An expected uncertainty reduction of reliability: adaptive sampling convergence criterion for Kriging-based reliability analysis

Reliability analysis has been widely used in engineering problems to determine the probability of failure of a system by considering its inputs as random variables. An important issue in reliability analysis is to keep to a minimum the number of performance function calls at the desired level of accuracy. Adaptive strategies for coupling sampling-based method and Kriging have been proposed, which allows refining the metamodel construction based on learning functions until a predefined level of accuracy is satisfied. Regarding convergence criteria, which are used to terminate the training of surrogate models, it is important to estimate expected reduction of the reliability by considering an untried sample. This study aims to provide robust information that helps a user decide whether an additional performance function call is necessary compared to the computational cost from a reliability perspective before performing the simulation. This paper first proposes the expected reliability analysis method by considering the posterior distribution of an untried sample. Then, the confidence interval of reliability (CIR) and confidence interval of expected reliability (CIER) are defined to quantify the expected uncertainty reduction of reliability (EURR). Finally, two numerical examples and Korean electrical multiple units (K-EMU) carbody engineering example are introduced to verify the robustness of the proposed adaptive sampling convergence criterion EURR.