Reduced order modelling of hysteretic structural response in seismic risk assessment

Abstract

Modern seismic risk/loss estimation practices require simulation of structural behavior for different levels of earthquake shaking through time-history analysis. This behavior can be strongly inelastic/hysteretic and evaluating it through high-fidelity finite element models introduces a significant computational burden. A reduced order modeling approach is discussed here to alleviate this burden. The reduced order model is developed using data from the original high-fidelity finite element model (FEM). Static condensation is first used to obtain the stiffness matrix and linear equations of motion for the dynamic degrees of freedom. The restoring forces prescribed by the linear stiffness matrix are then substituted with hysteretic ones, calibrated by comparing the reduced order model time-history to the time-history of the initial FEM for a range of different excitations. This is posed as a least squares optimization problem and its efficient solution is facilitated through a sequential approach. The accuracy and the computational savings of the reduced order model are then examined for seismic risk assessment applications by comparing to the FEM predictions. A stochastic ground motion model is used to describe the seismic hazard and the accuracy for different levels of intensity is separately examined.