耦合模块度优化与谱聚类的供水管网分区算法

Coupling Modularity Optimization and Spectral Clustering of Water Supply Network Partition Algorithm

摘要:

为降低供水管网漏损，实现供水管网快速准确分区，提出一种耦合模块度优化与谱聚类的供水管网分区算法。该算法采用快速模块度优化算法对供水管网进行社区划分，以每个社区为节点、社区间连接关系为边，结合各社区内的水力特征和空间区位特征计算差异性作为边权重，构建对偶图。利用谱聚类算法完成供水管网分区。结果表明，该算法求解的管网分区结果相比快速模块度优化和谱聚类算法，将空间上更邻近的管段划分在同一分区，不会产生狭长型无效分区，且在模块度及边界管道数量上表现较为均衡，管网分区方案不仅模块度高，而且边界管道数量少。

Abstract:

In order to reduce the leakage of the water supply network， a coupling modularity optimization and spectral clustering algorithm is proposed to implement pipe network partitioning. First， the modularity optimization algorithm is used in this algorithm to obtain the coarse partition of the maximum modularity in the water supply network. Next， a dual graph is constructed with each partition as a node and the partition connection relationship as an edge. The divisional structure of the pipeline network is affected by the combination of the topology of the pipeline network and the layout of the street， land use， and population distribution. After that， the edge weights are calculated based on the number of points of interest in each district， the average degree of the district， the average pipe diameter， the average pipe length， and the average node elevation. Finally， Laplace matrix decomposition and K-means clustering are used to complete the partition. The experiments verify that the community structure of the pipe network identified by the algorithm is consistent with the actual spatial distribution. A comparison of the algorithm with the modularity optimization and spectral clustering algorithms in the modularity and the number of boundaries indicates that the result obtained by the algorithm is more tightly connected within the partition， the connection between the partitions is sparse， and the boundary pipe is fewer.