Efficient subset simulation with active learning Kriging model for low failure probability prediction

For low failure probability prediction, subset simulation can reduce the number of simulations significantly compared to the traditional MCS method for a target prediction error limit. To further reduce the computational effort for cases where the performance function evaluation is tedious and time-consuming, the performance f unction is approximated by a sequentially updated (instead of a global) Kriging model. For this purpose, an active learning technique with a new learning and stopping criterion is employed to efficiently select points to train the computationally cheaper Kriging model at each simulation level, which is used to estimate the intermediate threshold and generate a new simulation sample. The updated Kriging model at the final subset simulation level is used to compute the conditional failure probability. The failure probability is estimated based on an initial simulation sample size N, and an updated N is computed and employed to obtain the final failure probability within a desired bound on the variability. The efficiency (in terms of the number of expensive evaluations using the actual performance function) and prediction error (represented by the mean square error (MSE)) of the proposed method are benchmarked using several examples. The method is shown to be more efficient (using lesser expensive evaluations) with smaller MSE for problems having low failu r e probabilities compared with selected existing methods.