甘油连续生物歧化过程的参数辨识与非线性分析  

Parameter identification and nonlinear analysis of the continuous bio-dissimilation process of glycerol

作　　者：张菁朔 徐恭贤[1] ZHANG Jingshuo;XU Gongxian(College of Mathematical Sciences,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《河北大学学报（自然科学版）》2023年第3期230-236,共7页Journal of Hebei University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11101051);辽宁省自然科学基金资助项目(20180550839);辽宁省教育厅科学研究项目(LJ2020015)。

摘　　要：为了给出能够较好描述甘油连续生物歧化为1,3-丙二醇过程的数学模型以及模型的非线性特性,研究了其参数辨识与非线性分析问题.首先,建立了甘油连续歧化过程的GMA-系统,给出了以模型的计算值与实验测量值误差最小为优化目标、以甘油连续发酵过程的稳态条件为约束的参数辨识优化问题.采用序列二次规划算法,获得了相应动力学系统的最优参数值.结果表明,构建的GMA-系统的参数辨识优化模型能够得到更准确的参数值.其次,将辨识出的参数结果代入到甘油连续歧化过程的GMA-系统中,进行了平衡点计算与稳定性分析等.采用符号化实根隔离法求解了系统的平衡点,依据几乎线性系统的稳定性理论研究了平衡点的稳定性.In order to give a mathematical model that can better describe the continuous bio-dissimilation process of glycerol to 1,3-propanediol and the nonlinear characteristics of the model,the problems of parameter identification and nonlinear analysis are studied.Firstly,the GMA-system for the continuous bio-dissimilation process of glycerol is established.A parameter identification optimization problem is given,which takes the minimum error between the calculated value of the model and the experimental measurement value as the optimization objective and the steady-state conditions of continuous fermentation process of glycerol as constraints.By using the sequential quadratic programming algorithm,the optimal parameter values of the corresponding dynamic system are obtained.The results show that the parameter identification optimization model of the GMA-system can provide more accurate parameter values.Secondly,by substituting the results of the identified parameters into the GMA-system of continuous bio-dissimilation process of glycerol,the equilibrium point calculation and stability analysis are carried out.The equilibrium points of the system are numerically calculated by the method of the symbolic real root isolation,the stability of the equilibrium point is studied according to the stability theory of almost linear system.

关 键 词：GMA-系统 参数辨识 平衡点 稳定性 

分 类 号：O29[理学—应用数学]