Article: A Taylor series approach to the robust parameter design of computer simulations using kriging and radial basis function neural networks Journal: International Journal of Quality Engineering and Technology (IJQET) 2017 Vol.6 No.3 pp.137 - 160 Abstract: Robust parameter design is used to identify a system's control settings that offer a compromise between obtaining desired mean responses and minimising the variability about those responses. Two popular combined-array strategies - the response surface model (RSM) approach and the emulator approach - are limited when applied to simulations. In the former case, the mean and variance models can be inadequate due to the high level of nonlinearity within many simulations. In the latter case, precise mean and variance approximations are developed at the expense of extensive Monte Carlo sampling. This paper extends the RSM approach to include nonlinear metamodels, namely kriging and radial basis function neural networks. The mean and variance of second-order Taylor series approximations of these metamodels are generated via the multivariate delta method and subsequent optimisation problems employing these approximations are solved. Results show that improved mean and variance prediction models, relative to the RSM approach, can be attained at a fraction of the emulator approach's cost. Inderscience Publishers - linking academia, business and industry through research

Title: A Taylor series approach to the robust parameter design of computer simulations using kriging and radial basis function neural networks

Authors: Joseph P. Bellucci; Kenneth W. Bauer Jr.

Addresses: Air Education and Training Command, Studies and Analysis Squadron, 100 H Street East, Suite #3, JBSA-Randolph, TX 78150, USA ' Department of Operational Sciences, Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, Ohio 45433, USA

Abstract: Robust parameter design is used to identify a system's control settings that offer a compromise between obtaining desired mean responses and minimising the variability about those responses. Two popular combined-array strategies - the response surface model (RSM) approach and the emulator approach - are limited when applied to simulations. In the former case, the mean and variance models can be inadequate due to the high level of nonlinearity within many simulations. In the latter case, precise mean and variance approximations are developed at the expense of extensive Monte Carlo sampling. This paper extends the RSM approach to include nonlinear metamodels, namely kriging and radial basis function neural networks. The mean and variance of second-order Taylor series approximations of these metamodels are generated via the multivariate delta method and subsequent optimisation problems employing these approximations are solved. Results show that improved mean and variance prediction models, relative to the RSM approach, can be attained at a fraction of the emulator approach's cost.

Keywords: robust parameter design; RPD; Taylor series; simulations; kriging; neural networks; radial basis function neural networks; RBFNN; delta method; dual response optimisation; metamodelling; response surface modelling; emulators.

DOI: 10.1504/IJQET.2017.088860

International Journal of Quality Engineering and Technology, 2017 Vol.6 No.3, pp.137 - 160

Received: 18 Aug 2016
Accepted: 11 May 2017
Published online: 21 Dec 2017 *

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Title: A Taylor series approach to the robust parameter design of computer simulations using kriging and radial basis function neural networks

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