Practical Identifiability Analysis and Optimal Experimental Design for the Parameter Estimation of the ASM2d-Based EBPR Anaerobic Submodel

Abstract

Identifiability analysis is a precondition for reliable parameter estimation. Building on previous work on structural identifiability, this paper focuses on the practical identifiability and optimal experimental design (OED) of the EBPR anaerobic submodel. The nonnegative determinant of the Fisher information matrix (FIM) found in this study clearly demonstrates that the parameters YPO4, KA, qPHA, and XPAO in the submodel are practically identifiable using SA and SPO4 as the measured variables and fixing KPP as the default value. Furthermore, fixing KPP to study the practical identifiability of the other parameters and to estimate their values is shown to be valid. Subsequently, a modeling-based procedure for the OED for parameter estimation was proposed and applied successfully to anaerobic phosphorus release experiments. According to the FIM D-criterion, the optimal experimental condition was determined to be an initial SA concentration of 300 mg/L. Under the optimal experimental condition, errors in the values of YPO4, KA, qPHA, and XPAO are all below 20%, and the estimated values were 0.35 ± 0.02 mg P/mg COD, 3.88 ± 0.41 mg COD/L, 3.35 ± 0.27 mg P/(mg CODd-1), and 1500 ± 72 mg COD/L, respectively. Compared to the results from the nonoptimal experimental condition, the practical identifiability and the estimation precision of the four parameters were improved.