Robust Optimal Experiment Design: A Multi-Objective Approach

Abstract Optimal Experiment Design (OED) is an indispensable tool in order to reduce the amount of labour and cost intensive experiments in the modelling phase. The unknown parameters are often non-linearly present in the dynamic process models. This means that the Fisher Information Matrix also depends on the current guess for the parameters. In the early stage of the modelling phase these estimates are often highly uncertain. So designing an optimal experiment without taking this uncertainty into account is troublesome. In order to obtain an informative experiment, a robust optimisation approach is necessary. In recent work a formulation using an implicit weighted sum approach is proposed where the objective function is split in a nominal optimal experiment design part and a robust counterpart. This weighted sum has well known drawbacks in a Multi-Objective Optimisation approach. In this work these objectives are studied using advanced methods like the Normal Boundary Intersection and the Normalised Normal Constraint. In this way, the experimenter gets an overview of the different experiments possible. Furthermore, in past work the necessary third order derivatives are approximated using a finite different approach. The results in this work are obtained using exact third order and fourth order derivatives by exploiting the symbolic and automatic derivation methods implemented in the ACADO-toolkit.