An independent measurement optimization partitioning method based on graph partitioning algorithm

Abstract

The present invention discloses an independent metering optimization partitioning method based on a graph partitioning algorithm, which is divided into three stages: simplification, partitioning and refinement. In the simplification stage, nodes are continuously paired and merged until the number of nodes is reduced to a predetermined value; in the partitioning stage, each node is used as a partition to obtain an initial partitioning scheme; in the refinement stage, nodes are first moved with the help of a multi-objective optimization algorithm to obtain a variety of partitioning schemes, and then the positions of valves and water meters are determined with the help of another optimization algorithm to obtain a Pareto optimal solution; then the pipeline network is restored according to the reverse process of the simplification stage, and the above steps are repeated until the pipeline network is restored to the initial state; finally, the best solution is selected from all Pareto optimal solutions. Compared with the existing graph partitioning algorithm, the present invention combines hydraulic simulation and optimization algorithm, which can expand the solution space of the existing method, and at the same time realize the automatic partitioning of the pipeline network, ensure the hydraulic and water quality conditions of the partitioning scheme, and improve the speed and scientificity of pipeline network partitioning.

Description

Technical Field

[0001] The invention relates to the technical field of leakage control of municipal engineering, and in particular to an independent metering optimization partitioning method based on a graph partitioning algorithm. Background Art

[0002] With the advancement of urbanization, the scale of water supply pipelines has continued to expand and the structure has become increasingly complex. The characteristics of urban water supply pipelines are as follows:

[0003] (1) With the increase in urban users, the water supply network is huge, and the pipe materials, specifications, and service life are different, resulting in a complex overall structure;

[0004] (2) The water supply network is buried deep underground, which makes it difficult to observe and maintain, and it is difficult to manage;

[0005] (3) There was a lack of rational planning during the early construction of the water supply network, the pipes were laid in a disorderly manner, and no complete information was retained.

[0006] The complexity of the pipeline network structure increases the difficulty of pipeline network management, resulting in serious pipeline network leakage problems and a series of hidden dangers:

[0007] A large amount of water is lost, which increases the cost of water supply;

[0008] Groundwater and pollutants enter the water supply system through leaking parts of the pipe network, causing water pollution problems;

[0009] When the pipe bursts, water rushes out of the ground and causes water to accumulate on the road; …

[0010] Therefore, it is imperative to strengthen pipeline management and quickly identify and deal with water supply pipeline leakage when leakage occurs.

[0011] Zone metering is one of the effective means to identify network leakage and assist in the daily management of urban water supply networks. Zone metering is to separate the water supply network into a certain number of areas by installing valves, metering equipment, etc., so as to measure and analyze the flow in and out of the area, perform pressure control, and identify leakage in each zone. By analyzing the minimum nighttime flow in each zone and assisting with leak detection equipment, the scope of network leakage identification can be narrowed, the speed of network leakage repair can be increased, and the replacement frequency of the main equipment of the network can be reasonably customized.

[0012] There are two methods of zoning: empirical method and computational method. The empirical method is that engineers use their experience to partition after comprehensive consideration of the network topology, background geographic information, administrative divisions, etc., which is suitable for networks with simple structures, small scales, and many branch pipes; the computational method is to automatically partition the network with the help of computer programming technology and hydraulic simulation software, which is suitable for networks with complex structures, large scales, and many ring structures. The graph partitioning algorithm is a method system in the computational partitioning method, which can be mainly divided into three steps: simplification, partitioning, and refinement. In the simplification stage, the original network topology is simplified to reduce the time cost of obtaining a preliminary partitioning scheme; in the partitioning stage, the simplified network is partitioned by binary search, optimization algorithm, etc. to obtain a preliminary partitioning scheme; the refinement stage is the inverse process of the simplification process, and the partitioning scheme is adjusted in the process of gradually restoring the network.

[0013] However, conventional graph partitioning algorithms have the following problems:

[0014] (1) Hydraulic simulation is not combined during refinement. Valves and flowmeters at the partition boundary are arranged after the partition. The optimization goal is to minimize the weight of the partition boundary, which limits the solution space of the method. For example, the DMA automatic partitioning method for water supply network based on graph partitioning uses the MLRB algorithm to obtain the partitioning scheme, and then uses the genetic algorithm to determine the layout of the flowmeter and valve. The refinement adjustment of the graph partitioning algorithm is separated from the hydraulic simulation.

[0015] (2) The layout method of flow meters and valves at the partition boundary is generally based on experience or a single indicator, which cannot fully explain the hydraulic and water quality safety of the pipe network after partitioning. For example, the "DMA Automatic Partitioning Method for Water Supply Pipeline Network Based on Graph Partitioning" uses the cost of partition transformation as the objective function when selecting the layout plan of valves and flow meters, which is a single-objective optimization. Summary of the invention

[0016] In view of the above-mentioned problems existing in the prior art, the present application provides an independent metering optimization partitioning method based on a graph partitioning algorithm, and constructs a method with a graph partitioning algorithm as the core and a hierarchical analysis method as an auxiliary decision-making method to carry out the zoning design of independent metering areas. First, simplify the partitioning, randomly traverse the nodes and preferentially pair and merge adjacent nodes with smaller weights, and repeat this step to gradually simplify the original pipe network graph until the number of nodes is consistent with the number of partitions. At this time, each node represents an initial partition. The pipe network is refined according to the inverse process of simplification. On the basis of each round of restored pipe network, an optimization algorithm is used to move the partition boundary points, and another optimization algorithm is nested to determine the installation position of the instrument in combination with the hydraulic simulation of the pipe network. Then, several Pareto optimal solutions are selected from all the solutions, and saved as the Pareto optimal solutions for this round of refinement. These solutions are used as the starting point for the next round of refinement, and the refinement steps are repeated until the pipe network is restored to its original state. Finally, the best solution is selected from all Pareto optimal solutions as the final partitioning solution using the solution optimization method.

[0017] The technical solution of the present invention is as follows:

[0018] An independent measurement optimization partitioning method based on a graph partitioning algorithm comprises the following steps:

[0019] S1. Collect the topological structure information of the pipe network, including but not limited to: nodes, node water demand, pipes, pipe diameters, average factory pressure of water sources, and total basic water demand; the collection of all topological structure information is called the pipe network status G. i ;

[0020] S2. Set a partition quantity, i.e., the partition quantity setting value; the current pipe network state is G0;

[0021] S3, starting from G0, set node weights and pipeline weights, perform node pairing and merging, and connect the pipeline network from G i Simplify to G i+1 ; When the number of network nodes is equal to the set value of the number of partitions, the network state at this time is recorded as G m ;

[0022] S4, G m Each node of is taken as a partition to obtain the initial partitioning scheme;

[0023] S5, adopt the opposite operation of step S3, and connect the pipe network from G m Restore to G m-1 , and then do the following:

[0024] S51, using a multi-objective optimization algorithm to move the partition boundary nodes, and obtain a series of new partition schemes, i.e., a partition scheme sequence;

[0025] S52, for each partition scheme in the partition scheme sequence, optimizing the arrangement of boundary instruments in the scheme by means of another optimization algorithm; the boundary instruments include but are not limited to: flow meters, water meters, valves;

[0026] S53, for each zoning scheme in the zoning scheme sequence, combining hydraulic simulation to obtain evaluation indicators of the scheme; the evaluation indicators include: pipe network elasticity coefficient Ir, average water age of pipe network avgWA, zoning scale difference UB, zoning transformation cost C;

[0027] S54. Select the partition scheme corresponding to the Pareto solution from the partition scheme sequence as G m-1 Pareto optimal solution under the state;

[0028] S6, taking the Pareto optimal solution as a new starting point, repeat step S5 until the pipe network is restored to the original state G0; step S5 is repeated m-1 times in total, and m-1 different Pareto optimal solutions are obtained, forming a Pareto optimal solution sequence;

[0029] S7. Use the hierarchical analysis method to select the best partitioning scheme from the Pareto optimal scheme sequence.

[0030] Furthermore, in step S3, the node weight is the node water demand, and the pipeline weight is the pipeline diameter.

[0031] Furthermore, when moving the partition boundary nodes in step S5, the multi-objective optimization algorithm used is the NSGA-II algorithm;

[0032] When optimizing the boundary instruments of the arrangement scheme in step S5, the optimization algorithm used is a genetic algorithm.

[0033] Furthermore, when performing node pairing and merging in step S3, the specific steps are as follows:

[0034] S31, establishing a pairing node set, where the initial pairing node set is an empty set;

[0035] S32, randomly traverse the pipe network nodes that are not in the paired node set, search for the adjacent nodes of the node, find the adjacent node that is not in the paired node set and has the smallest weight, define the two nodes as paired nodes, and add the paired node to the paired node set; the adjacent node refers to other nodes that are directly connected to the node through a pipeline;

[0036] S33. According to the pipe network topology, the paired nodes in the paired set are merged. The specific operations are as follows:

[0037] (1) Merge nodes with small weights into nodes with large weights;

[0038] (2) Update the weight of the node with the larger weight to the sum of the weight values ​​of the two nodes;

[0039] (3) Hide the pipeline between paired nodes;

[0040] In the process of executing the above operation, if the pipelines overlap, the weight of the pipeline is updated to the weight value of the pipeline with the largest weight among all the overlapping pipelines;

[0041] S34: If the number of network nodes is not equal to the set value of the number of partitions, continue to execute S32; otherwise, stop pairing and merging nodes to obtain the network state G. m .

[0042] Furthermore, the pipe network elastic coefficient Ir is used to represent the relationship between the pressure of the water source point and the user node. The lower the value, the lower the overall residual pressure of the pipe network and the lower the leakage risk. The formula of the pipe network elastic coefficient Ir is as follows:

[0043]

[0044] Where: N represents the number of connected nodes; S represents the number of water source nodes; T represents the hydraulic simulation duration, in h; It represents the water demand of node n at hour t, in L / s; represents the free water head at node n at hour t, in m; It represents the water output of water source s at hour t, in L / s; represents the outflow head of water source s at hour t, in m; p * It indicates the minimum service head of the connection node, in L / s;

[0045] The average water age avgWA of the pipe network is used to indicate the overall level of the water age of the pipe network and is an indicator for determining the overall water quality of the pipe network. The formula for the average water age avgWA of the pipe network is as follows:

[0046]

[0047] in: It represents the water age of the nth connection node at time t, in h;

[0048] The sub-area size difference UB is used to represent the relative difference between the maximum and minimum sizes of an area, measured by the water consumption of users within the sub-area; the formula for the sub-area size difference UB is as follows:

[0049]

[0050] Where: Area max Indicates the maximum partition size among all partitions, in L / s; Area min Indicates the minimum partition size among all partitions, in L / s;

[0051] The formula for the zoning transformation cost C is as follows:

[0052]

[0053] in: Indicates the nth m Cost of a metering device, yuan; N m Indicates the total number of installed metering devices; Indicates the nth v Cost of a valve, Yuan; N mIndicates the total number of valves installed.

[0054] Further, step S7 includes the following steps:

[0055] S61. Using the analytic hierarchy process, a hierarchical structure is established, which includes three levels: target level, criterion level, and scheme level. The target level is the evaluation system A; the criterion level includes four evaluation indicators: system elasticity coefficient Ir, average water age of the pipe network avgWA, zone scale difference UB, and zone cost C; the scheme level is the Pareto optimal scheme sequence;

[0056] S62. According to experience, the importance of the four evaluation indicators of the criterion layer to the evaluation system A is judged, and then the four evaluation indicators are assigned importance values, namely: the importance value of the system elasticity coefficient Ir is B1, the importance value of the average water age of the pipe network avgWA is B2, the importance value of the partition scale difference UB is B3, and the importance value of the partition cost C is B4;

[0057] S63, construct a judgment matrix W according to B1, B2, B3, and B4, that is:

[0058] W=(a ij ) 4×4

[0059]

[0060] Where: i = 1, 2, 3, 4, j = 1, 2, 3, 4;

[0061] S64, checking the consistency of the judgment matrix W;

[0062] S65. Use the geometric mean method to calculate the weights of the four evaluation indicators of the criterion layer to the solution layer. The formula is as follows:

[0063]

[0064] Where: i = 1, 2, 3, 4, j = 1, 2, 3, 4, n = 1, 2, 3, 4, a ij is the element of the judgment matrix W, ω1 (2) is the weight of the system elasticity coefficient Ir on the solution layer, ω2 (2) is the weight of the average water age avgWA of the pipe network on the scheme layer, ω3 (2) is the weight of the partition size difference UB on the solution layer, ω4 (2) is the weight of the zoning transformation cost C on the scheme layer;

[0065] S66, weight vector w of the synthesis criterion layer to the target layer (2) :

[0066] w (2) =(ω1(2) ,ω2 (2) ,ω3 (2) ,ω4 (2) ) T ;

[0067] S67. The Pareto optimal solution sequence of the solution layer contains m-1 partition solutions. The importance value p of each partition solution to the four evaluation indicators of the criterion layer is obtained according to the hydraulic simulation results. j1 (3) 、p j2 (3) 、p j3 (3) 、p j4 (3) , where p j1 (3) represents the importance of the jth partition scheme to the system elasticity coefficient Ir, p j2 (3) represents the importance of the jth partition scheme to the average water age avgWA of the pipe network, p j3 (3) represents the importance value of the jth partitioning scheme to the partition size difference UB, p j4 (3) Represents the importance of the j-th zoning scheme to the zoning transformation cost C, and the value range of j is 0 to m-1;

[0068] S68, m-1 p ji (3) The resultant vector P i (3) :

[0069] P i (3) =(p 1i (3) , p 2i (3) , ..., p ji (3) ) T ;

[0070] S69, 4 P i (3) Merge into an n×4 weight matrix:

[0071] P (3) =(P1 (3) , P2 (3) , P3 (3) , P4 (3) );

[0072] S610, through w (2) and P (3)Obtain the synthetic weight w of the solution layer to the target layer (3) :

[0073] w (3) =P (3) w (2) ;

[0074] S611. Check the consistency of the total order of the hierarchy. The formula is as follows:

[0075]

[0076] Where: i Indicates the relative weight of each element in the criterion layer to the overall goal; CI i Represents the consistency index of the solution layer to each element of the criterion layer; RI i Represents the average random consistency index of each element of the scheme layer for the criterion layer.

[0077] Furthermore, in step S62, the importance values ​​assigned to the four evaluation indicators of the criterion layer based on experience are as follows:

[0078] The importance value of the system elasticity coefficient Ir is 9;

[0079] The importance value of the average water age avgWA of the pipe network is 5;

[0080] The importance value of partition size difference UB is 3;

[0081] The importance value of the partition cost C is 7.

[0082] The beneficial technical effects of the present invention are:

[0083] (1) A method based on graph partitioning algorithm and analytic hierarchy process (AHP) as auxiliary decision-making is constructed to design the zoning of independent metering areas. First, the partition is simplified, nodes are randomly traversed, and adjacent nodes with smaller weights are preferentially paired and merged. This step is repeated to gradually simplify the original network until the number of nodes in the network is the number of partitions. At this time, each node represents an initial partition. Then, refinement is performed. A multi-objective optimization algorithm (such as NSGA-II algorithm) is used to move the partition boundary points, and another optimization algorithm (such as genetic algorithm) is nested to combine with the hydraulic simulation of the network to determine the meter installation location of the scheme. Then, several Pareto solutions are selected from the scheme as the Pareto optimal scheme and saved. This is used as the starting point for the next refinement until it is refined to the original state. The final scheme is selected from the saved Pareto optimal scheme using a scheme optimization method (such as AHP). Based on this method, a better zoning scheme can be obtained.

[0084] (2) Evaluation indicators that take into account hydraulic, water quality, and economic factors are set up, such as the elasticity coefficient of the pipeline network, the average water age of the nodes, the difference in the scale of the zones, and the cost of zone transformation. At the same time, the best solution with the best comprehensive conditions can be obtained through screening.

[0085] (3) The framework of the partitioning scheme optimization method (such as the hierarchical analysis method) was established. By establishing a hierarchical structure and constructing a pairwise comparison judgment matrix, the entire method system was established; the effectiveness of the method system was verified by calculating relative weights and consistency tests and calculating composite weights and consistency tests. Based on this, a reliable optimization scheme selection system can be obtained.

[0086] (4) The multi-objective optimization algorithm for mobile partition boundary nodes of the present invention is not limited to the NSGA-II algorithm, and has the following characteristics: it can select the best comprehensive solution based on a number of evaluation indicators, has a fast running speed, and has good convergence.

[0087] (5) The optimization algorithm used by the present invention to optimize the layout of boundary instruments is not limited to genetic algorithms, and has the following characteristics: it starts searching from several solutions and processes multiple solutions simultaneously, and is not easily trapped in local optimality; it has self-organization, self-adaptation and self-learning properties.

[0088] (6) The node weight of the present invention has the characteristic of making the partition water consumption of the simplified node closer, and is not limited to setting the node weight as the node water demand.

[0089] (7) The pipe section weight of the present invention has the characteristic of protecting large diameter pipes during the simplification process so that they are not easily turned into boundary pipes (such as boundary pipes where valves may be placed), and is not limited to the pipe diameter. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 is a flow chart of the present invention;

[0091] Figure 2 It is the initial topological structure of the water supply network in a certain district of YX City;

[0092] Figure 3 It is a schematic diagram of the analytic hierarchy process;

[0093] Figure 4 This is a Pareto solution diagram for the first zoning of the water supply network in a district of YX City;

[0094] Figure 5 It is the scope of each zone when the pipe network of a district in YX City is first zoned;

[0095] Figure 6 It is the scope of each zone when the pipeline network in a district of YX city was divided for the second time. DETAILED DESCRIPTION

[0096] The present invention is described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0097] The embodiment is a water supply network in a certain district of YX City. The embodiment is divided into different areas by the present invention, and the steps are as follows: Figure 1 As shown:

[0098] S1. Collect the topological structure information of the pipe network, including but not limited to: nodes, node water demand, pipes, pipe diameters, average factory pressure of water sources, and total basic water demand; the collection of all topological structure information is called the pipe network status G. i .

[0099] like Figure 2 As shown, the water supply network in a certain district of YX City contains 1162 nodes and 1237 pipelines. The average factory pressure of the water source is 36.67m, and the total basic water demand is 1434.65L / s.

[0100] S2. Set a partition quantity, that is, the partition quantity setting value. The current pipe network state is G0.

[0101] The partition quantity setting value of the embodiment is 5.

[0102] S3, starting from G0, set the node weight and pipeline weight, pair and merge the nodes, and connect the pipeline network from G i Simplify to G i+1 ; The specific steps are as follows:

[0103] S31, establishing a pairing node set, where the initial pairing node set is an empty set;

[0104] S32, randomly traverse the pipe network nodes that are not in the paired node set, search for the adjacent nodes of the node, find the adjacent node that is not in the paired node set and has the smallest weight, define the two nodes as paired nodes, and add the paired node to the paired node set; the adjacent node refers to other nodes that are directly connected to the node through a pipeline;

[0105] S33. According to the pipe network topology, the paired nodes in the paired set are merged. The specific operations are as follows:

[0106] (1) Merge nodes with small weights into nodes with large weights;

[0107] (2) Update the weight of the node with the larger weight to the sum of the weight values ​​of the two nodes;

[0108] (3) Hide the pipeline between paired nodes;

[0109] In the process of executing the above operation, if the pipelines overlap, the weight of the pipeline is updated to the weight value of the pipeline with the largest weight among all the overlapping pipelines.

[0110] When the number of network nodes is equal to 5, the network status at this time is recorded as G m .

[0111] S4, G m Each node of is regarded as a partition to obtain the initial partitioning scheme.

[0112] S5, adopt the opposite operation of step S3, and connect the pipe network from G m Restore to G m-1 , and then do the following:

[0113] S51, using the NSGA-II algorithm to move the partition boundary nodes, a series of new partition schemes are obtained, namely, a partition scheme sequence;

[0114] S52, for each partition scheme in the partition scheme sequence, optimizing the arrangement of boundary instruments in the scheme by means of a genetic algorithm; the boundary instruments include but are not limited to: flow meters, water meters, valves;

[0115] S53. For each partition scheme in the partition scheme sequence, the evaluation index of the scheme is obtained by combining hydraulic simulation. There are 4 evaluation indexes in total:

[0116] (1) Pipeline network elastic coefficient Ir

[0117] The pipe network elastic coefficient Ir is used to represent the relationship between the pressure of the water source point and the user node. The lower the value, the lower the overall residual pressure of the pipe network and the lower the leakage risk. The formula of the pipe network elastic coefficient Ir is as follows:

[0118]

[0119] Where: N represents the number of connected nodes; S represents the number of water source nodes; T represents the hydraulic simulation duration, in h; It represents the water demand of node n at hour t, in L / s; represents the free water head at node n at hour t, in m; It represents the water output of water source s at hour t, in L / s; represents the outflow head of water source s at hour t, in m; p * Indicates the minimum service head of the connection node, in L / s.

[0120] (2) Average water age of the pipe network avgWA

[0121] The average water age avgWA of the pipe network is used to indicate the overall level of the water age of the pipe network and is an indicator for determining the overall water quality of the pipe network. The formula for the average water age avgWA of the pipe network is as follows:

[0122]

[0123] in: Represents the water age of the nth connected node at time t, in h.

[0124] (3) Partition size difference UB

[0125] The sub-area size difference UB is used to represent the relative difference between the maximum and minimum sizes of an area, measured by the water consumption of users within the sub-area; the formula for the sub-area size difference UB is as follows:

[0126]

[0127] Where: Area max Indicates the maximum partition size among all partitions, in L / s; Area min Indicates the minimum partition size among all partitions, in L / s.

[0128] (4) Zoning renovation costs C

[0129] The formula for the zoning transformation cost C is as follows:

[0130]

[0131] in: Indicates the nth m Cost of a metering device, yuan; N m Indicates the total number of installed metering devices; Indicates the nth v Cost of a valve, Yuan; N m Indicates the total number of valves installed.

[0132] S54. Select the partition scheme corresponding to the Pareto solution from the partition scheme sequence as G m-1 The Pareto optimal solution under the state.

[0133] S6. Taking the Pareto optimal solution as a new starting point, repeat step S5 until the pipeline network is restored to the original state G0; step S5 is repeated m-1 times in total, and m-1 different Pareto optimal solutions are obtained, forming a Pareto optimal solution sequence.

[0134] S7. Use the hierarchical analysis method to select the best partitioning scheme from the Pareto optimal scheme sequence. The specific steps are as follows:

[0135] S71, such as Figure 3 As shown in the figure, the hierarchical analysis method is used to establish a hierarchical structure, which includes three levels: target level, criterion level, and solution level:

[0136] (1) The target layer is the evaluation system;

[0137] (2) The criterion layer includes four evaluation indicators: system elasticity coefficient Ir, average water age of the pipe network avgWA, zone size difference UB, and zone transformation cost C;

[0138] (3) The solution layer is a sequence of Pareto optimal solutions.

[0139] S62. Based on the experience, the importance of the four evaluation indicators of the criterion layer to the evaluation system A is determined, and then the importance values ​​are assigned to the four evaluation indicators respectively, namely: the importance value of the system elasticity coefficient Ir is B1=9, the importance value of the average water age of the pipe network avgWA is B2=5, the importance value of the partition scale difference UB is B3=3, and the importance value of the partition transformation cost C is B4=7. The results are shown in Table 1.

[0140] Table 1 Importance values ​​of evaluation indicators

[0141]

[0142] S63, construct a judgment matrix W according to B1, B2, B3, and B4, that is:

[0143] W=(a ij ) 4×4

[0144]

[0145] Among them: i=1,2,3,4, j=1,2,3,4.

[0146] The results are shown in Table 2.

[0147] Table 2 Judgment matrix W

[0148]

[0149]

[0150] S64, check the consistency of the judgment matrix W. The maximum eigenvalue of the judgment matrix W is 4, and the consistency index CI is as follows:

[0151]

[0152] The table shows that when n=4, the average random consistency index RI is 0.89, and the consistency ratio CR is as follows:

[0153]

[0154] Here, the consistency ratio CR of the fourth-order judgment matrix W is < 0.09, so the consistency of the judgment matrix W is considered acceptable.

[0155] S65. Use the geometric mean method to calculate the weight of the criterion layer to the solution layer. The formula is as follows:

[0156]

[0157] Where: i = 1, 2, 3, 4, j = 1, 2, 3, 4, n = 1, 2, 3, 4, a ij is the element of the judgment matrix W, ω1 (2) is the weight of the system elasticity coefficient Ir on the solution layer, ω2 (2) is the weight of the average water age avgWA of the pipe network on the scheme layer, ω3 (2) is the weight of the partition size difference UB on the solution layer, ω4 (2) It is the weight of the zoning transformation cost C to the scheme layer.

[0158] The calculation process of the embodiment is shown in Table 3. The "product" column in the table is the product of the four indicator values ​​of the judgment matrix in this row, and the "root" column is the fourth power of the elements in the "product" column. The weight of the criterion layer to the solution layer is obtained by normalizing the "root" column.

[0159] Table 3 Weights of the criterion layer to the solution layer

[0160]

[0161]

[0162] S66, weight vector w of the synthesis criterion layer to the target layer (2) :

[0163] w (2) =(ω1 (2) ,ω2 (2) ,ω3 (2) ,ω4 (2) ) T =(0.38,0.21,0.13,0.29) T .

[0164] S67. The Pareto optimal solution sequence of the solution layer contains m-1 partition solutions. The importance value p of each partition solution to the four evaluation indicators of the criterion layer is obtained according to the hydraulic simulation results. j1 (3) 、p j2 (3) 、p j3 (3) 、pj4 (3) , where p j1 (3) represents the importance of the jth partition scheme to the system elasticity coefficient Ir, p j2 (3) represents the importance of the jth partition scheme to the average water age avgWA of the pipe network, p j3 (3) represents the importance value of the jth partitioning scheme to the partition size difference UB, p j4 (3) Represents the importance of the j-th partition scheme to the partition transformation cost C, and the value range of j is 0 to m-1.

[0165] There are 44 groups of Pareto optimal solutions in the embodiment, and the evaluation indicators before and after the partition are shown in Table 4. The system elasticity coefficient Ir of the 44 groups of solutions is between 0.540-0.594, the average water age avgWA of the pipe network is between 11.9-12.4h, the partition scale difference UB is between 0.024-16.478, and the partition transformation cost C is between 433,000-1.131 million yuan. According to the size of the partition scale difference UB, the 44 groups of solutions are divided into 5 groups, represented by five different graphics, and displayed in a three-dimensional coordinate system, such as Figure 4 As shown, the x-axis represents the system elasticity coefficient Ir, the y-axis represents the average water age avgWA of the pipeline network, and the z-axis represents the partition transformation cost C.

[0166] Table 4 Comparison of evaluation indicators before and after partitioning

[0167]

[0168]

[0169] Among them, the reference costs of flow meters and valves are shown in Table 5:

[0170] Table 5 Reference costs of flow meters and valves

[0171]

[0172]

[0173] S68, m-1 p ji (3 ) Synthesized vector P i (3) :

[0174] P i (3) =(p 1i (3) , p 2i (3), ..., p ji (3) ) T ;

[0175] S69, 4 P i (3) Merge into an n×4 weight matrix:

[0176] P (3) =(P1 (3) , P2 (3) , P3 (3) , P4 (3) );

[0177] S610, through w (2) and P (3) Obtain the synthetic weight w of the solution layer to the target layer (3) :

[0178] w (3) =P (3) w (2) :

[0179] S611. Check the consistency of the total order of the hierarchy. The formula is as follows:

[0180]

[0181] Where: i Indicates the relative weight of each element in the criterion layer to the overall goal; CI i Represents the consistency index of the solution layer to each element of the criterion layer; RI i Represents the average random consistency index of each element of the scheme layer for the criterion layer.

[0182] The execution results of steps S68 to S611 are shown in Table 6. In the hierarchical structure of the evaluation system, the weight vector of the criterion layer to the target layer is (0.38, 0.21, 0.13, 0.29) T . When calculating the weight vector of the scheme layer to the criterion layer, first calculate the importance value of each scheme corresponding to each criterion, and then calculate the synthetic weight according to the formula of step S610. The results are shown in Table 6. Among them, the smaller the values ​​of the system elasticity coefficient Ir, the average water age of the pipeline network avgWA and the partition renovation cost C, the better the scheme, and the importance values ​​of these three elements are the reciprocals of the original values. The partition scale difference UB is divided into 5 levels according to the numerical value. When 0≤UB<0.5, the importance value is 4; when 0.5≤UB<1, the importance value is 3; when 1≤UB<5, the importance value is 2; when 5≤UB<10, the importance value is 1; when UB≥10, it is considered that the scale difference of the partition scheme is large, and this solution should be discarded, and the importance value is 0.001.

[0183] Table 6 Calculation of composite weights of partitioning schemes

[0184]

[0185]

[0186] After calculation, among all the schemes, the scheme with the largest synthetic weight is C33, with a weight value of 0.0254 and a consistency ratio CR (3) =0, the total hierarchical order is considered to have passed the consistency test.

[0187] Select C33 as the final partition scheme, and its independent metering partition is shown in Figure 5 .

[0188] The sizes of the five partitions are shown in Table 7 below:

[0189] Table 7 Scale of independent measurement area

[0190] Partition number Partition size (L / s) 1 793.490 2 242.368 3 103.115 4 104.239 5 187.999

[0191] It is expected that there will be 10 secondary zones with a zone size of 131.4 L / s. Combined with the size of the primary independent metering area, the secondary independent metering area is divided using the same method. Zone 1 is further divided into 5 secondary independent metering areas, zone 2 is divided into 2 independent metering areas, and zones 3, 4 and 5 are no longer subdivided. The secondary independent metering areas are as follows: Figure 6 shown.

[0192] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and implementation modes, and can be fully applicable to various fields suitable for the present invention. For those familiar with the art, for those of ordinary skill in the art, various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present invention. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to specific details.

Claims

1. An independent measurement optimization partitioning method based on a graph partitioning algorithm, characterized in that: The following steps are involved: S1. Collect the topological structure information of the pipe network, including but not limited to: nodes, node water demand, pipes, pipe diameters, average factory pressure of water sources, and total basic water demand; the collection of all topological structure information is called the pipe network status G. i ; S2. Set a partition quantity, i.e., the partition quantity setting value; the current pipe network state is G0; S3, starting from G0, set node weights and pipeline weights, perform node pairing and merging, and connect the pipeline network from G i Simplify to G i+1 ; When the number of network nodes is equal to the set value of the number of partitions, the network state at this time is recorded as G m ; The specific steps are as follows: S31, establishing a pairing node set, where the initial pairing node set is an empty set; S32, randomly traverse the pipe network nodes that are not in the paired node set, search for the adjacent nodes of the node, find the adjacent node that is not in the paired node set and has the smallest weight, define the two nodes as paired nodes, and add the paired node to the paired node set; the adjacent node refers to other nodes that are directly connected to the node through a pipeline; S33. According to the pipe network topology, the paired nodes in the paired set are merged. The specific operations are as follows: (1) Merge nodes with small weights into nodes with large weights; (2) Update the weight of the node with the larger weight to the sum of the weight values ​​of the two nodes; (3) Hide the pipeline between paired nodes; In the process of executing the above operation, if the pipelines overlap, the weight of the pipeline is updated to the weight value of the pipeline with the largest weight among all the overlapping pipelines; S34: If the number of network nodes is not equal to the set value of the number of partitions, continue to execute S32; otherwise, stop pairing and merging nodes to obtain the network state G. m ; S4, G m Each node of is taken as a partition to obtain the initial partitioning scheme; S5, adopt the opposite operation of step S3, and connect the pipe network from G m Restore to G m-1 , and then do the following: S51, using a multi-objective optimization algorithm to move the partition boundary nodes, and obtain a series of new partition schemes, i.e., a partition scheme sequence; S52, for each partition scheme in the partition scheme sequence, optimizing the arrangement of boundary instruments in the scheme by means of another optimization algorithm; the boundary instruments include but are not limited to: flow meters, water meters, valves; S53, for each zoning scheme in the zoning scheme sequence, combining hydraulic simulation to obtain evaluation indicators of the scheme; the evaluation indicators include: pipe network elasticity coefficient Ir, average water age of pipe network avgWA, zoning scale difference UB, zoning transformation cost C; S54. Select the partition scheme corresponding to the Pareto solution from the partition scheme sequence as G m-1 Pareto optimal solution under the state; S6, taking the Pareto optimal solution as a new starting point, repeat step S5 until the pipe network is restored to the original state G0; step S5 is repeated m-1 times in total, and m-1 different Pareto optimal solutions are obtained, forming a Pareto optimal solution sequence; S7. Use the hierarchical analysis method to select the best partitioning scheme from the Pareto optimal scheme sequence.

2. According to claim 1, the independent measurement optimization partitioning method based on the graph partitioning algorithm is characterized in that: In step S3, the node weight is the node water demand, and the pipeline weight is the pipeline diameter.

3. The independent measurement optimization partitioning method based on graph partitioning algorithm according to claim 2 is characterized in that: When moving the partition boundary nodes in step S5, the multi-objective optimization algorithm used is the NSGA-II algorithm; When optimizing the boundary instruments of the arrangement scheme in step S5, the optimization algorithm used is a genetic algorithm.

4. The independent measurement optimization partitioning method based on graph partitioning algorithm according to claim 3 is characterized by: The pipe network elastic coefficient Ir is used to represent the relationship between the pressure of the water source point and the user node. The lower the value, the lower the overall residual pressure of the pipe network and the lower the leakage risk. The formula of the pipe network elastic coefficient Ir is as follows: Where: N represents the number of connected nodes; S represents the number of water source nodes; T represents the hydraulic simulation duration, in h; It represents the water demand of node n at hour t, in L / s; represents the free water head at node n at hour t, in m; It represents the water output of water source s at hour t, in L / s; represents the outflow head of water source s at hour t, in m; p * It indicates the minimum service head of the connection node, in L / s; The average water age avgWA of the pipe network is used to indicate the overall level of the water age of the pipe network and is an indicator for determining the overall water quality of the pipe network. The formula for the average water age avgWA of the pipe network is as follows: in: It represents the water age of the nth connection node at time t, in h; The sub-area size difference UB is used to represent the relative difference between the maximum and minimum sizes of an area, measured by the water consumption of users within the sub-area; the formula for the sub-area size difference UB is as follows: Where: Area max Indicates the maximum partition size among all partitions, in L / s; Area min Indicates the minimum partition size among all partitions, in L / s; The formula for the zoning transformation cost C is as follows: in: Indicates the nth m Cost of a metering device, yuan; N m Indicates the total number of installed metering devices; Indicates the nth v Cost of a valve, Yuan; N m Indicates the total number of valves installed.

5. The independent measurement optimization partitioning method based on graph partitioning algorithm according to claim 4 is characterized in that: Step S7 includes the following steps: S61. Using the analytic hierarchy process, a hierarchical structure is established, which includes three levels: target level, criterion level, and scheme level. The target level is the evaluation system A; the criterion level includes four evaluation indicators: system elasticity coefficient Ir, average water age of the pipe network avgWA, zone scale difference UB, and zone cost C; the scheme level is the Pareto optimal scheme sequence; S62. According to experience, the importance of the four evaluation indicators of the criterion layer to the evaluation system A is judged, and then the four evaluation indicators are assigned importance values, namely: the importance value of the system elasticity coefficient Ir is B1, the importance value of the average water age of the pipe network avgWA is B2, the importance value of the partition scale difference UB is B3, and the importance value of the partition cost C is B4; S63, construct a judgment matrix W according to B1, B2, B3, and B4, that is: W=(a ij ) 4×4 Where: i = 1, 2, 3, 4, j = 1, 2, 3, 4; S64, checking the consistency of the judgment matrix W; S65. Use the geometric mean method to calculate the weights of the four evaluation indicators of the criterion layer to the solution layer. The formula is as follows: Where: i = 1, 2, 3, 4, j = 1, 2, 3, 4, n = 1, 2, 3, 4, a ij is the element of the judgment matrix W, ω1 (2) is the weight of the system elasticity coefficient Ir on the solution layer, ω2 (2) is the weight of the average water age avgWA of the pipe network on the scheme layer, ω3 (2) is the weight of the partition size difference UB on the solution layer, ω4 (2) is the weight of the zoning transformation cost C on the scheme layer; S66, weight vector w of the synthesis criterion layer to the target layer (2) : w (2) =(ω1 (2) ,ω2 (2) ,ω3 (2) ,ω4 (2) ) T ; S67. The Pareto optimal solution sequence of the solution layer contains m-1 partition solutions. The importance value p of each partition solution to the four evaluation indicators of the criterion layer is obtained according to the hydraulic simulation results. j1 (3) 、p j2 (3) 、p j3 (3) 、p j4 (3) , where p j1 (3) represents the importance of the jth partition scheme to the system elasticity coefficient Ir, p j2 (3) represents the importance of the jth partition scheme to the average water age avgWA of the pipe network, p j3 (3) represents the importance value of the jth partitioning scheme to the partition size difference UB, p j4 (3) Represents the importance of the j-th zoning scheme to the zoning transformation cost C, and the value range of j is 0 to m-1; S68, m-1 p ji (3) The resultant vector P i (3) : P i (3) =(p 1i (3) ,p 2i (3) ,...,p ji (3) ) T ; S69, 4 P i (3) Merge into an n×4 weight matrix: P (3) =(P1 (3) ,P2 (3) ,P3 (3) ,P4 (3) ); S610, through w (2) and P (3) Obtain the synthetic weight w of the solution layer to the target layer (3) : w (3) =P (3) w (2) ; S611. Check the consistency of the total order of the hierarchy. The formula is as follows: Where: i Indicates the relative weight of each element in the criterion layer to the overall goal; CI i Represents the consistency index of the solution layer to each element of the criterion layer; RI i Represents the average random consistency index of each element of the scheme layer for the criterion layer.

6. The independent measurement optimization partitioning method based on graph partitioning algorithm according to claim 5 is characterized in that: In step S62, the importance values ​​assigned to the four evaluation indicators of the criterion layer based on experience are as follows: The importance value of the system elasticity coefficient Ir is 9; The importance value of the average water age avgWA of the pipe network is 5; The importance value of partition size difference UB is 3; The importance value of the partition cost C is 7.

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