High-dimensional dependence modelling using Bayesian networks for the degradation of civil infrastructures and other applications

Abstract : This thesis explores high-dimensional deterioration-related problems using Bayesian networks (BN). Asset managers become more and more familiar on how to reason with uncertainty as traditional physics-based models fail to fully encompass the dynamics of large-scale degradation issues. Probabilistic dependence is able to achieve this while the ability to incorporate randomness is enticing.In fact, dependence in BN is mainly expressed in two ways. On the one hand, classic conditional probabilities that lean on thewell-known Bayes rule and, on the other hand, a more recent classof BN featuring copulae and rank correlation as dependence metrics. Both theoretical and practical contributions are presented for the two classes of BN referred to as discrete dynamic andnon-parametric BN, respectively. Issues related to the parametrization for each class of BN are addressed. For the discrete dynamic class, we extend the current framework by incorporating an additional dimension. We observed that this dimension allows to have more control on the deterioration mechanism through the main endogenous governing variables impacting it. For the non-parametric class, we demonstrate its remarkable capacity to handle a high-dimension crack growth issue for a steel bridge. We further show that this type of BN can characterize any Markov process.
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Alex Kosgodagan. High-dimensional dependence modelling using Bayesian networks for the degradation of civil infrastructures and other applications. Probability [math.PR]. Ecole nationale supérieure Mines-Télécom Atlantique, 2017. English. ⟨NNT : 2017IMTA0020⟩. ⟨tel-01596030⟩

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