Efficient updating of kriging estimates and variances

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To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions.When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging.It is used as a substitute of high-fidelity codes representing physical phenomena and aims to reduce the computational time of a particular process.For instance, the kriging model is used successfully in several optimization problems [6–11].The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging.During the last years, the kriging model [1–4], which is referred to as the Gaussian process model [5], has become one of the most popular methods in computer simulation and machine learning.

The PLS technique reduces dimension and reveals how inputs depend on output.This method is able to reduce the number of hyperparameters of a kriging model, such that their number becomes equal to the number of principal components retained by the PLS method.The KPLS method is thus able to rapidly build a kriging model for high-dimensional problems (100 ) while maintaining a good accuracy.Institut Clément Ader, CNRS, ISAE-SUPAERO, Université de Toulouse, 10 Avenue Edouard Belin, 31055 Toulouse Cedex 4, France Received 31 December 2015; Revised ; Accepted Academic Editor: Erik Cuevas Copyright © 2016 Mohamed Amine Bouhlel et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the following, we use (a coefficient) contain the regression coefficients.

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