Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness

Abstract

In this paper, the nonlinear enzyme-catalytic kinetic system of batch and continuous fermentation in the process of glycerol bio-dissimilation is investigated. On the basis of both glycerol and 1,3-PD pass the cell membrane by active and passive diffusion under substrate-sufficient conditions, we consider the delay of concentration changes on both extracellular substances and intracellular substances. We establish a nonlinear delay dynamical system according to the batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-propanediol(1,3-PD) and we propose an identification problem, in which the biological robustness is taken as a performance index, constrained with nonlinear delay dynamical system. An algorithm is constructed to solve the identification problem and the numerical result shows the values of time delays of glycerol, 3-HPA, 1,3-PD intracellular and extracellular substances. This work will be helpful for deeply understanding the metabolic mechanism of glycerol in batch and continuous fermentation.

Parameter identification and steady-state optimization of microbial continuous fermentation based on two-stage and interior point methods

“…The parameters in the original GMA system are then identified by the two-stage method. Compared with the error results of existing literature [5,6,10,20,22,25], smaller error values have been achieved. This shows that our proposed GMA system can better describe the microbial continuous fermentation process.…”

“…In recent years, scholars have conducted extensive research on parameter identification, process optimization, and control in microbial fermentation production processes, and have achieved a series of research results [1,[4][5][6][10][11][12][13][14]17,[20][21][22][23][24][25][26][27]29]. For example, Abdullah et al [1] solved the parameter identification problem of biochemical systems based on hybrid optimization algorithms, resulting in higher accuracy and shorter time for the calculated parameters.…”

“…Zhao et al [29] applied the improved particle swarm optimization (PSO) algorithm to study the multi-stage parameter identification problem. Wang [22] studied the parameter identification problem of microbial fermentation system. Liu et al [11] established a two-stage fractional order dynamic system and used the penalty method and parallel particle swarm optimization algorithm to find the parameter values.…”

“…Although the mathematical modeling or parameter identification methods for the microbial continuous fermentation of glycerol to 1,3-propanediol have been addressed in the literature [5,6,10,20,22,25], a comparison study suggested that the steady-states computed by these literatures significantly violate the experimental data (See Tables 2-3 of Section 5). This concludes that the models given in the literature [5,6,10,20,22,25] cannot satisfactorily represent the microbial continuous fermentation. Thus, we must propose the new mathematical modeling or parameter identification approaches to describe the microbial continuous fermentation.…”

“…In order to identify the parameter values of the GMA system, a two-stage method is proposed in Section 4. The optimal values of the parameters are presented in Section 5, which results in the smaller concentration error values compared to the existing literature [5,6,10,20,22,25]. In Section 6, a corresponding steady-state optimization model was established by optimizing the maximum volume yield of 1,3-propanediol.…”