Real-time data assimilation on systems with damage

This PhD project deals with real-time state evaluation and model updating on damageable structures, from in-situ measurements (in particular rich data coming from optic fibres used as distributed sensors). This research topic is critical in modern structural health monitoring applications, in order to early detect some critical defects inside structures and anticipate appropriate actions into a numerical feedback loop (DDDAS framework). In order to conduct effective data assimilation, we first wish to combine model reduction, Kalman filtering, and the constitutive relation error (CRE) concept which has been used in various applications. This last concept brings a deterministic variational inversion method, with primal-dual formulation and regularisation from physics (using duality and thermodynamics of continuum media). It is associated with many advantages such as convexity properties or robustness to measurement noise. The CRE concept also naturally involves a modelling error term that we wish to use to conduct adaptive multiscale modelling along the assimilation process, dynamically selecting the most suited model (among a hierarchy of damage models with increasing complexity) with respect to available data, and with coupling between concurrent models (restricting complex models in local zones where damage occurs). In addition, in order to better localise damage effects, we wish to complement the CRE concept with sparse L1 regularisation (coming from compressed sensing). Eventually, we wish to investigate on-the-fly data-based model enrichment, using deep learning techniques, in order to take into account features of the structure which are not captured a priori by physical models. In other words, the goal is to correct model bias (learning ignorance from suitable algorithms and data) so that the simulation outputs remain constantly consistent with the physical system. 

Doctoral Researcher: Antoine Benady

Scientific Advisors: Ludovic Chamoin, Insa Neuweiler, Philipp Junker