Incorporating experimental uncertainties into multivariate granulation modelling

A methodology that carries experimental uncertainties into model predictions is studied and applied to a multidimensional population balance model for granulation processes. This complex model contains 27 parameters. A portion of them such as material constants can be measured or estimated, whereas some of the model parameters need to be established through granulation experiments and subsequent fitting to the model. As uncertainties are associated with every measurement, these are used in the presented methodology for the computation of uncertainties in the model predictions. This allows one to assess the quality of a model and to identify outliers in the experimental observations. As the evaluation of the complex model framework is computationally expensive, the granulation process is approximated with response surfaces in the studied example, allowing the quick computation of the model response in the optimisation procedure. Using eight sets of experimental observations, model-specific rate constants for particle coalescence, compaction, breakage, and reaction are calculated. Additionally, uncertainties of these parameters are estimated, allowing for the calculation of the model prediction and its uncertainty. Whereas the a priori uncertainties are relatively large, the uncertainties are significantly reduced by the method proposed. In addition to this, a possible mismatch between the model and the experimental observations is identified, giving hints for further investigations.