Moreover, this inversion’s problem induces difficulty in the classical hyperparameters estimation through the maximization of the likelihood function.
A recent method, called KPLS , is developed to reduce computational time which uses, during a construction of the kriging model, the dimensional reduction method “Partial Least Squares” (PLS).
Under hypothesis that kernels used for building the KPLS model are of exponential type with the same form (all Gaussian kernels, e.g.), we choose the hyperparameters found by the KPLS model as an initial point to optimize the likelihood function of a conventional kriging model.
In fact, this approach is performed by identifying the covariance function of the KPLS model as a covariance function of a kriging model.
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.
Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models.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.In the following, we use (a coefficient) contain the regression coefficients.For more details of how PLS method works, please see [19–21].Finally, numerical results are shown to confirm the efficiency of our method followed by a summary of what we have achieved.