Real-time demand estimation and confidence limit analysis for water distribution systems

A real-time estimation of water distribution system state variables such as nodal pressures and chlorine concentrations can lead to savings in time and money and provide better customer service. While a good knowledge of nodal demands is prerequisite for pressure and water quality prediction, little effort has been placed in real-time demand estimation. This study presents a real-time demand estimation method using field measurement provided by supervisory control and data acquisition systems. For real-time demand estimation, a recursive state estimator based on weighted least-squares scheme and Kalman filter are applied. Furthermore, based on estimated demands, real-time nodal pressures and chlorine concentrations are predicted. The uncertainties in demand estimates and predicted state variables are quantified in terms of confidence limits. The approximate methods such as first-order second-moment analysis and Latin hypercube sampling are used for uncertainty quantification and verified by Monte Carlo simulation. Application to a real network with synthetically generated data gives good demand estimations and reliable predictions of nodal pressure and chlorine concentration. Alternative measurement data sets are compared to assess the value of measurement types for demand estimation. With the defined measurement error magnitudes, pipe flow data are significantly more important than pressure head measurements in estimating demands with a high degree of confidence.