Adaptive Kriging-based failure probability estimation for multiple responses

Many systems have multiple stochastic responses, which correspond to multiple Limit-State Functions (LSFs). Over the past decade, researches on adaptive Kriging-based failure probability estimation have been focused on enhancing its performance for single response, whereas few efforts have been devoted to simultaneously coping with multiple responses of a system. Those methods have to estimate multiple responses in the same system one by one, potential repeated calculation is inevitable. This paper proposes a novel methodology for multiple responses within a single run, which includes an Adaptive Kriging-Monte Carlo Simulation for multiple responses (AK-MCS-m) and an Adaptive Kriging-Generalized Subset Simulation (AK-GSS). Once the surrogate for a certain LSF meets the requirement, the others are kept updating until the accuracy of ones for all are accepted. Two learning schemes considering the optimal effect and the averaging effect for all the LSFs are proposed. A heuristic comparative study on learning schemes for simultaneously constructing the Kriging models for multiple responses are conducted on AK-MCS-m. GSS is adopted to simultaneously estimate all the failure probabilities upon the constructed Kriging models and hence accelerate convergence for the outer loop of the simulation. Four examples are used to demonstrate the performance of the methodology.