Aerospace design requirements mandate acceptable levels of structural failure risk. Probabilistic fatigue models enable estimation of the likelihood of fatigue failure. A key step in the development of these models is the accurate inference of the probability distributions for dominant parameters. Since data sets for these inferences are of limited size, the fatigue model parameter distributions are themselves uncertain. A hierarchical Bayesian approach is adopted to account for the uncertainties in both the parameters and their distribution. Variables specifying the distribution of the fatigue model parameters are cast as hyperparameters whose uncertainty is modeled with a hyperprior distribution. Bayes' rule is used to determine the posterior hyperparameter distribution, given available data, thus specifying the probabilistic model. The Bayesian formulation provides an additional advantage by allowing the posterior distribution to be updated as new data becomes available through inspections. By updating the probabilistic model, uncertainty in the hyperparameters can be reduced, and the appropriate level of conservatism can be achieved. In this work, techniques for Bayesian inference and updating of probabilistic fatigue models for metallic components are developed. Both safe-life and damage-tolerant methods are considered. Uncertainty in damage rates, crack growth behavior, damage, and initial flaws are quantified. Efficient computational techniques are developed to perform the inference and updating analyses. The developed capabilities are demonstrated through a series of case studies.

Les travaux de la présente thèse portent sur le recalage de modèles dynamiques d’aubes de turbinecomposites à matrice céramique. Ils s’inscrivent dans le cadre de la quantification d’incertitudes pour la validation de modèles et ont pour objectif de fournir des outils d’aide à la décision pour les ingénieurs desbureaux d’études. En effet, la dispersion importante observée lors des campagnes expérimentales invalidel’utilisation des méthodes de recalage déterministe. Après un état de l’art sur la relation entre les incertitudeset la physique, l’approche de Vérification & Validation a été introduite comme approche permettantd’assurer la crédibilité des modèles numériques. Puis, deux méthodes de recalages stochastiques, permettantde déterminer la distribution statistique des paramètres, ont été comparées sur un cas académique. La priseen compte des incertitudes n’élude pas les potentielles compensations entre paramètres. Par conséquent, desindicateurs ont été développés afin de détecter la présence de ces phénomènes perturbateurs. Ensuite, lathéorie info-gap a été employée en tant que moyen de modéliser ces méconnaissances. Une méthode derecalage stochastique robuste a ainsi été proposée, assurant un compromis entre la fidélité du modèle auxessais et la robustesse aux méconnaissances. Ces outils ont par la suite été appliqués sur un modèle éléments / This work is focused on the stochastic updating of ceramic matrix composite turbine blade model. They arepart of the uncertainty quantification framework for model validation. The aim is to enhance the existing toolused by the industrial decision makers. Indeed, consequent dispersion was measured during the experimentalcampaigns preventing the use of deterministic approaches. The first part of this thesis is dedicated to therelationship between mechanical science and uncertainty. Thus, Verification and Validation was introduced asthe processes by which credibility in numerical models is established. Then two stochastic updatingtechniques, able to handle statistic distribution, were compared through an academic example. Nevertheless,taking into account uncertainties doesn’t remove potential compensating effects between parameters.Therefore, criteria were developed in order to detect these disturbing phenomena. Info-gap theory wasemployed as a mean to model these lack of knowledge. Paired with the stochastic updating method, a robuststochasticapproach has been proposed. Results demonstrate a trade-off relationship between the model’sfidelity and robustness. The developed tools were applied on a ceramic matrix composite turbine blade finiteelement model.