Physics-Informed Machine Learning-Assisted State Estimation for Degrading System Considering Sensor Degradation Impacts
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
Degradation estimation is a fundamental component of prognostics, yet it is often compromised by the idealized assumption of perfect sensor fidelity. In harsh industrial environments, the concurrent degradation of both primary assets and monitoring sensors introduces severe observational ambiguity. Traditional state estimation methods, such as Kalman Filters (KF) or standard Sequential Monte Carlo (SMC), often fail to track states when sensor degradation causes the observation model to become non-stationary and complex. To address this, this paper proposes a hybrid degradation estimation framework that integrates Physics-Informed Machine Learning (PIML) into SMC inference. The joint evolution of asset and sensor degradation is modeled through stochastic Wiener processes, capturing both deterministic drift and diffusion. A learnable observation model is then implemented using a Multilayer Perceptron (MLP) to map the relationship between degradation states and measurements within a recursive Bayesian optimization framework. Numerical validation demonstrates that the proposed method achieves robust tracking accuracy under non-stationary conditions, performing competitively with model-based filtering approaches, presenting a promising approach in supporting prognostics frameworks considering sensor degradation.
How to Cite
##plugins.themes.bootstrap3.article.details##
Prognostics and Health Management (PHM), Sensor Degradation, Measurement Degradation, Hybrid Approach, Online Learning, Monte Carlo Inference
Cancelliere, F., Girard, S., Bourinet, J. M., & Broggi, M. (2023). A grey-box approach for the prognostic and health management of lithium-ion batteries. In Proceedings of the Annual Conference of the PHM Society (pp. 1–8). New York, NY.
Chen, Z., Yang, C., Peng, T., Dan, H., Li, C., & Gui, W. (2018). A cumulative canonical correlation analysis-based sensor precision degradation detection method. IEEE Transactions on Industrial Electronics, 66(8), 6321–6330.
Combette, A., Venaille, A., & Pustelnik, N. (2025). A new initialisation to control gradients in sinusoidal neural network. arXiv preprint arXiv:2512.06427.
Csuzdi, D., Bécsi, T., & Törő, O. (2026). Physics-informed neural particle flow for the Bayesian update step. arXiv preprint arXiv:2602.23089.
Farea, A., Yli-Harja, O., & Emmert-Streib, F. (2024). Understanding physics-informed neural networks: Techniques, applications, trends, and challenges. AI, 5(3), 1534–1557.
Fink, O., Nejjar, I., Sharma, V., Niresi, K. F., Sun, H., Dong, H., ... Zhao, M. (2025). From physics to machine learning and back: Part II—Learning and observational bias in PHM. arXiv preprint arXiv:2509.21207.
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
Guo, G., You, H., Li, C., Tang, Z., & Li, O. (2023). A physics-informed automatic neural network generation framework for emerging device modeling. Micromachines, 14(6), 1150.
Hachem, H., Vu, H. C., & Fouladirad, M. (2024). Different methods for RUL prediction considering sensor degradation. Reliability Engineering & System Safety, 243, 109897.
Jiang, L., Djurdjanovic, D., Ni, J., & Lee, J. (2006). Sensor degradation detection in linear systems. In Engineering Asset Management: Proceedings of the 1st World Congress on Engineering Asset Management (WCEAM) (pp. 1252–1260). London, UK.
Jung, D. (2022). Automated design of grey-box recurrent neural networks for fault diagnosis using structural models and causal information. In Learning for Dynamics and Control Conference (pp. 8–20). PMLR.
Kahle, W., & Lehmann, A. (2009). The Wiener process as a degradation model: Modeling and parameter estimation. In W. Kahle & A. Lehmann (Eds.), Advances in degradation modeling: Applications to reliability, survival analysis, and finance (pp. 127–146). Birkhäuser.
Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.
Li, H., Si, X., Zhang, Z., & Li, T. (2024). A critical review on prognostics for stochastic degrading systems under big data. Fundamental Research.
Li, J., & Ying, Y. (2018). A method to improve the robustness of gas turbine gas-path fault diagnosis against sensor faults. IEEE Transactions on Reliability, 67(1), 3–12.
Li, Z., Zhang, Y., & Wang, C. (2013). A sensor-driven structural health prognosis procedure considering sensor performance degradation. Structure and Infrastructure Engineering, 9(8), 764–776.
Liu, B., Do, P., Iung, B., & Xie, M. (2019). Stochastic filtering approach for condition-based maintenance considering sensor degradation. IEEE Transactions on Automation Science and Engineering, 17(1), 177–190.
Liu, X., Matias, J., Jäschke, J., & Vatn, J. (2022). Gibbs sampler for noisy transformed gamma process: Inference and remaining useful life estimation. Reliability Engineering & System Safety, 217, 108084.
Ma, S. L., Jiang, S. F., & Li, J. (2019). Structural damage detection considering sensor performance degradation and measurement noise effect. Measurement, 131, 431–442.
Mehdizadeh, M., John, S., Wang, C. H., Ghorbani, K., & Rowe, W. S. (2012). Distinguishing the degradation of the interdigital piezoelectric fibre transducers from structural damage in multifunctional composites. In Smart Materials, Adaptive Structures and Intelligent Systems (pp. 869–877). Stone Mountain, GA, USA.
Mo, H., Wang, W., Xie, M., & Xiong, J. (2017). Modeling and analysis of the reliability of digital networked control systems considering networked degradations. IEEE Transactions on Automation Science and Engineering, 14(3), 1491–1503.
Tang, J., Jiang, M., & Mao, Y. (2025). Reliability assessment for multivariate degradation system based on uncertainty and Chatterjee correlation coefficient. Systems, 13(11), 953.
Wang, P., & Gao, R. X. (2014). Particle filtering-based system degradation prediction applied to jet engines. Annual Conference of the PHM Society, 6(1).
Yoo, M., Kim, T., Yoon, J. T., Kim, Y., Kim, S., & Youn, B. D. (2020). A resilience measure formulation that considers sensor faults. Reliability Engineering & System Safety, 199, 106393. doi: 10.1016/j.ress.2019.106393
Zhang, J. X., Si, X. S., Du, D. B., & Hu, C. H. (2018). Specification analysis of the deteriorating sensor for required lifetime prognostic performance. Microelectronics Reliability, 85, 71–83.

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.