Journal ArticleDOI
Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula
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TLDR
A PMA-based RBDO method for problems with correlated random input variables using the Gaussian copula is developed, which can accurately estimates joint normal and some lognormal CDFs of the input variable that cover broad engineering applications.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.read more
Citations
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Journal ArticleDOI
Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems
Chao Hu,Byeng D. Youn +1 more
TL;DR: The proposed adaptive-sparse polynomial chaos expansion method is highly efficient and accurate for reliability analysis and its sensitivity analysis, and it is capable of handling a nonlinear correlation.
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Sampling-based RBDO using the stochastic sensitivity analysis and Dynamic Kriging method
TL;DR: New efficiency and accuracy strategies such as a hyper-spherical local window for surrogate model generation, sample reuse, local window enlargement, filtering of constraints, and an adaptive initial point for the pattern search are proposed.
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Uncertainty quantification in multiscale simulation of woven fiber composites
Ramin Bostanabad,Biao Liang,Jiaying Gao,Wing Kam Liu,Jian Cao,Danielle Zeng,Xuming Su,Hongyi Xu,Yang Li,Wei Chen +9 more
TL;DR: The top-down sampling method is introduced that allows to model non-stationary and continuous (but not differentiable) spatial variations of uncertainty sources by creating nested random fields (RFs) where the hyperparameters of an ensemble of RFs is characterized by yet another RF.
Journal ArticleDOI
Impact of copulas for modeling bivariate distributions on system reliability
TL;DR: A copula-based method is presented to investigate the impact of copulas for modeling bivariate distributions on system reliability under incomplete probability information and indicates that the system probability of failure of a parallel system under incomplete probabilities information cannot be determined uniquely.
References
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Book
An Introduction to Copulas
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Book
Structural Reliability: Analysis and Prediction
TL;DR: Measures of Structural Reliability Assessment, including second-Moment and Transformation Methods, and Probabilistic Evaluation of Existing Structures.
Journal ArticleDOI
Remarks on a Multivariate Transformation
Book
Introduction to Optimum Design
TL;DR: This fourth edition of the introduction to Optimum Design has been reorganized, rewritten in parts, and enhanced with new material, making the book even more appealing to instructors regardless of course level.
Book
Structural Reliability Methods
Ove Ditlevsen,H. O. Madsen +1 more
TL;DR: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometricreliability Index Generalized Reliability index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis.