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Cristina Sarmiento Ferrero, Qian Chai, Marta Dueñas Díez, Sverre H. Amrani, Bernt Lie

### Systematic Analysis of Parameter Identifiability for Improved Fitting of a Biological Wastewater Model to Experimental Data

In this paper, we describe a Biological Wastewater Plant situated at Duvbacken in Gävle, Sweden. A dynamic model based on the ASM2d description is developed, and is implemented in Matlab. The model is qualitatively verified based on the nominal parameter values available for ASM2d Henze et al., 1999.

It is of interest to adjust the parameters in the model such that the developed model fits better to experimental data from the Gävle plant. One problem with the ASM2d model is that of parameter identifiability the model holds a large number of parameters, and few measurements are available. This leads to problems related to both output insensitivity to parameters, and correlation between parameters some parameters may be unidentifiable. Three strategies for avoiding this problem are i to find the theoretically identifiable parameters, and only include these in the parameter updating algorithm, ii to remove numerically insensitive and correlated parameters from the parameter list, and only update the remaining parameters, and iii to project the parameters into the numerically identifiable subspace, where the parameter updating takes place. Strategy ii and iii use the available experimental data in a numerical analysis, while strategy i makes the unrealistic assumption that the system is persistently excited.

In this paper, we use a method proposed by Brun et al. 2002 which is based on strategy ii, see also Duenñas Díez et al. 2005 for an application. When a low number of identifiable parameters have been found, a standard least squares technique is used to calculate the improved parameter estimates. The adjusted model is validated against experimental data, and the consequence of many parameters combined with few measurements is highlighted.

Finally, possible uses of the dynamic model are discussed briefly.