Modeling and parameter identification of microbial bioconversion in fed-batch cultures

a b s t r a c tDeveloping suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a global optimization method is developed to seek the optimal key parameters. Numerical results show that the nonlinear time-delay system can describe the fed-batch fermentation process reasonably.

“…Obviously, (27) and (28) in conjunction with (29) is the solution of time-delay system (23) and (24). Thereby completing the proof.…”

Section: Sensitivity Functionsmentioning

confidence: 55%

Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process

Liu

2014

“…The relative errors e i between the computational values and the experimental data are listed in Table 3. From Table 3, we can see that the relative errors between the computational values and the experimental data are considerablly decreased than that in the impulsive system in [5]. Under the obtained optimal parameter vector u * , we plot the concentration changes with respect to time as shown in Figures 1-3.…”

Section: Optimization Algorithmmentioning

confidence: 99%

“…Otherwise, change the velocity A C C E P T E D M A N U S C R I P T error e i between the computational values and the experimental data is defined as follows [5]:…”

Section: Optimization Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear state-dependent impulsive system and its parameter identification in microbial fed-batch culture

Shen

Zhai

Gao

et al. 2016

Self Cite

Nonlinear state-dependent impulsive system and its parameter identification in microbial fed-batch culture, Applied Mathematical Modelling (2015), Highlights• A nonlinear impulsive system is proposed to formulate the fed-batch culture.• Some important properties of the system are investigated.• A parameter identification model is presented to identify the parameters.• We construct an improved PSO algorithm to find the optimal parameters.• Numerical results show that the system can describe the fed-batch culture well. AbstractIn fed-batch culture of glycerol to 1,3-propanediol by Klebsiella pneumoniae, glycerol and alkali are fed in batches into the bioreactor to provide sufficient nutrition and maintain a suitable environment for cells growth. In this paper, taking the feeding process as a state-dependent impulses process, a nonlinear state-dependent impulsive system is proposed to formulate the fed-batch process. Some important properties of the solution to the system are discussed, i.e., the existence, uniqueness and regularity of solution to the system and continuous dependence of the solution on initial value and parameters. Regarding the errors between the experimental results and calculated values as the performance index, a parameter identification model is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to seek the optimal parameters. Numerical results show that the nonlinear state-dependent impulsive system can be used to describe the fed-batch culture reasonably.

“…Unstructured and nonsegregational models have been used for optimization studies by a number of researchers [13][14][15][16][17]. Recently, based on an assumption that the feeding of glycerol only occurs at impulsive time, nonlinear impulsive systems have been extensively investigated to formulate the fermentation process [18][19][20][21]. Nonetheless, since the feeding rate of glycerol is finite, it is not reasonable to describe the actual fed-batch culture by the impulsive dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Modelling and optimization for a switched system in microbial fed-batch culture

Gong¹,

Liu²,

Feng³

et al. 2011

Self Cite

a b s t r a c tThis paper considers modelling and optimization of a microbial fed-batch fermentation process. A switched system with variable switching instants is proposed to describe the fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). Taking the concentration of 1,3-PD at the terminal time as the cost function and the switching instants as optimization variables, an optimization model involving switched system and subject to continuous state inequality constraints is then presented. By introducing a time-scaling transform, the optimization model is transcribed into an equivalent one with parameters and fixed switching instants. A computational approach to seek the optimal solution is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD can be increased considerably compared with previous results.