Single-Loop Sampling for Estimating Failure-Probability Upper-Bound Function

Under random-interval mixed uncertainties of structures, failure-probability upper-bound function (FPUBF), which varies with the distribution parameters of random inputs, can not only provide the influence of distribution parameters on the failure-probability upper bound (FPUB), but also contribute to decoupling a reliability-based design optimization model. Although FPUBF can be estimated by repeatedly evaluating FPUBs at different distribution parameter realizations, it suffers from unaffordable computational cost resulting from this double-loop framework. To address this issue, this paper proposes a single-loop sampling strategy (SL) to estimate FPUBF at arbitrary realizations in the interested distribution parameter region. Instead of the huge computational cost of a double-loop framework, the SL estimates the entire FPUBF only by one simulation analysis. Moreover, importance sampling (IS) variance reduction technique is introduced, and a single-loop IS probability density function (PDF), or SL-IS-PDF, is constructed to more efficiently estimate FPUBF by reducing the required size of the candidate sample pool. For approximating the optimal SL-IS-PDF and identifying the states of candidate samples efficiently, the double-loop adaptive Kriging model of performance function is introduced to further reduce the number of performance function evaluations. A numerical example and two composite structure examples are employed to verify the accuracy, efficiency, and feasibility of the proposed methods.