BEA: An efficient Bayesian emulation-based approach for probabilistic seismic response

This paper presents an advanced Bayesian emulation-based approach (hereafter BEA) that allows a reduced number of analyses to be carried out to compute the probabilistic seismic response and fragility of buildings. The BEA, which is a version of kriging, uses a mean function as a first approximation of the expected Engineering Demand Parameter given Intensity Measure (EDP|IM) and then models the approximation errors as a Gaussian Process (GP). A main advantage of the BEA is its flexibility, as it does not impose a fixed mathematical form on the EDP|IM relationship (unlike other approaches such as the standard cloud method). In addition, BEA makes fewer assumptions than standard methods, and provides improved characterization of uncertainty. This paper first presents the BEA approach and then assesses its computational efficiency as compared to the standard cloud method. This is done through the creation of EDP|IM relationships and fragility functions using the outputs of nonlinear dynamic and nonlinear static analyses for two case-study buildings representing Pre- and Special-Code seismic vulnerability classes. The nonlinear dynamic and static analysis methods represent different levels of accuracy i.e., are of high and low fidelity, respectively. The BEA and standard cloud methods are compared in their ability to recreate three “pseudo-realities”, each represented by an artificially generated EDP|IM relationship derived from a large set of analysis runs. Several input configurations are tested, including, reduced sets of training inputs (analysis runs), training inputs of high and low fidelity, two sampling processes for these inputs (i.e., random and stratified sampling) and two different IM representations. The results demonstrate that BEA yields both an improved accuracy in terms of mean estimates, as well as smaller uncertainty bounds compared to the cloud method. The improved performance of the BEA is maintained for all “pseudo-realities” tested regardless of whether it is trained with high or low fidelity analysis data, with the improvement particularly pronounced in cases when the advanced IM INp is used. It is demonstrated that good accuracy can be achieved with BEA even with reduced samples, yielding a saving in 25% in number of analyses required to generate the EDP|IM relationship. Finally, the use of BEA drastically improves both the accuracy and efficiency of the resultant seismic fragility functions.