Approches numériques avancées pour le recalage de modèles en dynamique vibratoire et en contexte industriel

In structural dynamics, the modified constitutive relation error is a widely used functional for model updating. The method involves a two-step iterative process to minimize the functional: first, regions with high modeling errors are localized, then their associated parameters are updated. The localization step requires solving large linear systems at each iteration, which makes the method less suitable for industrial models.In this work, a domain decomposition formulation is proposed. It makes the method more flexible, as subdomains can use different models and modify them during the updating algorithm without any additional cost. Moreover, this approach is very efficient numerically as it benefits from the same advantages as domain decomposition methods. In its standard form, it lacks a coarse problem which seems problematic; this is however solved by using a multi-preconditioned solver such as MPGMRES.Two other research areas are investigated to make the mCRE method even more suitable for industrial models. The first one deals with uncertainty quantification related to sensors placement, which is a real industrial problem in such a context. The second refers to the use of the POD to build reduced models of local problems arising from the new formulation. All these numerical methods are developed, implemented and validated using an academic platform then in code_aster, the industrial solver of EDF.