This study presents a novel hybrid entropy-clustering framework for placing pressure sensors in water distribution systems (WDS) to detect leakage. Leakages are simulated at all potential nodes of WDS, and then potential pressure sensors (PPS) in WDS are classified using a K-means clustering algorithm. Transinformation entropy for each potential pair of PPS was also computed, which in turn helped to reduce redundant information. PPS locations were subsequently optimized using a multi-objective optimization model. Furthermore, to capture the sensitivity of sensors' layout in WDS to sensor error, a fuzzy-based analysis is integrated with a multi-objective optimization model. Finally, the best compromise solution of PPS placement in each category was selected using an ELECTRE multi-criteria decision making model. Reducing redundant information of pressure sensors based on information theory and choosing the best possible solution based on the ELECTRE model are the main novelties of this study. Results of C-Town WDS attest to the proposed framework' efficiency.

这项研究提出了一种新颖的混合熵聚类框架，用于在水分配系统（WDS）中放置压力传感器以检测泄漏。在WDS的所有潜在节点上模拟泄漏，然后使用K均值聚类算法对WDS中的潜在压力传感器（PPS）进行分类。还计算了每个潜在PPS对的转换信息熵，这又有助于减少冗余信息。随后使用多目标优化模型对PPS位置进行了优化。此外，为了捕获WDS中传感器布局对传感器错误的敏感性，将基于模糊的分析与多目标优化模型集成在一起。最后，使用ELECTRE多标准决策模型选择了每个类别中PPS放置的最佳折衷解决方案。基于信息论的方法来减少压力传感器的冗余信息，并基于ELECTRE模型选择最佳的解决方案是本研究的主要新颖之处。C镇WDS的结果证明了所提出框架的效率。