Journal
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
Volume 38, Issue 1, Pages 1-16Publisher
SPRINGER
DOI: 10.1007/s00158-008-0277-9
Keywords
Correlated input variables; Reliability-based design optimization (RBDO); Inverse reliability analysis; Rosenblatt transformation; Nataf transformation; Gaussian copula
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Funding
- US Army TARDEC
- Automotive Research Center
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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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