Research On District Metered Areas Of Water Distribution Network Based On Improved Differential Evolution

District Metered Area(DMA)of W ater Distribution Network(WDN)is an important measure of refined water supply management,and it is also the trend of scientific and intelligent development of water su pply industry.It is of great significance in leakage control.Nowadays,the boundary partitioning of DMA generally uses scientific and efficient computational partitioning techniques to replace subjectively limited emp irical partitioning techniques.However,the widely used community detection algorithms still have some limitations,and the related research is not comprehensive enough.In view of this,this paper carried out the following work :(1)Aiming at the problem of poor uniformity of the number of nodes in the partition when the community discovery algorithm(CNM)optimizes the modularity of the partition,combined with graph theory knowledge and clustering algorithm,a method combining the shortest path between nodes and K-means++ algorithm is pro posed.Firstly,Floyd algorithm is used to solve the shortest path matrix between nodes and principal component analysis is used to extract feature vectors.Then,the K-means++ algorithm with optimized initial clustering center is used to perform prelimina ry node clustering.Finally,the Warshall algorithm is used to detect abnormal outlier branches and correct them according to the connection density to form the final partition scheme.The algorithm is applied to two networks with annular characteristics a nd compared with the partition results of CNM.The results show that the partition scheme formed by the proposed algorithm has higher modularity and better uniformity of node number,which can reduce the difficulty of partition maintenance and management.(2)The community detection algorithm(CNM)is easy to fall into the local optimal solution,resulting in the unsatisfactory structure of the partition and the lack of tightness of the connection.Based on the differential evolution algorithm(DE),this pa per proposes Differential Evolution based Boundary Detection algorithm(DEBD).Firstly,the initial population based on partition number is generated,and the preference operation is used to reduce the abnormal outlier branches in the individual.Then,the mutation and crossover steps of DE are improved and the correction operation is introduced to improve the accuracy of partition.Finally,the modularity is used as the fitness function to determine the next generation population by the preferred sorting s election strategy and iteratively evolve to form the final partition scheme.The algorithm is applied to DMA partition test in four networks with different scales and topological properties,and compared with the actual partition scheme and the partition s cheme of CNM.The results show that the partition scheme of DEBD is very consistent with the actual partition scheme,and the algorithm has certain practical guiding significance.The modularity of the partition scheme of the DEBD is better than that of th e CNM under any partition,and it has certain advantages in improving the modularity and the connection tightness of the partition.In addition,the basic framework of DEBD is flexible and extensible,and different partitioning purposes can be achieved by modifying the modularity function or the weighting form of the pipe.(3)In view of the current situation that the research on the hydraulic interdependence between modules is not perfect,this paper uses a visual analysis method to measure and visualize t he hydraulic interdependence between all modules.Firstly,the DEBD is used to divide the networks.Then,the internal state of a single module(simulating a single pipe failure condition and a single node water demand surge scenario)is changed to constru ct an interdependence matrix.Finally,a directed graph is used to represent the interdependence between modules.This method is used to analyze three networks with different characteristics.The results show that the interdependence between modules changes with the change of the scene and is affected by the inherent attributes of the pipe(topology and components).Revealing the interdependence at the module level can provide guidance and suggestions for the maintenance,management,hydraulic model calibr ation,and DMA design of the WDNs.