Towards a model-order reduction strategy for nonlinear dynamics parametric simulations

Assessing the risk of failure of a structure subjected to seismic hazard often requires numerous costly computations. When computing fragility curves, for instance, the nonlinear damageable behaviour of structures needs to be considered, and the dynamics response of the latter must be computed for a wide range of likely ground motion inputs. This work uses a space-frequency Proper Generalised Decomposition (PGD) when solving the dynamics aspect of the history-dependent nonlinear problem, thus coupling the efficiency of model-order reduction with the numerical benefits of frequency computations. In this work, the parametric variability lies in the loading scenario, raising the need to derive a new multiquery framework to decrease the computation cost of such risk predictions. This framework relies on a wise initialisation process of the space-time nonlinear solver and the smart usage of previously computed reduced bases. The effectiveness of the method is based on the specificities of the LATIN solver used in the context of nonlinear dynamics. It is indeed the non-incremental nature of the LATIN approach that allows the use of a priori model-order reduction techniques such as the PGD as well as the spatio-temporal wise initialisation inspired from previous work on material variability in a multi-query context. This approach allows taking advantage of the redundant information embedded in the different solutions of the multiple computations scenario. The final computational cost is significantly lower than the cumulative cost of independently performing the different cases.