Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules

Authors:
D. L. Wei;Z. S. Cui;J. Chen
Affiliations:
National Die and Mold CAD Engineering Research Center, Shanghai Jiao Tong University, Shanghai 200030, China;National Die and Mold CAD Engineering Research Center, Shanghai Jiao Tong University, Shanghai 200030, China;National Die and Mold CAD Engineering Research Center, Shanghai Jiao Tong University, Shanghai 200030, China
Venue:
Computers and Structures
Year:
2008

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Abstract

This paper proposes an efficient method for estimating uncertainty propagation and identifying influence factors contributing to uncertainty. In general, the system is dominated by some of the main effects and lower-order interactions due to the sparsity-of-effect principle. Therefore, the construction of polynomial chaos expansion with points of monomial cubature rules is particularly attractive in dealing with large computational model. This approach has advantages over many others as it needs far fewer sampling points for multivariate models and all of the points can be sampled. The proposed approach is validated via two mathematical functions and an engineering problem.