Model-order reduction framework for non-linear dynamics problems involving multiple non-parametrised loading configurations for damage assessment

Predicting the probability of failure of structures submitted to uncertain loading requires a large number of non-linear computations corresponding to as many realisations of probable inputs needed to represent loading variability. This paper proposes an enhanced Reduced-Order Modelling (ROM) strategy for taking advantage of the redundancy between solutions associated with similar inputs. It reduces the overall computational cost when the dynamic response of a structure to a family of loading configurations must be calculated. In a preliminary stage, a proximity indicator involving an energy-weighted Grassmann distance between elastic solutions is investigated to assess the presumed distance between solutions. A genetic algorithm orchestrates the sequencing of computations. For each computation, a so-called ‘parent simulation’ (assumed sufficiently close) is identified, and the ROM strategy enables (1) an informed initialisation of the current solution and (2) a reuse of previously computed reduced-order basis onto which the equations of the problem will be projected, both inherited from the parent simulation. The advantages of the proposed approach are illustrated using an academic structure inspired by earthquake engineering and subjected to plasticity-induced damage and a resonance phenomenon.