(343d) Parameter Estimation and Sensitivity Analysis in Beer Fermentation Modelling and Dynamic Optimisation
AIChE Annual Meeting
2017
2017 Annual Meeting
Computing and Systems Technology Division
Complex and Networked Chemical and Biochemical Systems
Tuesday, October 31, 2017 - 1:27pm to 1:46pm
The complexity of the fermentation biochemical system (Vanderhaegen et al., 2006) renders comprehensive dynamic model formulation cumbersome and the required parameter estimation prohibitive. Numerous previous publications (Engasser, 1981; Gee and Ramirez, 1988; de Andrés-Toro 1998; Trelea et al., 2001) have postulated reduced order models, which are concise enough to allow for parameter estimation on the basis of experimental campaign data, but also suitably descriptive by considering the most essential subset of important biochemical reactions via selective aggregation. Subsequent process optimisation studies have been successfully performed on the basis of these foregoing models, primarily addressing batch time minimisation or ethanol yield maximisation (de Andrés-Toro, 1998; Carrillo-Ureta, 2001), or both (Rodman and Gerogiorgis, 2016). A necessary assumption of process optimisation studies is that all parameter datasets published in the original fermentation modelling papers are accurate and consistent.
The present paper has relied on a comprehensive compilation of original time-dependent concentration data for beer fermentation campaigns (Gee, 1990; de Andrés-Toro, 1996) in order to perform an parameter estimation study (Dochain, 2003) for the respective reduced-order dynamic models. The Simulink environment has been used within MATLAB®, enabling the implementation of a nonlinear least squares method on the basis of the trust-region reflective algorithm for systematic parameter vector estimation. Remarkable discrepancies have been identified between the originally published parameter vectors and the corresponding ones determined herein, with the latter (our own results) universally improving dynamic model fidelity - and remarkably so, for certain critical parameters. Furthermore, we have performed systematic sensitivity analyses in order to assess and elucidate the relative significance of parametric discrepancy on the validity of dynamic simulation and optimisation results; the evolution of certain concentration observables is of particular interest, inasmuch as the latter govern process performance (: ethanol) and flavour (: diacetyls, ethyl acetate).
This comprehensive sensitivity analysis illustrates how state trajectory model predictions are affected by individual model parameters (DiStefano, 2013). Our new parameter set is subsequently used for further dynamic simulations towards attainable fermentation envelope visualisation. Multi-objective dynamic optimisation (time minimisation and ethanol maximisation) has also been performed with the new parameter vector we have determined, to investigate how and to what extent optimal operation is affected by parametric uncertainty, and thereby assess the validity of prior optimisation studies.
LITERATURE REFERENCES
Carrillo-Ureta, G., P. Roberts, and V. Becerra, 2001. Genetic algorithms for optimal control of beer fermentation. Proc. IEEE Int. Symp. Intell. Control, 391-396.
de Andrés-Toro, B., 1996. Modelling, Simulation, and Optimal Control of and Industrial Beer Fermentation Process (in Spanish). PhD Thesis, University Complutense of Madrid, Spain.
de Andrés-Toro, B., et al., 1998. A kinetic model for beer production under industrial operational conditions. Math. Comput. Simulat. 48(1): 65-74.
DiStefano, J, 2013. Dynamic Systems Biology Modelling and Simulation, Academic Press.
Dochain, D., 2003. State and parameter estimation in chemical and biochemical processes: a tutorial, J. Proc. Control 13(8): 801-818.
Engasser, J. M., Marc, I., Moll & M. Duteurte, B. Kinetic modelling of beer fermentation. Proceedings of the 18th Congress of the European Brewery Convention, 1981 Copenhagen. 579-86.
Gee, D. A., Ramirez, W. F. 1988. Optimal temperature control for batch beer fermentation. Biotechnol. Bioengineering, 31, 224-234.
Gee, D. A., 1990. Modelling, optimal control, state estimation, and parameter identification as applied to a batch fermentation process, PhD Thesis, The University of Colorado, Boulder, USA.
Rodman, A. D., Gerogiorgis, D.I., 2016. Multi-objective process optimisation of beer fermentation via dynamic simulation, Food Bioprod. Proc. 100(A): 255-274.
Trelea, I. C., Titica, M., Landaud, S., Latrille, E., Corrieu, G. & Cheruy, A. 2001. Predictive modelling of brewing fermentation: From knowledge-based to black-box models. Math. Comput. Simulat. 56, 405-424.
Vanderhaegen, B., et al., 2006. The chemistry of beer aging â a critical review. Food Chem. 95(3): 357-381.
Xiao, J., Zhou, Z., Zhang, G., 2003. Ant colony system algorithm for the optimization of beer fermentation control. J. Zhejiang Univ. 5(12): 1597-1603.