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 radialbased 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 fl-sphere, and only those samples outside the optimal fl-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 fl-sphere are updated adaptively. In each iteration of determining the optimal fl-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 fl-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 fl-sphere. The updating iteration of the fl-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.

Automated summary

This paper proposes an efficient algorithm that combines PCK and ARBIS for reliability analysis, updating both models adaptively. By sequentially updating the PCK model based on an active learning function and updating the fl-sphere in iterations until the optimal sphere is found, the algorithm demonstrates high accuracy and efficiency in five representative examples.