Journal article
Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula
Structural and multidisciplinary optimization, Vol.38(1), pp.1-16
03/2009
DOI: 10.1007/s00158-008-0277-9
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.
Details
- Title: Subtitle
- Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula
- Creators
- Yoojeong Noh - Department of Mechanical and Industrial Engineering, College of Engineering The University of Iowa Iowa City IA 52242 USAK Choi - Department of Mechanical and Industrial Engineering, College of Engineering The University of Iowa Iowa City IA 52242 USALiu Du - Department of Mechanical and Industrial Engineering, College of Engineering The University of Iowa Iowa City IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Structural and multidisciplinary optimization, Vol.38(1), pp.1-16
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- DOI
- 10.1007/s00158-008-0277-9
- ISSN
- 1615-147X
- eISSN
- 1615-1488
- Language
- English
- Date published
- 03/2009
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064228602771
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