Kriging metamodeling for seismic response distribution estimation

Abstract

AbstractThis paper revisits the implementation of surrogate modeling (metamodeling) techniques within seismic risk assessment, for applications that the seismic hazard is described through stochastic ground motion models. Emphasis is placed on how to efficiently address the aleatoric uncertainty in the ground motions, stemming in this case from the stochastic sequence utilized within the excitation model. Previous work has accommodated this uncertainty by approximating the statistics of the engineering demand parameters (EDPs), something that required a large number of replication simulations (for different stochastic sequences) for each training point that was used to inform the metamodel calibration. Using kriging (Gaussian Process regression) as surrogate model, an alternative formulation is discussed here, aiming to minimize the replications for each training point. This is achieved by approximating directly the EDP distribution. It is shown that accommodating heteroscedastic behavior with respect to the aleatoric uncertainty is absolutely critical for achieving an accurate approximation, and two different approaches are presented for establishing this objective. The first approach adopts a stochastic kriging formulation, utilizing a small number of replications for judicially selected inputs, leveraging a secondary surrogate model over the latter inputs to address the heteroscedastic behavior. The second approach uses no replications, establishing a heteroscedastic nugget formulation to accommodate the EDP distribution estimation. A functional relationship is introduced between the nugget and the excitation intensity features to approximate the heteroscedastic behavior. This relationship is explicitly optimized during the metamodel calibration.