Cross-validation based single response adaptive design of experiments for Kriging metamodeling of deterministic computer
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RESEARCH PAPER
Cross-validation based single response adaptive design of experiments for Kriging metamodeling of deterministic computer simulations V. Aute · K. Saleh · O. Abdelaziz · S. Azarm · R. Radermacher
Received: 14 February 2012 / Revised: 1 February 2013 / Accepted: 2 March 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract A new approach for single response adaptive design of deterministic computer experiments is presented. The approach is called SFCVT, for Space-Filling CrossValidation Tradeoff. SFCVT uses metamodeling to obtain an estimate of cross-validation errors, which are maximized subject to a constraint on space filling to determine sample points in the design space. The proposed method is compared, using a test suite of forty four numerical examples, with three DOE methods from the literature. The numerical test examples can be classified into symmetric and asymmetric functions. Symmetric examples refer to functions for which the extreme points are located symmetrically in the design space and asymmetric examples are those for which the extreme regions are not located in a symmetric fashion in the design space. Based upon the comparison results
for the numerical examples, it is shown that SFCVT performs better than an existing adaptive and a non-adaptive DOE method for asymmetric multimodal functions with high nonlinearity near the boundary, and is comparable for symmetric multimodal functions and other test problems. The proposed approach is integrated with a multi-scale heat exchanger optimization tool to reduce the computational effort involved in the design of novel air-to-water heat exchangers. The resulting designs are shown to be significantly more compact than mainstream heat exchanger designs. Keywords Design optimization · Design of experiments · Kriging metamodeling · Heat exchanger design
Nomenclature A previous version of this paper was presented at: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, British Columbia, Canada, Sep 10–12, 2008; Aute, V., Abdelaziz, O., Azarm, S., Radermacher, R. 2008, “Cross-validation Based Single Response Adaptive Design of Experiments” V. Aute () · K. Saleh · S. Azarm · R. Radermacher Mechanical Engineering Department, University of Maryland, College Park, MD 20742, USA e-mail: [email protected] K. Saleh e-mail: [email protected] S. Azarm e-mail: [email protected] R. Radermacher e-mail: [email protected] O. Abdelaziz Oak Ridge National Lab, Oak Ridge, TN 37831, USA e-mail: [email protected]
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kth component of the weight vector Cross Validation Error Dimension of input space Current design Number of sample points in design D Inner diameter Outer diameter Cluster threshold Determinant Scaled distance Relative error Leave-one-out error Predicted leave-one-out error Entropy Identity matrix or vector Maximum number of function calls Leave-One-Out
V. Aute et al.
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Maximum Entropy Design Maxi-Min Scaled Distance Number of poi
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