A Two-Phase Approach for Model-Based Design of Experiments Applied in Chemical Engineering
Optimal (model-based) experimental design (OED) aims to determine the interactions between input and output quantities connected by an, often complicated, mathematical model as precisely as possible from a minimum number of experiments. While statistical design techniques can often be proven to be optimal for linear models, this is no longer the case for nonlinear models. In process engineering applications, where the models are characterized by physico-chemical laws, nonlinear models often lead to nonconvex experimental design problems, thus making the computation of optimal experimental designs arduous. On the other hand, the optimal selection of experiments from a finite set of experiments can be formulated as a convex optimization problem for the most important design criteria and, thus, solved to global optimality. Since the latter represents an approximation of common experimental design problems, we propose a two-phase strategy that first solves the convex selection problem, and then uses this optimal selection to initialize the original problem. Finally, we illustrate and evaluate this generic approach and compare it with two statistical approaches on an OED problem from chemical process engineering.