Optimal experimental design for optimal process design: A trilevel optimization formulation

Abstract

Typical optimal experimental design (OED) methods aim at minimizing the covariance matrix of the estimated parameters regardless of the intended application of the model that is being estimated. This can unnecessarily increase the experimental costs. Herein, we propose a new OED method, which tailors the designed experiments to the model application. The method is demonstrated for model-based process design and aims at mitigating a worst-case realization of the process design. The proposed formulation results in a min–max–min problem and is based on bounded-error OED. The method is illustrated via an ad hoc solution method using two examples, a simple illustrative example and the van de Vusse reaction, that show the differences between typical and the new tailored OED method: experimental designs can be considered good using the latter method, while the same design would be considered bad with the former methods.