A simplified method to assess structurally identifiable parameters in Monod-based activated sludge models

The first step in the estimation of parameters of models applied for data interpretation should always be an investigation of the identifiability of the model parameters. In this study the structural identifiability of the model parameters of Monod-based activated sludge models (ASM) was studied. In an illustrative example it was assumed that respirometric (dissolved oxygen or oxygen uptake rates) and titrimetric (cumulative proton production) measurements were available for the characterisation of nitrification. Two model structures, including the presence and absence of significant growth for description of long- and short-term experiments, respectively, were considered. The structural identifiability was studied via the series expansion methods. It was proven that the autotrophic yield becomes uniquely identifiable when combined respirometric and titrimetric data are assumed for the characterisation of nitrification. The most remarkable result of the study was, however, that the identifiability results could be generalised by applying a set of ASM1 matrix based generalisation rules. It appeared that the identifiable parameter combinations could be predicted directly based on the knowledge of the process model under study (in ASM1-like matrix representation), the measured variables and the biodegradable substrate considered. This generalisation reduces the time-consuming task of deriving the structurally identifiable model parameters significantly and helps the user to obtain these directly without the necessity to go too deeply into the mathematical background of structural identifiability.