Nonuniform rational B-splines (NURBs) have unique properties that make them attractive for engineering metamodeling applications. NURBs are known to accurately model many different continuous curve and surface topologies in one- and two-variate spaces. However, engineering metamodels of the design space often require hypervariate representations of multidimensional outputs. In essence, design space metamodels are hyperdimensional constructs with a dimensionality determined by their input and output variables. To use NURBs as the basis for a metamodel in a hyperdimensional space, traditional geometric fitting techniques must be adapted to hypervariate and hyperdimensional spaces composed of both continuous and discontinuous variable types. In this paper, we describe the necessary adaptations for the development of a NURBs-based metamodel called a hyperdimensional performance model or HyPerModel. HyPerModels are capable of accurately and reliably modeling nonlinear hyperdimensional objects defined by both continuous and discontinuous variables of a wide variety of topologies, such as those that define typical engineering design spaces. We demonstrate this ability by successfully generating accurate HyPerModels of ten trial functions laying the foundation for future work with -dimensional NURBs in design space applications.
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e-mail: cturner@mines.edu
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September 2009
Research Papers
-Dimensional Nonuniform Rational B-Splines for Metamodeling
Cameron J. Turner,
Cameron J. Turner
Assistant Professor
Mem. ASME
Division of Engineering,
e-mail: cturner@mines.edu
Colorado School of Mines
, 1500 Illinois Street, Golden, CO 80401
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Richard H. Crawford, P.E.
Richard H. Crawford, P.E.
Professor
Mem. ASME
Department of Mechanical Engineering,
e-mail: rhc@mail.utexas.edu
University of Texas at Austin
, 1 University Station, C2200, Austin, TX 78712
Search for other works by this author on:
Cameron J. Turner
Assistant Professor
Mem. ASME
Division of Engineering,
Colorado School of Mines
, 1500 Illinois Street, Golden, CO 80401e-mail: cturner@mines.edu
Richard H. Crawford, P.E.
Professor
Mem. ASME
Department of Mechanical Engineering,
University of Texas at Austin
, 1 University Station, C2200, Austin, TX 78712e-mail: rhc@mail.utexas.edu
J. Comput. Inf. Sci. Eng. Sep 2009, 9(3): 031002 (13 pages)
Published Online: August 19, 2009
Article history
Received:
November 5, 2007
Revised:
November 25, 2008
Published:
August 19, 2009
Citation
Turner, C. J., and Crawford, R. H. (August 19, 2009). "-Dimensional Nonuniform Rational B-Splines for Metamodeling." ASME. J. Comput. Inf. Sci. Eng. September 2009; 9(3): 031002. https://doi.org/10.1115/1.3184599
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