A Tri-Level Approach for T-Criterion-Based Model Discrimination

Model discrimination (MD) aims to determine the inputs, called design points, of two or more models at which these models differ most under the additional condition that the models are fitted to these points, in the case of T-optimal designs. On the one hand, nonlinear models often lead to nonconvex MD problems, on the other hand, the optimal number of design points must be determined, too. Thus, the computation of T-optimal designs is very arduous. However, if one considers finitely many design points, a well-solvable bi-level problem arises. Since the latter only represents an approximation of the original model discrimination problem, we refine the design space discretization using the equivalence theorem of MD. This yields a tri-level approach whose iterates converge to a T-optimal design. We demonstrate that the approach can outperform known solution methods on an example from chemical process engineering.