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Parameter identification in dynamical models of anaerobic waste water treatment. (English) Zbl 0999.92040

Summary: Biochemical reactions can often be formulated mathematically as ordinary differential equations. In the process of modeling, the main questions that arise are concerned with structural identifiability, parameter estimation and practical identifiability. To clarify these questions and the methods how to solve them, we analyze two different second order models for anaerobic waste water treatment processes using two data sets obtained from different experimental setups. In both experiments only biogas production rate was measured which complicates the analysis considerably. We show that proving structural identifiability of the mathematical models with currently used methods fails. Therefore, we introduce a new, general method based on the asymptotic behavior of the maximum likelihood estimator to show local structural identifiability. For parameter estimation we use the multiple shooting approach which is described. Additionally we show that the Hessian matrix approach to compute confidence intervals fails in our examples while a method based on Monte Carlo simulation works well.

MSC:

92D40 Ecology
92C40 Biochemistry, molecular biology
62P12 Applications of statistics to environmental and related topics
92E20 Classical flows, reactions, etc. in chemistry
93B30 System identification

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