Enhanced Dimension-Reduction (eDR) method for sensitivity-free uncertainty quantification

In this paper, the enhanced Dimension Reduction (eDR) method is proposed for uncertainty quantification that is an improved version of the DR method. It has been acknowledged that the DR method is accurate and efficient for assessing statistical moments of mildly nonlinear system responses. However, the recent investigation on the DR method has found difficulties of instability and inaccuracy for large-scale nonlinear systems, while maintaining reasonable efficiency. The eDR method is composed of four new technical elements: one-dimensional response approximation, Axial-Design of Experiment (A-DOE), numerical integration scheme, and a modified Pearson system. First, the Stepwise Moving Least Squares method is employed to accurately approximate the responses. Second, 2N+1 and 4N+1 A-DOEs are proposed to maintain high accuracy of the eDR method for UQ analysis. Third, in aid of approximated responses, any numerical integration scheme can be used with accurate but free response values at any set of integration points. Fourth, a modified Pearson system will be proposed to avoid its singular behavior while precisely predicting reliability and quality of engineering systems. Results for some engineering examples indicate that the eDR method is better than any other probability analysis methods in estimating statistical moments, reliability, and quality of the systems.

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