Stochastic Emulation with Enhanced Partial Replication Strategy for Seismic Response Estimation

Abstract

Modern performance earthquake engineering practices typically entail a large number of time-consuming nonlinear time history simulations to appropriately incorporate excitation and model uncertainties in the decision making process. Surrogate modeling techniques have emerged as attractive tool for alleviating this computational burden, while allowing for the use of high-fidelity numerical models to describe hysteretic structural response. A key challenge arises in this setting for accurately capturing the aleatoric uncertainty associated with the seismic hazard. This uncertainty is typically expressed as high-dimensional or non-parametric uncertainty (depending on the approach adopted for modeling ground motion time histories), and so cannot be easily incorporated within standard surrogate modeling frameworks. Recent work has shown how stochastic emulation techniques can be leveraged to address this challenge, utilizing Gaussian Process regression (GP) as foundational surrogate model technique. The established formulation requires, for some of the parametric configurations examined, the replication of the simulations to capture the aleatoric response variability. The simulations with replications are leveraged to inform a secondary GP to describe the heteroscedastic aleatoric variability, whereas all simulations and the secondary GP are then used to establish a primary GP for predicting the response distribution. This formulation has two challenges: (i) it requires replications for some of the configurations; (ii) it only uses the configurations with replications to inform the secondary GP development. Here, an enhancement is proposed to address both these challenges: a GP-based approximation is first established for the median response, and leveraging this approximation, all simulations are utilized for developing the secondary GP. Case study examples demonstrate the benefits of the alternative formulation and the fact that it addresses both aforementioned challenges.