Capability of high intrinsic quality Space Filling Design for global sensitivity analysis and metamodelling of interference optical systems

摘要

In the field of computer experiments, when the relations between the outputs and the inputs of the computer code are complex, the Space Filling Designs (SFD) are used to study the outputs all over the domain or to build metamodels. It is necessary that the points of these designs are distributed as uniformly as possible in the domain of interest. The methodology of Minimum Spanning Tree (MST) was proposed to evaluate the quality of the distribution of the points of an experimental design in a multidimensional space. We introduce here the results obtained in high dimensional case (dimension higher than 20) and we point out the bad quality of the classical designs or the designs based on low discrepancy sequences but mainly the advantages of WSP designs. Empirical results point out the need to qualify SFD in the original space due to the insufficiency of the conclusions obtained using projections onto 2D subspaces. We define the intrinsic quality of SFD as the characteristic of the distribution of the points in the space. Likewise, the extrinsic quality of SFD describes the performances of the results obtained by the use of SFD on an application case. The results obtained with different SFD in the case of interference optical system sensitivity analysis are presented. Finally, the intrinsic quality of SFD is assessed by MST criterion and is proved to be in accordance with the results of the interference optical system sensitivity analysis. So, this study can be considered as an empirical step to connect intrinsic quality and extrinsic quality of SFD designs.