3.2.4 Transformation

For both input (x) and output parameters (y), transformations can be specified, so additional knowledge about the system behavior can be included. A detailed discussion of the transformation is given in Section 3.1.17.

Figure 3.6 the transformation of the controls and the responses are Response Surface Methodology is applied to the dataset.

Figure 3.6: Structure of the Response Surface Methodology program with transformations.

It should be noticed that a transformation for input parameters of the response surface should be used in the DoE step.

Additionally, it is also possible to automatically select the best out of a given set of transformation functions for a given set of sample points. This is done by computing several response surfaces where any possible variation of available transformations is applied to all input parameters. The selection criteria for the best set of transformations is determined by the minimum fit error of the sample points calculated by the total sum of squares of the residuals. For all these surfaces the fit error of the sample points (the sum of squares) is used to select the best combination of transformations.