Dynamical Variational Autoencoders for Estimating the Remaining Useful Life of Machinery
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Published
Oct 21, 2025
Marco Star
Kristoffer McKee
https://orcid.org/0000-0003-0547-1525
Kristoffer McKee
Abstract
The purpose of this work is to show the effectiveness of using generative models, specifically Dynamical Variational Autoencoders (DVAEs) for Remaining Useful Life (RUL) estimation. Many deep learning methods simply output point estimates of the RUL, generative models have the benefit of being optimized to learn an underlying probability distribution, this allows for uncertainty quantification. This work showcases how to construct a conditional DVAE to learn how to sample from p(y1:T |x1:T ), where y1:T is a sequence of RUL estimates and x1:T are a sequence of sensor signals. It is shown why noncausal sensors are important when constructing this conditional model and how one can achieve state of the art results using DVAEs. Because the DVAE is a generative model and learns to sample from p(y1:T |x1:T ), one can also quantify the uncertainty of the RUL estimates directly with this model. This is tested on NASA’s CMAPSS turbofan engine dataset and an open dataset from a dust filter experimental setup and it is demonstrated it is able to achieve state of the art results.
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Keywords
Generative models, Deep Learning, Remaining Useful Life, Uncertainty Quantification, Machinery Prognostics
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Gao, G., Que, Z., & Xu, Z. (2020). Predicting remaining useful life with uncertainty using recurrent neural process. Proceedings - Companion of the 2020 IEEE 20th International Conference on Software Quality, Reliability, and Security, QRS-C 2020, 291-296. doi: 10.1109/QRS-C51114.2020.00057
Gao, Y., Wen, Y., & Wu, J. (2021, 1). A neural network-based joint prognostic model for data fusion and remaining useful life prediction. IEEE Transactions on Neural Networks and Learning Systems, 32, 117-127. doi: 10.1109/TNNLS.2020.2977132
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González-Muñiz, A., Díaz, I., Cuadrado, A. A., & García-Pérez, D. (2022, 8). 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
Guo, L., Li, N., Jia, F., Lei, Y., & Lin, J. (2017). A recurrent neural network based health indicator for remaining useful life prediction of bearings. Neurocomputing, 240, 98-109. Retrieved from http://dx.doi.org/10.1016/j.neucom.2017.02.045 doi: 10.1016/j.neucom.2017.02.045
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Jonschkowski, R., Rastogi, D., & Brock, O. (2018, June). Differentiable particle filters: End-to-end learning with algorithmic priors. In Proceedings of robotics: Science and systems (pp. 1–9). Pittsburgh, Pennsylvania. doi: 10.15607/RSS.2018.XIV.001
Kim, M., & Liu, K. (2020). A bayesian deep learning framework for interval estimation of remaining useful life in complex systems by incorporating general degradation characteristics. IISE Transactions, 53, 326-340. Retrieved from https://www.tandfonline.com/doi/abs/10.1080/24725854.2020.1766729 doi: 10.1080/24725854.2020.1766729
Kingma, D. P., & Welling, M. (2014). Auto-encoding variational bayes. CoRR, abs/1312.6114.
Lai, J., Domke, J., & Sheldon, D. (2021). Variational marginal particle filters. Proceedings of The International Conference on Artificial Intelligence and Statistics (AISTATS). Retrieved from https://par.nsf.gov/biblio/10359646
Lee, J., & Mitici, M. (2023). Deep reinforcement learning for predictive aircraft maintenance using probabilistic remaining-useful-life prognostics. Reliability Engineering & System Safety, 230, 108908. Retrieved from https://www.sciencedirect.com/science/article/pii/S0951832022005233 doi: https://doi.org/10.1016/j.ress.2022.108908
Li, A. H., Wu, P., & Kennedy, M. (2021). Replay overshooting: Learning stochastic latent dynamics with the extended kalman filter. In 2021 ieee international conference on robotics and automation (icra) (p. 852-858). doi: 10.1109/ICRA48506.2021.9560811
Li, X., Ding, Q., & Sun, J. Q. (2018). Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability Engineering and System Safety, 172(December 2017), 1–11. Retrieved from https://doi.org/10.1016/j.ress.2017.11.021 doi: 10.1016/j.ress.2017.11.021
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