An Advanced Point Estimate Method for Uncertainty and Sensitivity Analysis Using Nataf Transformation and Dimension-Reduction Integration

This article presents an advanced point estimate method (APEM) with the purposes of estimating the moments of model outputs and identifying the sensitivities of inputs variables. The APEM consists of four ingredients, i.e. (1) Nataf transformation, (2) a generalized dimension-reduction method, (3) the Gauss–Hermite integration (GHI), and (4) a global sensitivity index. Nataf transformation enables the APEM to deal with the practical engineering problems generally involving the random variables often given the marginal distributions and correlations. The generalized dimension-reduction method with the univariate and the bivariate formulas is adopted to decompose a high-dimension function into several one- and two-dimension functions, respectively. Consequently, the moments of the high-dimension function are approximated by that of the decomposed low-dimension functions, which are further calculated by the GHI. As a complement to the APEM, a global sensitivity index is additionally proposed. Through three numerical examples and two applications, the APEM shows good performance at estimating the moments of random functions, and the global sensitivity index is validated for defining the influence of a variable’s variation in standard normal space on model responses.