Fast numerical methods for robust optimal design

References

• Allen , J. , Seepersad , C. , Choi , J. and Mistree , F. 2006 . Robust design for multiscale and multidisciplinary applications . Journal of Mechanical Design , 128 : 832 – 843 .
   Web of Science ®Google Scholar
• Babus˘ka , I. , Tempone , R. and Zouraris , G. 2004 . Galerkin finite element approximations of stochastic elliptic differential equations . SIAM Journal on Numerical Analysis , 42 : 800 – 825 .
   Web of Science ®Google Scholar
• Belegundu , A. and Zhang , S. 1992 . Robustness of design through minimum sensitivity . Journal of Mechanical Design , 114 : 213 – 220 .
   Web of Science ®Google Scholar
• Bergounioux , M. and Kunisch , K. 1997 . Augmented Lagrangian techniques for elliptic state constrained optimal control problems . SIAM Journal on Control and Optimization , 35 : 1524 – 1543 .
   Web of Science ®Google Scholar
• Chen , W. , Allen , J. , Mavis , D. and Mistree , F. 1996 . A concept exploration method for determining robust top-level specifications . Engineering Optimization , 26 : 137 – 158 .
   Web of Science ®Google Scholar
• Chen , W. , Sahai , A. , Messac , A. and Sundararaj , G. 2000 . Exploration of the effectiveness of physical programming in robust design . Journal of Mechanical Design , 122 : 155 – 163 .
   Web of Science ®Google Scholar
• Chen , W. , Wiecek , M. and Zhang , J. 1999 . Quality utility: a compromise programming approach to robust design . Journal of Mechanical Design , 121 ( 2 ) : 179 – 187 .
   Web of Science ®Google Scholar
• Chorin , A. 1971 . Hermite expansion in Monte-Carlo simulations . Journal of Computational Physics , 8 : 472 – 482 .
   Web of Science ®Google Scholar
• Du , X. and Chen , W. 2002 . Efficient uncertainty analysis methods for multi-disciplinary robust design . AIAA Journal , 40 ( 3 ) : 545 – 552 .
   Web of Science ®Google Scholar
• Eggert , R. and Mayne , R. 1993 . Probabilistic optimal-design using successive surrogate probability density functions . Journal of Mechanical Design , 115 ( 3 ) : 385 – 391 .
   Google Scholar
• Fowlkes , W. and Creveling , C. 1995 . Engineering methods for robust product design using Taguchi methods in technology and product development , Reading, MA : Addison-Wesley .
   Google Scholar
• Frauenfelder , P. , Schwab , C. and Todor , R. 2005 . Finite elements for elliptic problems with stochastic coefficients . Computer Methods in Applied Mechanics Engineering , 194 : 205 – 228 .
   Web of Science ®Google Scholar
• Ghanem , R. 1999 . Ingredients for a general purpose stochastic finite element formulation . Computer Methods in Applied Mechanics Engineering , 168 : 19 – 34 .
   Web of Science ®Google Scholar
• Ghanem , R. and Spanos , P. 1991 . Stochastic finite elements: a spectral approach , Berlin : Springer .
   Google Scholar
• Gunawan , S. and Azarm , S. 2005 . Multi-objective robust optimization using a sensitivity region concept . Structural and Multidisciplinary Optimization , 29 : 50 – 60 .
   Web of Science ®Google Scholar
• Le Maitre , O. , Knio , O. , Najm , H. and Ghanem , R. 2004 . Uncertainty propagation using Wiener-Haar expansions . Journal of Computational Physics , 197 : 28 – 57 .
   Web of Science ®Google Scholar
• Loève , M. 1977 . Probability Theory , 4 , Berlin : Springer .
   Google Scholar
• Murphy , T. , Tsui , K.-L. and Allen , J. 2005 . A review of robust design methods for multiple responses . Research in Engineering Design , 15 : 201 – 215 .
   Web of Science ®Google Scholar
• Nair , V. 1992 . Taguchi's parameter design: a panel discussion . Technometrics , 34 : 127 – 161 .
   Web of Science ®Google Scholar
• Ramakrishnan , B. and Rao , S. 1996 . A general loss function based optimization procedure for robust design . Engineering Optimization , 25 : 255 – 276 .
   Web of Science ®Google Scholar
• Rao , S. 1996 . Engineering optimization: theory and practice , New York : Wiley .
   Google Scholar
• Shoemaker , A. , Tsui , K.-L. and Wu , C. 1991 . Economical experimentation methods for robust design . Technometrics , 33 : 415 – 427 .
   Web of Science ®Google Scholar
• Taguchi , G. 1986 . Introduction to quality engineering: design quality into products and processes , Tokyo : Asian Productivity Organization .
   Google Scholar
• Wiener , N. 1938 . The homogeneous chaos . American Journal of Mathematics , 60 : 897 – 936 .
   Web of Science ®Google Scholar
• Xiu , D. 2007 . Efficient collocational approach for parametric uncertainty analysis . Communications in Computational Physics , 2 ( 2 ) : 293 – 309 .
   Web of Science ®Google Scholar
• Xiu , D. and Hesthaven , J. 2005 . High-order collocation methods for differential equations with random inputs . SIAM Journal on Scienific Computing , 27 ( 3 ) : 1118 – 1139 .
   Web of Science ®Google Scholar
• Xiu , D. and Karniadakis , G. 2002 . The Wiener-Askey polynomial chaos for stochastic differential equations . SIAM Journal on Scienific Computing , 24 ( 2 ) : 619 – 644 .
   Web of Science ®Google Scholar
• Xiu , D. and Karniadakis , G. 2003 . Modeling uncertainty in flow simulations via generalized polynomial chaos . Journal of Computational Physics , 187 : 137 – 167 .
   Web of Science ®Google Scholar