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Parameter identification in microbial population dynamics models of anaerobic wastewater treatment

Thorsten Müller, Neli Noykova, Mats Gyllenberg, Jens Timmer, Parameter identification in microbial population dynamics models of anaerobic wastewater treatment. Mathematical Biosciences , 2002.

Abstract:

In this paper we investigate two second order models of batch anaerobic digestion processes: one includes the Monod model of the specific growth rate of methanogenic bacteria, while the other describes the noncompetitive substrate inhibition phenomena. We assume that only biogas production rate is measurable, and the other two state variables – substrate and microorganisms concentrations - are not. Here we discuss the problems related to structural and practical identifiability of the model parameters. We show that even for these relatively simple models almost all existing methods for investigating the structural identifiability fail. For the simpler Monod model we were still able to apply the Taylor series or Wu-Ritt method after some model transformations, while for the substrate inhibition model all methods failed. Therefore, we introduce a new, general method based on the asymptotic behaviour of the maximum likelihood estimator to show local structural identifiability. We apply it both for initial parameter values and for parameter estimates.
After that we were able to estimate the chosen parameters using the data sets from the third paper. Here we use the multiple shooting estimation method. After that we conduct an uncertainty analysis of the parameter estimates. For this purpose we introduce a new method for uncertainty analysis, based on Monte Carlo Simulation. One of the advantages of this method is that we use the original nonlinear model instead of a linear approximation in the neighbourhood of the best parameter estimates. 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.

BibTeX entry:

@ARTICLE{jMuNoGyTi02a,
  title = {Parameter identification in microbial population dynamics models of anaerobic wastewater treatment},
  author = {Müller, Thorsten and Noykova, Neli and Gyllenberg, Mats and Timmer, Jens},
  journal = {Mathematical Biosciences},
  year = {2002},
  keywords = {parameter estimation, structural identifiability, practical identifiability, confidence intervals, waste water treatment processes},
}

Belongs to TUCS Research Unit(s): Biomathematics Research Unit (BIOMATH)

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