Water supply network water pressure sensor layout method based on minimum pipe burst detection threshold value

Abstract

The invention discloses a water supply network water pressure sensor layout method based on a minimum pipe burst detection threshold value. A water supply network hydraulic model is constructed and preliminary correction is carried out; simulating and generating pipe explosion pressure drop data according to the water supply network hydraulic model, and creating a pipe explosion detectable threshold matrix; based on the tube explosion detectable threshold matrix, a multi-objective optimization problem of minimizing a tube explosion detection threshold and minimizing the number of sensors is constructed, and a non-dominated sorting differential evolution algorithm is adopted for solving; and according to the solved Pareto optimal leading edge, the optimal number and the optimal layout of the water pressure sensors are determined in combination with cost-benefit analysis and distance measurement indexes. According to the method, the water pressure sensor layout is optimized by minimizing the pipe explosion detection threshold value for the first time, and the water pressure sensor layout which is higher in robustness and practicability and better in leakage and pipe explosion monitoring performance is obtained by utilizing the characteristic that the relative size of detectable threshold values of different pipelines is irrelevant to noise; the method has the advantages of high calculation efficiency and high engineering application convenience.

Description

Technical Field

[0001] The invention belongs to the field of municipal engineering and urban water supply network safety, and in particular relates to a water supply network water pressure sensor layout method based on minimizing a pipe burst detection threshold. Background Art

[0002] The water supply network is the lifeline of the city, and its stable operation is crucial to ensuring people's living and production water. However, factors such as pipeline aging and insufficient maintenance of the network inevitably lead to pipe bursts, resulting in a large amount of water waste and threatening the normal operation of the system. With the development of sensor technology, communication technology and data processing algorithms, real-time pipe burst monitoring of the water supply network can be carried out by analyzing the abnormal pressure drop in the monitoring data. However, considering the construction and maintenance costs of the monitoring network, it is not practical to install water pressure sensors at each node of the water supply network. Therefore, it is necessary to comprehensively consider economic benefits and monitoring capabilities, and reasonably arrange water pressure sensors to achieve effective pipe burst detection.

[0003] The current method for optimizing the layout of water pressure sensors in water supply networks is to use a coverage matrix of leakage and pipe burst events to optimize the layout of water pressure sensors. However, this method has problems under uncertain background noise or sensor accuracy. For example, an increase in background noise or an improvement in sensor accuracy will cause changes in matrix elements, which in turn affects the final optimized layout results, making the layout lack of robustness and making it difficult to obtain a reliable water pressure sensor layout solution. In addition, previous methods usually construct the layout of water pressure sensors as a single-objective optimization problem, which requires a cumbersome solution process when determining the optimal number of water pressure sensors, and cannot handle larger pipe bursts and smaller leakage problems at the same time. Summary of the invention

[0004] The present invention provides a water supply network water pressure sensor layout method based on minimizing the burst detection threshold. The method makes the relative size of the detectable threshold of different pipelines independent of noise, thereby solving the problem that the water pressure sensor layout changes with the background noise or sensor accuracy.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for arranging water pressure sensors in a water supply network based on minimizing a burst pipe detection threshold, characterized in that it comprises the following steps:

[0007] 1.1 Construct a hydraulic model of the water supply network and make preliminary corrections;

[0008] 1.2 Generate burst pressure drop data based on the water supply network hydraulic model simulation and create a burst detectable threshold matrix;

[0009] 1.3 Based on the burst pipe detectable threshold matrix, a multi-objective optimization problem of minimizing the burst pipe detection threshold and minimizing the number of sensors is constructed, and the non-dominated sorting differential evolution algorithm is used to solve it;

[0010] 1.4 Based on the Pareto optimal frontier obtained by solving the problem, combined with cost-benefit analysis and distance measurement indicators, determine the optimal number and optimal layout of water pressure sensors.

[0011] The method for creating the burst pipe detectable threshold matrix in step 1.2 is as follows:

[0012] 2.1 Calculation of the maximum possible burst flow rate of each pipeline

[0013] By adding virtual nodes in the middle of each pipe section, a node flow rate of 10,000 L / s is assigned in turn to simulate pipe bursting, and then the pressure-driven algorithm in EPANET2.2 is used to calculate the hydraulic balance of the pipe network, thereby obtaining the maximum possible burst flow rate Q of each pipeline. max :

[0014]

[0015] Among them, Q max is the maximum possible burst flow rate of each pipeline, and m is the total number of pipelines in the pipeline network;

[0016] 2.2 Calculation of node pressure drop under different burst flow rates

[0017] First, generate the flow rate Q from 0 L / s to the maximum possible burst flow rate Q of each pipe. max The arithmetic progression of different levels of burst flow matrix Q is obtained, and then the burst flow in matrix Q is used to perform burst simulation in turn to obtain the pressure drop values ​​of all nodes and create the node pressure change matrix ΔP;

[0018]

[0019] Where n is the total number of network nodes; m is the total number of pipe segments; l is the total number of items; P i It refers to the water pressure value at node i under normal working conditions; P′ i，k represents the water pressure value at node i when pipe burst simulation is performed using the node flow corresponding to item number k; ΔP j It indicates the node pressure drop corresponding to each burst flow rate when the pipe segment j is subjected to burst simulation; i is the node number, i=1, 2, ..., n; j is the pipe segment number, j=1, 2, ..., m; k is the item number, k=1, 2, ..., l;

[0020] 2.3 Construction of detectable threshold matrix based on linear interpolation

[0021] Compare each element in ΔP with the background noise threshold ΔP C For comparison, ΔPC The value range is 0.6~1.5m. i -P′ i，k )≥ΔP C And (P i -P′ i，k-1 )<ΔP C When the voltage drop at node i is estimated by linear interpolation, it is just equal to the background noise threshold ΔP C The burst flow rate Q′ j，i , thus obtaining the detectable threshold matrix DT min ;

[0022]

[0023] Among them, Q′ j，i It is represented as the minimum detectable burst flow at node i when a burst occurs in pipe segment j.

[0024] The process of step 1.3 is as follows:

[0025] 3.1 Construction of objective function

[0026] The water pressure sensor layout scheme N (m×n) is a 0-1 binary matrix, where m rows equal the population size, n columns equal the total number of pipe network nodes, and each element is randomly assigned a value of 0 or 1, indicating whether the node is equipped with a sensor; the purpose of the first objective function N is to minimize the number of sensors to obtain a more economical layout, and the purpose of the second objective function ADT is to improve the performance of the sensor layout in burst pipe detection leakage by minimizing the detectable threshold after weighted processing; therefore, there is a conflict between these two objectives, because reducing the number of sensors will lead to an increase in the detectable threshold, thereby converting the water pressure sensor layout into a multi-objective optimization problem; based on this representation method, the objective function for optimizing the water pressure sensor layout can be expressed as follows:

[0027]

[0028] Among them, X i Indicates whether node i is equipped with a water pressure sensor; represents the detectable threshold of pipe j under the water pressure sensor layout defined by X; L j and D j represents the length and diameter of the pipeline; N represents the total number of water pressure sensors in a certain layout scheme; ADT is the detectable threshold after weighted processing in a certain layout scheme;

[0029] 3.2 Start the non-dominated sorting differential evolution algorithm

[0030] The non-dominated sorting differential evolution algorithm uses a 0-1 binary encoding method, and the number of chromosomes is the total number of pipe network nodes; the chromosomes are randomly assigned 0 and 1, 0 means that the node is not equipped with a water pressure sensor, and 1 means that the node is equipped with a water pressure sensor; before running the algorithm, some key parameters need to be set, including population size, maximum number of iterations, crossover factor and mutation factor. The execution steps of the algorithm are as follows:

[0031] ① Randomly select 3 individuals from the population, generate new individuals through mutation and crossover strategies, and obtain a sub-population with the same size as the initial population;

[0032] ② Mix the parent generation and the offspring generation to generate new individuals with exactly the same chromosomes, and calculate their objective function value using formula (6);

[0033] ③ Perform non-dominated sorting and crowding calculation on the individuals in the population. Non-dominated sorting is a method of sorting individuals according to their relative merits in all objectives. Crowding can be determined by calculating the distance between each individual. This step is done by retaining the highest-ranked and least crowded individual as the parent.

[0034] ④The above steps are repeated until the preset maximum number of iterations G is reached. max , thus the Pareto optimal frontier of the objective function for optimizing the layout of water pressure sensors constructed in step 3.1 can be obtained.

[0035] The method for step 1.4 is as follows:

[0036] 4.1 Determine the optimal number of water pressure sensors

[0037] The present invention introduces an economic evaluation index, namely, the net cost NC, through cost-benefit analysis. The number of water pressure sensors corresponding to the minimum value of NC represents the optimal number of sensors. Due to the difference between units, the cost IC and the detectable threshold ADT are normalized using equations (7) and (8). The net cost NC of sensor placement is the normalized cost IC nor and normalized return ADT nor The difference between:

[0038]

[0039] NC(N)=IC nor (δ, N)+1-ADT nor (N) (9)

[0040] Among them, ADT nor is the normalized detectable threshold; IC nor is the normalized water pressure sensor investment cost, N max is the maximum number of sensors, Nmin is the minimum number of sensors, C(δ) is the unit cost of sensors, and N is the number of sensors.

[0041] 4.2 Determine the optimal layout of water pressure sensors

[0042] The average geographic plane distance (AGPD) and the average shortest path distance (ASPD) are distance metrics used to describe layout characteristics; AGPD measures the two-dimensional spatial discreteness of the water pressure sensor layout, while ASPD evaluates the discreteness of the sensor layout based on the pipe network topology, as shown in Equations (10) and (11):

[0043]

[0044] Among them, GD min and SD min represents the distance between each water pressure sensor and its nearest neighbor sensor; n is the total number of water pressure sensors; where GD min By determining the geographical location in two-dimensional space, SD min It is calculated using the Dijkstra shortest path algorithm.

[0045] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0046] (1) The present invention proposes for the first time to optimize the layout of water pressure sensors by minimizing the pipe burst detection threshold, and utilizes the characteristic that the relative size of the detectable threshold of different pipelines is independent of noise, thereby obtaining a water pressure sensor layout with higher robustness, practicality, and better leakage and pipe burst monitoring performance.

[0047] (2) The present invention transforms the layout of water pressure sensors into a multi-objective optimization problem, and introduces a multi-objective optimization model based on a non-dominated sorting differential evolution algorithm, so as to obtain the optimal layout under different numbers of water pressure sensors in one optimization operation. Compared with the current single-objective optimization method, the present invention has the advantages of high computational efficiency and strong convenience in engineering application.

[0048] (3) The present invention proposes a detectable threshold to optimize the layout of water pressure sensors with a larger average shortest path distance and average geographic plane distance, and exhibits better performance in simultaneously detecting larger pipe bursts and smaller leaks, and is more practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flowchart of the algorithm for laying out the water pressure sensor.

[0050] Figure 2 To estimate the maximum burst flow rate of the pipe network using a pressure-driven algorithm.

[0051] Figure 3Because pipeline P1( Figure 2 a) and pipeline P2( Figure 2 b) Pressure drops at node 1 (dashed line) and node 2 (solid line) for different burst flow rates.

[0052] Figure 4 There are three water supply network diagrams, among which Figure 4 a is a simple pipe network, Figure 4 b is the net3 pipe network, Figure 4 c is the L-town pipe network.

[0053] Figure 5 The method of the present invention ( Figure 5 a~c) and traditional method 1( Figure 5 d~f) and traditional method 1( Figure 5 The optimization results of g~i) are applied to a simple pipe network.

[0054] Figure 6 The influence of three methods applied to the simple pipe network optimization layout on the detectable threshold in the net3 pipe network is shown in Figure 2. Figure 6 a compares the detectable thresholds of the method of the present invention and two traditional methods; Figure 6 b, 6c and 6d are the optimized layouts of the method of the present invention, conventional method 1 and conventional method 2 respectively; the pipelines in bold and marked with numbers indicate that their detectable thresholds are much higher than those of the method of the present invention.

[0055] Figure 7 The optimal layout of the method of the present invention under different background noise and demand multipliers in the net3 network, where Figure 7 a is the optimal sensor layout with a background noise threshold of 0.1 m. The relative error of the average detectable threshold caused by the change in sensor position is 0.45%; Figure 7 b is the optimal sensor layout with a background noise threshold of 1.5 m, with a relative error of 0.49%; Figure 7 c is the optimal sensor layout with a water demand multiplier of 0.7, and a relative error of 0.96%; Figure 7 d is the optimal sensor layout with a water multiplier of 2, and the relative error is 0.70%.

[0056] Figure 8 The optimal layout of water pressure sensors obtained by applying four methods to the L-Town pipe network is shown in Figure 2. Figure 8 a is the optimal layout of sensors under expert guidance; Figure 8 b is the optimal layout of sensors in the method of the present invention; Figure 8 c is the optimal sensor layout of traditional method 1; Figure 8 d is the optimal sensor layout of traditional method 2.

[0057] Fig. 9In order to optimize the sensor layout of the L-town network under different background noise thresholds and water demand multipliers, the method of minimizing the detectable threshold is used. Fig. 9 a is the optimized sensor layout when the background noise threshold is 0.1m and the water demand multiplier is 1.0; Fig. 9 b is the background noise threshold of 0.6 m and the water multiplier of 1.0; Fig. 9 c is the background noise threshold of 1.5 m and the water multiplier of 1.0; Fig. 9 d is the background noise threshold of 0.1 m and the water multiplier of 0.35; Fig. 9 e is the background noise threshold of 0.6 m and the water multiplier of 0.35; Fig. 9 f is the background noise threshold of 1.5 m, and the water multiplier is 0.35; Fig. 9 g is the background noise threshold of 0.1 m, and the water multiplier is 1.68; Fig. 9 h is the background noise threshold of 0.6 m, and the water multiplier is 1.68; Fig. 9 i is the background noise threshold of 1.5 m and the water multiplier is 1.68.

[0058] Fig.10 The sensor layout of the L-town pipe network is optimized by maximizing the burst coverage under different background noise thresholds, water demand multipliers, and simulated burst intensities. Fig.10 a is the optimized sensor layout under the background noise threshold of 0.6 m, water demand multiplier of 1.0 and pipeline flow velocity increment of 1.2 m / s; Fig.10 b represents the background noise threshold of 1.0 m, the water demand multiplier of 1.0, and the pipe velocity increment of 1.2 m / s; Fig.10 c is the background noise threshold of 1.5 m, the water demand multiplier of 1.0 and the pipe velocity increment of 1.2 m / s; Fig.10 d is the background noise threshold of 0.6 m, the water demand multiplier of 0.35 and the pipe velocity increment of 1.2 m / s; Fig.10 e represents the background noise threshold of 0.6 m, the water demand multiplier of 1.0 and the pipe velocity increment of 1.2 m / s; Fig.10 f is the background noise threshold of 0.6 m, the water demand multiplier of 1.68 and the pipe velocity increment of 1.2 m / s; Fig.10 g is the background noise threshold of 0.6 m, the water demand multiplier of 1.0 and the pipe velocity increment of 0.8 m / s; Fig.10 h is the background noise threshold of 0.6 m, the water demand multiplier of 1.0, and the pipe velocity increment of 1.0 m / s; Fig.10 i represents the background noise threshold of 0.6 m, the water demand multiplier of 1.0 and the pipe velocity increment of 1.2 m / s.

[0059] Fig.11To optimize the sensor layout of the L-town network by maximizing the leakage detection rate under different sensor accuracies and water demand multipliers, Fig.11 a is the optimized sensor layout with a sensor accuracy of 0.03psi and a water multiplier of 0.35; Fig.11 b means the sensor accuracy is 0.05psi and the water multiplier is 0.35; Fig.11 c is the sensor accuracy of 0.07psi, and the water multiplier is 0.35; Fig.11 d is the sensor accuracy of 0.03psi, and the water multiplier is 1.0; Fig.11 d is the sensor accuracy of 0.03psi, and the water multiplier is 1.0; Fig.11 e is the sensor accuracy of 0.05psi, and the water multiplier is 1.0; Fig.11 f is the sensor accuracy of 0.07psi, and the water multiplier is 1.0; Fig.11 g is the sensor accuracy of 0.03psi, and the water multiplier is 1.68; Fig.11 h is the sensor accuracy of 0.05psi, and the water multiplier is 1.68; Fig.11 i represents the sensor accuracy of 0.07 psi and the water multiplier is 1.68. DETAILED DESCRIPTION

[0060] Example 1

[0061] The present invention aims to propose a water supply network water pressure sensor layout method based on minimizing the burst detection threshold. The innovation point is easy to understand. The implementation method of the present invention is further described in detail below with reference to the accompanying drawings and examples. Figure 1 , the specific steps are as follows:

[0062] Step 1. Build a hydraulic model of a dual-pipeline network and perform preliminary calibration;

[0063] like Figure 2 As shown, the diameter of the double-pipe network is 200 mm, the length is 500 m, the node water demand is set to 5 L / s, and the node elevation is 0 m.

[0064] Step 2. Generate pipe burst pressure drop data based on hydraulic simulation and create a pipe burst detectable threshold matrix;

[0065] (1) Estimation of the maximum possible burst flow rate of each pipeline

[0066] By adding a virtual node between pipelines P1 and P2, a node flow rate of 10,000 L / s is assigned in turn to simulate pipeline bursting, and then the pressure-driven algorithm in EPANET2.2 is used to calculate the hydraulic balance of the pipeline network, thereby obtaining the maximum possible burst flow rate Q of each pipeline in the pipeline network. max :

[0067]

[0068] (2) Estimation of node pressure drop under different burst flow rates

[0069] First, generate the flow rate Q from 0 L / s to the maximum possible burst flow rate Q of each pipe. max The arithmetic progression is 20 intervals, and the number of items l is 21. The burst flow matrix Q of different levels is obtained. Then, the burst flow in the matrix Q is used to perform burst simulation in turn to obtain the pressure drop values ​​of all nodes (such as Figure 3 As shown), create the node pressure change matrix ΔP:

[0070]

[0071] (3) Construction of detectable threshold matrix based on linear interpolation

[0072] Compare each element of ΔP with the background noise threshold ΔP C For comparison, in this case, ΔP C The value of is 0.6m. When a burst occurs in pipeline P1, the burst simulation is performed using a flow rate of 12.86L / s with a term number of 3. When the pressure drop at node 1 is 0.96m≥0.6m and the pressure drop at the next position is 0.4m<0.6m, the linear interpolation method is used to estimate that the pressure drop at node 1 is just equal to the burst flow rate Q′ with a background noise threshold of 0.6m. j，i , calculated to be 8.72L / s, and the burst detection thresholds of node 1 and node 2 in pipeline 1 and pipeline 2 are calculated in turn, so as to obtain the detectable threshold matrix DT min :

[0073]

[0074] Example 2

[0075] Step 1. Build a hydraulic model of a simple pipe network and make preliminary corrections; basic information of the pipe network is as follows: Figure 4 As shown in a.

[0076] Step 2. Generate pipe burst pressure drop data based on hydraulic simulation and create a pipe burst detectable threshold matrix;

[0077] According to the above detailed steps and the steps of the first embodiment, the burst detectable threshold matrix DT of a simple pipe network can be obtained: min , as shown in Table 1.

[0078] Table 1. Detectable threshold matrix DT with background noise threshold of 1.3m min

[0079]

[0080] Step 3. Based on the detectable threshold matrix, a multi-objective optimization problem is constructed to minimize the burst pipe detection threshold and minimize the number of sensors, and a non-dominated sorting differential evolution algorithm is used to solve it;

[0081] (1) Construction of objective function

[0082] The water pressure sensor layout scheme N (m × n) is a 0-1 binary matrix, where m rows equal the population size, n columns equal the total number of pipe network nodes, and each element is randomly assigned a value of 0 or 1, indicating whether the node is equipped with a sensor. According to Equation 6, the average detectable threshold matrix can be calculated, as shown in Table 2.

[0083] Table 2. Average detectable threshold matrix

[0084]

[0085]

[0086] (2) Start the non-dominated sorting differential evolution algorithm

[0087] The non-dominated sorting difference algorithm uses 0-1 binary encoding to randomly assign chromosomes 0 and 1. The algorithm needs to set some key parameters, including the population size of 500, the maximum number of iterations of 1000, the number of chromosomes is the same as the total number of network nodes, the crossover factor is 0.7, and the mutation factor is 0.5. The algorithm execution steps are as follows:

[0088] ① Randomly select 3 individuals from the population, generate new individuals through mutation and crossover strategies, and obtain a sub-population with the same size as the initial population;

[0089] ② Mix the parent generation and the offspring generation to generate new individuals with exactly the same chromosomes, and calculate their objective function value (Formula 6);

[0090] ③ Perform non-dominated sorting and crowding calculation on the individuals in the population. Non-dominated sorting is a method of sorting individuals according to their relative merits in all objectives. Crowding can be determined by calculating the distance between each individual. This step is done by retaining the highest-ranked and least crowded individual as the parent.

[0091] ④ The above steps are iterated repeatedly until the preset maximum number of iterations 1000 is reached, so that the Pareto optimal frontier of the objective function can be obtained.

[0092] Step 4. Determine the optimal number and layout of water pressure sensors based on the Pareto optimal frontier obtained by solving the problem and combining cost-benefit analysis and distance measurement indicators.

[0093] (1) Determine the optimal number of water pressure sensors

[0094] Due to the difference between units, the cost IC and detectable threshold ADT are normalized using equations (7) and (8). The net cost NC of sensor placement is the normalized cost IC nor and normalized return ADT nor The difference between (Formula 9):

[0095] IC nor (δ, N)=[0 0.2 0.4 0.6 0.8 1.0];

[0096] ADT nor (N) = [0 1 1 1 1 1];

[0097] NC(N)=[1.0 0.2 0.4 0.6 0.8 1.0].

[0098] Among them, ADT nor is the normalized detectable threshold; IC nor is the normalized water pressure sensor investment cost.

[0099] From the calculation results of the above formula, we can see that the minimum value of NC is 2, which means that the optimal number of sensors is 2. Then two sensors are placed at the positions of node 1 and node 5 (such as Figure 5 c).

[0100] Its average detectable threshold ADT:

[0101] 127.14+1.31+5.45+0.59+0.03+40.50=175.02L / s;

[0102] The results are as follows Figure 5 (a) shown.

[0103] (2) Determine the optimal layout of water pressure sensors

[0104] In EPANET2.2, the geographical locations of node 1 and node 5 in two-dimensional space are (-777.7, 7144.7) and (1472.2, 7144.7) respectively. The average geographic plane distance (AGPD) can be calculated by formula 16; the average shortest path distance (ASPD) can be calculated according to formula 17:

[0105]

[0106] Comparative Example 1

[0107] The method of the present invention is applied to a simple pipe network (such as Figure 4 As shown in a), the water supply network system includes 1 water source, 6 pipes, and 6 water demand nodes. Figure 5The Pareto optimal frontier and optimized layout of the method of the present invention and the traditional method (i.e., optimizing the layout of water pressure sensors by pipe burst coverage and leakage detection rate) on a simple pipe network are given. Tables 3, 4 and 5 are the detectable threshold matrix and pipe burst coverage matrix of the background noise threshold of 0.6m and the leakage detection matrix of the sensor accuracy of 0.014m, respectively. It can be clearly seen that the method of the present invention establishes a unique optimal layout regardless of whether one or two water pressure sensors are arranged. In contrast, the traditional method provides two and four equivalent layout strategies for the optimal layout of one and two sensors, respectively. In the optimized layout of the method of the present invention, one sensor is arranged at the terminal node of the large-diameter pipe on the left side, thereby enhancing the pipe burst detection capability of the large pipe on that side. For the layout of two sensors, the sensors are located at the terminal nodes of the pipes on the left and right sides, respectively, which meets the actual needs of the pipe network project. In addition, this layout maximizes the average geographical plane distance and the average shortest path distance between the two sensors, realizes the optimal decentralized layout of the sensors in the entire pipe network, and meets the requirements of engineering intuition and practical application.

[0108] Table 3. Detectable threshold matrix using 0.6m background noise threshold

[0109]

[0110] Table 4. Explosion pipe coverage matrix using 0.6m background noise threshold

[0111]

[0112] Table 5. Leakage detection matrix using 0.014m sensor accuracy

[0113]

[0114] The method of the present invention minimizes the burst detection threshold of each pipe. Under the background noise threshold of 0.6 m, the thresholds of pipes 1 to 6 are 215.98 L / s, 5.21 L / s, 16.62 L / s, 3.68 L / s, 0.31 L / s and 73.38 L / s, respectively. In addition, adding additional sensors does not cause a further decrease in the detectable threshold, and the relative size of the detectable threshold of different pipes is independent of the background noise threshold, indicating its effectiveness. In contrast, placing sensors at nodes 1 or 2, as well as nodes 4 or 5, has the same effect in terms of burst coverage or leak detection. Therefore, the method of the present invention optimizes the sensor layout by minimizing the burst detection threshold, which is not affected by the background noise threshold, and is proven to be a more suitable method for determining the optimal location of sensors in practical applications.

[0115] Comparative Example 2

[0116] The method of the present invention is applied to the net3 pipe network (such as Figure 4 b), the water supply network is a benchmark network widely used for sensor layout optimization, including 2 water sources, 3 water towers, 92 nodes, and 117 pipes. Table 6 compares the performance of the layout optimization method of the present invention with that of two traditional methods. Figure 6 The effects of the layout optimization method of the present invention and two traditional methods on the detectable threshold of each pipeline are given. Figure 7 The optimal sensor layout of the method of the present invention under different background noise thresholds and water demand multipliers is given. It can be clearly seen that the method of the present invention has a sharp contrast with the layout of the other two traditional methods through an average shortest path distance of up to 10,443 feet between sensors, and shows excellent performance in terms of detectable threshold, burst coverage and leakage detection rate. In contrast, the detectable thresholds of 6 and 23 pipelines in the two traditional methods are significantly higher than those of the method of the present invention.

[0117] Under different background noise thresholds (0.1m and 1.5m) and water demand multipliers (0.7 and 2), among the 11 water pressure sensors included in the optimized layout of the method of the present invention, only 1 to 3 sensors change positions with the changes in the background noise threshold and the water demand multiplier, and the remaining sensors remain unchanged. In addition, cross-validation shows that the relative error of the average detectable threshold due to the change in sensor position is always less than 1%, which has little impact on the detection performance. In summary, the method of the present invention uses the detectable threshold as the objective function, combines the 0-1 binary coding method and the non-dominated sorting differential evolution algorithm to optimize the water pressure sensor, and can provide a highly robust and practical water pressure sensor layout under different noise conditions. At the same time, it significantly improves the detection capability of pipe bursts and leakage events in the pipe network, and provides a strong guarantee for the safe operation of the pipe network system.

[0118] Table 6. Performance comparison of three sensor layout methods applied to the net3 network

[0119]

[0120] Comparative Example 3

[0121] The method of the present invention is applied to the L-town pipe network (such as Figure 4 c), the water supply network is the new benchmark water supply network for the "Battle of Leakage Detection and Isolation Methods" competition, including 2 water sources, 1 water tower, 782 nodes, and 905 pipes. Table 7 is a performance comparison of the layout optimization method of the present invention and three traditional methods. Fig. 9 Four methods are given to apply to the optimal sensor layout of the L-town pipe network. Among them, the number and location of sensors proposed by Vrachimis et al. are predetermined by the organizers of BattLeDIM and are the optimal design under the guidance of experts. Fig. 9 , Fig.10 and Fig.11 The optimal sensor layouts of the method of the present invention, traditional method 1 and traditional method 2 under different background noise thresholds and water demand multipliers are given respectively. It can be clearly seen that the method of the present invention, traditional method 1 and traditional method 2 achieve the best results in average detectable threshold, pipe burst coverage and leakage detection rate, respectively, because each method optimizes the detectable threshold, pipe burst coverage and leakage detection rate, but the leakage detection rate of traditional method 1 is the lowest, which is 74.24%, while the pipe burst coverage value of traditional method 2 is the lowest, which is 61.45%. This means that there is a mutually restrictive relationship between the leakage detection rate and pipe burst coverage indicators, indicating that fully maximizing the coverage of larger pipe bursts will reduce the ability of the sensor layout to detect smaller leaks, and vice versa. On the contrary, the method proposed by the present invention focuses on minimizing the detectable threshold, and has achieved satisfactory results in detecting larger pipe bursts and smaller leaks. Among the four methods considered, the pipe burst coverage and leakage detection rate of the method of the present invention are 70.46% and 79.26%, respectively, ranking second. This highlights that the method of the present invention can effectively detect large pipe bursts and small leaks at the same time, avoiding the dilemma of giving priority to detecting pipe bursts or leaks. For the expert-guided sensor layout (Vrachimis et al.), although it is better than Traditional Method 1 and Traditional Method 2 in terms of detectable threshold, pipe burst coverage rate for Traditional Method 2, and leak detection rate for Traditional Method 1, it is inferior to the method of the present invention in all three indicators. In particular, its performance is about 20% lower than that of the method of the present invention in terms of detectable threshold. Therefore, the method of the present invention is expected to play a better role in optimizing sensor layout in practical applications.

[0122] The water pressure sensor layout optimized by the method of the present invention has a larger average shortest path distance and an average geographic plane distance second only to the expert-guided sensor layout (Vrachimis et al.), and its sensor distribution is more uniform. In contrast, the monitoring points arranged by the two traditional methods in the lower left corner of the pipe network are too concentrated or too sparse, indicating that there is a large deviation in the engineering practice of uniformly distributing water pressure sensors in the pipe network. Therefore, the sensor arrangement of the method of the present invention is more uniform and shows better performance in detecting larger pipe bursts and smaller leaks at the same time.

[0123] In the L-town pipe network, only 3 to 6 of the 33 water pressure sensors changed position, while the positions of the remaining sensors remained unchanged. In contrast, the traditional method of maximizing pipe burst coverage and leakage detection rate showed high sensitivity to background noise thresholds, and the optimized sensor layout showed significant changes. The method proposed in this paper to minimize the detectable threshold of pipe bursts always maintains a stable and highly robust sensor layout under different background noise thresholds and water demand multipliers, highlighting its practical value in engineering applications.

[0124] Table 7 Performance comparison of four sensor layout methods applied to the L-town pipe network

[0125]

Claims

1. A method for arranging water pressure sensors in a water supply network based on minimizing the burst detection threshold, characterized in that: The following steps are involved: 1.1 Construct a hydraulic model of the water supply network and make preliminary corrections; 1.2 Generate burst pressure drop data based on the water supply network hydraulic model simulation and create a burst detectable threshold matrix; 1.3 Based on the burst pipe detectable threshold matrix, a multi-objective optimization problem of minimizing the burst pipe detection threshold and minimizing the number of sensors is constructed, and the non-dominated sorting differential evolution algorithm is used to solve it; 1.4 Based on the Pareto optimal frontier obtained by solving the problem, combined with cost-benefit analysis and distance measurement indicators, determine the optimal number and optimal layout of water pressure sensors.

2. A method for arranging water pressure sensors in a water supply network based on minimizing pipe burst detection threshold according to claim 1, characterized in that: The method for creating the burst pipe detectable threshold matrix in step 1.2 is as follows: 2.1 Calculation of the maximum possible burst flow rate of each pipeline By adding virtual nodes in the middle of each pipe section, a node flow rate of 10,000 L / s is assigned in turn to simulate pipe bursting, and then the pressure-driven algorithm in EPANET2.2 is used to calculate the hydraulic balance of the pipe network, thereby obtaining the maximum possible burst flow rate Q of each pipeline. max : Among them, Q max is the maximum possible burst flow rate of each pipeline, and m is the total number of pipelines in the pipeline network; 2.2 Calculation of node pressure drop under different burst flow rates First, generate the flow rate Q from 0 L / s to the maximum possible burst flow rate Q of each pipe. max The arithmetic progression of different levels of burst flow matrix Q is obtained, and then the burst flow in matrix Q is used to perform burst simulation in turn to obtain the pressure drop values ​​of all nodes and create the node pressure change matrix ΔP; Where n is the total number of network nodes; m is the total number of pipe segments; l is the total number of items; P i It refers to the water pressure value at node i under normal working conditions; P′ i，k represents the water pressure value at node i when pipe burst simulation is performed using the node flow corresponding to item number k; ΔP j It indicates the node pressure drop corresponding to each burst flow rate when the pipe segment j is subjected to pipe burst simulation; i is the node number, i=1, 2, ..., n; j is the pipe segment number, j=1, 2, ..., m; k is the item number, k=1, 2, ..., l; 2.3 Construction of detectable threshold matrix based on linear interpolation Compare each element in ΔP with the background noise threshold ΔP C For comparison, ΔP C The value range is 0.6~1.5m. i -P′ i，k )≥ΔP C And (P i -P′ i，k-1 )<ΔP C When the linear interpolation method is used to estimate the voltage drop at node i, it is just equal to the background noise threshold ΔP C The burst flow rate Q′ j，i , thus obtaining the detectable threshold matrix DT min ; Among them, Q′ j，i It is represented as the minimum detectable burst flow at node i when a burst occurs in pipe segment j.

3. A method for arranging water pressure sensors in a water supply network based on minimizing pipe burst detection threshold according to claim 1, characterized in that: The process of step 1.3 is as follows: 3.1 Construction of objective function The water pressure sensor layout scheme N (m × n) is a 0-1 binary matrix, where m rows equal the population size, n columns equal the total number of pipe network nodes, and each element is randomly assigned a value of 0 or 1, indicating whether the node is equipped with a sensor; The purpose of the objective function N is to minimize the number of sensors to obtain a more economical layout, and the purpose of the objective function ADT is to improve the performance of the sensor layout in burst pipe detection leakage by minimizing the detectable threshold after weighted processing; based on this representation method, the objective function for optimizing the water pressure sensor layout can be expressed as follows: Among them, X i Indicates whether node i is equipped with a water pressure sensor; represents the detectable threshold of pipe j under the water pressure sensor layout defined by X; L j and D j represents the length and diameter of the pipeline; N represents the total number of water pressure sensors in a certain layout scheme; ADT is the detectable threshold after weighted processing in a certain layout scheme; 3.2 Start the non-dominated sorting differential evolution algorithm The non-dominated sorting differential evolution algorithm uses a 0-1 binary encoding method, and the number of chromosomes is the total number of pipe network nodes; the chromosomes are randomly assigned 0 and 1, 0 means that the node is not equipped with a water pressure sensor, and 1 means that the node is equipped with a water pressure sensor; before running the algorithm, key parameters including population size, maximum number of iterations, crossover factor and mutation factor need to be set. The execution steps of the algorithm are as follows: ① Randomly select 3 individuals from the population, generate new individuals through mutation and crossover strategies, and obtain a sub-population with the same size as the initial population; ② Mix the parent generation and the offspring generation to generate new individuals with exactly the same chromosomes, and calculate their objective function value using formula (6); ③ Perform non-dominated sorting and crowding calculation on the individuals in the population, and retain the individuals with the highest ranking and the lowest crowding as the parents; ④The above steps are repeated until the preset maximum number of iterations G is reached. max , so that the Pareto optimal frontier of the objective function for optimizing the water pressure sensor layout described in step 3.1 can be obtained.

4. According to the method for arranging water pressure sensors in a water supply network based on minimizing the pipe burst detection threshold value according to claim 1, it is characterized in that the method of step 1.4 is as follows: 4.1 Determine the optimal number of water pressure sensors Through cost-benefit analysis, an economic evaluation index, namely net cost NC, is introduced. The cost IC and detectable threshold ADT are normalized using equations (7) and (8). The net cost NC of sensor placement is the normalized cost IC nor and normalized return ADT nor The difference between: NC(N)=IC nor (δ,N)+1-ADT nor (N) (9) Among them, ADT nor is the normalized detectable threshold; IC nor is the normalized water pressure sensor investment cost, N max is the maximum number of sensors, N min is the minimum number of sensors, C(δ) is the unit cost of sensors, and N is the number of sensors. 4.2 Determine the optimal layout of water pressure sensors The average geographic plane distance (AGPD) and the average shortest path distance (ASPD) are determined by equations (10) and (11). in, SD min and SD min represents the distance between each water pressure sensor and its nearest neighbor sensor; n is the total number of water pressure sensors; where GD min By determining the geographical location in two-dimensional space, SD min It is calculated using the Dijkstra shortest path algorithm.

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