4. Modeling the response surface

The analysis of the experimental design consists in modeling the different response values as a function of the different values of the factors defined by this design. This modeling can take several forms, but the objective of the study determines the type of modeling. In fact, a metamodel can have at least two objectives. The first is to describe or predict the behavior of the modeled system as a function of the combination of values taken by the factors. In this context, we'll be looking more closely at regression-type modeling. The second objective may be to find the optimum (minimum or maximum) value for the system, in which case we'll use kriging models.

To create a metamodel, we need a matrix X constituting the experimental design and the corresponding vector of outputs Y. The latter is obtained using a finite element model. The latter is obtained using a...