In this paper, we consider mathematical modelling and parameter identification problem in bioconversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae. In view of the dynamic behavior with memory and heredity and experimental results in batch culture, a two-stage fractional dynamical system with unknown fractional orders and unknown kinetic parameters is proposed to describe the fermentation process. For this system, some important properties of the solution are discussed. Then, taking the weighted least-squares error between the computational values and the experimental data as the performance index, a parameter identification model subject to continuous state inequality constraints is presented. An exact penalty method is introduced to transform the parameter identification problem into the one only with box constraints. On this basis, we develop a parallel Particle Swarm Optimization algorithm to find the optimal fractional orders and kinetic parameters. Finally, numerical results show that the model can reasonably describe the batch fermentation process, as well as the effectiveness of the developed algorithm. Keywords: fractional dynamical system, parameter identification, parallel optimization,

中文翻译：

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微生物批处理过程中两阶段分数动力系统的建模与参数识别

在本文中，我们考虑了肺炎克雷伯菌将甘油生物转化为 1,3-丙二醇的数学建模和参数识别问题。针对具有记忆和遗传的动态行为以及分批培养的实验结果，提出了一种分数阶数未知、动力学参数未知的两阶段分数动力学系统来描述发酵过程。对于这个系统，讨论了解决方案的一些重要性质。然后，以计算值与实验数据的加权最小二乘误差为性能指标，提出了一种受连续状态不等式约束的参数辨识模型。引入了一种精确的惩罚方法，将参数识别问题转化为只有框约束的问题。以这个为基础，我们开发了一种并行的粒子群优化算法来找到最佳的分数阶和动力学参数。最后，数值结果表明该模型能够合理地描述批量发酵过程，以及所开发算法的有效性。关键词：分数动力系统，参数辨识，并行优化，