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Optimisation de politiques séquentielles d'emploi et de maintenance prédictive de systèmes multi-composants

Abstract : We present an optimization problem for the maintenance of a multi-component system designed by Thales. This system is subject to random deteriorations and failures of its components, during the missions for which it is required, leading to the evolution of its state and an unavailability penalty in case of failure. The challenge is then to define an optimal policy for the use and maintenance of the system, in order to guarantee the good progress of the missions, while minimizing its management costs. It is a question of determining a compromise between intervening too early, generating unnecessary maintenance costs, and intervening too late, leading to the failure of the system and to paying penalties and more expensive operations.One of the specificities of this work is to consider a sequential decision making on the system. Then, it is about differentiating the maintenance operations according to the state of each of its components. The main idea of this work is then to define a mathematical model for the evolution of the system via the formalism of a Markovian Decision Process (MDP). Thus, the objective is to solve the associated optimization problem, i.e. to determine for each decision date and each state of the system, the action that minimizes the sum of the costs generated over the whole horizon. This is called a policy. We define several preventive and corrective reference policies and compare their performances in terms of costs and failure statistics, by Monte-Carlo simulations. This illustrates the interest of grouping the maintenances during the workshop visits, and of considering the operating times of the components for decision making, in order to reduce both the costs and the failure rate.The model specified for this industrial problem gives rise to a non-standard optimization problem in the MDP framework, because the system state space is continuous and the transition kernel is not analytically explicit, but only simulatable. In order to be able to search for an optimal policy over a finite set of admissible policies, we discretize the MDP decision rule. This allows decisions to be made over a finite number of states, without discretizing the MDP dynamics. The costs of the reference policies are used to calibrate this discretization. The goal is to determine a compromise between precision, leading to consider a very large number of states, and numerical complexity, leading to the smallest possible number of states. Finally, as the transition kernel is still not explicit, we implement and compare two stochastic optimization methods based on simulations in order to approach and make explicit an optimal policy. Particular attention is given to identifying the origin of the benefits, in order to interpret the determined optimal policy.
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https://tel.archives-ouvertes.fr/tel-03676320
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Submitted on : Monday, May 23, 2022 - 6:14:11 PM
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Tiffany Cherchi. Optimisation de politiques séquentielles d'emploi et de maintenance prédictive de systèmes multi-composants. Probabilités [math.PR]. Université Montpellier, 2021. Français. ⟨NNT : 2021MONTS131⟩. ⟨tel-03676320⟩

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