Nonlinear estimation of water network demands form limited measurement information

Access to clean drinking water is very important to the health and well-being of the population. Mathematical modeling, optimization, and online estimation are needed to solve challenging problems in water network applications such as the requirement to meet the new dynamic regulations in the Safe Drinking Water Act and the Clean Water Act. This includes providing sufficient capacity to satisfy uncertain and changing water demands, maintaining consistent water quality, and identifying and responding to abnormal events. In most of these applications, reliable knowledge of the water flow velocity is necessary. However, in practice, few measurements are usually available. This work uses a nonlinear optimization framework to estimate the unknown water demands and velocities from limited measurements. The problem is formulated as a constrained nonlinear least squares estimation problem. The constraints represent the basic governing mass and energy conservation laws as well as some operational constraints. Given the limited number of flow measurements, the estimation problem is ill-posed. Non-unique solutions may exist in which many demand profiles can match the limited number of measurements. Offline estimates of the demand patterns based on historical data are used to regularize the problem and force a unique solution. In the first phase of this project, a hydraulic model was developed for water distribution systems. This model showed very good agreement when it was validated against the simulator EPANET using 3 case studies. In the second phase, the estimation formulation was tested using the same 3 case studies with different sensor configurations. In each of the case studies, estimation results are reasonable with fewer sensors than the available degrees of freedom.