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

Non-uniform rational B-splines (NURBs) demonstrate properties that make them attractive as metamodels, or surrogate models, for engineering design purposes. Previous research has resulted in the development of algorithms capable of fitting NURBs-based metamodels to engineering design spaces, and optimizing these models. This article presents an approach to robust optimization that employs NURBs-based metamodels. This robust optimization technique exploits the unique structure of NURBs-based metamodels to derive a simple but effective robustness metric. An algorithm is demonstrated that uses this metric to weigh robustness against optimality, and visualizes the trade-offs between these metamodel properties. This approach is demonstrated with test problems of increasing dimensionality, including several practical design challenges.

[1]  John E. Renaud,et al.  Worst case propagated uncertainty of multidisciplinary systems in robust design optimization , 2000 .

[2]  Jaume Paradís,et al.  A Singular Function and its Relation with the Number Systems Involved in its Definition , 1999 .

[3]  Timothy M. Mauery,et al.  COMPARISON OF RESPONSE SURFACE AND KRIGING MODELS FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION , 1998 .

[4]  Abiola Moruf Ajetunmobi.  Robust optimization using NURBs based metamodels , 2007 .

[5]  Richard H. Crawford,et al.  Adapting Non-Uniform Rational B-Spline Fitting Approaches to Metamodeling , 2005 .

[6]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[7]  Bernhard Sendhoff,et al.  Trade-Off between Performance and Robustness: An Evolutionary Multiobjective Approach , 2003, EMO.

[8]  Jaume Paradís,et al.  A new light on Minkowski's? $(x)$ function , 1998 .

[9]  Richard H. Crawford,et al.  Global optimization of NURBs-based metamodels , 2007 .

[10]  R. Gibson.  Principles of Composite Material Mechanics , 1994 .

[11]  Shapour Azarm,et al.  Non-Gradient Based Parameter Sensitivity Estimation for Single Objective Robust Design Optimization , 2004 .

[12]  Panos Y. Papalambros,et al.  Principles of Optimal Design: Author Index , 2000 .

[13]  Jeong Sam Han,et al.  Robust optimization using a gradient index: MEMS applications , 2004 .

[14]  Richard H. Crawford,et al.  Selecting an Appropriate Metamodel: The Case for NURBs Metamodels , 2005, DAC 2005.

[15]  N. Cressie.  The origins of kriging , 1990 .

[16]  Xiaoping Du,et al.  The use of metamodeling techniques for optimization under uncertainty , 2001 .

[17]  Panos Y. Papalambros,et al.  Principles of Optimal Design: Optimization Models , 2000 .

[18]  P. Siarry,et al.  Multiobjective Optimization: Principles and Case Studies , 2004 .

[19]  Akira Oyama,et al.  A new efficient and useful robust optimization approach - design for multi-objective six sigma , 2005, 2005 IEEE Congress on Evolutionary Computation.

[20]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[21]  Cameron J. Turner,et al.  HyPerModels: Hyperdimensional Performance Models for engineering design , 2005 .

[22]  Timothy W. Simpson,et al.  Analysis of support vector regression for approximation of complex engineering analyses , 2003, DAC 2003.

[23]  Richard H. Crawford,et al.  N -Dimensional Nonuniform Rational B-Splines for Metamodeling , 2009, J. Comput. Inf. Sci. Eng..

[24]  S. Azarm,et al.  Multi-objective robust optimization using a sensitivity region concept , 2005 .

[25]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[26]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[27]  Jack P. C. Kleijnen,et al.  A methodology for fitting and validating metamodels in simulation , 2000, Eur. J. Oper. Res..

[28]  Kwon-Hee Lee,et al.  Robust optimization considering tolerances of design variables , 2001 .

[29]  Florian Jurecka,et al.  Robust Design Optimization Based on Metamodeling Techniques , 2007 .

[30]  Farrokh Mistree,et al.  A procedure for robust design: Minimizing variations caused by noise factors and control factors , 1996 .

[31]  Greg Turk,et al.  Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[33]  Hans-Martin Gutmann,et al.  A Radial Basis Function Method for Global Optimization , 2001, J. Glob. Optim..

[34]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[35]  Byung Chai Lee,et al.  Development of a simple and efficient method for robust optimization , 2002 .

[36]  G. Matheron.  Principles of geostatistics , 1963 .