Reduced order modeling of hysteretic structural response and applications to seismic risk assessment

Abstract

A reduced order modeling approach is presented to alleviate the computational burden associated with using high-fidelity finite element models (FEMs) to describe hysteretic structural response for earthquake engineering time-history analysis. The reduced order model (ROM) is developed using data from the original high-fidelity FEM. Static condensation is first used to obtain the condensed stiffness matrix and the linear equations of motion for the dynamic degrees of freedom (DoFs). The restoring forces prescribed by the linear stiffness matrix are then substituted with hysteretic ones by replacing the linear springs connecting each of the DoFs with hysteretic ones. Different hysteretic models are considered, including peak-oriented, Masing and Bouc-Wen type of hysteresis, whereas more complex relationships obtained by combining multiple simpler hysteretic models are also discussed. The hysteretic spring parameters are calibrated by comparing the reduced order model time-history response to the time-history response of the initial FEM for a range of different excitations. The characteristics for each of the considered springs are separately selected and an efficient solution of the associated calibration problem is facilitated through a sequential, hierarchical approach. The excitations utilized for the reduced order model calibration are carefully selected so that nonlinear characteristics of the FEM are appropriately excited to support the tuning of all the important hysteretic spring features. The accuracy and the computational savings of the calibrated reduced order model are evaluated for risk assessment applications, separately examining different levels of intensity. Comparison extends to three structures, with the high-fidelity FEMs developed in OpenSees.