Information entropy and clustering-based sensor placement in water distribution networks for leak detection

The optimal sensor placement (OSP) within water distribution networks (WDNs) is a critical research area, driven by the need for effective leak detection, localization, and data-driven decision support. Due to the large scale, complex topology, and uncertain hydraulic behavior of WDNs, identifying sensor locations that are both informative and spatially representative remains a challenging task. This study proposes an information-entropy and clustering-based framework for optimal sensor placement, aimed at enhancing leak detection and localization through machine learning in smart water networks.

Hydraulic pressure data are generated using EPANET by introducing a single leak at a time, modeled as an additional demand at each demand node in the network. The pressure signal at each node is treated as a random variable, and its probability distribution is estimated using a histogram-based approach. Shannon information entropy is employed to quantify the uncertainty and sensitivity of nodal pressure responses, where nodes with higher entropy are considered more informative and responsive to system disturbances such as leaks. Mutual information is incorporated to compute shared information between candidate sensor locations. By penalizing nodes that exhibit high redundancy with previously selected sensors, the proposed framework ensures that each sensor contributes unique and complementary information. Furthermore, to guarantee spatially distributed sensors and network-wide coverage, spectral clustering is applied using nodal coordinates and elevation (X, Y, Z), partitioning the network into geographically coherent clusters. Sensors are placed within each cluster at the nodes with maximum penalized entropy score. A greedy search algorithm is employed to maximize this score. Consequently, this integrated framework effectively balances information maximization, redundancy reduction, and spatial representativeness.

The methodology is validated on the benchmark Modena network, a medium-sized gravity-fed WDN consisting of 268 demand nodes, 317 pipes, and four reservoirs. The performance of the information-entropy and clustering-based sensor placement framework was evaluated using spatial classification accuracy metrics at varied distance tolerances (0m to 500m). The multilayer perceptron (MLP) based leak localization model trained using data from the information-entropy and clustering-based OSP at nodes {7, 42, 162, 228, 257} achieved training accuracy of 97.62% and test accuracy of 85.73%. Spatial accuracy results further validate robustness, with localization accuracies of 93.94% within 100 m, improving to 97.95% and 99.72% within 200 m and 500 m tolerance, respectively. Robust performance was maintained even after introducing noise into the data; however, under noisy conditions, the use of spatial accuracy metrics is recommended to effectively predict the leak zone rather than exact node locations. The high spatial accuracies demonstrate the frameworks effectiveness for machine learning–based predictive analytics. The framework supports informed decision-making and provides an efficient solution for smart water network monitoring and management.