Real time water demand estimation in water distribution system

Accurate modeling of chemical transport in water distribution systems depends on accurate knowledge of temporally and spatially variable water demands. Typical network models would include water demands that are allocated from billing or census data, and thus may not be appropriate for specific operational analysis, such as emergency events arising from intentional or accidental contamination. During such an event, water consumption patterns may be significantly different from those assumed when developing the hydraulic model, and may change significantly over short time periods due to the unusual circumstances of the event. To allow accurate hydraulic and water quality prediction in real-time, the water demands should be updated continuously to reflect current conditions. The development of such a real-time water demand calibration method poses many complex issues such as identifiability and uncertainty of the water demand estimates. Given the sparsity of data that are likely to be available in real time, prior statistical information about water demands must be incorporated in the calibration procedure. In this paper, a method and algorithms are proposed for a real time water demand calibration process. A predictor-corrector methodology is proposed to predict statistical hydraulic behavior based on prior estimation of water demands, and then correct this prediction using new, real-time measurements. The problem is solved using the extended Kalman filter, which is a linear algorithm that calculates the estimate of water demands and their uncertainty. As part of the Kalman filter calculation, we calculate direct sensitivities of system hydraulic responses with respect to water demands. Results of numerical experiments illustrate the impacts of statistical demand variability, hydraulic measurement accuracy and sampling design on demand estimation. Copyright ASCE 2006.