谱聚类在给水管网分区优化中的应用

Spectral clustering for optimal design of district metered areas in water distribution systems

利用图划分技术和图论算法实现给水管网分区。根据给水管网分析,确定分区数量,建立权重邻接矩阵并计算图拉普拉斯矩阵及其特征向量,通过多路图划分对隐藏在特征向量中的聚类信息进行数据挖掘,采用遗传算法和K均值方法实现最佳节点聚类。利用PageRank和最短路径算法确定水表和阀门位置,最终实现给水管网优化分区。实际给水管网模型分区实例表明所提方法在给水管网分区的有效性。

Design of district metered areas（DMAs）in water distribution system was performed based on complex network spectral clustering and graph theory.First the number of DMAs was determined,and graph weighted adjacency matrix and Laplacian matrix were established.Then k-way spectral clustering algorithm was used to discover the optimal clusters hidden behind eigenvectors of Laplacian matrix,leading to the best layout of DMAs using genetic algorithm and K-means.PageRank and shortest path algorithm were adopted to ascertain the location of meters in DMAs and valves between DMAs to achieve the optimal design of DMAs eventually.And a real water distribution system was tested and the results showed that the proposed method was effective in DMAs design.