Efficient Algorithm for Estimating the Quantile of Performance Function

A sequential quantile-guided decoupling strategy can efficiently solve reliability-based design optimization constrained by target failure probability, in which a critical task is estimating the quantile of the performance function (Q-PF) with respect to the required target failure probability. Q-PF is defined as the inverse cumulative distribution function of the performance function corresponding to the target failure probability. However, it is time-consuming for existing methods to estimate the Q-PF in the case of extremely low target failure probability and high-dimensional performance function. To this end, this paper uses the monotonicity of the cumulative distribution function to propose an algorithm by combining bisection with stratified clustering mixture importance sampling (B-SC-MIS). In the proposed algorithm, the stratified clustering and mixture importance sampling are alternately executed to trace the interval of the Q-PF with respect to the extremely low target failure probability. Within the traced interval, the bisection searches the Q-PF accurately. Since stratified clustering reduces the difficulty of exploring the high-dimensional rare failure region, mixture importance sampling is explicitly and regularly constructed to reduce the numerical simulation variance, and the performance function information is shared in the bisection search, the proposed B-SC-MIS can be more efficient and robust than several existing methods for estimating the Q-PF. Several numerical and engineering examples are demonstrated to verify the superiority of the proposed algorithm over several existing methods.