The fragility curve is defined as the conditional probability of failure of a structure, or its critical components, at given values of seismic intensity measures (IMs). The conditional probability of failure is usually computed adopting a log-normal assumption to reduce the computational cost. In this paper, an artificial neural network (ANN) is constructed to improve the computational efficiency for the calculation of structural outputs. The following aspects are addressed in this paper: (a) Implementation of an efficient algorithm to select IMs as inputs of the ANN. The most relevant IMs are selected with a forward selection approach based on semi-partial correlation coefficients; (b) Quantification and investigation of the ANN prediction uncertainty computed with the delta method. It consists of an aleatory component from the simplification of the seismic inputs and an epistemic model uncertainty from the limited size of the training data. The aleatory component is integrated in the computation of fragility curves, whereas the epistemic component provides the confidence intervals; (c) Computation of fragility curves with Monte Carlo method and verification of the validity of the log-normal assumption. This methodology is applied to estimate the probability of failure of an electrical cabinet in a reactor building studied in the framework of the KARISMA benchmark.

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In seismic reliability analysis the total failure probability is determined by combining the fragility curverepresenting the response of the structure to seismic excitation -with the seismic hazard curve. The determination of fragility curves has a long tradition in the nuclear industry and reaches back to the 1970s. Since the late 1990s also for ordinary buildings seismic reliability analysis became more important and formed the bases for the development of new seismic standards. Several methods are available to build fragility curves relying on different assumptions and restrictions, level of detail and type of failure modes under consideration. In this paper, different fragility analysis methods are described and their advantages and disadvantages are discussed: (i) the safety factor method, in which the fragility curve is estimated on an existing deterministic quasi-static design; the numerical simulation method, in which the parameters of the fragility curve are obtained by (ii) regression analysis or (iii) maximum likelihood estimation from a set of nonlinear time history analysis at different seismic levels; (iv) the incremental dynamic analysis which is based on numerical simulation and the scaling of accelerograms until failure. These four fragility analysis methods are applied to determine fragility curves for the 3-storey reinforced concrete shear wall building of the SMART2013 benchmark project. Advantages and disadvantages of the methods are illustrated and the impact of the simplifying assumptions (e.g. lognormal curves, scaling) are accessed.

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