Simultaneous solution approach to model-based experimental design



A model-based experimental design is formulated and solved as a large-scale NLP problem. The key idea of the proposed approach is the extension of model equations with sensitivity equations forming an extended sensitivities-state equation system. The resulting system is then totally discretized and simultaneously solved as constraints of the NLP problem. Thereby, higher derivatives of the parameter sensitivities with respect to the control variables are directly calculated and exact. This is an advantage in comparison with proposed sequential approaches to model-based experimental design so far, where these derivatives have to be additionally integrated throughout the optimization steps. This can end up in a high-computational load especially for systems with many control variables. Furthermore, an advanced sampling strategy is proposed which combines the strength of the optimal sampling design and the variation of the collocation element lengths while fully using the entire optimization space of the simultaneous formulation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4169–4183, 2013