Multi-fidelity Monte Carlo for seismic risk assessment applications

Modern probabilistic seismic risk assessment practices frequently require a considerable number of nonlinear time-history analyses of the structural behavior for estimating risk. Use of high-fidelity finite element models (FEMs) in this setting has the potential to accurately capture all essential features of the inelastic/hysteretic structural behavior but introduces a large associated computational burden. This study examines a multi-fidelity Monte Carlo (MC) implementation to alleviate this burden. Approach leverages low computational cost, biased evaluations from a low-fidelity numerical model to accelerate the MC estimation process, and uses simulations of the computationally expensive, high-fidelity FEM, to establish an unbiased MC estimation. It specifically exploits the correlation between the two models following a control variate formulation. The number of simulations from each of the models is optimally selected to minimize the variability of the MC-based risk predictions for the given computational budget. Since seismic risk assessment requires simultaneous estimation of the risk for multiple quantities of interest, related to different engineering demand parameters or different thresholds describing performance, guidelines for achieving satisfactory computational savings across all of them are discussed. As low-fidelity model, the reduced order modeling framework recently proposed by the authors is adopted in this study, though implementation can support any other modeling approach. The computational savings and accuracy improvement established by using the multi-fidelity estimator, when compared against the use of only the high- or low-fidelity models, is examined within an illustrative implementation that considers two structures, corresponding to different heights and materials, with high-fidelity FEMs developed in OpenSees.

Automated summary

This study examines a multi-fidelity Monte Carlo implementation to reduce computational burden in probabilistic seismic risk assessment. By leveraging biased evaluations from a low-fidelity model and using simulations from a high-fidelity finite element model, an unbiased Monte Carlo estimation process is established. Optimal simulation numbers from each model are selected to minimize variability in risk predictions.