Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula |
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Authors: | Yoojeong Noh K K Choi Liu Du |
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Affiliation: | (1) Department of Mechanical and Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242, USA |
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Abstract: | The reliability-based design optimization (RBDO) using performance measure approach for problems with correlated input variables
requires a transformation from the correlated input random variables into independent standard normal variables. For the transformation
with correlated input variables, the two most representative transformations, the Rosenblatt and Nataf transformations, are
investigated. The Rosenblatt transformation requires a joint cumulative distribution function (CDF). Thus, the Rosenblatt
transformation can be used only if the joint CDF is given or input variables are independent. In the Nataf transformation,
the joint CDF is approximated using the Gaussian copula, marginal CDFs, and covariance of the input correlated variables.
Using the generated CDF, the correlated input variables are transformed into correlated normal variables and then the correlated
normal variables are transformed into independent standard normal variables through a linear transformation. Thus, the Nataf
transformation can accurately estimates joint normal and some lognormal CDFs of the input variable that cover broad engineering
applications. This paper develops a PMA-based RBDO method for problems with correlated random input variables using the Gaussian
copula. Several numerical examples show that the correlated random input variables significantly affect RBDO results. |
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Keywords: | Correlated input variables Reliability-based design optimization (RBDO) Inverse reliability analysis Rosenblatt transformation Nataf transformation Gaussian copula |
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