247
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Robust engineering design optimization with non-uniform rational B-splines-based metamodels

, &
Pages 767-786 | Received 24 Sep 2011, Accepted 05 Jun 2012, Published online: 22 Aug 2012

References

  • Ajetunmobi , A. M. 2007 . “ Robust optimization using NURBs based metamodels ” . The University of Texas at Austin . Master's thesis.
  • Box , G. E.P. and Wilson , K. B. 1951 . On the experimental attainment of optimum conditions . Journal of the Royal Statistical Society , 9 ( 1 ) : 1 – 45 .
  • Brusse , W. 2006 . All about Six Sigma , New York : McGraw-Hill .
  • Chen , W. , Allen , J. K. and Tsui , L.-K. 1996 . A procedure for robust design: minimizing variations caused by noise factors and control factors . Journal of Mechanical Design , 118 ( 4 ) : 478 – 485 . (doi:10.1115/1.2826915)
  • Clarke , S. M. , Griebsch , J. H. and Simpson , T. W. 2005 . Analysis of support vector regression for approximation of complex engineering analyses . Journal of Mechanical Design , 127 ( 6 ) : 1077 – 1088 . (doi:10.1115/1.1897403)
  • Collette , Y. and Siarry , P. 2003 . Multiobjective optimization: principles and case studies , 19 – 24 . New York : Springer .
  • Cressie , N. 1990 . The origins of kriging . Mathematical Geology , 22 ( 3 ) : 239 – 252 . (doi:10.1007/BF00889887)
  • Dinh , H. Q. , Turk , G. and Slabaugh , G. 2002 . Reconstructing surfaces by volumetric regularization using radial basis functions . IEEE Transactions on Pattern Analysis and Machine Intelligence , 24 ( 10 ) : 1358 – 1371 . (doi:10.1109/TPAMI.2002.1039207)
  • Friedman , J. H. 1991 . Multivariate adaptive regression splines . Annals of Statistics , 19 ( 1 ) : 1 – 141 . (doi:10.1214/aos/1176347963)
  • Gibson , R. F. 1994 . Principles of composite material mechanics , 190 – 200 . New York : McGraw-Hill .
  • Gu , X. 2000 . Worst case propagated uncertainty of multidisciplinary systems in robust design optimization . et al. , 20 ( 3 ) : 190 – 213 .
  • Gunawan , S. and Azarm , S. 2004a . Non-gradient based parameter sensitivity estimation for single objective robust design optimization . Journal of Mechanical Design, ASME , 126 ( 3 ) : 395 – 402 . (doi:10.1115/1.1711821)
  • Gunawan , S. and Azarm , S. 2004b . Multi-objective robust optimization using a sensitivity region concept . Journal of Structural and Multidisciplinary Optimization , 29 ( 1 ) : 50 – 60 . (doi:10.1007/s00158-004-0450-8)
  • Gutmann , H. M. 2001 . A radial basis function method for global optimization . Journal of Global Optimization , 19 ( 3 ) : 201 – 227 . (doi:10.1023/A:1011255519438)
  • Han , J. S. and Kwak , B. M. 2004 . Robust optimization using a gradient index: MEMS applications . Journal of Structural and Multidisciplinary Optimization , 21 : 300 – 308 .
  • Jin , R. , Chen , W. and Simpson , T. W. 2001 . Comparative studies of metamodeling techniques under multiple modeling criteria . Journal of Structural and Multidisciplinary Optimization , 23 : 1 – 13 . (doi:10.1007/s00158-001-0160-4)
  • Jin , R. , Du , X. and Chen , W. 2003 . The use of metamodeling techniques for optimization under uncertainty . Structural Multidisciplinary Optimization , 25 : 99 – 116 . (doi:10.1007/s00158-002-0277-0)
  • Jin , Y. and Sendhoff , B. Trade-off between performance and robustness: an evolutionary multiobjective approach. LNCS 2632 . April 8–11 , Faro , Portugal. In: Proceedings of the second international conference on evolutionary multi-criteria optimization , pp. 237 – 251 . Berlin : Springer .
  • Jung , D. H. and Lee , B. C. 2002 . Development of a simple efficient method for robust optimization . International Journal for Numerical Methods in Engineering , 53 : 2201 – 2215 . (doi:10.1002/nme.383)
  • Jurecka , F. 2007 . “ Robust design optimization based on metamodeling techniques ” . Technischen Universitat Munchen . Dissertation.
  • Kleijnen , J. P.C. and Sargent , R. G. 2001 . A methodology for fitting and validating metamodels in simulation . European Journal of Operational Research , 120 ( 1 ) : 14 – 29 . (doi:10.1016/S0377-2217(98)00392-0)
  • Kouvelis , P. and Yu , G. 1997 . Robust optimization and its applications , Dordrecht : Kluwer .
  • Lee , K. and Park , G. J. 2001 . Robust optimization considering tolerances of design variables . Journal of Computers and Structures , 79 : 77 – 86 . (doi:10.1016/S0045-7949(00)00117-6)
  • Matheron , G. 1963 . Principles of geostatistics . Economic Geology , 58 ( 8 ) : 1246 – 1266 . (doi:10.2113/gsecongeo.58.8.1246)
  • Myers , R. H. , Montgomery , D. C. and Anderson-Cook , C. M. 2009 . Response surface methodology: process and product optimization using designed experiments , Hoboken , NJ : Wiley .
  • Papalambros , P. Y. and Wilde , D. J. 2000 . Principles of optimal design , 1 – 2 . New York : Cambridge University Press .
  • Pardis , J. , Viader , P. and Bibiloni , L. 1999 . A singular function and its relation with the number systems involved in its definition Economics Working Articles, Universitat Pompeu Fabra.
  • Piegel , L. A. and Tiller , W. 1997 . The NURBs book , New York : Springer .
  • Shimoyama , K. , Oyama , A. and Fujii , K. A new efficient and useful robust optimization approach—design for multi-objective Six Sigma . September 2–5 , Edinburgh , Scotland. In: Proceedings of the 2005 IEEE congress on evolutionary computation , pp. 950 – 957 . Danvers , MA : IEEE Press . 1
  • Simpson , T. W. 1998 . Comparison of response surface and kriging models for multidisciplinary design optimization. 1998 NASA technical documentation , Reston , VA : American Institute of Aeronautics and Astronautics .
  • Taguchi , G. , Chowdhury , S. and Taguchi , S. 2000 . Robust engineering , New York : McGraw-Hill .
  • Turner , C. 2005 . “ HyPerModels: hyperdimensional performance models for engineering design ” . The University of Texas at Austin . Doctoral dissertation.
  • Turner , C. and Crawford , R. Adapting non-uniform rational B-spline fitting techniques to metamodeling. CIE-85544 . Proceedings of the 2005 ASME/IDETC/CIE conferences . September 24–28 , Long Beach , CA . pp. 165 – 178 . 3
  • Turner , C. and Crawford , R. Selecting an appropriate metamodel: the case for NURBs metamodels. DAC-85043 . Proceedings of the 2005 ASME/IDETC/CIE conferences . September 24–28 . pp. 759 – 771 . Long Beach , CA 2
  • Turner , C. and Crawford , R. 2009 . N-dimensional nonuniform rational B-splines for metamodeling . Journal of Computing and Information Science in Engineering, ASME , 9 ( 3 ) : 1 – 13 .
  • Turner , C. , Crawford , R. and Campbell , M. 2007 . Global optimization with NURBs-based metamodels . Engineering Optimization , 39 ( 3 ) : 245 – 269 . (doi:10.1080/03052150601077260)
  • Viader , P. , Paradis , J. and Bibiloni , L. 1998 . A new light on Minkowski's ?(x) function . Journal of Number Theory , 73 ( 2 ) : 212 – 227 . (doi:10.1006/jnth.1998.2294)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.