An efficient method for accessing structural reliability indexes via power transformation family

Evaluating the large reliability index of an implicit and nonlinear performance function (PF) is still a challenging problem in practical engineering. To overcome this problem, an efficient method by using multiple techniques is proposed. A strategy is proposed to select the optimal transformation parameter (OTP) that makes the transformed PF approximately normally distributed. This strategy is established based on the power transformation family including Box-Cox and dual power transformation, in which three formulations, i.e., maximum likelihood estimation, Jarque–Bera test, and absolute skewness minimization criterion are first introduced to estimate the transformation parameters. Further, the selective factors corresponding to the three different formulations can be estimated based on the minimum distance between the pair of the skewness and kurtosis of the transformed PF and that of a normal random variable, where the first four moments of the transformed PF are evaluated from the high-order unscented transformation. Then, the OTP can be chosen as the one with minimum selective factor. Eventually, the reliability index can be obtained based on the first four moments of the transformed PF and the cubic normal distribution. The accuracy and efficiency of the proposed method are demonstrated through four numerical examples with nonnormal, nonlinear and implicit PFs.