Drinking Water Distribution System Network Clustering Using Self-Organizing Map for Real-Time Demand Estimation

Consumer demand estimation is a key step in real-Time drinking water system (DWS) modeling used for demand forecasting, optimal operations, and water quality management. Consumer nodes in a DWS are generally clustered to reduce the number of unknown demands to be estimated from a limited number of measurement locations. A clustering methodology using the self-organizing map (SOM) is presented, which groups consumer nodes based on sensitivity of measurements to perturbations in the consumer demands and through the use of exogenous consumer information representative of, for example, socioeconomic information. The SOM algorithm not only developed demand clusters, but also provided intuitive visualization of the high-dimensional sensitivity space, which can provide important visual clues about the clustering problem such as the maximum number of clusters that can reasonably be formed and sharpness of the clusters. When applied to an example network, the sensitivity-based SOM clusters improved the performance in representing the observed measurements and demand estimate uncertainty, but reduced the performance in representing the overall network hydraulics relative to the actual clusters. Incorporating exogenous information about the actual clusters demonstrated the potential for providing trade-offs between representing the limited observed hydraulic information and the overall network hydraulics. The results from the SOM algorithm clearly demonstrate a need for clustering approaches that incorporate network-specific information (e.g., measurement locations, sensitivity information, and exogenous data) to develop demand estimates that are capable of representing observed information while adequately capturing overall system dynamics.