Identifiability Analysis of Wall Decay Coefficients in Water Distribution Water Quality Model

Often, parameter estimation is not the only focus of a calibration process. The final aim of the calibration process is to use the estimated parameters for accurate model predictions. It is understood that the estimated parameters with higher uncertainty will poorly predict the system. For a nonlinear high-dimensional system like a water distribution system, point estimation of the model parameter is not adequate. It is important to identify the confidence intervals of the estimated parameters for such a system. A parameter may be estimated but it may not be identifiable for the set of data collected. The profile likelihood based confidence interval can be used to analyze the identifiability of the parameters. Confidence intervals for three-wall decay parameters in the water distribution systems were calculated from profile likelihood using chi-squared distribution in this paper. Results show that additional field data may be required for a parameter to be completely identifiable.