  Construction of kinetic models has become an indispensable step in the
development and scale up of processes in the industry. Model-based design of
experiments (MBDoE) has been widely used for the purpose of improving parameter
precision in nonlinear dynamic systems. This process needs to account for both
parametric and structural uncertainty, as the feasibility constraints imposed
on the system may well turn out to be violated leading to unsafe experimental
conditions when an optimally designed experiment is performed. In this work, a
Gaussian process is utilized in a two-fold manner: 1) to quantify the
uncertainty realization of the physical system and calculate the plant-model
mismatch, 2) to compute the optimal experimental design while accounting for
the parametric uncertainty. This method provides a guarantee for the
probabilistic satisfaction of the constraints in the context of model-based
design of experiments. The method is assisted with the use of adaptive
trust-regions in order to facilitate a satisfactory local approximation. The
proposed method is able to allow the design of optimal experiments starting
from limited preliminary knowledge of the parameter set, leading to a safe
exploration of the parameter space. The performance of this method is
demonstrated through illustrative case studies regarding the parameter
identification of the kinetic model in flow reactors.
