An efficient method combining polynomial-chaos kriging and adaptive radial-based importance sampling for reliability analysis

This paper develops an efficient algorithm that combines polynomial-chaos kriging (PCK) and adaptive radial-based importance sampling (ARBIS) for reliability analysis. The key idea of ARBIS is to adaptively determine a sphere with the center at the origin and radius equal to the smallest distance of the failure domain to the origin, also known as the optimal β-sphere, and only those samples outside the optimal β-sphere have a possibility of failure and thus need to evaluate the limit-state function to judge their states (safe or failure). In the proposed algorithm, both the PCK model and β-sphere are updated adaptively. In each iteration of determining the optimal β-sphere, the PCK model is updated sequentially based on an active learning function, which is used to select the most informative sample from the samples between the last and current β-spheres. Once the stopping criterion is met, the learning process of PCK in this iteration terminates, and the obtained PCK model is then used to determine the next β-sphere. The updating iteration of the β-sphere proceeds until the optimal sphere is found. Five representative examples are revisited, in which the results demonstrate the high accuracy and efficiency of the proposed PCK-ARBIS algorithm.