A method for implementing DMA zoning of a water supply network in a minimal pressure reduction space

Abstract

The present invention discloses a method for implementing DMA zoning of a water supply network in a minimal pressure reduction space. This method first defines a calculation formula for the similarity between nodes, and then optimizes the coefficients in the similarity formula through the function gamultiobj in MATLAB to determine the boundary pipe segments of the zones. Then, different minimum service water pressures are set and used as constraint conditions respectively. Taking the average water age of nodes and the zoning cost after zoning as objectives, multiple equipment layout schemes on the boundary pipe segments are obtained by using the function gamultiobj, and the optimal layout scheme is selected from them according to three principles. Finally, the simulated annealing algorithm is used to find the best pipe replacement scheme, so that the water pressure of the network after zoning can meet the requirements of the specified minimum service water pressure. The DMA zoning method provided by the present invention can successfully complete the zoning without having too much impact on the overall water quality of the network after zoning, and can provide a certain theoretical basis for local water supply companies to accelerate the implementation of DMA zoning, reduce the network leakage rate, and build a smart water supply system.

Description

Technical Field

[0001] This application belongs to the technical field of urban water supply network design, and specifically relates to a method for DMA zoning of water supply networks, especially a method for implementing DMA zoning of water supply networks with extremely small pressure reduction space. Background Technique

[0002] DMA zoning is to divide the entire water supply network into several relatively closed independent metering areas by closing valves and installing flow meters on boundary pipe segments. By monitoring the flow rates at the entrances and exits of each area and regulating the pressure at the entrances, the purpose of controlling network leakage and the pressure of the control management system can be achieved. Since boundary valves need to be closed during zoning, it will inevitably cause an increase in the head loss of the water supply network, thereby reducing the redundancy of the pressures at each node in the network. For nodes with extremely small pressure reduction space at the end of the network, this will result in the water pressure after zoning being difficult to meet the minimum service water pressure, thus affecting the normal operation of the water supply network.

[0003] Currently, there are deficiencies in the treatment of the pressures at the end nodes of the water supply network in the research on DMA zoning. Zhou Lidian et al. used the condition that the pressure fluctuation range at the nodes is within 10% as a constraint when optimizing the layout of equipment, which may cause the pressures at the end nodes of the water supply network not to meet the regulations. Zeng Han et al. restricted the water pressure of nodes with a water pressure exceeding 16m before zoning to not be lower than 16m after zoning, and for nodes with a water pressure lower than 16m before zoning, their water pressure should not be lower than 0m after zoning. Obviously, this constraint method creates a relatively large pressure reduction space for the water supply network, and it is very likely that the water pressure of nodes with a low water pressure originally will be even lower after zoning. Zhou Zhongjian et al. applied the regulation in the "Urban Water Supply Service" specification that the pressure at the end of the water supply network should not be lower than 14m to the Modena water supply network in Italy, increasing the pressure reduction space of the water supply network and then completing the DMA zoning. Summary of the Invention

[0004] In order to solve the problem of zoning of the water supply network with extremely small pressure reduction space, the present invention first combines the spectral clustering algorithm and the function gamultiobj in MATLAB to determine the ideal boundary pipe segments for zoning. Then, by setting a series of different minimum service water pressures and using them as constraint conditions respectively, the optimal layout scheme of the equipment on the boundary pipe segments is obtained by using the function gamultiobj. Finally, the simulated annealing algorithm is used to find the pipe segments that need to change the pipe diameter, so that the pressures of all nodes in the water supply network after zoning can meet the minimum service pressure.

[0005] The technical solution for the present invention to achieve the above object is as follows.

[0006] The present invention provides a method for implementing DMA zoning of a water supply network with extremely small pressure reduction space, including the following steps:

[0007] A1: Call the EPANET dynamic link library in MATLAB, and obtain the basic data of the pipe network after performing hydraulic analysis;

[0008] A2: Specify the number of partitions, and define the calculation formula for the similarity between two nodes in the pipe network;

[0009] A3: Take the number of boundary pipe segments after partitioning by the spectral clustering algorithm, and their average flow rate, pipe diameter, and length as the objective function, and optimize the parameters in the similarity calculation formula through the function gamultiobj to determine the boundary pipe segments of the partition;

[0010] A4: Set a series of different minimum service water pressures and use them as constraint conditions. Take the average node water age and partition cost after partitioning as the objective function, and obtain the Pareto optimal solution set through gamultiobj optimization calculation. Select the optimal equipment layout plan through three principles;

[0011] A5: Take the minimum cost of replacing pipe segments as the objective, and use the simulated annealing algorithm to find the best pipe segment replacement plan.

[0012] In the present invention, a hydraulic model of the water supply pipe network is established in EPANET 2.2, and the EPANET dynamic link library is called in MATLAB to obtain the basic data of the pipe network.

[0013] The present invention uses the spectral clustering algorithm to partition the pipe network. The water supply pipe network is regarded as an undirected graph model composed of nodes and pipe segments. The spectral clustering algorithm is used to transform the clustering problem into a graph partitioning problem, and different nodes of the water supply pipe network are clustered, so that the weight of the boundary pipe segments between different partitions after partitioning is small, and the sum of the weights of the pipe segments in the same partition is high, obtaining an ideal partition result.

[0014] In the preferred technical solution of the present invention, the similarity between two nodes in the water supply pipe network is defined according to formula (1), mainly considering that if the valve is closed on the boundary pipe segment with a large flow rate, it will cause energy dissipation in the pipe network, resulting in a significant reduction in the node water pressure in the pipe network, and it is extremely easy for the water pressure at the end nodes of the pipe network not to meet the specified minimum service water pressure. On the other hand, if the pipe diameter of the boundary pipe segment is too large, it will invisibly increase the cost of partition transformation, because the price of both valves and flow meters will increase exponentially with the increase of the pipe diameter. In addition, a large pipe diameter often corresponds to a high flow rate, so the pipe diameter of the boundary pipe segment should be avoided as large as possible. Installing a closing valve on the boundary pipe segment, the risk of water quality deterioration will increase with the increase of the DMA cut-off pipe length. Therefore, pipe segments with a small flow rate, a small pipe diameter, and a short length should be selected as the boundary pipe segments of the partition.

[0015] The similarity value of the pipe segment between two nodes in the water supply pipe network is shown in formula (1):

[0016]

[0017] Where: ω ij , Q ij , D ij , L ij and are the similarity value, flow rate, m 3 / s, pipe diameter, mm, and length, m of the pipe section between nodes i and j respectively; N is the set of all nodes in the pipe network; α, β, and γ are parameters in the similarity calculation formula

[0018] In formula (1), the selection of the three values of α, β, and γ will directly affect the result of the boundary pipe section of the partition. By optimizing the values of these three parameters, the purpose of selecting the optimal boundary pipe section is achieved.

[0019] The objective function for optimizing the three parameters α, β, and γ is

[0020] Where f n is the number of boundary pipe sections, pieces; f q is the average flow rate of the boundary pipe sections, L / s; f d is the average pipe diameter of the boundary pipe sections, mm; f l is the average length of the boundary pipe sections, m; n b is the number of boundary pipe sections; Q r , D r , L r are the flow rate, L / s, pipe diameter, mm, and length, m of the r-th boundary pipe section respectively.

[0021] Use the function gamultiobj in MATLAB for solving multi-objective optimization problems to determine the values of the three parameters.

[0022] The coding method uses real number coding. The decision variables are the three parameters in the similarity calculation formula. During the optimization process, their ranges are restricted to the interval (0, c), where c can be determined through multiple experiments: specifically, it is to make α, β, and γ within this interval, so that the resulting normalized Laplacian matrix does not have imaginary numbers when calculating eigenvalues and eigenvectors in MATLAB. For different pipe networks, the selection of the c value is also different, but for different water usage states of the same pipe network, the determination of the c value can refer to the previous water usage state, and the difference between the two is very small or remains unchanged.

[0023] For nodes with extremely limited pressure reduction space at the end of the pipe network, once a valve is newly closed in the pipe network, the node pressure will easily fall below the specified minimum service water pressure. Therefore, when optimizing the equipment layout on the boundary pipe sections, if the specified minimum service water pressure is used as a constraint, there is a high probability of having no solution or a very poor solution quality. Therefore, a series of different minimum service water pressures are set as the constraints for optimizing the equipment layout, and the solutions under each pressure constraint are observed to determine the optimal layout plan.

[0024] When optimizing the equipment layout on the boundary pipe sections, the water quality safety of the pipe network after zoning and the economy of zoning should be considered. At the same time, the node continuity equation, the energy conservation equation, and the water pressure constraints of the nodes must also be satisfied.

[0025] The objective function and constraints for optimizing the equipment layout on the boundary pipe sections are

[0026] In the formula: M is the total number of nodes in the pipe network except for the water sources; t i is the node water age of node i in the pipe network, h; T v is the number of valves installed on the boundary pipe sections, units; C valve,v is the price of the v-th valve on the boundary pipe sections, yuan; T m is the number of flow meters installed on the boundary pipe sections, units; C meter,m is the price of the m-th flow meter on the boundary pipe sections, yuan. A is the connection matrix of the pipe network; q is the column vector of pipe section flows; Q is the column vector of node flows; L is the loop matrix of the pipe network; h is the column vector of pipe section head losses; H i is the actual water pressure of node i in the pipe network, m; H smin is the set minimum water pressure of the pipe network, m; H i,max is the maximum allowable water pressure of node i in the pipe network, m.

[0027] Use the function gamultiobj in MATLAB to obtain the equipment layout plan.

[0028] The decision variables are to install valves or flow meters on the boundary pipe sections, and their dimension is equal to the number of boundary pipe sections. The coding method uses binary coding, where "0" represents installing a flow meter on the boundary pipe section, and "1" represents installing a valve on the boundary pipe section.

[0029] Select the optimal layout plan from the Pareto optimal solution set according to the following three principles.

[0030] Principle ① The maximum number of entrances to each DMA is 2.

[0031] Principle ② The average node water age after arranging the equipment should not be higher than the water age before zoning.

[0032] Principle ③: On the basis of meeting the requirements of the number of DMA entries and the average node water age limit, select the equipment layout plan that can minimize the number of nodes with a service water pressure lower than the specified minimum service water pressure in the pipe network after operation.

[0033] After determining the equipment layout plan, establish the hydraulic model of the water supply pipe network under this plan (using EPANET 2.2 software).

[0034] For nodes that do not meet the specified minimum service water pressure of the pipe network, the pipe diameter of the pipe section flowing to this node can be enlarged to reduce the energy loss during water transfer, thereby increasing the node pressure of this node and making the node pressure meet the specified minimum service pressure of the pipe network.

[0035] During the replacement process, it is necessary to control the number, length, and diameter of the replaced pipe sections to save costs. After replacement, the two basic equations of the pipe network still need to be satisfied, and the average node pressure of the pipe network after replacement should not be greater than the average pressure before replacement, because an increase in pressure will lead to an increase in the leakage volume in the pipe network.

[0036] The objective function and constraints for replacing pipe sections are

[0037] In the formula: D i , l i are the diameter, in mm, and length, in m, of pipe section i respectively; U is the total number of pipe sections whose diameters need to be replaced in the pipe network; a, b, and σ are statistical parameters in the pipe section cost formula, taking a = 112.9, b = 3135, and σ = 1.5; are the average node pressures of the pipe network after replacing the pipe diameter and the original pipe network respectively, in m; H i,now is the actual water pressure of node i after replacing the pipe diameter, in m.

[0038] Use the simulated annealing algorithm to optimize the pipe section replacement plan. The coding method uses integer coding, and the decision variable is the pipe diameter specification that can be replaced for the pipe section, and its dimension is the number of pipe sections whose diameters are to be replaced.

[0039] For the convenience of coding and decoding, natural numbers from 1 to 9 are used to represent the pipe diameter specifications that can be replaced, and 0 represents that the pipe diameter of this pipe section remains unchanged. For example, a solution x = [0, 3, 5, 8] means that there are a total of 4 pipe sections whose diameters are to be replaced. The diameter of the first pipe section remains unchanged, and the diameters of the second, third, and fourth pipe sections are replaced with 150 mm, 250 mm, and 400 mm respectively.

[0040] First, find the set of nodes S1 in the pipe network where the node pressures do not meet the specified minimum service pressure after installing the equipment. Then, find the set of nodes S2 that are adjacent to them and the water flow is directed towards them. The set of pipe segments P formed by these nodes is the first batch of pipe segments for which the pipe diameters are to be replaced. Use the simulated annealing algorithm to find the pipe diameter replacement plan that minimizes the objective function and satisfies the constraints. If there is a solution after optimization, a more economical pipe diameter replacement plan is obtained at this time. If there is no solution, continue to find the set of nodes S3 that are adjacent to S2 and the water flow is directed towards them, and then update the set of pipe segments P to obtain the second batch of pipe segments for which the pipe diameters are to be replaced. Continue to use the simulated annealing algorithm to find the optimal solution until a pipe diameter replacement plan can be found and the algorithm stops. At this time, it can be considered that the global optimal solution has been obtained.

[0041] When the pipe diameter replacement plan is first found, it can be considered that the global optimal solution has been obtained because each subsequent search downward means that the elements in the set P will gradually increase, causing the search space of the algorithm to expand rapidly, making it much more difficult to find a feasible solution, thereby increasing the probability of the algorithm falling into a local optimum and making it difficult for the algorithm to converge to the global optimal solution.

[0042] The beneficial effects of the present invention are as follows:

[0043] 1. A method for DMA zoning of urban water supply pipe networks in a minimal pressure reduction space is proposed. During the zoning process, the economy of zoning, the safety of water quality after zoning, and the effectiveness of implementing DMA zoning are fully considered, which can greatly improve the quality of DMA zoning.

[0044] 2. A specific calculation method for the similarity between nodes in the pipe network is proposed. The boundary pipe segments obtained thereby can greatly reduce the impact of closing valves on the water pressure of the entire pipe network, can also greatly reduce the cost of zoning, and ensure the water quality safety of the pipe network after zoning. Description of the Drawings

[0045] Figure 1 It is a flowchart of a method for implementing DMA zoning of a water supply pipe network in a minimal pressure reduction space according to the present invention.

[0046] Figure 2 It is a topological diagram of the case pipe network in the present invention.

[0047] Figure 3 It is a comparison of the relevant indicators of the boundary pipe segments obtained after zoning the case pipe network using the zoning method of the present invention and the zoning methods proposed by other studies.

[0048] Figure 4 It is a graph of the trend of the number of cooling times and the optimal value of the simulated annealing algorithm in the present invention.

[0049] Figure 5 It is a diagram of the final zoning result of the case pipe network in the present invention. Detailed Embodiment

[0050] The present invention will be described in detail below in conjunction with specific embodiments.

[0051] As Figure 1 shown, a method for implementing DMA zoning of a water supply network under an extremely small pressure reduction space of the present invention includes the following steps:

[0052] Step 1: Call the EPANET dynamic link library in MATLAB, and obtain the basic data of the pipe network after performing hydraulic analysis;

[0053] Step 2: Specify the number of zones, and define the calculation formula for the similarity between two nodes of the pipe network;

[0054] Step 3: Take the number of boundary pipe segments, their average flow rate, pipe diameter and length after zoning by the spectral clustering algorithm as the objective function, and optimize the parameters in the similarity calculation formula through the function gamultiobj to determine the boundary pipe segments of the zoning;

[0055] Step 4: Set a series of different minimum service water pressures and use them as constraint conditions, take the average node water age and zoning cost after zoning as the objective function, obtain the Pareto optimal solution set through gamultiobj optimization calculation, and screen out the optimal equipment layout plan through three principles;

[0056] Step 5: Take the minimum cost of replacing pipe segments as the objective, and use the simulated annealing algorithm to find the best pipe segment replacement plan;

[0057] The following will be described by taking a specific example.

[0058] The topological structure of the case pipe network is as Figure 2 shown. The pipe network has a total of 272 nodes (including 4 water source nodes) and 317 pipe segments, belonging to a medium-sized urban pipe network. The maximum pipe diameter in the pipe network is 400 mm, the minimum pipe diameter is 100 mm, and each node has a limit of a minimum pressure of 20 m and a maximum pressure of 32.67 - 44.11 m. When operating under single-condition conditions, the minimum node pressure in the pipe network is 20.09 m, and there are 13 nodes with a pressure not exceeding 20.5 m.

[0059] DMA zoning of the case pipe network has also been completed in other studies. After comprehensively considering factors such as economy and management, the number of zones is determined to be 4 in each case. The zoning schemes obtained from other studies are denoted as Scheme B and Scheme C respectively. The number of zones adopted for DMA zoning of the case pipe network in the present invention is also set to 4. Scheme B is derived from the prior art "Research on the DMA Zoning Method of Water Supply Pipe Networks Based on Node Natural Neighbors" (see: Zhou Zhongjian, Wang Qi, Ji Ruibo, etc. Research on the DMA Zoning Method of Water Supply Pipe Networks Based on Node Natural Neighbors [J]. Water & Wastewater Engineering, 2019, 55(07): 118-123.). Scheme C is derived from the prior art "Research on the Automatic DMA Zoning of Urban Water Supply Pipe Networks Based on Node Energy Redundancy" (see: Jiang Hao. Research on the Automatic DMA Zoning of Urban Water Supply Pipe Networks Based on Node Energy Redundancy [D]. Guangzhou: Guangdong University of Technology, 2017.).

[0060] The function gamultiobj is used to determine the boundary pipe segments of the zones, and the parameter settings are as follows: the optimal front coefficient is 0.3, the population size is 100, the maximum number of generations for evolution is 600, the stopping generation is also 600, the deviation of the fitness function value is 0.01, and other parameters are default values. Through experiments, the value of c can be 3.5, so the values of the three parameters are limited to the range of (0, 3.5). After calculation by MATLAB, the Pareto optimal solution set is obtained. On this basis, the values of the three parameters in the similarity calculation formula are determined to be α = 0.198, β = 2.41, and γ = 0.674 respectively, and the boundary pipe segments and zoning results are obtained accordingly, which are denoted as Scheme A.

[0061] Figure 3 The relevant indicators of the three zoning schemes are compared. The sum of the flow rates, the sum of the pipe diameters, and the sum of the lengths of the boundary pipe segments are represented by f tq 、f td and f tl respectively.

[0062] As Figure 3 can be seen, in Scheme A, both the average flow rate and the total flow rate of the boundary pipe segments are less than 50% of those of the other two schemes, while the total pipe diameter length and the average pipe diameter length are both in the range of 55% - 86% of those of the other two schemes, and the number of boundary pipe segments is also the lowest among the three.

[0063] After determining the boundary pipe segments of the zones, the optimal layout of the equipment on the boundary pipe segments is carried out, that is, valves and flow meters are installed on the boundary pipe segments.

[0064] Set different minimum service water pressures to 20m, 19m, 18m, and 17m respectively, and use them as constraint conditions. Import the costs of valves and flow meters under different pipe diameters into MATLAB, and optimize the layout scheme of equipment on the sectional boundary pipes through the gamultiobj function. The parameter settings are as follows: the optimal front coefficient is 0.1, the population size is 100, the maximum number of evolutionary generations is 50, the stopping generation is also 50, the deviation of the fitness function value is 0.01, and other parameters are default values.

[0065] After MATLAB calculation, the number of Pareto optimal solutions obtained under different pressure constraints are 3, 4, 3, and 5 respectively, and 2 solutions coincide when the pressure constraints are 17m and 18m. Table 1 lists the two objective function values of 15 Pareto optimal solutions, the number of flow meters required for zoning, the number of nodes n with water pressure below 20m after equipment layout p and the number of water inlets in each area after zoning.

[0066] Table 1 Pareto frontiers and other relevant information under different pressure constraints

[0067]

[0068]

[0069] Note: * indicates that this solution appears repeatedly when the minimum service water pressure constraint is 17m

[0070] Screen the Pareto optimal solution sets obtained under different pressure constraints according to the following three principles: 1) The number of water inlets for a single DMA shall not exceed two; 2) The average water age of the nodes in the pipe network shall not be higher than 0.72h; 3) The number of nodes with water pressure below 20m after operation is the least.

[0071] Solution s-11 meets the above principles, and the corresponding scheme is the optimal layout scheme of equipment on the boundary pipes. Therefore, 8 valves and 6 flow meters are installed in the case pipe network, the equipment installation cost is 93,928 yuan, the average water age of the nodes after equipment installation is 0.70h, the lowest water pressure of the pipe network nodes after operation under single-condition is 17.61m, and there are 13 nodes with water pressure below 20m.

[0072] The specified minimum service water pressure of the nodes in the case pipe network is 20m. After zoning, 13 nodes do not meet the requirements. Therefore, it is necessary to increase the pipe diameter of some pipes in the pipe network to reduce the head loss of the pipe network so that the pressure of all nodes can meet the requirements.

[0073] Execute hydraulic simulation in MATLAB, find the set of pipe segments whose pipe diameters are to be replaced, optimize the pipe diameter sizes of the replaced pipe segments, and obtain the optimal solution through the simulated annealing algorithm. The algorithm parameters are set as follows: the initial temperature is 200 °C, the end temperature is 0.001 °C, the cooling rate is 0.98, and the length of the Markov chain is 50. The encoded numbers are consecutive natural numbers from 0 to 9. 0 represents that the pipe diameter of the pipe segment remains unchanged, and 1 to 9 respectively correspond to the pipe diameter changes of 100 mm to 450 mm.

[0074] After the set of pipe segments to be replaced is updated twice, the calculation stops. The operation process of the simulated annealing algorithm is as Figure 4 shown. The algorithm converges when the number of cooling times E is 290 times, that is, the global optimal solution is obtained.

[0075] It can be seen from the calculation results that 10 pipe segments need to be replaced, which only accounts for 3.2% of the total number of pipe segments in the pipe network. The cost of replacing the pipe segments is 847,350 yuan. After replacing the pipe diameters of the case pipe network with equipment arranged on the boundary pipe segments, the pressures of all nodes during single-condition operation are greater than the specified minimum service water pressure. The final zoning results are as Figure 5 shown.

[0076] Table 2 is a comparison of various operation performance indicators of the Modena pipe network before and after implementing DMA zoning. In the table, g w is the comprehensive water age index of the pipe network, which can reasonably reflect the water quality situation of the entire pipe network, especially the water quality of large-flow users and the pipe network end areas.

[0077] Table 2 Operation performance indicators of the pipe network before and after DMA zoning

[0078]

[0079] It can be seen from Table 2 that:

[0080] The node water age after zoning has not changed compared with that before zoning, indicating that the implementation of DMA zoning in the case pipe network has not had too much impact on the water quality of the pipe network. The comprehensive water age index of the pipe network after zoning has decreased, indicating from this perspective that the water quality of the pipe network after zoning, especially the water quality of the pipe network end and large-flow users, has been significantly improved.

[0081] On the premise of ensuring that the minimum water pressure of the pipe network is greater than the specified minimum service water pressure, the average water pressure of the pipe network after zoning decreases, and the leakage volume of the pipe network also decreases slightly. Although the decrease amplitude is very small, the time to detect leakage and find the leakage points will be greatly shortened after implementing DMA zoning, which can further reduce the leakage of the pipe network and the production and sales difference of the water supply company.

[0082] It should be understood that for those of ordinary skill in the art, improvements or transformations can be made according to the above description, and all such improvements and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for implementing DMA zoning of a water supply network in an extremely small pressure reduction space, characterized in that, It includes the following steps: A1: Call the EPANET dynamic link library in MATLAB, and obtain the basic data of the pipe network after performing hydraulic analysis; A2: Specify the number of partitions, and define the calculation formula for the similarity between two nodes in the pipe network; A3: Take the number of boundary pipe segments after partitioning by the spectral clustering algorithm, and their average flow rate, pipe diameter and length as the objective function, and optimize the parameters in the similarity calculation formula through the function gamultiobj to determine the boundary pipe segments; A4: Set a series of different minimum service water pressures and use them as constraints. Take the average node water age and partition cost after partitioning as the objective function, and obtain the Pareto optimal solution set through gamultiobj optimization calculation. Then, select the optimal equipment layout plan according to three principles; A5: Take the minimum cost of replacing pipe segments as the objective, and use the simulated annealing algorithm to find the best pipe segment replacement plan; specifically: the coding method uses integer coding, the decision variable is the pipe diameter specification that can be replaced for the pipe segment, and its dimension is the number of pipe segments with the pipe diameter to be replaced; Use natural numbers from 1 to 9 to represent the pipe diameter specifications that can be replaced, and 0 represents that the pipe diameter of this pipe segment remains unchanged; First, find the set of nodes in the pipe network whose nodal pressures do not meet the specified minimum service pressure after installing the equipment. S 1. Then, find the set of nodes adjacent to them and with water flowing towards them. S 2. The set of pipe segments formed by these nodes P is the first batch of pipe segments for which the pipe diameters are to be replaced. Use the simulated annealing algorithm to find the pipe diameter replacement plan that minimizes the objective function and satisfies the constraints. If there is a solution after optimization, a relatively economical pipe diameter replacement plan is obtained at this time. If there is no solution, continue to search for nodes S adjacent to 2 and with water flowing towards them. S 3. Then, update the set of pipe segments P to obtain the second batch of pipe segments for which the pipe diameters are to be replaced, and continue to use the simulated annealing algorithm to find the optimal solution until the algorithm stops when a pipe diameter replacement plan can be found. At this time, it can be considered that the global optimal solution has been obtained.

2. The method for implementing DMA zoning of a water supply network in an extremely small pressure reduction space as described in claim 1, wherein In step A2, the similarity value between two pipe segments between two nodes in the water supply pipe network is shown in formula (1): （1） In the formula: ω ij , Q ij , D ij , L ij and are the similarity value, flow rate in m³ / s, pipe diameter in mm, and length in m of the pipe section between nodes i and j respectively; N is the set of all nodes in the pipe network; α , β , γ are the parameters in the similarity calculation formula.

3. A method for implementing DMA zoning of a water supply network in an extremely small pressure reduction space, characterized in that, In step A3: Taking the minimum number of boundary pipe segments, their average flow rate, pipe diameter, and length after partitioning by the spectral clustering algorithm as the objectives, the parameters in the similarity calculation formula are determined through the multi-objective optimization function gamultiobj in MATLAB α , β , γ , and the corresponding partition boundary pipe segments are obtained.

4. A method for implementing DMA zoning of a water supply network in a minimal pressure reduction space, as described in claim 3, characterized in that In step A3: Optimize α , β , γ The objective function of the three parameters is: In the formula f n is the number of boundary pipe segments, in pieces; f q is the average flow rate of the boundary pipe segments, in L / s; f d is the average pipe diameter of the boundary pipe segments, in mm; f l is the average length of the boundary pipe segments, in m; n b is the number of boundary pipe segments; Q r , D r , L r are respectively the flow rate, in L / s, pipe diameter, in mm, and length, in m, of the r th boundary pipe segment; Use the function gamultiobj in MATLAB that solves multi-objective optimization problems to determine the values of the three parameters; The coding method adopts real number coding. The decision variables are the three parameters in the similarity calculation formula. During the optimization process, their ranges are restricted to the interval (0, c ), where c can be determined through multiple experiments: specifically, it is to make α , β , γ within this interval, so that the resulting normalized Laplacian matrix does not produce imaginary numbers when calculating eigenvalues and eigenvectors in MATLAB; for different pipe networks, c the selected values are also different, but for different water usage states of the same pipe network, c the value can be determined by referring to the previous water usage state, and the difference between the two is very small or remains unchanged.

5. A method for implementing DMA zoning of a water supply network in an extremely small pressure reduction space, characterized in that, In step A4: The objective function and constraints for optimizing the equipment layout on the boundary pipe segments are: （3） In the formula: M is the total number of nodes in the pipe network except the water source; t i is the node water age of node i in the pipe network, h; T v is the number of valves installed on the boundary pipe section, unit; C valve,v is the price of the v th valve on the boundary pipe section, yuan; T m is the number of flow meters installed on the boundary pipe section, unit; C meter,m is the price of the m th flow meter on the boundary pipe section, yuan; A is the connection matrix of the pipe network; q is the column vector of the pipe segment flow rate; Q is the column vector of the node flow rate; L is the loop matrix of the pipe network; h is the column vector of the pipe segment head loss; H i is the node i in the pipe network, with the actual water pressure, m; H smin The minimum water pressure of the set pipe network, m; H i,max For a node in the pipe network i Maximum allowable water pressure, m; Use the function gamultiobj in MATLAB to obtain the equipment layout plan; The decision variable is to install a valve or a flowmeter on the boundary pipe segment, and its dimension is equal to the number of boundary pipe segments. The coding method uses binary coding, where "0" represents installing a flowmeter on the boundary pipe segment, and "1" represents installing a valve on the boundary pipe segment.

6. A method for implementing DMA zoning of a water supply network in an extremely small pressure reduction space, characterized in that, In step A4: The three principles for screening the optimal layout plan are respectively: 1) The number of inlets of a single DMA shall not exceed two; 2) The average node water age after arranging the equipment shall not be higher than the water age before partitioning; 3) On the basis of meeting the requirements for the number of inlets of each DMA and the limit of the average node water age, select the equipment layout plan that can minimize the number of nodes with a water pressure lower than the specified minimum service water pressure in the pipe network after operation.

7. A method for implementing DMA zoning of a water supply network in an extremely small pressure reduction space, characterized in that, In step A5: The objective function and constraints for replacing pipe segments are: （4） Wherein: D i and l i are respectively the diameter, in mm, and the length, in m, of the pipe segment i . U is the total number of pipe segments whose pipe diameters need to be replaced in the pipe network; a, b, σ is a statistical parameter in the pipe segment cost formula, taking a = 112.9, b = 3135, σ = 1.5; are the average nodal pressures of the replaced pipe diameter and the original pipe network, respectively, in m; H i,now is the actual water pressure at the node i after the pipe diameter is replaced, in m.

Images