Research On DMA Partition Of Water Distrubution Leakage Control In Mountainous Cities Based On Graph Theory

In recent years,the leakage of urban water supply network has always been a major problem in the water industry.It has been proved by practice that District Metered Area(DMA),with its advanced pipe network management mode and excellent leakage control performance,has gradually developed as one of the main technologies for leakage control of pipe network.Because of the undulating topography,the water supply environment between mountainous cities and plain cities is very different.The pressure of water supply in mountain cities is generally high and varies with the pressure of water demand of terminal users.The multi-stage pressurization in the pipe network is common,and the pipeline is circuitous and the topological structure of pipe network is complex.Therefore,this paper proposes a DMA partition method based on graph theory for mountain city network.Based on the idea of graph theory,the paper abstracts the topology map of real water supply network into a large graph model which is connected with the network topology between points and edges,and uses spectral clustering algorithm to establish the similarity matrix among nodes to cluster the nodes,thus realizing the division of the DMA region.This method can realize the automation of DMA partition,get rid of the dependence of traditional experience partition on subjective experience,and achieve good partition effect.This paper takes the water supply network in the central city of T District of Chongqing as an example,through a series of operations such as introducing the static topology data of the pipe network in the GIS system,the correction and simplification of the pipe network structure,the distribution of water consumption and the network checking of the network,the hydraulic model of water supply network in T district is established by using the professional modeling software MIKE URBEN.Considering that pressure is the main factor affecting the reliability of mountain city water supply,and the water demand of users should be guaranteed when zoning,this paper constructs similarity matrix from the point of view of ensuring the residual energy of users.Therefore,the similarity matrix is constructed from the point of view of energy redundancy between nodes,and the solution of spectral clustering algorithm is realized by calling the simulation results of the hydraulic model of the real case pipe network in EPANET by MATLAB.This method can ensure that the energy redundancy difference of each node in DMA area is as small as possible,and the energy redundancy difference of each node between areas is larger,thus realizing effective clustering among nodes.Finally,the paper divides the example pipe network into 22 DMA areas.Finally,three indexes of leak rate,pressure uniformity and hydraulic reliability of pipeline network are used to test the validity of DMA network partition results.Among them,the leakage rate before partition is calculated by water balance analysis,and the determination of leakage rate after partition is calculated by using the classical mathematical model between pressure and leakage amount.the results show that the leakage rate of nodes after partition is 3.2 percentage points lower than that before partition.The flow weighted index of the pressure between nodes is adopted to evaluate the pressure uniformity of the pipe network,and the results show that the pressure uniformity in each region is good.The verification results of hydraulic reliability of pipe network by using indirect evaluation index based on tolerance show that the pipe network has good hydraulic reliability after zoning.