Real-time data assimilation and control on mechanical systems under uncertainties

This research work deals with the implementation of so-called Dynamic Data-Driven Application Systems (DDDAS) in structural mechanics activities. It aims at designing a real-time numerical feedback loop between a physical system of interest and its numerical simulator, so that (i) the simulation model is dynamically updated from sequential and in situ observations on the system; (ii) the system is appropriately driven and controlled in service using predictions given by the simulator. In order to build such a feedback loop and take various uncertainties into account, a suitable stochastic framework is considered for both data assimilation and control, with the propagation of these uncertainties from model updating up to command synthesis by using a specific and attractive sampling technique. Furthermore, reduced order modeling based on the Proper Generalized Decomposition (PGD) technique is used all along the process in order to reach the real-time constraint. This permits fast multi-query evaluations and predictions, by means of the parametrized physics-based model, in the online phase of the feedback loop. The control of a fusion welding process under various scenarios is considered to illustrate the proposed methodology and to assess the performance of the associated numerical architecture.