Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis

Time-dependent reliability analysis using surrogate model has drawn much attention for avoiding the high computational burden. But the surrogate training strategies of existing methods do not directly consider the estimation error of failure probability, leading to the limitations that some computationally expensive samples are wasted or some algorithms tend to terminate prematurely. To address the challenges, this work proposes a real-time estimation error-guided sampling method. As the classification of random points may be not completely accurate, the wrong-classification probability is calculated by using the mean and variance of Kriging prediction. With this probability, the total numbers of wrongly classified points are obtained. Furthermore, the confidence intervals of the numbers are computed based on the probability theory, and the estimation error of failure probability is calculated through the confidence intervals. Subsequently, the point maximizing the probability is identified as the new sample for decreasing the estimation error, and the maximum error is used to guide when to stop the refinement of Kriging model. Results of three cases demonstrate the performance of the proposed method. (C) 2019 Elsevier Inc. All rights reserved.