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Multidimensional sequential sampling for NURBs-based metamodel development

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Abstract

Adaptive design of experiments approaches are intended to overcome the limitations of a priori experimental design by adapting to the results of prior runs so that subsequent runs yield more significant information. Such approaches are valuable in engineering applications with metamodels, where efficiently collecting a dataset to define an unknown function is important. While a variety of approaches have been proposed, most techniques are limited to sampling for only one phenomenon at a time. We propose a multicriteria optimization approach that effectively simultaneously samples for multiple phenomena. In addition to determining the next sequential sampling point, such an algorithm also can be formulated to support conclusions about the adequacy of the experiment through the use of convergence criteria. A multicriteria adaptive sequential sampling algorithm, along with convergence metrics, is defined and demonstrated on five trial problems of engineering interest. The results of these five problems demonstrate that a multicriteria sequential sampling approach is a useful engineering tool for modeling engineering design spaces using NURBs-based metamodels.

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Acknowledgments

The assistance and support of Troy Harden, Chris James, and Kane Fisher of Los Alamos National Laboratory and the students of The University of Texas at Austin Manufacturing and Design Laboratory to complete this work is greatly appreciated.

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Authors and Affiliations

  1. Plutonium Manufacturing and Technology Division, Los Alamos National Laboratory, P.O. Box 1663, MS J580, Los Alamos, NM, 87545, USA

    Cameron J. Turner

  2. Department of Mechanical Engineering, The University of Texas at Austin, 1 University Station, C2200, Austin, TX, 78712-0292, USA

    Richard H. Crawford & Matthew I. Campbell

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  1. Cameron J. Turner
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  2. Richard H. Crawford
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  3. Matthew I. Campbell
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Correspondence to Cameron J. Turner.

Additional information

This paper is approved for release by Los Alamos National Laboratory under LA-UR-06-6651 and is based upon research originally presented at the 2003 and 2004 ASME IDETC/CIE Conferences. Funding provided by Los Alamos National Laboratory and the National Science Foundation under Grant No. DMI-0323838. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or Los Alamos National Laboratory.

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Turner, C.J., Crawford, R.H. & Campbell, M.I. Multidimensional sequential sampling for NURBs-based metamodel development. Engineering with Computers 23, 155–174 (2007). https://doi.org/10.1007/s00366-006-0051-9

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