Open Access

ARTICLE

Optimal Design of Computer Experiments for Metamodel Generation Using I-OPT^TM

Selden B. Crary¹, Peter Cousseau², David Armstrong¹, David M. Woodcock³, Eva H. Mok¹, Olivier Dubochet⁴, Philippe Lerch⁴, Philippe Renaud²

1 Ctr. for Integrated MicroSystems, U. Mich., Ann Arbor, MI, USA
2 Institute for Microsystems, EPFL, Ecublens, CH
3 Lab. for Scientific Computation, U. Mich., Ann Arbor, MI, USA
4 Leister Process Technologies, Sarnen, CH

Computer Modeling in Engineering & Sciences 2000, 1(1), 127-140. https://doi.org/10.3970/cmes.2000.001.127

Abstract

We present a new and unique software capability for finding statistical optimal designs of deterministic experiments on continuous cuboidal regions. The objective function for the design optimization is the minimization of the expected integrated mean squared error of prediction of the metamodel that will be found, subsequent to the running of the computer simulations, using the best linear unbiased predictor (BLUP). The assumed response-model function includes an unknown, stochastic term, Z. We prove that this criterion, which we name I_Z-optimality, is equivalent to I-optimality for non-deterministic experiments, in the limit of zero correlations among the Z's for different inputs. An example is presented of metamodel generation for a micromachined-silicon flow sensor. The I_Z-optimal set of inputs is found, finite-element (FE) simulations run, and the metamodel generated using a BLUP fit. The method is compared to other approaches. I_Z-optimality, coupled with BLUP fitting, provides a highly efficient means of non-parametric metamodel generation. I_Z-optimal design searching and BLUP fitting are new options of the I-OPT^TM program that is available on the World-Wide Web at URL http://www-personal.engin.umich.edu/~crary/iopt.

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