Abstract
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,
Highlights
Fractional calculus, known as noninteger-order calculus in the literature, is a generalization of the ordinary calculus
We have considered the parameter identification problem in batch process
Taking the error between the calculated values and the experimental data as the performance index, we present a parameter identification model subject to continuous state inequality constraints
Summary
Fractional calculus, known as noninteger-order calculus in the literature, is a generalization of the ordinary calculus. A fractional dynamic system in batch culture and its parameter identification problem have been investigated in [24]. Fractional dynamic system with only one stage cannot describe the whole batch fermentation process well. A two-stage fractional differential dynamical system in the sense of Caputo is proposed to formulate the batch fermentation process. For this system, some important properties of the solution are discussed. Numerical simulations show that the two-stage fractional dynamical system can reasonably describe the fermentation process, and the developed algorithm is applicable and effective.
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