A coupled subset simulation and active learning kriging reliability analysis method for rare failure events

It is widely recognized that the active learning kriging (AK) combined with Monte Carlo simulation (AK-MCS) is a very efficient strategy for failure probability estimation. However, for the rare failure event, the AK-MCS would be time-consuming due to the large size of the sample pool. Therefore, an efficient method coupling the subset simulation (SS) with AK is proposed to overcome the time-consuming character of AK-MCS in case of estimating the small failure probability. The SS strategy is firstly employed by the proposed method to transform the small failure probability into the product of a series of larger conditional failure probabilities of the introduced intermediate failure events. Then, a kriging model is iteratively updated for each intermediate failure event until all the conditional failure probabilities are obtained by the well-trained kriging model, on which the failure probability will be estimated by the product of these conditional failure probabilities. The proposed method significantly reduces the number of evaluating the actual complicated limit state function compared with AK-MCS, and it overcomes the time-consuming character of AK-MCS since the sample pool size of SS is significantly smaller than that of MCS. The presented examples demonstrate the efficiency and accuracy of the proposed method.