Error Quantification and Control for Adaptive Kriging-Based Reliability Updating with Equality Information

Abstract

• Two-phase reliability updating using adaptive Kriging (two-phase RUAK) is proposed • The maximum error induced by Kriging in posterior failure probability estimate is derived • The error estimate is used as the stopping criterion for the refinement of the Kriging model • This method allows balancing the accuracy and computational demand of reliability updating • Four examples demonstrate the accuracy of the estimated error bounds and updated reliability estimates New information obtained through measurements provide an opportunity to update estimates of a system's reliability. For equality type information, reliability updating is a daunting task. The current state-of-the-art method, reliability updating with equality information using adaptive Kriging (RUAK), integrates an adaptive Kriging process with a transformation of equality information into inequality information. The stopping criterion for training the Kriging model relies on the estimated error for prior failure probability, thus leaving the potential for the true error in posterior failure probability to exceed acceptable thresholds. This study presents an approach to estimate the maximum error in posterior failure probability for a given confidence level . Moreover, a two-phase approach is proposed for active learning and adaptive training of Kriging models in reliability updating problems. The new stopping criterion based on the maximum error of posterior failure probability ensures the accuracy of Kriging and thus the reliability estimates, while the two-phase scheme avoids unnecessary training hence improving the efficiency of reliability updating. Four numerical examples are considered to investigate the performance of the proposed approach. It is demonstrated that this method offers the ability to set and meet target accuracies for reliability updating, which is critical for applications where the consequences of decisions are significant.