Robust design with arbitrary distributions using Gauss-type quadrature formula |
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Authors: | S H Lee W Chen B M Kwak |
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Affiliation: | (1) Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Rd Tech B224, Evanston, IL 60201, USA;(2) Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea |
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Abstract: | In this paper, we present the Gauss-type quadrature formula as a rigorous method for statistical moment estimation involving
arbitrary input distributions and further extend its use to robust design optimization. The mathematical background of the
Gauss-type quadrature formula is introduced and its relation with other methods such as design of experiments (DOE) and point
estimate method (PEM) is discussed. Methods for constructing one dimensional Gauss-type quadrature formula are summarized
and the insights are provided. To improve the efficiency of using it for robust design optimization, a semi-analytic design
sensitivity analysis with respect to the statistical moments is proposed for two different multi-dimensional integration methods,
the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. Through several examples,
it is shown that the Gauss-type quadrature formula can be effectively used in robust design involving various non-normal distributions.
The proposed design sensitivity analysis significantly reduces the number of function calls of robust optimization using the
TPQ formulae, while using the UDR method, the savings of function calls are observed only in limited situations. |
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Keywords: | Robust design Gauss-type quadrature formula Tensor product quadrature Univariate dimension reduction method Analytical design sensitivity analysis Design optimization |
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