Effect of data collection on the estimation of wall reaction coefficients for water distribution models

During a model calibration process, errors in field measurements propagate to uncertainties in model parameter estimates and model predictions. This paper presents a means to quantify that effect in a water distribution water quality model and provides guidance on data collection experiment design. Water quality in the distribution systems is dominated by advective transport that is hydraulically driven. The hydraulic model, including the nodal demand, is assumed well calibrated and provides no uncertainty. Thus, only the wall decay coefficients are to be estimated and evaluated. The uncertainty assessment procedure consists of a parameter estimation model, parameter estimation uncertainty analysis, and model prediction uncertainty analysis. The shuffled frog leaping algorithm (SFLA), an optimization algorithm, is used to estimate the parameters in the water quality model in a least-squares regression given a set of field data. The parameter uncertainty is calculated using a first-order approximation and is further propagated to model prediction uncertainty. The model prediction uncertainty is calculated using a similar first-order analysis. The methodology is applied to two networks. Alternative conditions are analyzed in terms of data collection and model prediction conditions to examine the benefits of performing pulse injection test and data collection design. The results showed that pulse injection provides more information and better parameter estimates. As a result, parameters estimated from a data set with pulse injection produced lower model prediction uncertainty. For a given simulation time, earlier pulses remained in the system for a longer duration, providing more calibration information and, hence, improving parameter estimation accuracy.