Adaptive trust regions and response surfaces for reliability analysis

An efficient method for the reliability analysis of systems with non-linear limit states is presented in this paper. A trust-region-based adaptive response surface is used to search for the most probable point on the limit state. The adaptive response surface construction is aided by an optimal symmetric Latin hypercube sampling-based experimental design. First-order and second-order reliability estimates using the adaptive response surface are further improved with multi-modal adaptive importance sampling. Numerical examples including a vehicle side impact problem show that the proposed method has desirable efficiency and accuracy.