A Decoupling Algorithm for Efficient Estimation of Failure Probability Function Based on Statistical Moment Functions

Abstract Failure probability function (FPF) is an important index that reflects the influence of designable distribution parameters on the safety degree of a structure, and it can be used for decoupling reliability optimization models. Thus, its efficient solution is expected. A decoupling algorithm based on statistical moment functions (SMFs) of performance function is proposed to solve the FPF efficiently in this paper. The proposed algorithm first constructs an extended density weight function (EDWF), which can cover the interested region of the distribution parameters and is independent of the distribution parameters so that the statistical moment integrals corresponding to different realizations of the distribution parameters can share the same EDWF. Then, using the same EDWF, a strategy is dexterously designed to estimate the SMFs by sharing a set of integral characteristic nodes. Finally, the FPF is approximated by the SMFs, which varies with the distribution parameters in the interested design region. In addition, the proposed algorithm introduces the Box–Cox transformation of the performance function to guide the high accuracy of FPF approximated by the SMFs. The main contribution of the proposed algorithm is constructing the EDWF to decouple the dependence of solving SMFs on the realizations of the distribution parameters over the interested region and designing the strategy of estimating the SMFs by sharing the same integral characteristic nodes. Since the proposed algorithm employs a point estimation method to evaluate the FPF, it has higher efficiency than the competitive methods. Numerical and engineering examples demonstrate the superiority of the proposed algorithm.