Abstract
We establish radial importance sampling under directional stratification and construct its easy-to-implement algorithm for estimating the probability of failure in structural reliability analysis. The proposed algorithm is expected to run in a fully adaptive manner for averaging the increasing realizations towards the unknown stratum probability of failure, along with updating parameterized importance sampling and adjusting the allocation of computing budget only occasionally yet effectively, fully considering the decreasing stratum variances, all on a single set of replications. The formulation does not require a monotonicity condition on the radial distance in the polar coordinate system to justify a deterministic numerical procedure, such as the root finding of directional simulation in its standard form. A wide variety of numerical results were provided for illustrating the applicability and effectiveness of the proposed framework and algorithm.
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