Optimisation of Maintenance by Piecewise Deterministic Markov Processes under Conditions of Population Heterogeneity

The relevance of a maintenance decision hinges partly on the model's ability to estimate the current health of a system and predict its future evolution based on available information, particularly in cases where access to degradation data is severely limited. This is the context in which we undertake this work. Physics-based approaches can be used to overcome data scarcity, but their models are typically constrained to specific regions. Additionally, degradation phenomena can exhibit highly diverse behaviors that can result in suboptimal maintenance decisions if based solely on population-average degradation performance. Our study aims to explore the potential of Piecewise Deterministic Markov Process (PDMP) in a condition-based maintenance policy when there are variations in behavior within the available sample. We place a strong emphasis on the phenomenon of fatigue cracking. Our demonstration's first phase involves modeling crack evolution behaviors using PDMP-based approaches while identifying the limits of validity of physical models directly from data. We highlight the heterogeneous behaviors of crack evolution. Once we apply a classification algorithm, we define and evaluate a condition-based maintenance strategy tailored to each population.

Keywords: PDMP, Condition based maintenance, Population heterogeneity, Physic based approach, Machine Learning.

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