Hierarchical Grouping of Nodes for Improved Nodal Demand Calibration in Water Distribution Networks

Hydraulic models are critical tools for planning and managing water distribution networks (WDNs), yet inaccuracies in nodal demand estimates remain a key source of modeling errors. Demand calibration is essential to enhance model reliability but is challenging due to the large number of unknown demands and limited sensor availability, resulting in an underdetermined problem. This study introduces a novel hierarchical grouping methodology that integrates sensitivity analysis with graph-theoretic shortest-path to cluster nodes into demand groups, effectively reducing the dimensionality of the calibration problem. Building on this, a two-stage calibration framework is proposed: Stage 1 performs conventional calibration across demand groups, while Stage 2 targets sensors with high residual errors by hierarchically subgrouping nodes in their associated groups for focused recalibration. The approach is validated on two looped WDNs and one tree type WDN using synthetic data under multiple sensor configurations. Results demonstrate that the proposed methodology achieves up to 34% reduction in nodal demand estimation errors compared to conventional single-stage calibration, particularly in scenarios with limited sensor coverage. These findings highlight the effectiveness of hierarchical node grouping and two-stage calibration in improving demand estimation accuracy, providing a scalable and practical solution for utilities facing data constraints in WDN modeling and operation.