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

Abstract

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.

Multi-fidelity reduced-order surrogate modelling

“…In particular, computational costs can easily become prohibitive or intractable when parametrized, time-dependent systems of partial differential equations (PDEs) are solved with detailed full-order models (FOMs) in a multi-query context (i.e. at many instances of the input parameters characterizing the systems), such as in uncertainty quantification [1,2], optimal control [3,4], shape optimization [5], parameter estimation [6,7] and model calibration [8][9][10]. In such cases, the construction of efficient surrogate models is of paramount importance in order to produce model proxies that can cheaply and accurately characterize the PDE system.…”

Discrete-time formulations as time discretization strategies in data assimilation

“…Data assimilation emerged in the 1980s [75,3] as the set of techniques for estimating the past, present, or future state of atmospheric models from partial observations and a priori knowledge. The range of applications then grew to include all environmental sciences and even new applications such as in biology and life sciences [39,23], as well as in various engineering fields [83]. Data assimilation was also essentially the meeting point of control theory -more specifically, observation theory -and scientific computing, as the systems of interest were often represented by complex physical models with partial differential equations [60].…”