Stochastic maintenance for large numbers of bridges

Alain Bensoussan (1, 2) , Alexandre Brouste (3, 4) , F.B. Cartiaux (5) , Véronique Le Corvec (5) , Jorge Semiao (5) , Marie Amélie Morlais (3, 4) , Alain Ehrlacher (6)

1 ICDRiA - International Center for Decision and Risk Analysis
2 CUHK - City University of Hong Kong [Hong Kong]
3 LMM - Laboratoire Manceau de Mathématiques
4 UM - Le Mans Université
5 OSMOS GROUP [Paris]
6 ENPC - École des Ponts ParisTech

Maintenance of a large number of public bridges needs a statistical approach. Following [OCR], we use Markov chain degradation models with randomized maintenance strategies. Statistically, a randomized strategy represents the frequency of bridges on which a maintenance plan is implemented. We develop a Dynamic Programming approach for stationary optimal randomized strategies. In this setting, the Bellman equation becomes a functional equation, which we solve completely using the value iteration and policy iteration classical methodologies. They lead to algorithms to find the optimal solution which are used to the maintenance of a portfolio of bridges.

Mots clés: infinite state dynamic programming stochastic models maintenance replacement Area of review: Stochastic Models; infinite state dynamic programming; stochastic models; maintenance; replacement Area of review: Stochastic Models

Domaines: Sciences de l'ingénieur [physics]

Alain Bensoussan, Alexandre Brouste, F.B. Cartiaux, Véronique Le Corvec, Jorge Semiao, et al.. Stochastic maintenance for large numbers of bridges. 2023. ⟨hal-03918289⟩