, a Conditional Weibull Survival Analysis is used for Mean Residual Life estimation. For the degraded regime, a Probabilistic Neural Network with Monte Carlo Dropout captures both aleatoric and epistemic uncertainties. Rather than using rigid binary labels, a calibrated sigmoid function converts the autoencoder’s output into continuous state probabilities, dynamically weighting the final ensemble prediction. The primary strength of this framework is its generation of physically consistent uncertainty bands, yielding high-confidence predictions near end-of-life while accurately reflecting the inherent variance of early operation, providing a robust tool for risk-informed maintenance.
How to Cite
##plugins.themes.bootstrap3.article.details##
Uncertainty Quantification, Machine Learning, Remaining Useful Life, C-MAPSS
Asif, O., Haider, S. A., Naqvi, S. R., Zaki, J. F., Kwak, K.-S., & Islam, S. R. (2022). A deep learning model for remaining useful life prediction of aircraft turbofan engine on C-MAPSS dataset. IEEE Access, 10, 95425–95440.
Basora, L., Viens, A., Chao, M. A., & Olive, X. (2025). A benchmark on uncertainty quantification for deep learning prognostics. Reliability Engineering & System Safety, 253, 110513. doi: 10.1016/j.ress.2024.110513
Biggio, L., Wieland, A., Chao, M. A., Kastanis, I., & Fink, O. (2021). Uncertainty-aware prognosis via deep Gaussian process. IEEE Access, 9, 123517–123527. doi: 10.1109/ACCESS.2021.3110049
Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187–202. doi: 10.1111/j.2517-6161.1972.tb00899.x
Cui, B., Ahsan, S., Zhang, J., & Liang, X. (2026). An improved Cox proportional hazards model for reliability analysis of aviation gas turbines considering varying environmental conditions and operational settings. Reliability Engineering & System Safety, 265, 111451. doi: 10.1016/j.ress.2025.111451
Dersin, P., & Rocchetta, R. (2026). Analysis of RUL dynamics and uncertainty via time transformation. Reliability Engineering & System Safety, 266, 111730. doi: 10.1016/j.ress.2025.111730
Elsherif, S. M., Hafiz, B., Makhlouf, M. A., & Farouk, O. (2025). A deep learning-based prognostic approach for predicting turbofan engine degradation and remaining useful life. Scientific Reports, 15(1), 26251. doi: 10.1038/s41598-025-09155-z
Frederick, D. K., DeCastro, J. A., & Litt, J. S. (2007). User’s guide for the commercial modular aeropropulsion system simulation (C-MAPSS) (Tech. Rep. No. NASA/TM-2007-215026). Cleveland, OH: National Aeronautics and Space Administration, Glenn Research Center.
Gal, Y. (2016). Uncertainty in deep learning (Unpublished doctoral dissertation). University of Cambridge.
Gal, Y., & Ghahramani, Z. (2016). Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In Proceedings of the 33rd International Conference on Machine Learning (Vol. 48, pp. 1050–1059). JMLR.org.
González-Muñiz, A., Díaz Blanco, I., Cuadrado, A., & García Pérez, D. (2022). Health indicator for machine condition monitoring built in the latent space of a deep autoencoder. Reliability Engineering & System Safety, 224, 108482. doi: 10.1016/j.ress.2022.108482
Heimes, F. O. (2008). Recurrent neural networks for remaining useful life estimation. In 2008 International Conference on Prognostics and Health Management (pp. 1–6). doi: 10.1109/PHM.2008.4711422
Huang, C., Bu, S., Lee, H. H., Chan, C. H., Kong, S. W., & Yung, W. K. (2024). Prognostics and health management for predictive maintenance: A review. Journal of Manufacturing Systems, 75, 78–101. doi: 10.1016/j.jmsy.2024.05.021
Kim, N.-H., An, D., & Choi, J.-H. (2017). Prognostics and health management of engineering systems. Cham, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-44742-1
Lawless, J. F. (2003). Statistical models and methods for lifetime data (2nd ed.). Hoboken, NJ: Wiley.
Li, H., Zhang, Z., Li, T., & Si, X. (2024). A review on physics-informed data-driven remaining useful life prediction: Challenges and opportunities. Mechanical Systems and Signal Processing, 209, 111120. doi: 10.1016/j.ymssp.2024.111120
Li, X., Ding, Q., & Sun, J.-Q. (2018). Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability Engineering & System Safety, 172, 1–11. doi: 10.1016/j.ress.2017.11.021
Liu, L., Song, X., & Zhou, Z. (2022). Aircraft engine remaining useful life estimation via a double attention-based data-driven architecture. Reliability Engineering & System Safety, 221, 108330. doi: 10.1016/j.ress.2022.108330
Mitici, M., de Pater, I., Barros, A., & Zeng, Z. (2023). Dynamic predictive maintenance for multiple components using data-driven probabilistic RUL prognostics: The case of turbofan engines. Reliability Engineering & System Safety, 234, 109199. doi: 10.1016/j.ress.2023.109199
Nemani, V., Biggio, L., Huan, X., Hu, Z., Fink, O., Tran, A., ... Hu, C. (2023). Uncertainty quantification in machine learning for engineering design and health prognostics: A tutorial. Mechanical Systems and Signal Processing, 205, 110796. doi: 10.1016/j.ymssp.2023.110796
Ochella, S., Dinmohammadi, F., & Shafiee, M. (2024). Bayesian neural networks for uncertainty quantification in remaining useful life prediction of systems with sensor monitoring. Advances in Mechanical Engineering, 16(7), 16878132241239802. doi: 10.1177/16878132241239802
Peng, W., Ye, Z.-S., & Chen, N. (2020). Bayesian deep-learning-based health prognostics toward prognostics uncertainty. IEEE Transactions on Industrial Electronics, 67(3), 2283–2293. doi: 10.1109/TIE.2019.2907440
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
Saxena, A., Goebel, K., Simon, D., & Ekelund, N. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. In 2008 International Conference on Prognostics and Health Management (pp. 1–9). doi: 10.1109/PHM.2008.4711414
Song, Y., Shi, G., Chen, L., Huang, X., & Xia, T. (2018). Remaining useful life prediction of turbofan engine using hybrid model based on autoencoder and bidirectional long short-term memory. Journal of Shanghai Jiaotong University (Science), 23(1), 85–94. doi: 10.1007/s12204-018-2027-5
Sutharssan, T., Stoyanov, S., Bailey, C., & Yin, C. (2015). Prognostic and health management for engineering systems: A review of the data-driven approach and algorithms. The Journal of Engineering, 2015(7), 215–222. doi: 10.1049/joe.2014.0303
Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics.
Xuan, Q. L., Adhisantoso, Y. G., Munderloh, M., & Ostermann, J. (2023). Uncertainty-aware remaining useful life prediction for predictive maintenance using deep learning. Procedia CIRP, 118, 116–121. doi: 10.1016/j.procir.2023.06.021
Younus, R., & Cai, J. (2025). Weibull reliability modeling with quantified uncertainty for turbofan engine maintenance. In 2025 7th International Conference on System Reliability and Safety Engineering (SRSE) (pp. 673–678). doi: 10.1109/SRSE67406.2025.11357334
Zhan, Y., Kong, Z., Wang, Z., Jin, X., & Xu, Z. (2024). Remaining useful life prediction with uncertainty quantification based on multi-distribution fusion structure. Reliability Engineering & System Safety, 251, 110383. doi: 10.1016/j.ress.2024.110383
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). doi: 10.1109/ICPHM.2017.7998311
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.