This paper addresses the issue of designing experiments for a metamodel that needs to be accurate for a certain level of the response value. Such a situation is common in constrained optimization and reliability analysis. Here, we propose an adaptive strategy to build designs of experiments that is based on an explicit trade-off between reduction in global uncertainty and exploration of regions of interest. A modified version of the classical integrated mean square error criterion is used that weights the prediction variance with the expected proximity to the target level of response. The method is illustrated by two simple examples. It is shown that a substantial reduction in error can be achieved in the target regions with reasonable loss of global accuracy. The method is finally applied to a reliability analysis problem; it is found that the adaptive designs significantly outperform classical space-filling designs.
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e-mail: victor.picheny@ecp.fr
e-mail: david.ginsbourger@stat.unibe.ch
e-mail: haftka@ufl.edu
e-mail: nkim@ufl.edu
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July 2010
Research Papers
Adaptive Designs of Experiments for Accurate Approximation of a Target Region
Victor Picheny,
Victor Picheny
Postdoctorate Researcher
Department of Applied Mathematics and Systems,
e-mail: victor.picheny@ecp.fr
Ecole Centrale Paris
, Chatenay-Malabry 92295, France
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David Ginsbourger,
David Ginsbourger
Research Assistant Professor
Institute of Mathematical Statistics and Actuarial Science,
e-mail: david.ginsbourger@stat.unibe.ch
University of Bern
, Bern, CH-3012 Bern, Switzerland
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Raphael T. Haftka,
Raphael T. Haftka
Distinguished Professor
Department of Mechanical and Aerospace Engineering,
e-mail: haftka@ufl.edu
University of Florida
, Gainesville, FL 32611
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Nam-Ho Kim
Nam-Ho Kim
Associate Professor
Department of Mechanical and Aerospace Engineering,
e-mail: nkim@ufl.edu
University of Florida
, Gainesville, FL 32611
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Victor Picheny
Postdoctorate Researcher
Department of Applied Mathematics and Systems,
Ecole Centrale Paris
, Chatenay-Malabry 92295, Francee-mail: victor.picheny@ecp.fr
David Ginsbourger
Research Assistant Professor
Institute of Mathematical Statistics and Actuarial Science,
University of Bern
, Bern, CH-3012 Bern, Switzerlande-mail: david.ginsbourger@stat.unibe.ch
Olivier Roustant
Assistant Professor
Raphael T. Haftka
Distinguished Professor
Department of Mechanical and Aerospace Engineering,
University of Florida
, Gainesville, FL 32611e-mail: haftka@ufl.edu
Nam-Ho Kim
Associate Professor
Department of Mechanical and Aerospace Engineering,
University of Florida
, Gainesville, FL 32611e-mail: nkim@ufl.edu
J. Mech. Des. Jul 2010, 132(7): 071008 (9 pages)
Published Online: June 29, 2010
Article history
Received:
February 15, 2009
Revised:
May 12, 2010
Online:
June 29, 2010
Published:
June 29, 2010
Citation
Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R. T., and Kim, N. (June 29, 2010). "Adaptive Designs of Experiments for Accurate Approximation of a Target Region." ASME. J. Mech. Des. July 2010; 132(7): 071008. https://doi.org/10.1115/1.4001873
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