Sequential Geometric Programming Method for Parameter Estimation of a Nonlinear System in Microbial Continuous Fermentation

Abstract

This paper addresses the problem of parameter estimation for the microbial continuous fermentation of glycerol to 1,3-propanediol. A nonlinear dynamical system is first presented to describe the microbial continuous fermentation. Some mathematical properties of the dynamical system in the microbial continuous fermentation are also presented. A parameter estimation model is proposed to estimate the parameters of the dynamical system. The proposed estimation model is a large-scale, nonlinear, and nonconvex optimization problem if the number of experimental groups is large. A sequential geometric programming (SGP) method is proposed to efficiently solve the parameter estimation problem. The results indicated that our proposed SGP method can yield smaller errors between the experimental and calculated steady-state concentrations than the existing seven methods. For the five error indices considered, that is, the concentration errors of biomass, glycerol, 1,3-propanediol, acetic acid, and ethanol, the results obtained using the proposed SGP method are better than those obtained using the methods in the literature (Xiu et al., Gao et al., Sun et al., Sun et al., Li and Qu, Wang et al., and Zhang and Xu), with improvements of approximately 71.86–95.03%, 52.08–94.87%, 99.70–99.98%, 5.39–90.29%, and 12.67–80.83%, respectively. This concludes that the established dynamical system can better describe the microbial continuous fermentation. We also present that our established dynamical system has multiple positive steady states in some fermentation conditions. We observe that there are two regions of multiple positive steady states at relatively high values of substrate glycerol concentration in feed medium.