Optimal placement method of inflow and infiltration detection sensors in sewage pipe networks based on information entropy

Abstract

This invention relates to the field of wastewater pipe network optimization technology, and provides a method for optimizing the placement of inflow and infiltration detection sensors in wastewater pipe networks based on information entropy. The method includes: simulating a total of M random abnormal events to obtain the information content vector of each node in the wastewater pipe network; constructing a joint entropy matrix EM for the entire wastewater pipe network by calculating the joint entropy between every two nodes; performing a first-stage clustering based on the joint entropy, clustering the number of nodes into NS classes according to the required number of sensors; performing a second-stage re-clustering based on the wastewater pipe network topology to cluster the number of nodes into NC classes; sorting the NC class nodes according to their ADR values, and selecting one node from each of the NS classes with the highest ADR value to place the sensor, with the combination having the largest multivariate joint entropy as the final optimal placement scheme. This invention proposes for the first time an application method of information entropy in the detection of abnormal events in wastewater pipe networks, providing a new approach for the optimized placement of sensors in wastewater pipe networks.

Description

Technical Field

[0001] This invention relates to the field of sewage pipe network optimization technology, and in particular to a method for optimizing the arrangement of inflow and infiltration detection sensors in sewage pipe networks based on information entropy. Background Technology

[0002] Urban sewage pipe networks play a vital role in urban wastewater transportation, crucial for public health and environmental protection. Sewage pipes are widespread in urban areas, typically buried underground. However, due to aging and lack of timely maintenance, many pipes in sewage networks suffer from severe structural deterioration, such as corrosion or damage. Therefore, infiltration has become a common problem in many sewage pipe networks. Infiltration refers to water from the surrounding environment entering the system through manholes, faulty pipe joints, and pipe cracks. Infiltration can pose a significant threat to urban water security, including reducing wastewater concentration, thus decreasing the efficiency of wastewater treatment plants, causing sewer overflows, releasing untreated wastewater into the environment, and increasing the risk of basement flooding and surface flooding during heavy rains. Therefore, detecting large-scale infiltration events in sewage pipe networks is essential for ensuring the protection of the urban water environment.

[0003] Physical methods, such as smoke testing, dye testing, and CCTV inspection, can directly identify pipe damage points causing infiltration. While these methods can easily and effectively pinpoint the location of infiltration within a specific pipe, they are typically inefficient and costly, making them difficult to apply to the entire pipe network. In recent years, with the rapid development of the Internet of Things (IoT), online sensors are increasingly being used for infiltration detection in sewage pipe networks. These sensors are typically used to monitor high-temporal-resolution hydraulic variables, such as water level or flow rate. The collected data can be processed using advanced analytical techniques such as machine learning algorithms to identify the occurrence and presence of infiltration in sewage pipe networks.

[0004] However, due to the high cost of purchasing and maintaining sensors, placing a sensor at every inspection well in a sewage pipe network is impractical. Therefore, optimizing the placement of a limited number of sensors to maximize monitoring efficiency is an important research problem. Many heuristic optimization methods have been developed for sensor placement in sewage pipe networks, such as genetic algorithms, greedy algorithms, evolutionary algorithms, and multi-objective genetic algorithms. These heuristic optimization methods may determine the optimal sensor placement scheme, but their solutions often differ across optimization runs, and the quality of the solution may heavily depend on algorithm parameterization, making widespread application in practical engineering difficult. Furthermore, optimization algorithms typically require significant computation, which can lead to a severe reduction in computational efficiency for large-scale pipe networks. Summary of the Invention

[0005] This invention provides a method for optimizing the placement of inflow and infiltration detection sensors in sewage pipe networks based on information entropy. First, by simulating random abnormal events, the information content available at each node in the pipe network is quantified. Then, information entropy is calculated, and a first-stage clustering is performed based on this. Building upon the results of the first-stage clustering, a second-stage clustering is performed based on the topological characteristics of the pipe network, aiming to further improve the effectiveness of the sensor placement scheme. Finally, a node is selected from each category to place the sensor, and the combination with the highest information entropy is taken as the final optimal placement scheme. By using information entropy as an evaluation index for sensor placement schemes and developing a novel two-stage clustering method to identify the optimal placement scheme, a highly efficient sensor optimization placement method is obtained.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a method for optimizing the layout of inflow and infiltration detection sensors in sewage pipe networks based on information entropy. The optimization layout method includes:

[0008] (1) Simulate a total of M random abnormal events to obtain the information content vector of each node in the sewage pipe network;

[0009] (2) Construct the joint entropy matrix EM of the entire sewage network by calculating the joint entropy between every two nodes;

[0010] (3) Based on joint entropy, the first stage of clustering is performed, and the number of nodes is clustered into NS class according to the number of sensors to be deployed. Based on the sewage pipe network topology, the second stage of re-clustering is performed to cluster the number of nodes into NC class.

[0011] (4) Sort the NC class nodes according to their ADR values ​​(average detection rate), and select one node from each of the top NS classes with the highest ADR values ​​(average detection rate) to deploy the sensor. The combination with the largest multivariate joint entropy is taken as the final optimal deployment scheme.

[0012] Furthermore, the specific process of obtaining the information content vector of each node i of the sewage pipe network in step (1) is as follows:

[0013] (11) Assume there are N nodes in the sewage pipe network and the total number of abnormal events (such as inflow and seepage events) is M. Consider each node i in the pipe network as a potential location for sensor placement.

[0014] (12) For node i, use formula (1-1) to calculate its information content based on the abnormal event m.

[0015]

[0016] The method determines whether an abnormal event m is detected by node i by considering changes in flow rate, water depth, or water quality parameters that exceed a pre-specified threshold.

[0017] (13) For the total number of abnormal events M, use formula (1-2) to obtain the information content vector NI of each node i. i ;

[0018]

[0019] Furthermore, the specific process of step (2) is as follows:

[0020] (21) After obtaining the information content vector of each node i, calculate the information matrix IM of the entire sewage network:

[0021]

[0022] The information matrix IM is used to calculate the joint entropy H(NI) of node i and node j. i NI j ):

[0023]

[0024] Among them, R(NI) i ,s) and R(NI j ,k) are respectively NI i and NI j Different records in;

[0025] S and K are NI. i and NI j The number of different records in the data is 2, based on the given information content S and K.

[0026] p(R(NI i ,s),R(NI j ,k)) is R(NI i ,s) and R(NI j The probability of k and k occurring simultaneously;

[0027] (22) Construct a joint entropy matrix EM based on the joint entropy between every two nodes.

[0028]

[0029] Here, EM is a diagonal matrix containing the joint entropy between each pair of nodes in the sewage network.

[0030] Furthermore, the specific process of step (3) is as follows:

[0031] (31) Use the spectral clustering method to perform the first stage of clustering, and divide the information content vector of each node i into NI. i Treat it as a point in space; then estimate the similarity w between node i and node j. ij :

[0032]

[0033] (32) Construct a similarity matrix SM based on the results of all node combinations:

[0034]

[0035] (33) For the spectral clustering method, graph theory is used to implement clustering; an undirected graph G is constructed based on all node combinations, and then the minimum loss function is defined as the result of cutting the undirected graph G into different classes C, as shown in formula (3-3);

[0036] minL(C1,C2,...,C g )=min∑ (i,j)∈CT w ij (3-3)

[0037] Where L(C1,C2,...,C) g ) is the loss function for cutting out a total of g clusters from the original undirected graph G, where the total number of g is equal to the number of sensors required to be deployed NS (i.e., the number of clusters is NS), and CT is the set removed from the cut graph.

[0038] (34) Since some nodes located in different branches were grouped into one class after the first stage of clustering, the second stage of re-clustering was carried out based on the sewage pipe network topology to separate such nodes. Specifically, each class was traversed, and if any of the nodes were located in different branches, they were divided into two classes, which further increased the number of classes in the first stage of clustering. The number of clusters became NC classes, where NC>NS, to ensure that the nodes in each class have a low joint entropy when detecting abnormal events.

[0039] Furthermore, the specific process of step (4) is as follows:

[0040] (41) After two-stage clustering, the number of clusters NC is usually greater than the number of sensors NS. The clusters are sorted by the ADR value (average detection rate) of all nodes in each cluster, so that the NS cluster can be selected from the total NC clusters. For each node i, it represents the probability DR of all abnormal events detected if the sensor is placed at node i. i :

[0041]

[0042] ADR for each cluster kk The value is;

[0043]

[0044] Among them, Ω k S(Ω) is the set of nodes in the k-th class. k ) represents the total number of nodes in the k-th class;

[0045] (42) Sort the classes in descending order of average detection rate value, and select one node from each of the top few NS classes with high average detection rate values ​​to place the sensor;

[0046] (43) Given the NS classes, enumerate the joint entropy of each candidate sensor placement scheme for a single sensor in each class, and take the combination with the largest multivariate joint entropy as the final optimal placement scheme. The sensor placement strategy with the largest determined joint entropy represents the comprehensive information of these sensors. The multivariate joint entropy can be obtained by extending formula (2-2).

[0047] The present invention has the following beneficial effects:

[0048] (1) This invention abandons the use of heuristic search methods and proposes a two-stage clustering method based on information entropy to identify the optimal sensor placement scheme with determinism and efficiency, providing an optimal solution for a given sensor placement problem in an efficient manner, which facilitates the decision-making process compared with the many different available solutions provided by heuristic algorithms.

[0049] (2) This invention uses information entropy as an indicator to design an optimized layout scheme for sewage pipe network sensors. Information entropy, as an indicator for measuring information uncertainty, is reflected in the design of hydrological monitoring systems, but it has not yet been applied to the optimized layout of sewage pipe network sensors for abnormal event detection. This invention proposes for the first time a method for applying information entropy in the detection of abnormal events in sewage pipe networks, providing a new approach for the optimized layout of sewage pipe network sensors.

[0050] (3) The method proposed in this invention is a deterministic method. The optimization results of traditional heuristic optimization algorithms are related to parameter settings on the one hand, and the same solution is difficult to be obtained for each optimization because the search space is too large on the other hand. However, the method proposed in this invention greatly reduces the search space through clustering and finds the definite optimal solution by traversing all potential solutions, which has higher engineering application value.

[0051] (4) The method proposed in this invention greatly improves computational efficiency. Optimization algorithms require repeated model calls during iteration, which reduces computational efficiency for large-scale pipeline networks; while the method of this invention greatly reduces the computational load through two-stage clustering, making it a highly efficient optimization layout method.

[0052] (5) The sensor optimization layout method based on information entropy clustering proposed in this invention uses information entropy as the evaluation index of sensor layout scheme and introduces two-stage clustering, which can effectively detect the occurrence of abnormal events in sewage pipe network. It is an important supplement to the research field of urban sewage pipe network management, provides important technical support for the management of sewage pipe network system, and has good promotion and practical engineering application value. Attached Figure Description

[0053] Figure 1 This is a simplified flowchart of the overall process of this invention.

[0054] Figure 2 This is a topology diagram of the wastewater pipe network systems FUSN and USN1 in the embodiment.

[0055] Figure 3 This is a schematic diagram of the sensor's individual monitoring range.

[0056] Figure 4 This is a graph showing the correlation between joint entropy and detection rate.

[0057] Figure 5 This is a comparison chart of the detection rate and spatial distribution uniformity results of the method of the present invention and the GA optimization method in Example USN1.

[0058] Figure 6 This is a comparison diagram of the specific sensor arrangement schemes of the method of the present invention and the GA optimization method in embodiment USN1.

[0059] Figure 7 This is a comparison chart of the detection rate results of the present invention method, GA optimization method, and engineering scheme in the FUSN embodiment.

[0060] Figure 8 This is a comparison diagram of the specific layout schemes of the method and engineering scheme of the present invention in the embodiment FUSN.

[0061] Figure 9 This is a comparison of the computational overhead of the method of this invention and the optimized method. Detailed Implementation

[0062] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that the embodiments are only specific illustrations of the invention and should not be regarded as limitations on the invention. The purpose of the embodiments is to enable those skilled in the art to better understand and reproduce the technical solution of the present invention. The scope of protection of the present invention should still be determined by the scope defined in the claims.

[0063] This invention provides a method for optimizing the layout of inflow and infiltration detection sensors in sewage pipe networks based on information entropy. The optimization layout method includes:

[0064] S1, simulate a total of M random abnormal events to obtain the information content vector of each node in the sewage pipe network; the specific process is as follows:

[0065] S11, Assuming there are N nodes in the sewage pipe network and the total number of abnormal events (such as inflow and seepage events) is M, consider each node i in the pipe network as a potential location for sensor placement;

[0066] S12, For node i, use formula (1-1) to calculate its information content based on the abnormal event m.

[0067]

[0068] The method determines whether an abnormal event m is detected by node i by considering changes in flow rate, water depth, or water quality parameters that exceed a pre-specified threshold.

[0069] S13, for the total number of abnormal events M, use formula (1-2) to obtain the information content vector NI of each node i. i ;

[0070]

[0071] S2, construct the joint entropy matrix EM of the entire sewage network by calculating the joint entropy between every two nodes. The specific process is as follows:

[0072] S21, After obtaining the information content vector of each node i, calculate the information matrix IM of the entire sewage pipe network:

[0073]

[0074] The information matrix IM is used to calculate the joint entropy H(NI) of node i and node j. i NI j ):

[0075]

[0076] Among them, R(NI) i ,s) and R(NI j ,k) are respectively NI i and NI j Different records in;

[0077] S and K are NI. i and NI j The number of different records in the data is 2, based on the given information content S and K.

[0078] p(R(NI i ,s),R(NI j ,k)) is R(NIi ,s) and R(NI j The probability of k and k occurring simultaneously;

[0079] S22, construct the joint entropy matrix EM based on the joint entropy between every two nodes.

[0080]

[0081] Here, EM is a diagonal matrix containing the joint entropy between each pair of nodes in the sewage network.

[0082] S3, based on joint entropy, performs the first stage of clustering, clustering the number of nodes into NS classes according to the required number of sensors. Then, based on the sewage network topology, it performs the second stage of re-clustering, clustering the number of nodes into NC classes. The specific process is as follows:

[0083] S31, use spectral clustering to perform the first stage of clustering, and generate the information content vector NI for each node i. i Treat it as a point in space; then estimate the similarity w between node i and node j. ij :

[0084]

[0085] S32, Construct a similarity matrix SM based on the results of all node combinations:

[0086]

[0087] S33. For the spectral clustering method, graph theory is used to implement clustering. An undirected graph G is constructed based on all node combinations. Then, the minimum loss function is defined as the result of cutting the undirected graph G into different classes C, as shown in formula (3-3).

[0088] minL(C1,C2,...,C g )=min∑ (i,j)∈CT w ij (3-3)

[0089] Where L(C1,C2,...,C) g ) is the loss function for cutting out clusters with a total number of g from the original undirected graph G, where the total number of g is equal to the number of sensors required to be deployed NS, and CT is the set removed from the cut graph;

[0090] S34. After the first stage of clustering, some nodes located in different branches are grouped into one class. Then, based on the sewage pipe network topology, the second stage of re-clustering is performed to separate these nodes. Specifically, each class is traversed, and if any of the nodes are located in different branches, they are divided into two classes. This further increases the number of classes in the first stage of clustering, and the number of clusters becomes NC classes, where NC > NS. This ensures that the nodes in each class have a low joint entropy when detecting abnormal events.

[0091] S4. Sort the NC class nodes according to their ADR (Average Detection Rate) values. Select one node from each of the top NS classes with the highest ADR values ​​(average detection rates) to deploy the sensors. The combination with the highest multivariate joint entropy is taken as the final optimal deployment scheme. The specific process is as follows:

[0092] S41, after two-stage clustering, the number of clusters NC is usually greater than the number of sensors NS. The clusters are sorted based on the ADR (average detection rate) of all nodes in each cluster, allowing the selection of the NS cluster from the total NC clusters. For each node i, it represents the probability DR of detecting all anomalous events if the sensor is placed at node i. i :

[0093]

[0094] ADR for each cluster k k The value is;

[0095]

[0096] Among them, Ω k S(Ω) is the set of nodes in the k-th class. k ) represents the total number of nodes in the k-th class;

[0097] S42, sort the classes in descending order of average detection rate value, and select one node from each of the top few NS classes with high average detection rate values ​​to place the sensor;

[0098] S43, given the defined NS classes, enumerate the joint entropy of each candidate sensor placement scheme for a single sensor in each class, and select the combination with the largest multivariate joint entropy as the final optimal placement scheme. The determined sensor placement strategy with the largest joint entropy represents the comprehensive information of these sensors. The multivariate joint entropy can be obtained by extending formula (2-2).

[0099] Example

[0100] The practical application of the method of the present invention in engineering is illustrated by simulating real-world examples. These examples do not represent actual examples, but rather illustrate that the present invention can be used in engineering practice and achieve the desired technical effects.

[0101] Taking a city's sewage pipe network as an example, the network serves an area of ​​approximately 15 square kilometers, with a total pipe length of about 60 kilometers and pipe diameters ranging from 0.3 meters to 1.5 meters. The system's daily total flow rate is approximately 43,400 cubic meters per day. This city experiences frequent rain and has numerous rivers, making inflow and infiltration a significant issue for the sewage pipe network. The local water authority plans to install 20 flow meters in the sewage pipe network to detect large-scale inflow and infiltration events and to develop a pipeline maintenance plan accordingly.

[0102] First, a hydraulic model of the sewage pipe network was established using SWMM software. This model consists of 819 pipes, 760 inspection wells, 60 overflow nodes, and an outlet located in the eastern part of the study area. Figure 2 The model has been calibrated by the local water authority under drought conditions. To better explain the application of the proposed method, a relatively independent area was selected ( Figure 2 The small sewage network (shown in the shaded area) is referred to as Example USN1, and the complete sewage network is referred to as Example FUSN.

[0103] A total of M inflow / infiltration events (abnormal events) are generated, with M being 1000 for USN1 and 3000 for FUSN. For each event, the inflow rate into a single pipe of the wastewater network is Q, where the probability of each pipe being selected is based on its pipe length. Q is designed to be 5% of the total daily flow of the network, and this value remains constant throughout the simulation period (24 hours in this case). The alarm threshold for inflow / infiltration events is set to be 15% above the average daily wastewater flow.

[0104] To evaluate the effectiveness of sensor placement, two quantitative evaluation metrics were used: detection rate (DR) and distribution uniformity (DU). DR, defined in Equation (4-1), represents the probability of a single sensor responding to a total of M anomalous events (i.e., inflow / seepage events). For a system with multiple sensors, DR represents the proportion of events detected by any sensor out of the total M events. A higher DR indicates that the sensor placement scheme can detect more anomalous events. Simultaneously, sensor distribution uniformity is also important. This is because a system with uniform sensor distribution means that each sensor individually monitors a similar length of pipe. Figure 3 As shown, pipes of different colors are monitored by sensors S1, S2, and S3, respectively. If the pipe lengths monitored by each sensor individually are similar, then after an anomaly occurs, the pipe lengths that need to be investigated are similar, resulting in higher overall time efficiency. In this invention, DU can be approximated by the coefficient of variation of the pipe lengths monitored by all sensors individually. To better present the results, DU is defined as the reciprocal of the coefficient of variation; therefore, the larger the DU, the higher the overall spatial uniformity of the sensor placement.

[0105] This invention proposes using joint entropy to design sensor placement schemes. First, the effectiveness of joint entropy needs to be proven. A higher joint entropy indicates more information about anomalous events that the sensors can provide, representing higher coverage of anomalous events. For USN1 and FUSN, several random sensor placement schemes were generated to discuss the correlation between joint entropy and detection rate, and the Pearson correlation coefficient was used to quantify the correlation, such as... Figure 4 As shown, there is a strong correlation between joint entropy and detection rate. The Pearson coefficient r is above 0.95, indicating that the higher the joint entropy, the higher the detection rate of abnormal events. Therefore, joint entropy is an effective design indicator for sensor deployment schemes.

[0106] To illustrate the advantages of the proposed method, a comparison is made between this method and the GA algorithm, which optimizes joint entropy for a single objective. First, considering the USN1 case with seven sensors, the detection rate and spatial distribution uniformity of the proposed method are compared with those of the GA optimization method. Figure 5 As shown, the detection rate of the method of this invention is no lower than that of the GA method, further proving the effectiveness of joint entropy as a design index. Furthermore, the spatial uniformity of the method of this invention is superior to that of the GA method. This is because the method of this invention considers two-step clustering, avoiding the possibility of poor spatial uniformity due to overly close sensor placement. Meanwhile, it can be seen that the uniformity results of the GA method vary greatly in each optimization round. The specific placement schemes of the two methods are then compared, as follows... Figure 6 As shown, the arrangement schemes obtained by the GA optimization method vary greatly in different optimization rounds, indicating the pluralistic nature of the optimization method and its difficulty in practical engineering applications. In contrast, the method proposed in this invention, due to its small search space, can traverse all potential schemes, thus obtaining a definite sensor optimization arrangement scheme, which is more valuable for engineering applications.

[0107] The same comparison was then conducted in the FUSN pipeline network. In addition to the GA optimization method, the engineering plan was also compared, which was the plan proposed by the local water authority based on experience, with a total of 20 sensors deployed. Figure 7 A comparison of the detection rates of three methods is presented, considering three different Q values: 1%, 3%, and 5% of the total flow. It can be seen that the detection rate of the method proposed in this invention is significantly better than that of the GA optimization method and the engineering layout scheme. Figure 8 Comparing the specific layouts of the method and engineering scheme of this invention, it can be seen that the engineering scheme generally places the sensors at nodes traditionally considered important, such as busbar nodes and the end nodes of main pipelines. However, Figure 7 The detection rate results demonstrate that such an experience-based deployment scheme may lead to a decrease in the detection rate of abnormal events, proving the necessity of optimizing the deployment.

[0108] The computational efficiency will be discussed below on a computer equipped with an AMD Ryzen 7 5800H CPU @ 3.20GHz. Since computation time is related to the network size and accuracy settings, converting the computation time into the required number of simulations allows for more effective comparisons. For USN1 and FUSN, the proposed method requires 1000 and 3000 simulations respectively. Furthermore, the time required for clustering and enumeration in scheme computation and joint calculation is equivalent to 800 model simulations and 6.5 x 10^6 simulations, respectively. 6 This model simulation is performed twice. In the optimization algorithm, both the number of samples and the number of iterations are 200. For each sample, each iteration requires regenerating random events and calling the model for simulation, totaling 4 x 10^6 iterations. 7 and 1.2x10 8 Sub-model simulation. Figure 9 A comparison of the computational costs of the two optimization methods is presented. Specifically, the computational cost of the proposed method is only 0.0045% and 5.4% of that of the optimization methods used for USN1 and FUSN, respectively. Furthermore, it is worth noting that the proposed method, because the computational tasks do not conflict, can significantly improve computational efficiency through parallelization, while the optimization methods may depend on the results of the previous iteration for each iteration, making it difficult to improve computational efficiency through parallelization.

[0109] Therefore, the wastewater pipe network sensor optimization layout method based on information entropy clustering proposed in this invention quantifies the information content that each node in the pipe network can provide through the simulation of random abnormal events. Then, the joint entropy between every two nodes is calculated, and two-stage clustering is performed based on the joint entropy and the pipe network topology. Finally, a node is selected from each cluster to place the sensor, and the combination with the highest joint entropy is taken as the final optimal layout scheme. The method proposed in this invention shows good performance in both detection rate and spatial uniformity, overcomes the uncertainty of the solution of optimization methods, provides important technical support for solving the problem of abnormal event detection in wastewater pipe networks, and has practical engineering application value.

[0110] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0111] It should be noted that any technical features not described in detail in this invention can be implemented using any existing technology.

Claims

1. A method for optimizing the layout of inflow and infiltration detection sensors in a sewage pipe network based on information entropy, characterized in that, Optimization layout methods include: (1) Simulate a total of M random abnormal events to obtain the information content vector of each node in the sewage pipe network; The specific process of obtaining the information content vector of each node i in the sewage pipe network in step (1) is as follows: (11) Assume there are N nodes in the sewage pipe network and the total number of abnormal events is M. Consider each node i in the pipe network as a potential location for sensor placement. (12) For node i, use formula (1-1) to calculate its information content based on the abnormal event m. The method determines whether an abnormal event m is detected by node i by considering changes in flow rate, water depth, or water quality parameters that exceed a pre-specified threshold. (13) For the total number of abnormal events M, use formula (1-2) to obtain the information content vector NI of each node i. i ; (2) Construct the joint entropy matrix EM of the entire sewage network by calculating the joint entropy between every two nodes; The specific process of step (2) is as follows: (21) After obtaining the information content vector of each node i, calculate the information matrix IM of the entire sewage network: The information matrix IM is used to calculate the joint entropy H(NI) of node i and node j. i NI j ): Among them, R(NI) i ,s) and R(NI j ,k) are respectively NI i and NI j Different records in; S and K are NI. i and NI j The number of different records in the data is 2, based on the given information content S and K. p(R(NI i ,s),R(NI j ,k)) is R(NI i ,s) and R(NI j The probability of k and k occurring simultaneously; (22) Construct a joint entropy matrix EM based on the joint entropy between every two nodes. Wherein, EM is a diagonal matrix containing the joint entropy between each pair of nodes in the sewage pipe network; (3) Based on joint entropy, the first stage of clustering is performed, and the number of nodes is clustered into NS class according to the number of sensors to be deployed. Based on the sewage pipe network topology, the second stage of re-clustering is performed to cluster the number of nodes into NC class. (4) Sort the NC class nodes according to the average detection rate (ADR) value, select one node from each of the top NS classes with high ADR values ​​to deploy the sensor, and take the combination with the largest multivariate joint entropy as the final optimal deployment scheme.

2. The method for optimizing the layout of inflow and infiltration detection sensors in a sewage pipe network based on information entropy, as described in claim 1, is characterized in that... The specific process of step (3) is as follows: (31) Use the spectral clustering method to perform the first stage of clustering, and divide the information content vector of each node i into NI. i Treat it as a point in space; then estimate the similarity w between node i and node j. ij : (32) Construct a similarity matrix SM based on the results of all node combinations: (33) Construct an undirected graph G based on all node combinations, and then define the minimum loss function as the result of cutting the undirected graph G into different classes C, as shown in formula (3-3); minL(C1,C2,...,C g )=min∑ (i,j)∈CT w ij (3-3) Where L(C1,C2,...,C) g ) is the loss function for cutting out clusters with a total number of g from the original undirected graph G, where the total number of g is equal to the number of sensors required to be deployed NS, and CT is the set removed from the cut graph; (34) Since some nodes located in different branches were grouped into one class after the first stage of clustering, the second stage of re-clustering was carried out based on the sewage pipe network topology to separate such nodes. Specifically, each class was traversed, and if any of the nodes were located in different branches, they were divided into two classes, which further increased the number of classes in the first stage of clustering. The number of clusters became NC classes, where NC>NS, to ensure that the nodes in each class have a low joint entropy when detecting abnormal events.

3. The method for optimizing the layout of inflow and infiltration detection sensors in a sewage pipe network based on information entropy, as described in claim 1, is characterized in that... The specific process of step (4) is as follows: (41) After two-stage clustering, the number of clusters NC is usually greater than the number of sensors NS. The clusters are sorted by the ADR values ​​of all nodes in each cluster, so that the NS cluster can be selected from the total NC clusters. For each node i, it represents the probability DR of all abnormal events detected if the sensor is placed at node i. i : ADR for each cluster k k The value is; Among them, Ω k S(Ω) is the set of nodes in the k-th class. k ) represents the total number of nodes in the k-th class; (42) Sort the classes in descending order of average detection rate value, and select one node from each of the top few NS classes with high average detection rate values ​​to place the sensor; (43) Under the given NS class conditions, enumerate the joint entropy of each candidate sensor placement scheme for a single sensor in each class, and take the combination with the largest multivariate joint entropy as the final optimal placement scheme.

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