TY - JOUR

T1 - An efficient method for accessing structural reliability indexes via power transformation family

AU - Zhang, Long Wen

AU - Dang, Chao

AU - Zhao, Yan Gang

N1 - Funding Information: The research reported in this paper is partially supported by the National Natural Science Foundation of China (Grant No: 51738001 ), China Scholarship Council (Grant No: CSC201906130175 ), the Natural Science Foundation of Hunan Province (Grant No: 2022JJ40188 ), the Natural Science Foundation of Changsha City (Grant No: kq2202234 ), and the Excellent Youth Project of Hunan Provincial Department of Education, China Project (Grant No. 20B296 ). All of the sources of the support are gratefully acknowledged.

PY - 2023/5

Y1 - 2023/5

N2 - 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.

AB - 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.

KW - Cubic normal distribution

KW - Power transformation family

KW - Reliability index

KW - Statistical moments

KW - Structural reliability

UR - http://www.scopus.com/inward/record.url?scp=85147246140&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2023.109097

DO - 10.1016/j.ress.2023.109097

M3 - Article

AN - SCOPUS:85147246140

VL - 233

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 109097

ER -