Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula

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System reliability-based design optimization using the MPP-based dimension reduction method (2010, unknown): “It is known that σ ′f , b, and ε′f, c are highly negatively correlated (Noh et al. 2009a; Socie 2003; Annis 2004).”
Weighted stochastic response surface method considering sample weights (2011, methodology): “When input random variables are correlated, they should be first transformed into independent variables using Rosenblatt (1952) or Nataf transformation ( Noh et al. 2009 ).”
Bivariate distribution models using copulas for reliability analysis (2013, background): “Except for some special cases, the integration of equation (10) over the failure domain g(X) 4 0 cannot be performed analytically.”
Impact of copulas for modeling bivariate distributions on system reliability (2013, methodology): “Conventionally, the Nataf model [8,14,16,17] is used to construct the joint CDF or PDF based on incomplete probability information.”