Bayesian Cloud Analysis: efficient structural fragility assessment using linear regression

Cloud Analysis is based on simple regression in the logarithmic space of structural response versus seismic intensity for a set of registered records. A Bayesian take on the Cloud Analysis, presented herein, manages to take into account both record-to-record variability and other sources of uncertainty related to structural modelling. First, the structural response to a suite of ground motions, applied to different realizations of the structural model generated through a standard Monte Carlo, is obtained. The resulting suite of structural response is going to be used as “data” in order to update the joint probability distribution function for the two regression parameters and the conditional logarithmic standard deviation. In the next stage, large-sample MC simulation based on the updated joint probability distribution is used to generate a set of plausible fragility curves. The robust fragility is estimated as the average of the generated fragility curves. The dispersion in the robust fragility is estimated as the variance of the plausible fragility curves generated. The plus/minus one standard deviation confidence interval for the robust fragility depends on the size of the sample of “data” employed. Application of the Bayesian Cloud procedure for an existing RC frame designed only for gravity-loading demonstrates the effect of structural modelling uncertainties, such as the uncertainties in component capacities and those related to construction details. Moreover, a comparison of the resulting robust fragility curves with fragility curves obtained based on the Incremental Dynamic Analysis shows a significant dependence on both the structural performance measure adopted and the selection of the records.