On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations

We present a new method for determining optimally informative dynamic experiments for the purpose of model discrimination among several rival multiresponse nonlinear structured dynamic models generally described by systems of differential and algebraic equations (DAEs). A robust and efficient algorithm based on an extension to the dynamic case of the discrimination criterion put forth by Buzzi-Ferraris and Forzatti (Chem. Eng. Sci. 1984,39, 81) is developed to calculate dynamic input trajectories by reformulation of the experiment design problem as an optimal control problem. We show that the new approach, by taking parametric uncertainty into account, can provide significant improvements in the ability to distinguish among a series of rival dynamic models over previous attempts to design dynamic experiments primarily based on parameter point estimates and thus maximizes the divergence of the model predictions without regard for uncertainty (Espie, D. M.; Macchietto, S. AIChE J. 1989, 35, 223). We illustrate the experiment design concepts with a relatively simple, but pedagogical example of the dynamic modeling of the fermentation of baker's yeast, although the methods are general enough to be applied in other modeling exercises.