Two-stage sensor arrangement method for leakage detection of water supply network

Abstract

The invention discloses a two-stage sensor arrangement method for water supply network leakage detection, and relates to the technical field of water supply network leakage detection.The method comprises the steps that in consideration of uncertainty and controllable and reliable requirements of real environment water supply network leakage detection, firstly, a scene set is generated for uncertain events, and basic information needed for decision making is provided for an algorithm; secondly, dividing sensor arrangement into two stages according to whether an uncertain event occurs or not, designing an algorithm for common optimization, and finally analyzing the influence of different factors on a decision scheme to assist in regulation and control of the pipe network and improvement of basic information, so that the controllable and reliable leakage detection method in the water supply pipe network is completed. Therefore, regulation and control of algorithm decision basic information, visualization of algorithm results and a closed-loop sensor arrangement optimization process are realized, construction of a more perfect and more efficient sensor arrangement optimization scheme is facilitated, and extended practice is provided for controllable and reliable operation of a water supply pipe network.

Description

Technical Field

[0001] The invention relates to the technical field of water supply network leakage detection, and in particular to a two-stage sensor arrangement method for water supply network leakage detection. Background Art

[0002] With social development and population growth, the scale and complexity of water supply networks have also increased exponentially. The construction and maintenance of water supply networks will inevitably develop in the direction of automation and intelligence. Maintaining urban water supply networks requires considering equipment aging and pipeline leaks caused by various uncertain events, which will lead to a decline in water supply capacity and even affect water quality safety.

[0003] In order to prevent pipeline leakage, it is necessary to first detect whether the pipeline network is leaking and where it is leaking so that timely repairs can be carried out. The common method is to arrange sensors to collect data to monitor and analyze the working conditions of the water supply network. Considering the large scale and complexity of the urban water supply network, the research direction is mainly to optimize the arrangement of sensors to achieve a higher leak detection accuracy or use fewer sensors to reduce costs. The research method is mainly to estimate the sensitivity of different locations to pressure changes through simulation and simulation models, and then select locations where it is easy to detect changes in pipeline pressure to arrange sensors.

[0004] The Chinese patent "Optimal Layout Method of Pipeline Monitoring Points for Water Supply Network Node Water Demand Inversion" with publication number CN106870955A, the Chinese patent "A Method for Optimal Layout of Monitoring Points for Urban Water Supply Network" with publication number CN105894130A, and the Chinese patent "A Method for Layout of Pressure Detection Points in Water Supply Network" with publication number CN105938505A, all use sensitivity analysis to obtain locations that are sensitive to pipeline pressure changes as optional sensor layout locations, and then use clustering or sorting methods to obtain the most representative locations for sensor layout based on the results of the sensitivity analysis. Among them, the Chinese patent "Optimal Layout Method of Pipeline Monitoring Points for Water Supply Network Node Water Demand Inversion" with publication number CN106870955A takes into account the error caused by water demand to leak detection.

[0005] There are also solutions in the prior art that use software or hydraulic models to simulate the impact of leakage or even burst pipes on the pipe network, and then calculate sensitivity and similar indicators as the basis for sensor layout. Among them, the Chinese patent "Multi-objective layout method of water supply pipe network leakage detection sensors based on leakage probability" with publication number CN113887020A and the Chinese patent "A method for optimizing the layout of pressure monitoring points for water supply pipe networks" with publication number CN111119282A studied the multi-objective optimization problem of sensor layout. The Chinese patent "Optimal layout method of water supply pipe network leakage identification sensors based on joint information entropy" with publication number CN112464421A studied the optimal layout plan when the sensor fails, and used the exhaustive method to pre-calculate the layout plan for possible situations, but only assumed that one sensor failed each time, without considering the possibility of multiple sensors failing in the real environment, and did not introduce prior knowledge into the decision-making.

[0006] Unlike simulation models, there are a lot of uncertainties in the real environment, such as waterlogging, ground subsidence, geological disasters caused by small earthquakes, and even irregular construction and equipment failures. Autonomous decision-making is still unable to accurately predict or even quickly handle unknown uncertain events. It is necessary to introduce a priori or professional knowledge to ensure the reliable operation of the water supply network.

[0007] In order to cope with the impact of uncertain events in the real environment, it is necessary to introduce uncertainty into the sensor layout optimization plan. In order to ensure the reliability of the water supply network operation in the real environment, it is necessary to achieve closed-loop decision optimization. Therefore, it is necessary to provide explainability for the layout plan to tell the operator how to come up with the layout plan and what factors affect the layout plan. In addition, it is necessary to provide uncertainty control methods to facilitate operators to introduce prior knowledge into the decision model, thereby achieving a more controllable and reliable sensor layout plan. Summary of the invention

[0008] In order to solve the above technical problems, the present invention provides a two-stage sensor arrangement method for water supply network leakage detection, comprising the following steps: S1. Obtain relevant basic information of the water supply network for sensor layout decision-making. The sensors are used to monitor the pressure and flow of the pipeline; S2. For each pipeline that needs to be monitored for leakage, generate leakage scenarios based on the probability of different leakage levels according to the basic information related to the water supply network, regard the leakage conditions of all pipelines as one scenario, and then combine them into a scenario set with a specified number of scenarios; S3, the sensor layout is divided into two stages based on whether the uncertain event occurs. In the first stage, that is, before the uncertain event occurs, a part of sensors are deployed for monitoring; in the second stage, that is, after the uncertain event occurs, new sensors are deployed for monitoring, and the number of new sensors is greater than the number of sensors deployed in the first stage; all possible uncertain events are represented by the scene set of step S2, and the maximum leakage coverage rate and leakage identification accuracy of the pipeline network are taken as the objective function, and the two stages are jointly optimized and solved to obtain the layout plan x of the first stage and the layout plan y of the second stage; based on the solution results, when the uncertain event occurs, the corresponding scene is selected according to the estimated leakage range. When the sensor deployed in the first stage detects the occurrence of leakage, the leakage location is estimated and matched with the scene in the scene set, and the pre-calculated second stage layout plan y is directly executed according to the matched scene; S4. Analyze the influence of different factors on the final objective function value and perform closed-loop optimization of sensor layout.

[0009] The technical solution further defined in the present invention is: Furthermore, in step S1, the relevant basic information used for sensor layout decision-making includes optional sensor layout locations and leakage probabilities of different pipelines with different leakage levels; the degree and scope of impact of different levels of leakage on surrounding pipelines are estimated based on simulation software and hydraulic models, and the threshold of pipeline leakage is determined.

[0010] As described above, in a two-stage sensor deployment method for water supply network leakage detection, in step S1, the sensor deployment locations are given according to the field investigation of the operation and maintenance personnel, and are represented by a set R, where R=[r1,r2,...,r n ] indicates that there are n optional positions; the operation and maintenance personnel divide the leakage level into k levels based on their professional experience. The larger the k, the more serious the leakage.

[0011] As described above, in a two-stage sensor arrangement method for water supply network leakage detection, in step S1, EPANET software is used to build a hydraulic model, and different levels of leakage are simulated on different pipelines through EPANET software, and the impact range and pressure impact degree of pipelines at different distances are recorded, which is expressed as a matrix E: Where s represents the s nearest pipelines connected to the pipeline where the leak is located, and the order of the s pipelines is based on the distance from the center of the corresponding pipeline to the leak location, from near to far; e ks It indicates the influence of the kth leakage level on the pressure of the sth nearest pipeline.

[0012] As described above, in a two-stage sensor arrangement method for water supply network leakage detection, in step S1, the probability P of different leakage levels of different pipelines is estimated based on the environment of the urban pipeline network. The environment of the urban pipeline network includes the geological environment of different pipelines, the degree of equipment aging, and the quality of pipeline laying. The matrix P is expressed as: Among them, m means there are m pipelines in the urban pipe network, p mk represents the probability that the mth pipeline has a leakage of leakage level k, where the sum of the probabilities of all leakage levels of each pipeline is 1, that is, p m1 +p m2 +...+p mk =1; Based on the pressure standard required for normal water use by urban residents, the threshold for the pressure drop in the water supply network caused by leakage is set to Q.

[0013] As described above, in a two-stage sensor deployment method for water supply network leakage detection, in step S2, different scenarios are generated according to probability based on matrix P. Assuming that the probability of leakage of level k in the first pipeline is p 1k , when the scene of level k is generated by uniform distribution, the same operation is performed on all other pipelines, then the scene c=[c1,c2,...,c m ], generate z scenes through the sampling average approximation method to form a scene set C.

[0014] As described above, in the two-stage sensor deployment method for water supply network leakage detection, in step S3, an objective function is constructed to convert the network leakage problem into a two-stage stochastic programming problem, and the scenario set C is regarded as a random variable, which is converted into a corresponding deterministic problem through the sampling average approximation method. The objective function is expressed as: Where x represents the selection of g positions from n optional sensor placement positions for the first stage of sensor placement, and y represents the sensor placement position for the second stage; the average impact range of different leakage levels is calculated according to the matrix E: w = [w1, w2, ..., w k ] and then solve it through evolutionary algorithm.

[0015] As described above, in a two-stage sensor arrangement method for water supply network leakage detection, based on the threshold Q, the leakage level to be monitored in the first stage is estimated to be k, k>5, then the range sensed by the position selected in x is w k ,So Indicates that the selected g positions need to cover as many pipelines as possible, where x i It indicates that i positions are selected from n optional sensor placement positions for the first stage of sensor placement.

[0016] As described above, in the two-stage sensor arrangement method for water supply network leakage detection, in step S3, based on the sampling average approximation method, the two-stage stochastic programming problem is expressed as a corresponding deterministic problem, and the objective function of the overall application scenario is expressed as: Among them, C j represents the jth scene, w kn The sensors arranged in the second stage need to be able to detect leakage of level n, y represents the sensor arrangement position in the second stage, and w km The sensors deployed in the first stage need to be able to detect leakage of level m, x i It indicates that i positions are selected from n optional sensor placement positions for the first stage of sensor placement.

[0017] As described above, in a two-stage sensor arrangement method for water supply network leakage detection, in step S4, based on the decision result of step 3, the influence of different factors on the final objective function value is analyzed, and interpretability is achieved through graphical visualization. The content of the graphical visualization is the influence of different factors on the final objective function value. The different factors include different sensor locations and leakage probabilities of different pipelines. The influence of different factors is evaluated through feature importance analysis or sensitivity analysis.

[0018] The beneficial effects of the present invention are: (1) In the present invention, by introducing prior knowledge in the real environment, possible uncertain events are represented in the form of scene sets, which helps to improve the reliability and effectiveness of the algorithm; by considering the impact of uncertain events on sensor layout, the sensor layout is divided into two stages. The joint optimization of the two stages ensures that the sensor layout plan of the first stage has the ability to more effectively deal with uncertain events. In addition, the sensor layout plans for different scenarios are pre-calculated in the form of scene sets. When an uncertain event occurs, the pre-calculated sensor layout plan can be quickly executed, which has the ability to quickly respond to uncertain events; (2) In the present invention, the influence of different factors on the final target value is displayed through a visualization method, which is conducive to understanding the layout plan and discovering the limitations of the plan, providing a basis for the subsequent regulation of the pipe network and the improvement of the algorithm model, and is conducive to building a controllable and reliable sensor layout method; (3) In the present invention, the basic information of algorithm decision-making, the visualization of algorithm results and the closed-loop sensor layout optimization process are realized, which is conducive to building a more complete and efficient sensor layout optimization scheme, and provides an extended practice for the controllable and reliable operation of the water supply network. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1It is a schematic diagram of the overall process of the present invention; Figure 2 Schematic diagram of water network pipelines in actual application scenarios in an embodiment of the present invention. DETAILED DESCRIPTION

[0020] This embodiment provides a two-stage sensor arrangement method for water supply network leakage detection, such as Figure 1 As shown, the following steps are included: S1. Obtain relevant basic information of the water supply network for sensor layout decision-making. The sensor is used to monitor the pressure and flow of the pipeline and send the data to the monitoring server for data processing and analysis.

[0021] For water supply networks, operation and maintenance personnel or software provide relevant basic information for sensor layout decisions, including optional sensor layout locations and leakage probabilities of different pipelines with different leakage levels. In addition, it is also necessary to estimate the degree and scope of impact of different levels of leakage on surrounding pipelines based on simulation software and hydraulic models, and determine the threshold of pipeline leakage.

[0022] The sensor layout locations are given according to the field investigation of the operation and maintenance personnel, and are represented by a set R, where R=[r1,r2,...,r n ] indicates that there are n optional positions; the operation and maintenance personnel divide the leakage level into k levels based on their professional experience, and the larger the k, the more serious the leakage; based on simulation software and hydraulic models, the impact of leakage of different levels can be estimated, including the changes in pressure and flow caused by leakage of different levels, as well as the scope of the impact of such changes.

[0023] The hydraulic model of a specific city water supply network is constructed using EPANET software. Leakages of different levels are simulated on different pipelines through EPANET software, and the impact range and pressure impact degree of pipelines at different distances are recorded, which is expressed as matrix E: Where s represents the s nearest pipelines connected to the pipeline where the leak is located, and the order of the s pipelines is based on the distance from the center of the corresponding pipeline to the leak location, from near to far; e ks It indicates the influence degree of the kth leakage level on the pressure of the sth nearest pipeline. In this embodiment, in order to simplify the problem scenario, the monitored pipeline is assumed to be a pipeline of DN300 and above.

[0024] Next, it is necessary to estimate the probability P of different leakage levels of different pipelines based on the environment of the urban pipeline network, taking into account factors including but not limited to the geological environment of different pipelines, the degree of equipment aging, and the quality of pipeline laying. The matrix P is expressed as: like Figure 2Shown is the CY-DMA (Cypros Independent Metering Area) water network, a real network from a large water company in Cypros; Figure 2 R-1 in the figure is a pumping station; the solid black nodes represent residential consumers, and the numbers on the nodes represent the r-th residential houses; the lines represent the water network pipelines in the area, and the numbers on the lines represent the m-th pipelines.

[0025] p in matrix P mk represents the probability that the mth pipeline has a leakage of leakage level k, where the sum of the probabilities of all leakage levels of each pipeline is 1, that is, p m1 +p m2 +...+p mk =1; based on Figure 2 The simulation of the urban pipe network shown in the figure takes into account the pressure standard required for normal water use by urban residents and sets the threshold value of the pressure drop in the water supply network caused by leakage as Q.

[0026] S2. For each pipeline that needs to be monitored for leakage, a leakage scenario is generated based on the probability of different leakage levels according to the basic information related to the water supply network. The leakage conditions of all pipelines are regarded as one scenario, which is then combined into a scenario set with a specified number of scenarios.

[0027] Based on the matrix P in step S1, different scenarios can be generated according to probability. Assume that the probability of leakage of level k in the first pipeline is p 1k = 0.2, then when the scene of level k is generated by uniform distribution, the same operation is performed on all other pipelines, then the scene c = [c1,c2,...,c m ], in order to comprehensively consider the impact of different situations and uncertain events, the sample average approximation method (SAA) is used to generate z scenarios to form the scenario set C.

[0028] S3. The sensor layout is divided into two stages based on whether an uncertain event occurs. In the first stage, i.e., before the uncertain event occurs, a part of sensors are arranged for normal monitoring; in the second stage, i.e., after the uncertain event occurs, new sensors are arranged for key monitoring, and the number of new sensors is greater than the number of sensors arranged in the first stage; all possible uncertain events are represented by the scenario set of step S2, and the two stages are jointly optimized and solved with maximizing the pipeline leakage coverage and leakage identification accuracy as the objective function to obtain the layout plan x of the first stage and the layout plan y of the second stage; based on the solution results, when the uncertain event occurs, the corresponding scenario is selected according to the estimated leakage range, and the pre-calculated layout plan y of the second stage is directly executed.

[0029] Taking into account pipeline leakage caused by uncertain events such as geological disasters or equipment aging, the optional sensor layout location is used as the decision variable. Before the uncertain event occurs, only a small number of sensors are needed to monitor whether the pipeline network has leakage. The number of sensors in the first stage is a constraint. After the uncertain event occurs, the approximate range of the leakage is estimated based on the deployed sensors. In the second stage, a certain number of sensors are added to conduct more detailed monitoring in local areas to accurately locate the leakage area.

[0030] Based on the relevant data and information of step S1 and step S2, the objective function is constructed, and the pipe network leakage problem is converted into a two-stage stochastic programming problem. The scenario set C is regarded as a random variable, but it can be converted into a corresponding deterministic problem through the sampling average approximation method. Then the objective function is expressed as: Where x represents the selection of g locations from the n optional sensor placement locations for the first phase of sensor placement, with the goal of covering the entire urban pipe network as much as possible and ensuring that the level of leakage detected is as low as possible; y represents the sensor placement location for the second phase; the average impact range of different leakage levels is calculated based on the matrix E: w = [w1, w2, ..., w k ], and then solve it through evolutionary algorithms, which include but are not limited to genetic algorithms, differential evolution algorithms, etc.

[0031] To simplify scene understanding, the leakage level to be monitored in the first stage is estimated to be k (k>5) based on the threshold Q, so the range of the position selected in x is w k ,So Indicates that the selected g positions need to cover as many pipelines as possible, where x i It indicates that i positions are selected from n optional sensor placement positions for the first stage of sensor placement.

[0032] Based on the sampling average approximation method, the two-stage stochastic programming problem is expressed as the corresponding deterministic problem, so the objective function of the overall application scenario is expressed as: Among them, C j represents the jth scene, w kn The sensors arranged in the second stage need to be able to detect leakage of level n, y represents the sensor arrangement position in the second stage, and w km The sensors deployed in the first stage need to be able to detect leakage of level m, x i It indicates that i positions are selected from n optional sensor placement positions for the first stage of sensor placement.

[0033] The goal of the second phase is also to achieve accurate monitoring and positioning of the leakage location by deploying more sensors. It should be noted that the joint optimization of the two phases must cover the leakage location in the specific scenario as a constraint of the objective function.

[0034] Since no leakage incidents occurred in the first phase, if we only optimize the goals of the first phase and just cover as many pipelines as possible, we will lack consideration and response capabilities for the real environment.

[0035] The optimization of deterministic problems can be solved by selecting different solving methods according to the problem type, including but not limited to commercial solvers such as CPLEX, heuristic algorithms such as genetic algorithms, etc.

[0036] By jointly optimizing the two stages, we can obtain plans x and y. When the sensors deployed in the first stage detect a leak, the approximate location of the leak can be estimated and matched with the scenes in the scene set. Since the layout plan of the second stage is calculated in advance, the corresponding sensor deployment plan can be directly executed according to the corresponding scene, which improves the emergency response speed after an uncertain event occurs.

[0037] S4. Analyze the influence of different factors on the final objective function value and perform closed-loop optimization of sensor layout.

[0038] Based on the decision results of step 3, we can then analyze the impact of different factors on the final objective function value and make it interpretable in a visual way through charts to facilitate understanding of the decision process and basis, thereby improving the basic decision information or algorithm model, and adjusting the number of sensors invested, ultimately realizing a closed-loop optimization method for sensor layout.

[0039] The explainable implementation method is mainly through the method of graphical visualization. The visualization content is the impact of different factors on the final objective function value. The different factors include but are not limited to different sensor locations and leakage probabilities of different pipelines. The influence of different factors can be evaluated through feature importance analysis or sensitivity analysis.

[0040] This embodiment takes the sensitivity analysis method as an example, and can adjust the probability of leakage of different levels in a pipeline, and then calculate the impact of the change in probability on the final sensor layout plan and the objective function value. The same operation is performed on other pipelines, and the impact of the change in the probability of leakage of the pipelines on the sensor layout plan can be compared. Then, the pipeline can be maintained and the operation of the pipeline network can be regulated, and relevant information can be updated to obtain a more effective sensor layout plan.

[0041] This embodiment takes into account the uncertainty and controllable and reliable requirements of leakage detection in a real-world water supply network. First, a scenario set is generated for uncertain events and the algorithm is provided with basic information required for decision-making. Then, the sensor layout is divided into two stages based on whether the uncertain event occurs and an algorithm is designed for joint optimization. Finally, the impact of different factors on the decision-making scheme is analyzed to assist in regulating the network and improving the basic information, thereby completing a controllable and reliable leakage detection method in a water supply network, thereby realizing the regulation of the basic information of the algorithm decision, the visualization of the algorithm results and the closed-loop sensor layout optimization process, which is conducive to building a more complete and efficient sensor layout optimization scheme, and provides an extended practice for the controllable and reliable operation of the water supply network.

[0042] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solution formed by equivalent replacement or equivalent transformation falls within the protection scope required by the present invention.

Claims

1. A two-stage sensor arrangement method for water supply network leakage detection, characterized in that: The following steps are involved: S1. Obtain relevant basic information of the water supply network for sensor layout decision-making. The sensors are used to monitor the pressure and flow of the pipeline; S2. For each pipeline that needs to be monitored for leakage, generate leakage scenarios based on the probability of different leakage levels according to the basic information related to the water supply network, regard the leakage conditions of all pipelines as one scenario, and then combine them into a scenario set with a specified number of scenarios; S3, the sensor deployment is divided into two stages based on whether the uncertain event occurs. In the first stage, before the uncertain event occurs, a part of sensors are deployed for monitoring; In the second stage, that is, after the occurrence of an uncertain event, new sensors are deployed for monitoring, and the number of new sensors is greater than the number of sensors deployed in the first stage; all possible uncertain events are represented by the scene set of step S2, and the maximum network leakage coverage and leakage identification accuracy are used as the objective function. The two stages are jointly optimized and solved to obtain the layout plan x of the first stage and the layout plan y of the second stage; based on the solution results, when an uncertain event occurs, the corresponding scene is selected according to the estimated leakage range. When the sensor deployed in the first stage detects a leakage, the leakage location is estimated and matched with the scene in the scene set, and the pre-calculated second stage layout plan y is directly executed according to the matched scene; S4. Analyze the influence of different factors on the final objective function value and perform closed-loop optimization of sensor layout.

2. A two-stage sensor arrangement method for water supply network leakage detection according to claim 1, characterized in that: In step S1, the relevant basic information used for sensor layout decision-making includes optional sensor layout locations and leakage probabilities of different pipelines with different leakage levels; the degree and scope of impact of different levels of leakage on surrounding pipelines are estimated based on simulation software and hydraulic models, and the threshold of pipeline leakage is determined.

3. A two-stage sensor arrangement method for water supply network leakage detection according to claim 2, characterized in that: In step S1, the sensor layout locations are given according to the field investigation of the operation and maintenance personnel, and are represented by a set R, where R=[r1,r2,...,r n ] indicates that there are n optional positions; the operation and maintenance personnel divide the leakage level into k levels based on their professional experience. The larger the k, the more serious the leakage.

4. A two-stage sensor arrangement method for water supply network leakage detection according to claim 2, characterized in that: In step S1, the hydraulic model is constructed using EPANET software, and leakages of different levels are simulated on different pipelines through EPANET software, and the impact range and pressure impact degree of pipelines at different distances are recorded, which is expressed as a matrix E: Where s represents the s nearest pipelines connected to the pipeline where the leak is located, and the order of the s pipelines is based on the distance from the center of the corresponding pipeline to the leak location, from near to far; e ks It indicates the influence of the kth leakage level on the pressure of the sth nearest pipeline.

5. A two-stage sensor arrangement method for water supply network leakage detection according to claim 2, characterized in that: In step S1, the probability P of different leakage levels of different pipelines is estimated based on the environment of the urban pipeline network. The environment of the urban pipeline network includes the geological environment of different pipelines, the degree of equipment aging and the quality of pipeline laying. The matrix P is expressed as: Among them, m means there are m pipelines in the urban pipe network, p mk represents the probability that the mth pipeline has a leakage of leakage level k, where the sum of the probabilities of all leakage levels of each pipeline is 1, that is, p m1 +p m2 +...+p mk =1; Based on the pressure standard required for normal water use by urban residents, the threshold for the pressure drop in the water supply network caused by leakage is set to Q.

6. A two-stage sensor arrangement method for water supply network leakage detection according to claim 5, characterized in that: In step S2, different scenarios are generated based on the probability of the matrix P. Assume that the probability of leakage of level k in the first pipeline is p. 1k , when the scene of level k is generated by uniform distribution, the same operation is performed on all other pipelines, then the scene c=[c1,c2,...,c m ], generate z scenes through the sampling average approximation method to form a scene set C.

7. A two-stage sensor arrangement method for water supply network leakage detection according to claim 4, characterized in that: In step S3, an objective function is constructed to convert the pipe network leakage problem into a two-stage stochastic programming problem. The scenario set C is regarded as a random variable and converted into a corresponding deterministic problem by the sampling average approximation method. The objective function is expressed as: Where x represents the selection of g positions from n optional sensor placement positions for the first stage of sensor placement, and y represents the sensor placement position for the second stage; the average impact range of different leakage levels is calculated according to the matrix E: w = [w1, w2, ..., w k ] and then solve it through evolutionary algorithm.

8. A two-stage sensor arrangement method for water supply network leakage detection according to claim 5, characterized in that: Based on the threshold Q, the leakage level to be monitored in the first stage is estimated to be k, k>5, then the range sensed by the position selected in x is w k ,So Indicates that the selected g positions need to cover as many pipelines as possible, where x i It indicates that i positions are selected from n optional sensor placement positions for the first stage of sensor placement.

9. A two-stage sensor arrangement method for water supply network leakage detection according to claim 1, characterized in that: In step S3, based on the sampling average approximation method, the two-stage stochastic programming problem is expressed as a corresponding deterministic problem, and the objective function of the overall application scenario is expressed as: Among them, C j represents the jth scene, w kn The sensors arranged in the second stage need to be able to detect leakage of level n, y represents the sensor arrangement position in the second stage, and w km The sensors deployed in the first stage need to be able to detect leakage of level m, x i It indicates that i positions are selected from n optional sensor placement positions for the first stage of sensor placement.

10. A two-stage sensor arrangement method for water supply network leakage detection according to claim 1, characterized in that: In step S4, based on the decision result of step 3, the influence of different factors on the final objective function value is analyzed, and the explanation is achieved through graphical visualization. The content of the graphical visualization is the influence of different factors on the final objective function value. The different factors include different sensor locations and leakage probabilities of different pipelines. The influence of different factors is evaluated through feature importance analysis or sensitivity analysis.

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