Inversion Model of Water Distribution Systems for Nodal Demand Calibration

Abstract

Nodal demand calibration of a water distribution system (WDS) is a process of adjusting the nodal demand in WDS models to make its predictions consisting with measurements, which is an inversion problem compared to the conventional forward computation. Most existing methods rely on performing forward computation repeatedly to calculate the sensitivity matrix or generate offspring for searching for optimal solutions. This paper develops an alternative framework, namely an inversion model, to directly calibrate the nodal demand. The model is constructed by separating the known and unknown variables in continuity and energy equations of WDS using the matrix decomposition method. Specifically, the measured and unmeasured nodal demand, nodal head, and pipe flow are taken as knows and unknowns, respectively. The nodal demands with similar user characteristics are grouped (i.e., aggregated) to make the model overdetermined, and the Gauss-Newton based iteration method is applied to solve the model. To evaluate the calibration results when observation errors are involved, the standard deviations of unknowns are calculated using first-order second-moment method for uncertainty quantification, and the results are verified by Monte Carlo simulation. A simple network is used to illustrate the model construction in detail, and two numerical case studies, including a real highly looped network, are applied to further validate its effectiveness and feasibility. Encouraging results obtained clearly demonstrate the proposed method has potential for practical application in real-time nodal demand calibration, state estimation, and uncertainty quantification of WDSs.