An entropy-based approach to detect critical nodes for modelling future demand uncertainty in Water Distribution Networks

Water demand in urban distribution networks is similar to external forces in building design. While users withdraw water along pipelines, design methods concentrate demand at a few specific nodes. The load, i.e., the water demand on each node, varies based on population and urban facilities and services within the network's coverage area. Estimating the current number of users for each node in a water network is feasible; however, predicting these numbers over medium to long-term periods is uncertain, which poses challenges for maintaining the network's efficiency. Detecting demand nodes that have the greatest impact on efficiency under future load increases enables a more robust network design. This work presents an entropy-based method for identifying critical nodes of a Water Distribution Network (WDN). The method quantifies uncertainty arising from unknown demand to perform a global sensitivity analysis. By deriving entropy-based sensitivity indices, specifically the Direct Information Transfer at each node, it quantifies how changes in nodal water demand can affect system response. Knowledge of the most critical nodes helps create future water demand scenarios that can be used to solve a robust design optimisation problem. To achieve this aim, the work presents a multi-objective robust optimisation (RO) model that incorporates future uncertainty in the design of the WDN. Future demand scenarios are constructed by overloading critical nodes, while also considering statistical uncertainty related to unpredictable user behaviour, modelled using a methodology from the literature. A limited number of demand scenarios with assigned probabilities are created, as required by the robust optimisation models.