A method and model for multi-objective optimization arrangement of long-distance water delivery pipeline sensors based on MOPSO algorithm

Abstract

The application discloses a long-distance water conveying pipeline sensor multi-objective optimization arrangement method and model based on an MOPSO algorithm, and the method comprises the following steps: constructing a one-dimensional hydraulic transient simulation model; obtaining node pressure and flow response data before and after pipe explosion through simulation, and calculating a pipeline weight matrix and a sensor response difference matrix; taking a weighted monitoring coverage rate F1 maximization and a sensor response similarity F2 minimization as double-objective functions, and constructing a multi-objective optimization model; solving the double-objective optimization model by using an MOPSO multi-objective particle swarm algorithm, and calculating F1 and F2 values; and iteratively obtaining a Pareto optimal solution set through a Pareto dominance relationship, external archive maintenance, crowding distance selection and polynomial mutation operation; and selecting a sensor arrangement scheme from the optimal solution set according to engineering constraints, so that the monitoring coverage rate and the positioning degree are cooperatively optimized. The method breaks through the limitation of the existing method which focuses on single performance index optimization.

Description

Technical Field

[0001] This invention relates to the field of water pipeline monitoring technology, specifically to a multi-objective optimization layout method and model for long-distance water pipeline sensors based on the MOPSO algorithm. Background Technology

[0002] Pressure sensors are the core equipment for monitoring pipe bursts in pipeline networks. Due to the limitations of monitoring network construction costs and subsequent maintenance pressures, the number of sensors deployed is always subject to objective constraints. How to optimize their spatial location and quantity configuration to maximize the monitoring and location capabilities of pipe bursts has become a key issue in pipeline safety management.

[0003] Existing research on sensor optimization layout mainly focuses on urban ring-shaped pipe networks. Current optimization methods tend to prioritize optimizing single performance indicators in their objective function design, such as maximizing monitoring coverage or minimizing information redundancy. This fails to fully consider the inherent constraints and synergistic optimization requirements between monitoring range and response sensitivity. Consequently, optimized layout schemes struggle to balance the spatial detectability of pipe burst events with the distinguishability of pressure signals, leading to monitoring blind spots or insufficient positioning resolution in some pipe sections. Given the tree-like structure and hydraulic transient attenuation characteristics of long-distance water pipelines, where burst shock waves propagate over long distances and pressure signal attenuation is significant, the sensitivity requirements for sensor placement are far higher than in typical ring-shaped water supply networks. Traditional layout methods are difficult to directly apply. Summary of the Invention

[0004] This invention addresses the challenges of long-distance water pipelines where hydraulic transients propagate over long distances and attenuate significantly, necessitating higher sensitivity requirements for sensor placement. It proposes a comprehensive pressure sensor optimization process, based on the MOPSO multi-objective optimization algorithm, to construct a two-dimensional evaluation index system encompassing monitoring coverage and sensor response variability. This provides technical support for improving the reliability and accuracy of monitoring pipe bursts in long-distance water pipelines.

[0005] The present invention adopts the following technical solution:

[0006] A multi-objective optimization method for sensor placement in long-distance water transmission pipelines based on the MOPSO algorithm includes the following steps:

[0007] S1: Based on the topology, pipe material parameters, pipe diameter, length, node elevation and boundary conditions of long-distance water transmission pipelines, construct a one-dimensional hydraulic transient simulation model;

[0008] S2: Traverse the pipe burst conditions and sensor monitoring point combinations of each pipe section in the hydraulic model, obtain the pressure and flow response data of the nodes before and after the pipe burst through simulation, and calculate the pipe weight matrix and sensor response difference matrix.

[0009] S3: A multi-objective optimization model is constructed with the dual objective functions of maximizing the weighted monitoring coverage F1 and minimizing the sensor response similarity F2. The optimization variables are 0-1 decision variables of whether pressure sensors are deployed at candidate nodes.

[0010] S4: The MOPSO multi-objective particle swarm optimization algorithm is used to solve the bi-objective optimization model, and the F1 and F2 values ​​are calculated. The Pareto optimal solution set is obtained iteratively through Pareto dominance relation, external archive maintenance, crowding distance selection and polynomial mutation operation.

[0011] S5: Select a sensor layout scheme from the optimal solution set based on engineering constraints to achieve synergistic optimization of monitoring coverage and positioning discrimination.

[0012] While existing pressure sensor deployment schemes have the potential to cover a large number of burst pipes, in actual water supply networks, different pipes have significantly different functional roles. The bursting of critical pipes often triggers more severe cascading consequences such as widespread water outages and sudden drops in network pressure. Therefore, sensor deployment should not only focus on the number of pipes covered, but also emphasize targeted monitoring of important pipes to achieve the multiple objectives of comprehensive coverage and focused prevention and control.

[0013] Considering that quantifying the importance of pipelines is a prerequisite for achieving this goal, this invention introduces the Shapley value method, combining multiple dimensions of indicators to comprehensively characterize the importance weight of pipelines. Specifically, by simulating the condition of sequential bursting of single pipelines, the pressure and flow response data of each node in the pipeline network before and after the burst are compared, and the head response weight and flow response weight are calculated respectively. Simultaneously, the physical properties of the pipeline itself are considered; that is, the larger the pipeline diameter and the longer the length, the more important it is in the pipeline network water distribution system, and the higher its corresponding weight should be. To eliminate the dimensional differences between different indicators and ensure the rationality of the calculation results, this study normalizes the pressure response, flow response, pipeline diameter, and pipeline length parameters.

[0014] Based on the above ideas, this invention proposes the first optimization objective function F1: maximizing the monitoring coverage of pressure sensors. Here, coverage is not simply measured by the number of pipes covered, but rather by the importance of the pipes. The aim is to optimize sensor placement to prioritize monitoring of high-importance pipes, thereby maximizing the ability to prevent pipe bursts within limited sensor deployment costs.

[0015]

[0016] In Equation (1): F1 is the monitoring coverage rate, l represents the node / segment number of the pipeline, N is the total number of pipelines, and cl represents the set of leak points that can be effectively covered / detected by the sensors under the current sensor layout scheme. Only nodes l that belong to the detectable set will be included in the summation of the numerator. Let be the weight of the nth pipe;

[0017] In formula (2): The value represents the change in head caused by the leak. The superscript h represents the head, and the subscript l represents the l-th monitoring point. h(⋅) represents the head calculation function. α represents the set of operating parameters when the pipeline leaks. A set of parameters representing the leak-free operating condition of a pipeline;

[0018] In formula (3): Let q(·) represent the change in flow rate in the pipe section caused by the leak, q({α}) represent the flow rate calculation function for the pipe section, and q({α}) represent the flow rate value of pipe section l under the leak condition. This represents the flow rate of pipe section l under leak-free operating conditions.

[0019] In equation (4): To normalize the pipe length, The shortest pipe length, The longest pipe length, Let be the length of the i-th pipe segment;

[0020] In equation (5): To normalize the pipe diameter, Minimum pipe diameter, For the maximum pipe diameter, Let be the diameter of the i-th pipe segment;

[0021] In formula (6): To normalize the stress weights, As pressure weight, The maximum pressure weight, The minimum pressure weight;

[0022] In equation (7): To normalize traffic weights, For traffic weight, For maximum traffic weight, Minimum traffic weight;

[0023] In equation (8): Let be the weight of the i-th pipe segment;

[0024] In equation (9): This is a matrix representing the pipeline weights.

[0025] When a long-distance water supply pipeline bursts, if the pressure sensor signals from two different burst locations are very similar, existing location models will struggle to distinguish which location actually experienced the burst. The model may confuse the two locations, incorrectly identifying one as the other, leading to inaccurate location results and severely impacting accuracy. The core issue is that sensors lack sufficient differentiation in their response characteristics to bursts in different pipelines. Therefore, improving the accuracy of burst location depends on ensuring the uniqueness of the sensor response; that is, the pressure response curves output by the sensors should show significant differences when a burst occurs in different pipelines. This differentiated response characteristic helps the model quickly identify the specific pipeline corresponding to the burst, avoiding confusion between responses from different pipelines.

[0026] Based on this idea, this invention proposes a second optimization objective function F2: minimizing the similarity of pressure sensor responses. This objective constraint can drive the sensor placement scheme towards optimizing for differentiated responses to different pipe bursts, thereby improving the discriminative ability of the burst location model from the source and ensuring the accuracy of the location results.

[0027]

[0028] In the formula: r is the Pearson correlation coefficient, Let be the Pearson correlation coefficient between sensor n and sensor m when the i-th pipe bursts. The sensor response difference matrix characterizes the independence of different sensors' response signals to a leak event. Its matrix elements are calculated based on the Pearson correlation coefficient. For sensor i and sensor j, the difference index is defined as follows: = 1- ,Right now The elements in the matrix are When | The smaller the hour, The larger the value, the weaker the linear correlation between the response signals of the two sensors, and the stronger the leak location capability of the sensor combination. The total number of sensors to be deployed.

[0029] This invention employs the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to solve the aforementioned bi-objective optimization problem. The MOPSO algorithm is a multi-objective optimization algorithm extended from the traditional particle swarm optimization algorithm. By introducing Pareto dominance relations, an external archive maintenance strategy, and a global facilitator selection mechanism, it can effectively handle multiple conflicting objective functions while maintaining the convergence and diversity of solutions. Compared with traditional multi-objective evolutionary algorithms (such as NSGA-II), MOPSO has advantages such as fast convergence speed, simple parameter settings, and ease of implementation, making it particularly suitable for discrete combinatorial optimization problems such as the optimal placement of sensors in long-distance water pipelines.

[0030] The bi-objective optimization problem can be formally described as follows:

[0031]

[0032] In the formula: Let D be the decision vector, and D be the total number of candidate monitoring nodes. This indicates that the sensor is placed at the i-th candidate node. This indicates no deployment; F1 represents monitoring coverage (after taking the negative sign, it is transformed into a minimization problem), and F2 represents sensor response similarity. An upper limit constraint is imposed on the number of sensors that can be deployed.

[0033] This invention also discloses a multi-objective optimization layout model for sensors in long-distance water transmission pipelines based on the MOPSO algorithm, comprising:

[0034] One-dimensional hydraulic transient simulation module, pipe burst response calculation module, dual-objective optimization module, MOPSO solution module and scheme output module;

[0035] The one-dimensional hydraulic transient simulation module is used to construct a hydraulic model of the pipeline network and output pressure and flow data under normal operating conditions and pipe burst conditions.

[0036] The burst pipe response calculation module is used to receive pressure and flow data output by the one-dimensional hydraulic transient simulation module and calculate the pipe weight matrix and the sensor response difference matrix.

[0037] The dual-objective optimization module is used to construct an F1 objective function based on the pipeline weight matrix and an F2 objective function based on the sensor response difference matrix.

[0038] The MOPSO solver module is used to iteratively solve the bi-objective optimization model;

[0039] The scheme output module is used to output the Pareto optimal sensor layout scheme.

[0040] Furthermore, the monitoring coverage rate F1 is calculated using a weighted average based on the importance of the pipeline, prioritizing monitoring coverage of high-weight pipeline sections; the sensor response similarity F2 is minimized to reduce signal redundancy and improve the distinguishability of different burst locations.

[0041] The beneficial effects of this invention are:

[0042] This method constructs a two-dimensional evaluation index system that encompasses maximizing monitoring coverage and minimizing sensor response variability, overcoming the limitations of existing methods that focus on optimizing a single performance index. Monitoring coverage is weighted based on the importance of the pipeline, ensuring that high-importance pipelines receive priority for effective monitoring; sensor response variability is quantified using the Pearson correlation coefficient to assess the similarity between the response curves of different sensors under different pipe burst conditions, thereby improving the discriminative ability of the pipe burst location model from the source.

[0043] This method uses the MOPSO multi-objective particle swarm optimization algorithm as its core solution engine. Through an external archive maintenance strategy based on congestion distance and a global facilitator selection mechanism, it ensures the convergence and uniformity of the solution distribution. Compared to traditional multi-objective evolutionary algorithms, MOPSO can obtain a solution set that more closely approximates the true Pareto front with the same number of iterations, saving computation time. This method can provide strong technical support for the safe operation of long-distance water pipelines. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the sensor arrangement before optimization in Example 2;

[0045] Figure 2 This is a schematic diagram of the optimized sensor arrangement in Example 2;

[0046] Figure 3 Comparison of F1 numerical change curves between simultaneous optimization of two objectives and optimization of F1 only;

[0047] Figure 4 Comparison of the numerical change curves of F2 when optimizing both objectives simultaneously and when optimizing only F1;

[0048] Figure 5 Comparison of the numerical change curves of F1 when optimizing both objectives simultaneously and when optimizing only F2;

[0049] Figure 6 Comparison of the numerical change curves of F2 when optimizing for both objectives simultaneously and when optimizing only F2. Detailed Implementation

[0050] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0051] Example 1:

[0052] A multi-objective optimization method for sensor placement in long-distance water transmission pipelines based on the MOPSO algorithm includes the following steps:

[0053] Step S1: Construct a hydraulic model for a long-distance water transmission pipeline. Based on the pipeline topology, pipe material parameters, pipe diameter, length, node elevations, and upstream and downstream boundary conditions, establish a one-dimensional hydraulic transient simulation model in a numerical simulation environment. This provides a basic computing platform for subsequent simulation of pipe burst conditions and sensor response analysis.

[0054] This embodiment constructs a simulation system for a long-distance water transmission pipeline containing multiple branch pipes, the structure of which is as follows: Figure 1 As shown. The core parameters of the simulation system are set as follows: the main pipe has a total length of 4000m, with 9 branch pipes, each 400m long, and a branch pipe spacing of 400m; all pipe diameters are uniformly 0.1m, the friction coefficient is 0.022, and the pipe wave velocity is 1200.5m / s; the upstream pressure tank head is set to 44.33m. The system has a total of 19 monitoring nodes. The original pressure sensor layout scheme is as follows: 16 pressure sensors are arranged at nodes 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, and 19.

[0055] Step S2 involves iterating through the pipe burst and monitoring conditions and calculating the feature matrix. Based on the constructed hydraulic model, all combinations of pipe burst points and pressure sensor monitoring points at different locations are sequentially traversed. Nodal pressure response data for each condition is obtained through hydraulic simulation, and the pipe weight matrix is ​​calculated accordingly. Sensor response difference matrix .

[0056] Step S3: Construct a bi-objective optimization function. Based on the feature matrix obtained in step S2, establish a bi-objective evaluation function that maximizes the monitoring coverage rate F1 and minimizes the sensor response similarity F2. The optimization variables are 0-1 decision variables regarding whether pressure sensors are deployed at each candidate monitoring node.

[0057] Step S4 uses the MOPSO multi-objective particle swarm optimization algorithm to solve the bi-objective optimization model and calculates the values ​​of F1 and F2.

[0058] Based on the aforementioned one-dimensional hydraulic transient model, the bursting conditions of the main pipe and branch pipes were simulated respectively, and the pressure change ΔP at the time of bursting of each pipe section was obtained. i Substituting into formula (2), the change in head caused by the leakage is calculated. Simulation shows that after the main pipe bursts, the pressure drops sharply, and the head at the monitoring point is 25.73m. Main pipe = 44.33 - 25.73 = 18.6 m; the branch pipe burst has a small impact and a small pressure drop; the water head at the monitoring point is 37.45 m. The length of the branch pipe is 42.10 - 37.45 = 4.65 m. The flow rate change caused by the pipe burst is calculated using formula (3). When the main pipe bursts, the flow rate change is extremely large, Δ... Main flow rate = 26.4 L / s, branch pipe burst, flow rate change small, Δ Support = 6.6 L / s.

[0059] The total pipeline consists of 1 main pipe and 9 branch pipes, totaling 10 pipe segments. Formula 4 is used to calculate the normalized length of the main pipe as 1, and the normalized length of the branch pipes as 0. Formula 5 is used to calculate the normalized diameter of both the main and branch pipes as 1. Formula 6 is used to calculate the normalized pressure weights of the main and branch pipes. Because a burst main pipe causes a drastic change in the overall network pressure, its pressure weight is the largest, while a burst branch pipe has a smaller impact and therefore a smaller pressure weight. Therefore, the normalized pressure weight for the main pipe is simplified to 1.0, and for the branch pipes to 0.25. Similarly, the normalized flow weight for the main pipe is simplified to 1.0, and for the branch pipes to 0.25. According to Formula 8, the final weight for the main pipe is 4.0, and the final weight for the branch pipes is 1.0.

[0060] Total weight sum = W_main + 9 × W_branch = 4 + 9 × 1 = 13.

[0061] The main pipe has 100% coverage and is fully included with a weight of 4.0. Not all of the 9 branch pipes can be completely monitored by the 16 sensors. Some branch pipe ends and remote locations are not fully monitored. Therefore, the weighted coverage ratio of the 9 branch pipes is calculated according to the weight ratio. The weighted coverage ratio of the 9 branch pipes is 7.3581. The total coverage weight is: 4.0 + 7.3581 = 11.3581.

[0062] The monitoring coverage rate is calculated according to formula (1): F1 = 11.3581 ÷ 13 = 0.8737 = 87.37%.

[0063] Because there are 10 pipes and 16 sensors, in Formula 11, N=10 and N′=16. The effective number of sensor pair combinations under each operating condition is: C(16,2) = 16×15÷2 = 120 pairs. That is, there are 120 different Pearson correlation coefficients that need to be added under each operating condition. There are a total of 10 pipe burst conditions, so the final F2 is the sum of all 10 conditions, which is 10×120 = 1200. The final value is F2 = 326.166.

[0064] Step S5 iteratively obtains the Pareto optimal solution set through Pareto dominance relations, external archive maintenance, congestion distance selection, and polynomial mutation operations. Based on engineering constraints, a sensor deployment scheme is selected from the optimal solution set to achieve synergistic optimization of monitoring coverage and positioning discrimination.

[0065] An initial external archive is constructed, and a global leader is determined. Non-dominated solutions in the initial population are identified based on Pareto dominance and stored in the external archive REP. If the REP size exceeds the maximum capacity of the external archive, solutions in dense regions are deleted based on crowding distance. In each subsequent iteration, a global leader is selected from the REP for each particle based on crowding distance or an adaptive grid method, prioritizing solutions in sparsely distributed regions to maintain solution diversity.

[0066] The new velocity and position of each particle are calculated based on the particle swarm velocity and position update formula, and boundary handling is performed on out-of-bounds variables. The objective function values ​​F1 and F2 of the new population are evaluated, and the optimal position of each individual is updated according to the Pareto dominance relationship. Non-dominated solutions in the new population are incorporated into the REP, dominated members are removed, and truncation is performed based on crowding distance when the REP is overcapacity. Polynomial mutation is performed on the population or archive to prevent premature convergence of the algorithm.

[0067] If the current iteration count reaches If the change in the Pareto front is less than a preset threshold, the iteration is terminated, and all non-dominated solutions in the external archive REP are output as alternative optimal sensor layout schemes; otherwise, iterative optimization continues.

[0068] The identification of non-dominated solutions based on Pareto dominance relations, external archive maintenance mechanisms, global facilitator selection strategies based on crowding distance, individual optimal update rules based on Pareto dominance relations, and the principles of polynomial mutation operations are all existing technologies and will not be elaborated here.

[0069] In step S6, decision-makers can select the optimal compromise between monitoring coverage and response variability from the Pareto frontier based on actual engineering constraints.

[0070] In this embodiment, the algorithm parameters are set as follows: population size N=100, maximum number of iterations... =200, inertia weight w=0.5, individual learning factor c1=1.5, social learning factor c2=1.5, external archive capacity =50, mutation probability =0.1. Based on the collaborative optimization analysis of multi-dimensional indicators, the final optimal layout scheme is as follows: 12 pressure sensors are selected, and their placement positions correspond to nodes 1, 2, 3, 5, 6, 8, 10, 12, 14, 15, 17, and 18, respectively. Figure 2 As shown in the figure, the core performance parameters of this scheme are excellent: the monitoring coverage rate reaches 90.1%, and the sensor response similarity (F2) is 248.3. Compared with the original scheme, the monitoring coverage rate has increased by 2.73 percentage points, and the sensor response similarity has decreased by 23.9%. The optimized scheme has significantly improved the two sensor evaluation indicators and the computational accuracy and efficiency of the two types of models. At the same time, the number of sensors has been reduced by 4, which reduces the cost of pressure sensor deployment and further improves the overall performance of the long-distance water pipeline burst monitoring system.

[0071] To further verify the advantages of this method, Figures 3-6 This study compared the impact of simultaneous optimization strategies for two objectives with single-objective optimization strategies on two core indicators: monitoring coverage and sensor response variability. Comparative experiments were conducted with strategies that optimized only F1 (single objective) and only F2 (single objective). Experimental results show that when optimizing both objectives simultaneously, as the number of deployed sensors gradually increases from 2 to 16, F1 increases from 0.207 to 1, and F2 increases from 2.175 to 545.695. While the single-objective optimization algorithm slightly outperforms the dual-objective optimization algorithm in optimizing a single objective function, the dual-objective optimization algorithm exhibits a significant advantage in the other objective indicator. For example, the scheme that only optimizes F1 achieves an F2 value exceeding 380 when the coverage reaches 90%, far worse than this scheme (F2=248.3); while the scheme that only optimizes F2 achieves a lower F2 value, but the coverage is only around 63%. This result fully demonstrates the core value of the proposed dual-objective optimization method in balancing multi-dimensional performance indicators in practical applications.

[0072] Example 2:

[0073] A multi-objective optimization layout model for sensors in long-distance water transmission pipelines based on the MOPSO algorithm includes:

[0074] One-dimensional hydraulic transient simulation module, pipe burst response calculation module, dual-objective optimization module, MOPSO solution module and scheme output module;

[0075] The one-dimensional hydraulic transient simulation module is used to construct a hydraulic model of the pipeline network and output pressure and flow data under normal operating conditions and pipe burst conditions.

[0076] The burst pipe response calculation module is used to receive pressure and flow data output by the one-dimensional hydraulic transient simulation module and calculate the pipe weight matrix and the sensor response difference matrix.

[0077] The dual-objective optimization module is used to construct an F1 objective function based on the pipeline weight matrix and an F2 objective function based on the sensor response difference matrix.

[0078] The MOPSO solver module is used to iteratively solve the bi-objective optimization model;

[0079] The scheme output module is used to output the Pareto optimal sensor layout scheme.

[0080] The monitoring coverage rate F1 is calculated by weighting the importance of the pipeline, prioritizing the monitoring coverage of high-weight pipeline sections; the sensor response similarity F2 is minimized to reduce signal redundancy and improve the distinguishability of different burst locations.

[0081] It should be understood that any parts not described in detail in this invention belong to the prior art.

[0082] The above description, in conjunction with the accompanying drawings, is merely a specific implementation method and process of the present invention. However, the scope of protection of the present invention is not limited thereto. Any person skilled in the art should understand that this is only an example and various changes and substitutions can be made to this implementation method without departing from the essence of the present invention.

Claims

1. A multi-objective optimization layout method for sensors in long-distance water transmission pipelines based on the MOPSO algorithm, characterized in that, Includes the following steps: S1: Based on the topology, pipe material parameters, pipe diameter, length, node elevation and boundary conditions of long-distance water transmission pipelines, construct a one-dimensional hydraulic transient simulation model; S2: Traverse the pipe burst conditions and sensor monitoring point combinations of each pipe section in the hydraulic model, obtain the pressure and flow response data of the nodes before and after the pipe burst through simulation, and calculate the pipe weight matrix and sensor response difference matrix. S3: A multi-objective optimization model is constructed with the dual objective functions of maximizing the weighted monitoring coverage F1 and minimizing the sensor response similarity F2. The optimization variables are 0-1 decision variables of whether pressure sensors are deployed at candidate nodes. S4: The MOPSO multi-objective particle swarm optimization algorithm is used to solve the bi-objective optimization model, and the F1 and F2 values ​​are calculated. The Pareto optimal solution set is obtained iteratively through Pareto dominance relation, external archive maintenance, crowding distance selection and polynomial mutation operation. S5: Select a sensor layout scheme from the optimal solution set based on engineering constraints to achieve synergistic optimization of monitoring coverage and positioning discrimination.

2. The method according to claim 1, characterized in that, The weight W of the i-th pipe segment in step S2 i It is obtained by summing the four terms: normalized length, normalized diameter, normalized pressure weight, and normalized flow weight. ， Normalized length in equation (1) Normalized diameter Normalized pressure weights Normalized traffic weight Calculate according to formulas (4), (5), (6), and (7) respectively; the pressure weight is obtained from formula (2) of the change in water head before and after the pipe burst, and the flow weight is obtained from formula (3) of the change in flow rate before and after the pipe burst: ， In formula (2): The value represents the change in head caused by the leak. The superscript h represents the head, and the subscript l represents the l-th monitoring point. h(⋅) represents the head calculation function. α represents the set of operating parameters when the pipeline leaks. A set of parameters representing the leak-free operating condition of a pipeline; In formula (3): Let q(·) represent the change in flow rate in the pipe section caused by the leak, q({α}) represent the flow rate calculation function for the pipe section, and q({α}) represent the flow rate value of pipe section l under the leak condition. This represents the flow rate of pipe section l under leak-free operating conditions. In equation (4): To normalize the pipe length, The shortest pipe length, The longest pipe length, Let be the length of the i-th pipe segment; In equation (5): To normalize the pipe diameter, Minimum pipe diameter, For the maximum pipe diameter, Let be the diameter of the i-th pipe segment; In formula (6): To normalize the stress weights, As pressure weight, The maximum pressure weight, The minimum pressure weight; In equation (7): To normalize traffic weights, For traffic weight, For maximum traffic weight, The minimum traffic weight.

3. The method according to claim 2, characterized in that, The formula for calculating the weighted monitoring coverage rate F1 in step S3 is as follows: ， In Equation (8): F1 is the monitoring coverage rate, l represents the node number of the pipeline, N is the total number of pipelines, and cl represents the set of leak points that can be effectively covered / detected by the sensors under the current sensor layout scheme; Let be the weight of the nth pipe.

4. The method according to claim 1, characterized in that, The sensor response difference matrix mentioned in step S2 The elements are: ， in, Let be the Pearson correlation coefficient between the response signals of sensor m and sensor n. The larger the value, the stronger the sensor's independent response and the higher the accuracy of pinpointing burst pipe locations.

5. The method according to claim 4, characterized in that, The sensor response similarity F2 mentioned in step S3 is calculated using a three-layer summation formula: ， in, The total number of sensors to be deployed.

6. The method according to claim 1, characterized in that, The MOPSO algorithm in step S4 includes: Identifying non-dominated solutions based on Pareto dominance relations; An external archive maintenance strategy based on congestion distance is adopted to maintain solution set diversity; The solution with the largest crowding distance is used as the global leader; Introducing polynomial variation to avoid premature convergence; The particle swarm velocity-position formula is iteratively updated, and the Pareto optimal layout scheme is output after the maximum number of iterations or the convergence threshold is met.

7. A multi-objective optimization layout model for sensors in long-distance water transmission pipelines based on the MOPSO algorithm, characterized in that, include: One-dimensional hydraulic transient simulation module, pipe burst response calculation module, dual-objective optimization module, MOPSO solution module and scheme output module; The one-dimensional hydraulic transient simulation module is used to construct a hydraulic model of the pipeline network and output pressure and flow data under normal operating conditions and pipe burst conditions. The burst pipe response calculation module is used to receive pressure and flow data output by the one-dimensional hydraulic transient simulation module and calculate the pipe weight matrix and the sensor response difference matrix. The dual-objective optimization module is used to construct an F1 objective function based on the pipeline weight matrix and an F2 objective function based on the sensor response difference matrix. The MOPSO solver module is used to iteratively solve the bi-objective optimization model; The scheme output module is used to output the Pareto optimal sensor layout scheme.

8. The model according to claim 7, characterized in that, The monitoring coverage rate F1 is calculated by weighting the importance of the pipeline, prioritizing the monitoring coverage of high-weight pipeline sections; the sensor response similarity F2 is minimized to reduce signal redundancy and improve the distinguishability of different burst locations.

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