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

Average demands are estimated based on population densities, typical usage by consumers, customer billing records, and other factors but are not appropriate for real-time modeling. Good nodal demand estimates to analyze and respond to pressure and water quality events are critical, however, approaches to estimate them are lacking. This paper presents a real-time demand estimation method using a recursive state estimator that is based on a weighted least squares (WLS) scheme. It is shown that pipe flow field measurements contain the most information for estimating nodal demands. Since the number of measurements will typically be less than the number of nodes in the system, regions with similar user characteristics are grouped and assumed to have same demand patterns. The demand estimation uncertainties propagated from field measurement errors and model simplification errors are quantified in terms of confidence limits using first order second moment (FOSM) method and the results are verified by Monte Carlo simulation. Application to a simple network with synthetically generated demands shows promising results.