Abstract
In structural reliability analysis, the input variables are often nonnormal and correlated. A procedure for efficient normal transformation, i.e., transforming dependent nonnormal random variables into independent standard normal ones, is often required. In general, Rosenblatt transformation is available to realize the normal transformation when the joint probability density function (PDF) of basic random variables is available and Nataf transformation can be used when the marginal PDFs and correlation coefficients are known. However, the joint PDF and marginal PDFs of some random variables are often unknown in practice, and the probabilistic characteristics of these variables are easier to be expressed using the statistical moments and correlation matrix. It is in this regard that the objective of the present paper is to develop a methodology for normal transformation including correlated random variables with unknown joint PDF and marginal PDFs. Based on the third-moment transformation technique for transforming independent nonnormal random variables into independent standard normal ones, the third-moment transformation is further developed for transforming the correlated variables including unknown joint PDF and marginal PDFs into independent standard normal variables. A first-order reliability method for structural reliability analysis including correlated random variables with unknown joint PDF and marginal PDFs is developed based on the proposed transformation. Using the proposed method, the normal transformation and reliability analysis can also be achieved for correlated nonnormal random variables with knowledge of only the statistical moments and correlation matrix. The simplicity and efficiency of the proposed method is further demonstrated through several numerical examples.
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Acknowledgments
The research reported in this paper is partially supported by the National Natural Science Foundation of China (Grant Nos. 51422814, U1134209, U1434204), the Project of Innovation-Driven Plan in Central South University (2015CXS014), and the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (Grant No. IRT1296). The Fundamental Research Funds for the Central Universities of Central South University is also gratefully acknowledged.
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Published In
Journal of Structural Engineering
Volume 143 • Issue 8 • August 2017
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©2017 American Society of Civil Engineers.
History
Received: Jul 27, 2016
Accepted: Jan 13, 2017
Published online: Mar 24, 2017
Published in print: Aug 1, 2017
Discussion open until: Aug 24, 2017
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