Accelerated subset simulation with neural networks for reliability analysis

Subset Simulation (SS) is a powerful tool, simple to implement and capable of solving a broad range of reliability analysis problems. In many cases however, SS leads to reliability predictions that exhibit a large variability due to the fact that the robustness of the SS prediction depends on the selection of an adequate width of the proposal distribution when applying the modified Metropolis algorithm. In this work a Neural Network-based SS (SS-NN) methodology is proposed in which NN are effectively trained over smaller sub-domains of the total random variable space which are generated progressively at each SS level by the modified Metropolis algorithm. NN are then used as robust meta-models in order to increase the efficiency of SS by increasing significantly the samples per SS level with a minimum additional computational effort. In the numerical examples considered, it is demonstrated that the training of a sufficiently accurate NN meta-model in the context of SS simulation leads to more robust estimations of the probability of failure both in terms of mean and variance of the estimator.