EEK-SYS: System reliability analysis through estimation error-guided adaptive Kriging approximation of multiple limit state surfaces

Abstract In order to approximate the multiple limit state functions for different failure events, the active learning Kriging model proposed for component reliability analysis has been extended to system reliability analysis. Meanwhile, many efficient sampling strategies have been applied to reduce the high computational burden. However, these strategies meet a challenge in wasting some training points and terminating the training process inappropriately, since they do not directly relate to the estimation error of system failure probability. To address the challenge, this work proposes an estimation error-guided adaptive Kriging method. As Kriging prediction may be inaccurate before being well trained, the predicted system failure probability may deviate from the true result. To quantify this estimation error, the true number of failure points is approximated by adding the number of predicted failure points and the number of wrongly classified points. Since it is impossible to learn the exact number of wrongly classified points, its confidence interval is derived based on the probability of making wrong state classification. Subsequently, the refinement of Kriging is achieved by using the probability to identify new points and using the estimation error to determine the termination, which has been demonstrated by three different cases.