A Bayesian Framework for Probabilistic Seismic Fragility Assessment of Structures

A statistical framework is proposed to address the problem of evaluating and updating estimates of seismic fragility for structural systems in nuclear power plants and other critical infrastructure facilities. The main objective of the framework is to enable (i) integration of fragility estimates from existing studies with the new fragility data from experiments or finite element simulations; (ii) planning and allocation of resources for efficient collection of fragility data. Seismic fragility analyses of large-scale engineering structures is performed by conducting large-scale simulations involving multiple nonlinear time-history analyses using experimentally-validated finite element models. Accurate estimation of fragility often demands a formidable number of nonlinear time-history simulations which can be computationally prohibitive. A computational methodology based on Bayesian inference techniques is proposed to reduce the computational effort and efficient allocation of computing resources. Application of the proposed methodology to large-scale piping systems with localized nonlinearities is simplified further by proposing an equivalent linearization technique. A fragility model is developed for these systems where linearization of the localized nonlinearity enables us to evaluate a robust prior estimate of fragility using only elastic time-history analyses. The model is incorporated into the Bayesian framework to evaluate posterior estimates by updating the prior using a much reduced number of nonlinear time-history analyses. Modeling of uncertainties in the interdependencies between input parameters (material and model) is an important step in setting up probabilistic simulations. A sampling algorithm is suggested in order to facilitate simulation of closely-spaced random variables subjected to inequality constraints.