Analytical Health Indices: Towards Reliability-Informed Deep Learning for PHM
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https://orcid.org/0000-0003-2268-5277
Mr. Dario Goglio Dr. Kristupas Bajarunas Dr. Manuel Arias Chao
Abstract
Deep learning has demonstrated significant potential for prognostics in complex systems (Fink et al., 2020). Recent advances in physics-informed machine learning have integrated physics-of-failure principles within data-driven models (AriasChao, Kulkarni, Goebel, & Fink, 2022). Beyond physical laws, fleet-level time-to-failure (TTF) distributions provide valuable prior knowledge for individual asset life predictions.In this paper we derive a probabilistic analytical health index(HI) model based on power-law degradation, enabling a probabilistic description that reconciles individual variability with fleet-wide trends. We show that, under Weibull, Gamma, and Pareto-distributed TTFs, the HI evolution follows an analytical form, allowing explicit characterization of time to reach intermediate degradation levels. Therefore, this work provides a theoretical foundation for integrating reliability principles with deep learning, advancing towards Reliability-Informed Deep Learning (RIDL). The approach is validated on synthetic turbofan engine data and real-world battery degradation datasets. This work establishes a rigorous basis for embedding reliability engineering principles into deep learning, improving predictive maintenance and remaining useful life (RUL) estimation.
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Health Index, Reliability, Degradation, Deep Learning, Time to Failure
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