Parameter Estimation of a Monod-Type Model Based on Genetic Algorithms and Sensitivity Analysis
Mathematical models and their parameters used to describe cell behavior constitute the key problem of bioprocess modelling, in practical, in parameter estimation. The model building leads to an information deficiency and to non unique parameter identifica
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Abstract. Mathematical models and their parameters used to describe cell behavior constitute the key problem of bioprocess modelling, in practical, in parameter estimation. The model building leads to an information deficiency and to non unique parameter identification. While searching for new, more adequate modeling concepts, methods which draw their initial inspiration from nature have received the early attention. One of the most common direct methods for global search is genetic algorithm. A system of six ordinary differential equations is proposed to model the variables of the regarded cultivation process. Parameter estimation is carried out using real experimental data set from an E. coli MC4110 fed-batch cultivation process. In order to study and evaluate the links and magnitudes existing between the model parameters and variables sensitivity analysis is carried out. A procedure for consecutive estimation of four definite groups of model parameters based on sensitivity analysis is proposed. The application of that procedure and genetic algorithms leads to a successful parameter identification.
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Introduction
The costs of developing mathematical models for bioprocesses improvement are often too high and the benefits too low. The main reason for this is related to the intrinsic complexity and non-linearity of biological systems. In general, mathematical descriptions of growth kinetics assume hard simplifications. These models are often not accurate enough at describing the underlying mechanisms. Another critical issue is related to the nature of bioprocess models. Often the parameters involved are not identifiable. Additionally, from the practical point of view, such identification would require data from specific experiments which are themselves difficult to design and to realize. The estimation of model parameters with high parameter accuracy is essential for successful model development. All parameter estimation problems involve minimization and the choice of minimization algorithm is problem-dependent. There are many possible variants such as numerical methods [7,14]. During the last decade evolutionary techniques have been applied in a variety of areas. A concept that promises a lot is the genetic I. Lirkov, S. Margenov, and J. Wa´ sniewski (Eds.): LSSC 2007, LNCS 4818, pp. 601–608, 2008. c Springer-Verlag Berlin Heidelberg 2008
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technique. Genetic algorithm (GA) is global, parallel, stochastic search method, founded on Darwinian evolutionary principles. Since its introduction, and subsequent popularization [6], the GA has been frequently utilized as an alternative optimization tool to conventional methods. Specific particularities of the considered processes lead to estimation of a large-scale problem and as a successful tool for solving this problem are examined GA. The GA effectiveness and robustness have been already demonstrated for identification of fed-batch cultivation processes [2,15,16,17,18,19]. Even if experimental curves are successfully matched by fermentation process model outputs, it d
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