Second order plus dead time analysis of experimental data

An attractive feature of the technique is that the technique can adapt to either linear or nonlinear models without involving mathematical manipulations. However, the final results and the efficiency of this technique depends on the relations between the objective function and its independent variables. The relations are usually visualized as the contour surface of the objective function. Search of the optimum becomes difficult if two or more independent variables are all related to same characteristic of the objective function. On the contour surface this causes inclined ridges. Unfortunately, most nonlinear optimization methods were not particularly designed to deal with the ridge problem.

In this work it demonstrated that the ridge problem could be eliminated by proper selection of the independent variables and design of experiment. Also a nonlinear optimization method was modified to deal with objective functions with extremely narrow curved ridges. With proper design of experiment and the modified optimization technique, the ridge problem in experimental modeling was successfully overcome.