Dynamic Optimisation of Beer Fermentation under Parametric Uncertainty

Abstract

Fermentation is one of the most important stages in the entire brewing process. In fermentation, the sugars are converted by the brewing yeast into alcohol, carbon dioxide, and a variety of by-products which affect the flavour of the beer. Fermentation temperature profile plays an essential role in the progression of fermentation and heavily influences the flavour. In this paper, the fermentation temperature profile is optimised. As every process model contains experimentally determined parameters, uncertainty on these parameters is unavoidable. This paper presents approaches to consider the effect of uncertain parameters in optimisation. Three methods for uncertainty propagation (linearisation, sigma points, and polynomial chaos expansion) are used to determine the influence of parametric uncertainty on the process model. Using these methods, an optimisation formulation considering parametric uncertainty is presented. It is shown that for the non-linear beer fermentation model, the linearisation approach performed worst amongst the three methods, while second-order polynomial chaos worked the best. Using the techniques described below, a fermentation process can be optimised for ensuring high alcohol content or low fermentation time while ensuring the quality constraints. As we explicitly consider uncertainty in the process, the solution, even though conservative, will be more robust to parametric uncertainties in the model.