REFERENCES
- Eldred , M. S. , Webster , C. G. , Constantine , P. ( 2008 ). Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos. Proceedings of the 10th AIAA Nondeterministic Approaches Conference, Schaumburg, IL, No. AIAA-2008-1892 .
- Garcke , J. , Griebel , M. ( 2002 ). Classification with anisotropic sparse grids using simplicial basis functions . Intelligent Data Analysis 6 ( 6 ): 483 – 502 .
- Gerstner , T. , Griebel , M. ( 2003 ). Dimension-adaptive tensor-product quadrature . Computing 71 ( 1 ): 65 – 87 .
- Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1994 ). Continuous Univariate Distributions, 2nd edn. New York, NY: Wiley .
- Lee , S. H. , Chen , W. ( 2008 ). A comparative study of uncertainty propagation methods for black-box type functions . Structural and Multidisciplinary Optimization 37 ( 3 ): 239 – 253 .
- Lu , H. , Zhang , Y. ( 2011 ). Reliability-based robust design for structural system with multiple failure modes . Mechanics Based Design of Structures and Machines: An International Journal 39 ( 4 ): 420 – 440 .
- Nobile , F. , Tempone , R. , Webster , C. G. ( 2008 ). An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data . SIAM Journal on Numerical Analysis 46 ( 5 ): 2411 – 2442 .
- Penmetsa , R. C. , Grandhi , R. V. ( 2003 ). Uncertainty propagation using possibility theory and function approximations . Mechanics-Based Design of Structures and Machines: An International Journal 31 ( 2 ): 257 – 279 .
- Salttelli , A. , Marco , R. , et al. . ( 2008 ). Global Sensitivity Analysis: The Primer . New York , NY : Wiley .
- Smolyak , S. A. ( 1963 ). Quadrature and interpolation formulas for tensor products of certain classes of functions . Soviet Mathematics Doklady 4 : 240 – 243 .
- Sobol , I. M. ( 2001 ). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates . Mathematics and Computers in Simulation 55 ( 1–3 ): 271 – 280 .
- Xiong , F. , Xiong , Y. , et al. . ( 2009 ). A new sparse grid-based method for uncertainty propagation. Structural and Multidisciplinary Optimization 41(3): 335–349 .
- Xiong , F. , Xue , B. , Yang , S. ( 2011 ). Polynomial chaos expansion-based robust design optimization. Proceeding of ICQR2MSE 2011, Xi'an, China .
- Xu , H. , Rahman , S. ( 2004 ). A generalized dimension–reduction method for multidimensional integration in stochastic mechanics . International Journal for Numerical Methods in Engineering 61 : 1992 – 2019 .
- Xue , S. (2010). Research on Multidisciplinary Design Optimization of Aerodynamic & Structural on Wrap-Around-Wing Rockets. Ph.D. thesis, Beijing Institute of Technology, Beijing, China.
- Youn , B. D. , Choi , K. K. , Yi , K. ( 2007 ). Performance moment integration (PMI) method for quality assessment in reliability-based robust design optimization . Mechanics-Based Design of Structures and Machines: An International Journal 33 ( 2 ): 185 – 213 .
- Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lmbd