Cloud Analysis Revisited: Efficient Fragility Calculation and Uncertainty Propagation Using Simple Linear Regression

One of the most efficient non-linear dynamic analysis procedures for analytic fragility evaluation, known also as the Cloud Method, is based on simple regression of structural response versus seismic intensity for a set of registered records. This work presents a Bayesian take on the cloud method for efficient fragility assessment, considering both record-to-record variability and other sources of uncertainty related to structural modeling. The starting point of this method lies in the assumption of a prescribed probability distribution such as the Lognormal probability distribution. In the first stage, the structural response to a limited set of ground motions (applied to different realizations of the structural model generated through uncertainty modeling) is obtained. This is going to be used as data in order to update (through Bayesian updating) the joint probability distribution function for the Log Normal distribution parameters (i.e., two regression parameters and a conditional standard deviation). In the second stage, large-sample MC simulation based on the posterior joint probability distribution (calculated in the first stage) is used to generate a set of plausible fragility curves and their percentiles (e.g., 50th, 84th, etc.). This provides a confidence interval that takes into account also the effect of limited number of structural analyses. The application of the above-mentioned procedure for efficient fragility assessment by using the cloud method is demonstrated for a shear-critical existing RC frame designed only for gravity-loading.