A Bayesian framework for estimating fragility curves based on seismic damage data and numerical simulations by adaptive neural networks

In seismic risk assessment, the fragility curve is used to estimate the reliability of structures and equipment under seismic loads. The shape of fragility curves is usually approximated by the cumulative distribution function of a lognormal distribution. The estimation of the parameters of the fragility curves requires gathering different sources of information and quantifying the uncertainties coming from these sources. This paper proposes a methodology for the computation of fragility curves for nuclear power plant equipment, based on a Bayesian updating framework that combines the results of numerical simulations and damage data. An artificial neural network is trained iteratively by optimizing its prediction uncertainties over the ground motion sample space, and it is used to conduct numerical simulations. The results of the numerical simulations provide a prior estimation of the seismic capacity of the equipment. The estimation of the uncertainty related to the equipment capacity is taken from the literature. Damage data, collected from the in situ observation and the database of the seismic qualification utility group (SQUG), are used to construct the likelihood function for the Bayesian updating. The posterior equipment capacity is evaluated by Markov chain Monte Carlo simulation and posterior fragility curves are, then, obtained. The main contributions of the work are: (i) proposal of an adaptive training algorithm of artificial neural networks to improve the design of experiments for finite element simulations; (ii) proposal of a two-step transformation method to construct the likelihood function with existing damage data from the SQUG database. The methodology is applied to compute the fragility curves of a low-voltage switchgear of a nuclear power plant, within the so-called KARISMA benchmark.