A system active learning Kriging method for system reliability-based design optimization with a multiple response model

This paper proposes a system active learning Kriging (SALK) method to handle system reliability-based design optimization (SRBDO) problems, where responses of all constraints at an input can be obtained simultaneously by running a multiple response model. In SALK, to select update points around the limit-state surfaces, three new system active learning functions are respectively defined for parallel, series and combined systems. The confidence interval of estimation of system failure probability at intermediate SRBDO solutions is considered in the stopping condition of Kriging update to reduce unnecessary update points used for refining the region far from the final SRBDO solution. Based on updated Kriging models, system failure probability is estimated by Monte Carlo simulation (MCS), and its partial derivative with respect to random variables is calculated by stochastic sensitivity analysis. The efficiency of the proposed SALK method for SRBDO is validated by four examples, including a power harvester design. The results indicate that SALK can locally approximate the limit-state surfaces around the final SRBDO solution and efficiently reduce the computational cost on the refinement of the region far from the final SRBDO solution.