Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness
Lei Wang Jinlong Yuan Yingfang Li Enmin Feng Zhilong Xiu
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.
keywords: biological robustness parameter identification Nonlinear time-delay system continuous and batch fermentation.
Nonlinear dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol and their optimal controls
Caixia Gao Enmin Feng Zongtao Wang Zhilong Xiu
In this study simplified mathematical models of the nonlinear dynamic systems of dissimilation of glycerol to 1,3-propanediol by {\it Klebsiella pneumoniae} in continuous, batch and fed-batch cultures are investigated. Considering big errors between the experimental results and computational values in the existing models, the parameter identification models for these systems are established. The properties of the solutions for the nonlinear dynamic systems are discussed and the identifiability of the parameters is proved. In view of the sudden increase of the glycerol and alkali in fed-batch culture, this paper proposes a nonlinear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. Based on the nonlinear impulsive system, the paper constructs an optimal control model in view of the controllability of volumes of glycerol added to the reactor instantaneously, and the existence of the optimal control is obtained.
keywords: parameter identi¯cation optimal control. nonlinear impulsive system 3-PD microbial fermentation 1
The model of heat transfer of the arctic snow-ice layer in summer and numerical simulation
Yila Bai Haiqing Zhao Xu Zhang Enmin Feng Zhijun Li
For the Arctic ice layer with high temperature in summer, the concepts of enthalpy degree, specific enthalpy and enthalpy conduction coefficient etc. are introduced in terms of the concept of enthalpy in calorifics. Heat conduction equation of enthalpy is constructed in the process of phase transformation of the Arctic ice. The condition of determinant solution and the identification model of diffusion coefficient of enthalpy are presented. Half implicit difference scheme and Schwartz alternating direction iteration are applied to solve the enthalpy conduction equation and sensitivity equation. Furthermore the Newton-Raphson algorithm is used for identification. The numerical results illustrate that the mathematic model and optimization algorithm are precise and feasible by the data(2003.8)of the Second Chinese Arctic Research Expedition in situ.
keywords: sea ice the Arctic numerical simulation. parameter identification
A two-step algorithm for layout optimization of structures with discrete variables
Lianshuan Shi Enmin Feng Huanchun Sun Zhaosheng Feng
This paper presents a mathematical model for Layout optimization of structure with discrete variables. The optimization procedure is composed of two kinds of sub-procedures of optimization: the topological optimization and the shape optimization. In each one, a comprehensive algorithm is used to treat the problem. The two kinds of optimization procedures are used in turn until convergence appears. After the dimension of the structure is reduced, the delimiting combinatorial algorithm is used to search for the better objective value. A couple of classical examples are presented to show the efficiency of the method. Numerical results indicate that the method is efficient and the optimal results are satisfactory.
keywords: delimiting and combinatorial algorithm structural optimization layout optimization Discrete variable relative difference quotient.
Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture
Chongyang Liu Zhaohua Gong Enmin Feng Hongchao Yin
In this paper, we propose a new controlled multistage system to formulate the fed-batch culture process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by regarding the feeding rate of glycerol as a control function. Compared with the previous systems, this system doesn't take the feeding process as an impulsive form, but a time-continuous process, which is much closer to the actual culture process. Some properties of the above dynamical system are then proved. To maximize the concentration of 1,3-PD at the terminal time, we develop an optimal control model subject to our proposed controlled multistage system and continuous state inequality constraints. The existence of optimal control is proved by bounded variation theory. Through the discretization of the control space, the control function is approximated by piecewise constant functions. In this way, the optimal control model is approximated by a sequence of parameter optimization problems. The convergence analysis of this approximation is also investigated. Furthermore, a global optimization algorithm is constructed on the basis of the above descretization concept and an improved Particle Swarm Optimization (PSO) algorithm. Numerical results show that, by employing the optimal control policy, the concentration of 1,3-PD at the terminal time can be increased considerably.
keywords: Control parametrization Nonlinear multistage system Optimal control Fed-batch culture Improved PSO algorithm.
Parameter identification and numerical simulation for the exchange coefficient of dissolved oxygen concentration under ice in a boreal lake
Qinxi Bai Zhijun Li Lei Wang Bing Tan Enmin Feng

Dissolved oxygen (DO) is one of the main parameters to assess the quality of lake water. This study is intended to construct a parabolic distributed parameter system to describe the variation of DO under the ice, and identify the vertical exchange coefficient K of DO with the field data. Based on the existence and uniqueness of the weak solution of this system, the fixed solution problem of the parabolic equation is transformed into a parameter identification model, which takes K as the identification parameter, and the deviation of the simulated and measured DO as the performance index. We prove the existence of the optimal parameter of the identification model, and derive the first order optimality conditions. Finally, we construct the optimization algorithm, and have carried out numerical simulation. According to the measured DO data in Lake Valkea-Kotinen (Finland), it can be found that the orders of magnitude of the coefficient K varying from 10-6 to 10-1 m2 s-1, the calculated and measured DO values are in good agreement. Within this range of K values, the overall trends are very similar. In order to get better fitting, the formula needs to be adjusted based on microbial and chemical consumption rates of DO.

keywords: Dissolved oxygen parameter identification numerical simulation partial differential equation frozen lakes

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