Parameter estimation and sensitivity analysis for dynamic modelling and simulation of beer fermentation

Abstract

Beer fermentation efficiency improvements have the strongest potential to boost profitability, as its long batch time renders this particular unit operation the throughput bottleneck of this complex, multistage biochemical process which mankind has employed for several millennia. Accurate fermentation models are critical for reliable dynamic simulation and process optimization: empirical trial-and-error approaches are not viable, and incrementally altering proven recipes implies prohibitively expensive campaigns, in terms of equipment use, off-spec production and personnel time for sampling and analysis. This paper considers parameter estimation for a published beer fermentation model, demonstrating that estimating the complete unknown parameter set is an ill-posed problem, which can lead to inconsistent solutions. Systematic sensitivity analysis is pursued, elucidating the relative significance of parametric discrepancy on the validity of key species concentration trajectories. Parameters have been identified and ranked by decreasing importance, and a high-fidelity estimation is performed for a published dataset.

Modelling the effect of food composition on antimicrobial compound absorption and degradation in an active packaging

“…A sensitivity analysis was conducted using the software Athena Visual Studio by simulating the established model for the sample of food matrix containing 2.5% protein at 5 • C. The following first-order sensitivity functions were used to assess the relative effects of the model input (Rodman and Gerogiorgis, 2020),…”

“…where s(t; θ) is the dynamic sensitivity function of parameters (θ) on model state (y). To compare the effect of each parameter (k 1 , k 2 , k 3 , k 4 , mt 1 ,mt 2 , k f/g , Sin 0 , and AITC 0 ) on sinigrin and AITC content in the packaging system, the mean squared summary for each parameter, δmsqr, can be used as a means analysis by the following equation where the model has been evaluated at n discrete time points (Rodman and Gerogiorgis, 2020).…”

Numerical Study of a Helical Heat Exchanger for Wort Cooling in the Artisanal Beer Production Process

“…In the production of beer, the aim is to improve the methods to obtain a quality product, from the preparation of an established formula, to the treatment of the drink in each of the stages. Rodman [7] recognizes fermentation as the most important process when brewing beer, therefore, it is sought to improve the production times of this stage and generate a better yield [8], [9]. Specifically, through improvements in cooling, after the wort boil.…”

Antimicrobial packaging design : Exploring the potential of allyl isothiocyanate release from mustard seeds

“…where s(t; θ ) is the dynamic sensitivity function of parameters (θ) on the model state (y). To compare the effect of each parameter (k 1 , k 2 , k 3 , k 4 , mt 1 ,mt 2 , k f/g , Sin 0 , and AITC 0 ) on sinigrin and AITC content in the packaging system, the mean squared summary for each parameter, δmsqr, can be used as a means analysis by the following equation where the model has been evaluated at n discrete time points (Rodman and Gerogiorgis, 2020).…”

“…The k 4 has a negative correlation for AITC content in the headspace and the food matrix. The high correlations were regarded to be because of the state trajectory (Rodman and Gerogiorgis, 2020). Appendix 4.12 shows the most influential parameters for the sinigrin and AITC content in the packaging system; k 1 for the sinigrin content in mustard seeds, k 2 and k 4 for the AITC content and mustard seeds, k 4 and mt 2 for the AITC content in the headspace, and k 4 for the AITC content in the food matrix.…”