Reliability-based robust design optimization using the eigenvector dimension reduction (EDR) method

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A comparative study of probability estimation methods for reliability analysis (2011, methodology): “In recent years, these methods have been employed to approximate the PDF, probabilities, and reliabilities of system responses from the known statistical information (Farnum 1997; Chen and Kamburowska 2001; Soize 2001; Huang and Du 2006; Straeten and Beck 2008; Youn and Xi 2009).”
A modified Benders decomposition method for efficient robust optimization under interval uncertainty (2011, background): “For example, Youn and Xi (2009) modified a double loop problem (like robust optimization) into a single loop so that it becomes computationally easier.”
Robust design with arbitrary distributions using Gauss-type quadrature formula (2009, methodology): “By the univariate dimension reduction (UDR) method (Rahman and Xu 2004; Youn and Xi 2008), the multivariate function g(X) is approximated by a sum of univariate functions which depend on only one variable with the other variables fixed to their mean values.”