Non-Linear Modelling of Industrial Brewing Fermentations
R. Alex Speers 1, 4, Peter Rogers 2 and Bruce Smith 3
1 Department of Food Science and Technology, Dalhousie University, P.O. Box 1000, Halifax, NS, Canada B3J 2X4. Telephone: (902) 494-3146. Facsimile: (902) 420-0219. E-mail: Alex.Speers@Dal.Ca
2 National Operations, Carlton and United Breweries, 2-4 Southampton Crescent, Abbottsford, Victoria 3067, AUS.
3 Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada B3H 4R2.
4 Corresponding author. E-mail: Alex.Speers@Dal.Ca
J. Inst. Brew. 109(3), 229-235, 2003 | VIEW ARTICLE
ABSTRACT
This work reports on the non-linear regression modelling of brewing fermentations. Evaluation of the decline in Plato with time from commercial datasets found a sigmoidal-shaped logistic function best described the data. Four fermentation parameters, the initial and final gravities as well as the slope and midpoint at the inflection point of the curve were derived from a simplex search technique to minimize the residual sum of squares.
The number of times the yeast was repitched had no effect (p > 0.05) on the fermentation. The starting temperature increased the fermentation rate (p < 0.01) while decreasing (p < 0.001) the time to the fermentation midpoint. Final gravities were also positively influenced by initial fermentation temperature (p < 0.001).
This paper also illustrates the construction of prediction intervals about the predicted function and for the first time, allows the prediction of process deviations in the fermentation. Prediction intervals such as these can be used in a similar fashion to control charts.
The statistical techniques reported in this paper can be used to make informed decisions (Evidence Based Practice) regarding fermentation procedures. For example, one could determine the number of yeast croppings possible before a significant change is observed in any of the fermentation parameters. These techniques can be used to examine the effect of process changes (e.g., temperature, yeast strain or starting gravity) on the fermentation process by statistically examining for changes in the four fermentation parameters (i.e., the initial and final gravities as well as the slope and midpoint at the inflection point of the fermentation curve). These techniques can also be used to evaluate various fermentation treatments or when developing a new strain or higher gravity wort.
Key words:
Evidence Based Practice fermentation modelling, non-linear regression
Publication no. G-2003-0925-078 ©2003 The Institute & Guild of Brewing