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Adaptive Designs of Experiments for Accurate Approximation of a Target Region

Abstract : Author(s): Victor Picheny, Postdoctorate Researcher Department of Applied Mathematics and Systems, Ecole Centrale Paris, Chatenay-Malabry 92295, France David Ginsbourger, Research Assistant Professor Institute of Mathematical Statistics and Actuarial Science, University of Bern, Bern, CH-3012 Bern, Switzerland Olivier Roustant, Assistant Professor Ecole des Mines de St Etienne, Saint Etienne 42023, France Raphael T. Haftka, Distinguished Professor and Nam-Ho Kim, Associate Professor Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611 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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Submitted on : Monday, May 21, 2012 - 3:12:47 PM
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Victor Picheny, David Ginsbourger, Olivier Roustant, Raphael T. Haftka, Nam-Ho Kim. Adaptive Designs of Experiments for Accurate Approximation of a Target Region. Journal of Mechanical Design, 2010, 132 (7), 071008 (9 p.). ⟨10.1115/1.4001873⟩. ⟨emse-00699752⟩



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