Moment Method with Box–Cox Transformation for Structural Reliability
Publication: Journal of Engineering Mechanics
Volume 146, Issue 8
Abstract
Structural reliability analysis involving highly nonnormally distributed performance functions or relatively small failure probabilities is still a challenging problem in engineering practice. To overcome these problems, this paper developed the moment method combined with Box–Cox transformation. A new criterion is proposed to select the optimal Box–Cox transformation parameter that makes the transformed performance functions approximately normally distributed. This criterion was established based on the minimum distance between the pair of the skewness and kurtosis of the transformed performance function and that of a normal random variable, in which the statistical moments of the transformed performance function are evaluated from the point-estimate method. The failure probability was evaluated using a third-order moment reliability index. The accuracy and efficiency of the proposed method were demonstrated through several numerical examples, including structural reliability analysis with correlated random variables; stochastic processes; and nonnormal, nonlinear, and implicit performance functions.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The research reported in this paper is partially supported by the National Natural Science Foundation of China (Grant Nos. 51820105014, 51738001 and U1934217) and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2019zzts879). The support is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Oct 12, 2019
Accepted: Mar 31, 2020
Published online: Jun 13, 2020
Published in print: Aug 1, 2020
Discussion open until: Nov 13, 2020
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