A double-loop Kriging model algorithm combined with importance sampling for time-dependent reliability analysis

In Kriging model-based time-dependent reliability analysis algorithm, double-loop one (DLK) needs partial candidate sample pool (CSP) combination of random input and time variable, while single-loop one (SLK) needs complete CSP combination, thus DLK is more time-saving than SLK in training Kriging model. However, the existing DLK is inefficient since the CSP in outer loop is generated by the probability density function (PDF) of random input, and the expected improvement learning strategy may meet unstable convergence of estimating the minimum time-dependent performance function in the inner loop. To solve these issues, an importance sampling (IS)-based DLK (IS-DLK) is proposed. In the inner loop of IS-DLK, a new strategy of identifying convergence is proposed to improve the algorithm stability of the inner loop. In the outer loop of IS-DLK, by adaptively updating the Kriging model of minimum performance function, a strategy of approaching optimal importance sampling PDF (IS-PDF) is proposed to reduce the required random input CSP size for the convergent time-dependent reliability. Additionally, an expected relative error upper bound based convergence criterion is derived to further improve the computational efficiency. By cooperating the stable minimum estimation in the inner loop with IS variance reduction and derived convergence criterion in the outer loop, the IS-DLK is more efficient than the existing DLK, which is fully illustrated by the presented examples.