Practical identifiability of model parameters by combined respirometric-titrimetric measurements

Abstract

An earlier study on theoretical identifiability of parameters for a two-step nitrification model showed that a unique estimation of the yield YA1 is possible with combined respirometric-titrimetric data, contrary to the case where only one type of measurement is available. Here, the practical identifiability of model parameters was investigated via evaluation of the output sensitivity functions and the corresponding Fisher Information Matrix (FIM). It appeared that the FIM was not sufficiently powerful to predict the practical identifiability of this case with combined measurements as parameters could indeed be identified despite the fact that the FIM became singular. The accuracy of parameter estimates based on respirometric and titrimetric data and combination thereof was also investigated. Estimation on titrimetric data (Hp) was very accurate and a fast convergence of the objective function towards a minimum was obtained. The latter also holds for estimation on oxygen uptake rate data (rO), however with a lower accuracy. Parameter estimation based on oxygen concentration data (SO) was more complex but resulted in a higher accuracy. Thus, when the highest accuracy is needed it is recommended to estimate parameters initially on Hp and/or rO data, and to subsequently use these parameters as initial values for final, and more accurate estimation on SO data.