第38卷第6期 2016年12月
土木建筑与环境工程
Journal of Civil,Architectural &. Environmental Engineering
doi:10.11835/j.issn.1674-4764.2016.06.019
谱聚类在给水管网分区优化中的应用
刘俊，周鹏
（燕山大学建筑工程与力学学院，河北秦皇岛066004）
Vol. 38 No. 6 Dec.2016
回
摘要：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。
关键词：给水管网；分区：聚类：优化
中图分类号：TU991
文献标志码：A
文章编号：1674-4764(2016)06-0142-06
Spectral clusteringfor optimal design of districtmetered areas
in water distribution systems
Liu Jun, Zhou Peng
(College of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, Hebei, P. R. China)
Abstract: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.
Keywords: water distribution systems; district metered area; clustering; optimization
给水管网分区是在系统性能影响最小的情况下
通过安装阀门、水表形成独立供水区域，使于优化调度、漏损控制等各方面的管理，以适应信息化、智能化、精细化的要求[1-5]。管网分区目的是获得规模均
收稿日期：2016-03-10
等，压力、水质均衡的分区。由于管网的高度复杂性以及众多技术要求和制约因素，使得分区这一问题面临较大挑战。
目前，管网分区优化方法主要有图论算法和复
基金项目：国家自然科学基金（51508492)；河北省自然科学基金（E2015203079)；燕山大学博士基金（B864)
作者简介：刘俊（1982-），男，博士，主要从事水资源与给水排水系统设计与运行优化研究，（E-mail）sdlj2008@163.com。 Received:2016-0310
Foundation item: National Natural Science Foundation of China (No. 51508492); Natural Science Foundation of Hebei
Province (No. E2015203079); Doctor Foundation of Yanshan University (No. B864)
Author brief:Liu Jun (1982-), assistant professor, PhD, main research interests: optimal design and operation of water
万方数据sources and urban water distribution and drainage systems，（E-mail）sdlj2008@163.com.