Advanced methodologies for the identification of stochastic models in computational mechanics. Case of uncertainty quantification for dynamical systems and case of mesoscale elasticity random fields for heterogeneous microstructures
Résumé
The main concepts, the formulations and some advances are presented for the stochastic modeling and the identification of uncertainties and of random fields in computational mechanics. Then the identification of the generalized probabilistic approach of uncertainties in computational structural dynamics is introduced. The prior stochastic models of both uncertain model-system parameters and modeling errors, are introduced. The posterior stochastic model of the uncertain model-system parameters, in presence of the modeling errors, are carried out using the Bayes method and the experimental observations. Finally, an adavanced methodology for the experimenal identification of stochastic models for materials elasticity property is presented.