Modeling in microbial batch culture and its parameter identification

In this paper, the nonlinear dynamical system of batch fermentation is investigated in the bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae. Taking account of the kinetic behavior and experimental results in the batch cultures, we propose a two-stage dynamical system to formulate the fermentation process. Then some properties of the proposed system are proved. In view of the big errors between observations and numerical simulation results, we subsequently establish a parameter identification model to identify parameters in the system. The identifiability of the model is also discussed. Finally, in order to find the optimal parameters of the identification model, an improved simulated annealing algorithm combined with Hook-Jeeves local search is constructed. Numerical results show that the two-stage system can describe the factual fermentation better and the optimization algorithm is valid.