Sewage pipe network inflow and infiltration detection sensor optimization arrangement method based on information entropy

Abstract

The invention relates to the technical field of sewage pipe network optimization, and provides an information entropy-based sewage pipe network inflow and seepage detection sensor optimization arrangement method, which comprises the following steps of: performing random abnormal event simulation of which the total number is M, and obtaining an information content vector of each node of a sewage pipe network; a joint entropy matrix EM of the whole sewage pipe network is constructed by calculating the joint entropy between every two nodes; performing first-stage clustering on the basis of the joint entropy, clustering the number of nodes into an NS class according to the number of sensors needing to be arranged, and performing second-stage re-clustering on the basis of a sewage pipe network topological structure to cluster the number of the nodes into an NC class; nC class nodes are ranked according to ADR values, a node is selected from each of NS classes with the highest ADR value to arrange a sensor, and a combination with the maximum multivariate joint entropy serves as a final optimal arrangement scheme. The application method of the information entropy in sewage pipe network abnormal event detection is provided for the first time, and a new thought is provided for optimized arrangement of sewage pipe network sensors.

Description

Technical Field

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

[0002] Urban sewage pipe networks play a vital role in urban sewage transportation and are essential for public health and environmental protection. Sewer pipes are widely present in urban areas and are usually buried underground. However, due to aging and lack of timely maintenance, many pipes in sewage pipe networks suffer from severe structural deterioration, such as pipe corrosion or damage. As a result, infiltration has become a common problem in many sewage pipe networks. Infiltration refers to the entry of water from the surrounding environment into the system through manholes, poor pipe joints, and pipe cracks. Infiltration can pose a considerable threat to urban water security, including reducing sewage concentration, thereby reducing the efficiency of sewage treatment plants, and causing sewer overflows, untreated wastewater discharge into the environment, and also increasing the risk of basement flooding and surface flooding during heavy rains. Therefore, detecting large infiltration events in sewage pipe networks is essential to ensure the protection of urban water environment.

[0003] The damaged points of pipes that cause inflow and infiltration can be directly identified by physical methods, such as smoke testing, dye testing, CCTV detection, etc. Although these physical methods can simply and effectively locate the location where inflow and infiltration occur in a specific pipe, they are usually inefficient and costly, and difficult to apply to the entire pipe network. In recent years, with the rapid development of the Internet of Things, online sensors are increasingly used for inflow and infiltration detection in sewage pipe networks. These sensors are usually used to monitor hydraulic variables with high temporal resolution, such as water level or flow. The collected data can be processed using advanced analytical techniques such as machine learning algorithms to identify the occurrence and existence of inflow and infiltration in sewage pipe networks.

[0004] However, due to the high cost of purchasing and maintaining sensors, it is impractical to place a sensor at every inspection well in the sewage network. Therefore, optimizing the placement of a limited number of sensors with maximum monitoring efficiency is an important research problem. Many heuristic optimization methods have been developed for placing sensors in sewage networks, such as genetic algorithms, greedy algorithms, evolutionary algorithms, multi-objective genetic algorithms, etc. These heuristic optimization methods may determine the best sensor placement scheme, but their solutions are usually different in different optimization runs, and the quality of the solution may be heavily dependent on the algorithm parameterization, making it difficult to widely apply in actual engineering. In addition, the optimization algorithm usually requires a lot of computation, which may lead to a serious reduction in computational efficiency for large-scale networks. Summary of the invention

[0005] The present invention provides a method for optimizing the layout of inflow and infiltration detection sensors in a sewage pipe network based on information entropy. First, by simulating random abnormal events, the information content that can be provided by each node of the pipe network is quantified, and then the information entropy is calculated, and the first stage clustering is performed based on this. Based on the results of the first stage clustering, the second stage clustering is performed based on the topological structure characteristics of the pipe network, aiming to further improve the effectiveness of the sensor layout scheme. Finally, a node is selected from each category to arrange the sensor, and the combination with the largest information entropy is used as the final optimal layout scheme. Information entropy is used as an evaluation indicator of the sensor layout scheme and a new two-stage clustering method is developed to identify the optimal layout scheme, thereby obtaining an efficient sensor optimization layout method.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention provides a method for optimizing the arrangement of inflow and infiltration detection sensors in a sewage pipe network based on information entropy. The method for optimizing the arrangement includes:

[0008] (1) Simulate a total of M random abnormal events to obtain the information content vector of each node in the sewage 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) The first stage clustering is performed based on joint entropy, and the number of nodes is clustered into NS categories according to the number of sensors to be deployed. The second stage clustering is performed based on the topological structure of the sewage pipe network, and the number of nodes is clustered into NC categories;

[0011] (4) Sort the NC class nodes according to the ADR value (average detection rate), select a node from each of the top NS classes with the highest ADR value (average detection rate) to arrange the sensors, and take the combination with the largest multivariate joint entropy as the final optimal arrangement plan.

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

[0013] (11) Assume that there are N nodes in the sewage network, the total number of abnormal events (such as inflow and infiltration events) is M, and each node i in the network is considered as a potential location for sensor placement;

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

[0015]

[0016] Determine whether an abnormal event m is detected by node i by the change of the considered flow, water depth or water quality parameter exceeding 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, the information matrix IM of the entire sewage network is calculated:

[0021]

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

[0023]

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

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

[0026] p(R(NI i ,s),R(NI j ,k)) is R(NI i ,s) and R(NI j ,k) probability of simultaneous occurrence;

[0027] (22) According to the joint entropy between every two nodes, the joint entropy matrix EM is constructed.

[0028]

[0029] Here, EM is a diagonal matrix containing the joint entropy between every 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 clustering, and transform the information content vector NI of each node i into i is regarded as a point in space; then the similarity w between node i and node j is estimated ij :

[0032]

[0033] (32) Construct the 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 minimization 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] Among them, L(C1,C2,...,C g ) is the loss function of cutting out a total number of g clusters from the original undirected graph G, where the total number g is equal to the number of sensors to be arranged NS, (i.e., the number of clusters is NS), and CT is the set removed from the cutting graph;

[0038] (34) After the first stage of clustering, some nodes located in different branches are classified into one category. Then, based on the topological structure of the sewage pipe network, the second stage of clustering is performed to separate such nodes. Specifically, each category is traversed. If there are nodes located in different branches, they are divided into two categories, which further increases the number of clusters in the first stage. The number of clusters becomes NC categories, where NC>NS, ensuring that the nodes in each category have a lower 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 values ​​(average detection rate) of all nodes in each cluster, so that NS clusters 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 values ​​are;

[0043]

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

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

[0046] (43) Under the condition of the determined NS class, the joint entropy of each candidate sensor placement scheme for a single sensor in each class is enumerated, and the combination with the largest multivariate joint entropy is taken as the final optimal placement scheme. The sensor placement strategy with the largest joint entropy represents the comprehensive information of these sensors. The multivariate joint entropy can be expanded by formula (2-2).

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

[0048] (1) The present invention abandons the use of heuristic search methods and proposes a two-stage clustering method conditioned on information entropy to identify the optimal sensor placement scheme deterministically and efficiently, providing an optimal solution for a given sensor placement problem in an effective manner, facilitating the decision-making process compared to the many different available solutions provided by heuristic algorithms.

[0049] (2) The present invention uses information entropy as an indicator to design an optimal layout plan for sewage pipe network sensors. Information entropy, as an indicator to measure information uncertainty, has been reflected in the design of hydrological monitoring systems, but has not yet been applied to the optimal layout of sewage pipe network sensors for abnormal event detection. The present invention proposes for the first time an application method of information entropy in abnormal event detection in sewage pipe networks, providing a new idea for the optimal layout of sewage pipe network sensors.

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

[0051] (4) The method proposed in the present invention greatly improves the efficiency of calculation. The optimization algorithm needs to call the model repeatedly during the iteration process, which reduces the calculation efficiency for large-scale pipe networks. The method of the present invention greatly reduces the amount of calculation through two-stage clustering, which is an efficient optimization layout method.

[0052] (5) The sensor optimization layout method based on information entropy clustering proposed in the present 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 networks. It is an important supplement to the research field of urban sewage pipe network management and provides important technical support for the management of sewage pipe network systems. It has great promotion and practical engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a schematic diagram of the overall process of the present invention.

[0054] Figure 2 It is a topological relationship diagram of the sewage pipe network system of the embodiment FUSN and USN1.

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

[0056] Figure 4 It is the correlation diagram between joint entropy and detection rate.

[0057] Figure 5 It 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 It is a comparison diagram of the specific sensor arrangement schemes of the method of the present invention and the GA optimization method in Example USN1.

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

[0060] Figure 8 It is a comparison diagram of the specific arrangement of the method of the present invention and the engineering solution in Example FUSN.

[0061] Fig. 9 It is a comparison of the computational overhead between the method of the present invention and the optimization method. DETAILED DESCRIPTION

[0062] The specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings. It should be pointed out that the embodiments are only specific explanations of the invention and should not be regarded as limitations of the invention. The purpose of the embodiments is to enable those skilled in the art to better understand and reproduce the technical solutions of the present invention. The protection scope of the present invention shall still be based on the scope defined by the claims.

[0063] The present invention provides a method for optimizing the arrangement of inflow and infiltration detection sensors in a sewage pipe network based on information entropy. The method for optimizing the arrangement includes:

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

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

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

[0067]

[0068] Determine whether an abnormal event m is detected by node i by the change of the considered flow, water depth or water quality parameter exceeding 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:

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

[0073]

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

[0075]

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

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

[0078] p(R(NI i ,s),R(NI j ,k)) is R(NIi ,s) and R(NI j ,k) probability of simultaneous occurrence;

[0079] S22, construct a 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 every pair of nodes in the sewage network.

[0082] S3, based on the joint entropy, the first stage clustering is performed to cluster the number of nodes into NS categories according to the number of sensors to be deployed, and the second stage clustering is performed based on the sewage network topology to cluster the number of nodes into NC categories. The specific process is as follows:

[0083] S31, use the spectral clustering method to perform the first stage clustering, and transform the information content vector NI of each node i i is regarded as a point in space; then the similarity w between node i and node j is estimated 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, and then a minimization 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] Among them, L(C1,C2,...,C g ) is the loss function for cutting out a total number of g clusters from the original undirected graph G, where the total number g is equal to the number of sensors NS to be arranged, and CT is the set removed from the cutting graph;

[0090] S34,After the first stage of clustering, some nodes located in different branches are classified into one category, and then the second stage of re-clustering is performed based on the topological structure of the sewage network to separate such nodes. Specifically, each category is traversed, and if there are nodes located in different branches, they are divided into two categories, which further increases the number of clustering categories in the first stage, and the number of clusters becomes NC categories, where NC>NS, ensuring that the nodes in each class have a lower joint entropy when detecting abnormal events.

[0091] S4, sort the NC class nodes according to the ADR value (average detection rate), select a node from each of the top NS classes with the highest ADR value (average detection rate) to arrange the sensor, and take the combination with the largest multivariate joint entropy as the final optimal arrangement plan. 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, and the clusters are sorted by the ADR values ​​(average detection rate) of all nodes in each cluster, so that NS clusters 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 :

[0093]

[0094] ADR for each cluster k k The values ​​are;

[0095]

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

[0097] S42, sort the classes in descending order according to the average detection rate values, and select a node for each of the first few NS classes with high average detection rate values ​​to place the sensor;

[0098] S43, under the condition of the determined NS class, enumerate the joint entropy of each candidate sensor placement scheme of 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 joint entropy represents the comprehensive information of these sensors. The multivariate joint entropy can be expanded by formula (2-2).

[0099] Example

[0100] The practical application of the method of the present invention in engineering is illustrated by using examples that simulate actual practice. The examples do not represent real existing examples, but the description of the examples indicates that the present invention can be used in engineering practice and can achieve technical effects.

[0101] Take the sewage pipe network of a certain city as an example. The service area of ​​the sewage pipe network is about 15 square kilometers, the total length of the pipe is about 60 kilometers, the pipe diameter ranges from 0.3 meters to 1.5 meters, and the total daily flow of the system is about 43,400 cubic meters / day. The city is a city with many rainy days and many rivers, so inflow and infiltration is an important problem in the sewage pipe network system. The local water department plans to arrange 20 flow meters in the sewage pipe network to detect large inflow and infiltration events and formulate a pipeline maintenance plan accordingly.

[0102] Firstly, the hydraulic model of the sewage network was established using SWMM software. The model consists of 819 pipes, 760 inspection wells, 60 overflow nodes and an outlet located in the east of the study area ( Figure 2 ). The model has been calibrated by the local water department under drought conditions. In order to better explain the application of the proposed method, a relatively independent region ( Figure 2 The small sewage pipe network is illustrated by the shaded area in the figure. This small sewage pipe network is called embodiment USN1, and the complete sewage pipe network is called embodiment FUSN.

[0103] A total of M inflow and infiltration events (abnormal events) are generated, with M being 1000 and 3000 for USN1 and FUSN, respectively. For each event, a single pipe of the sewer network is injected with an inflow flow rate of 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 Q value remains constant throughout the simulation time (24 hours in this case). The alarm threshold for inflow and infiltration events is set to 15% above the daily mean sewage flow rate.

[0104] In order to evaluate the effectiveness of sensor placement, two quantitative evaluation indicators are used: detection rate (DR) and distribution uniformity (DU). The DR defined in formula (4-1) represents the probability that a single sensor responds to a total of M abnormal events (i.e., inflow and infiltration events). For a system with multiple sensors, DR represents the proportion of events detected by any sensor in the system to the total M events. The larger the DR, the more abnormal events the sensor layout can detect. At the same time, the uniformity of sensor distribution is also important. This is because a system with uniformly distributed sensors means that the length of the pipeline monitored by each sensor is close. For example Figure 3 As shown, pipes of different colors are monitored by sensors S1, S2, and S3, respectively. If the length of the pipes monitored by each sensor individually is close, then after an abnormal event occurs, the length of the pipes that need to be checked is close, and the overall time efficiency is high. In the present invention, DU can be approximated by the coefficient of variation of the length of the pipes monitored by all sensors individually. In order to better present the results, DU is defined as the inverse value of the coefficient of variation. Therefore, the larger the DU, the higher the overall spatial uniformity of the sensor placement.

[0105] This paper proposes to use joint entropy to design sensor layout schemes. First, it is necessary to prove the effectiveness of joint entropy. Because the larger the joint entropy, the more information about abnormal events the sensor can provide, which means a higher coverage of abnormal events. For USN1 and FUSN, several random sensor layout schemes are generated to discuss the correlation between joint entropy and detection rate, and the Pearson correlation coefficient is used to quantify the correlation, such as Figure 4 It can be seen that the joint entropy has a strong correlation with the detection rate, and the Pearson coefficient r is above 0.95, indicating that the larger the joint entropy, the higher the detection rate of abnormal events. The joint entropy is effective as a design indicator for sensor layout schemes.

[0106] In order to illustrate the advantages of the method proposed in the present invention, the present method is compared with the GA algorithm of single-objective optimization joint entropy. First, for the USN1 case, considering the arrangement of 7 sensors, the detection rate and spatial distribution uniformity of the method proposed in the present invention and the GA optimization method are compared. Figure 5 As shown. It can be seen that the detection rate of the method of the present invention is not lower than that of the GA method, which once again proves the effectiveness of joint entropy as a design indicator. In addition, the spatial uniformity of the method of the present invention is better than that of the GA method. This is because the method of the present invention considers two-step clustering, which avoids the possibility of poor spatial uniformity due to the arrangement of sensors too close. At the same time, it can be seen that the uniformity results of the GA method in each optimization round are very different. Then the specific arrangement schemes of the two methods are compared, as shown in Figure 6 As shown. It can be seen that in different optimization rounds, the layout schemes obtained by the GA optimization method are very different, which shows that the optimization method has multiple solutions and is difficult to apply in actual engineering. The method proposed in the present invention can traverse all potential solutions because of its small search space, so it obtains a definite sensor optimization layout scheme, which is more valuable for engineering application.

[0107] Then the same comparison was carried out in the FUSN pipe network. In addition to the GA optimization method, the engineering plan was also compared, that is, the plan that the local water department planned to arrange according to experience, with a total of 20 sensors deployed. Figure 7 A comparison of the detection rates of the three methods is given, considering three different Qs, namely 1%, 3% and 5% of the total flow rate. It can be seen that the detection rate of the method proposed in the present invention is significantly better than that of the GA optimization method and the engineering layout scheme. Figure 8 Comparing the specific layout of the method of the present invention with that of the engineering solution, it can be seen that the engineering solution generally places sensors at nodes that are traditionally considered important, such as confluence nodes, trunk pipe end nodes, etc. Figure 7 The detection rate results show that such an experience-based layout may lead to a decrease in the detection rate of abnormal events, proving the necessity of optimizing the layout.

[0108] The following discussion of the efficiency of the calculation is conducted on a computer equipped with an AMD Ryzen 7 5800H CPU @ 3.20GHz. Since the calculation time is related to the size of the network and the precision setting, converting the calculation time into the number of simulations required can make a more effective comparison. For USN1 and FUSN, the method proposed in this paper first requires 1000 and 3000 simulations. In addition, the time for clustering and enumeration in the scheme and calculating the union is equivalent to 800 model simulations and 6.5x10 6 The number of samples and iterations in the optimization algorithm are both 200. For each sample, each iteration needs to regenerate random events and call the model for simulation, a total of 4x10 7 and 1.2x10 8 Model simulation. Fig. 9 A comparison of the computational costs of the two optimization methods is given, that is, the computational cost of the method proposed in this invention is only 0.0045% and 5.4% of the computational cost of the optimization method for USN1 and FUSN, respectively. It is also worth pointing out that the method proposed in this article can greatly improve the computational efficiency through parallelization because there is no conflict between the computational tasks, while the calculation of each iteration of the optimization method may depend on the result of the previous iteration, and it is difficult to improve the computational efficiency through parallelization.

[0109] It can be seen that, through the sewage pipe network sensor optimization layout method based on information entropy clustering proposed by the present invention, the information content that can be provided by each node of the pipe network is quantified by simulating random abnormal events, and 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 structure, and then a node is selected from each cluster category to arrange the sensor, and the combination with the largest joint entropy is used as the final optimal layout plan. The method proposed by the present invention has good performance in both detection rate and spatial uniformity, overcomes the uncertainty of the solution of the optimization method, provides important technical support for solving the problem of abnormal event detection in sewage pipe networks, and has practical engineering application value.

[0110] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

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

Claims

1. A method for optimizing the arrangement of inflow and infiltration detection sensors in a sewage pipe network based on information entropy, characterized in that: Optimized layout methods include: (1) Simulate a total of M random abnormal events to obtain the information content vector of each node in the sewage network; (2) Construct the joint entropy matrix EM of the entire sewage network by calculating the joint entropy between every two nodes; (3) The first stage clustering is performed based on joint entropy, and the number of nodes is clustered into NS categories according to the number of sensors to be deployed. The second stage clustering is performed based on the topological structure of the sewage pipe network, and the number of nodes is clustered into NC categories; (4) Sort the NC class nodes according to the ADR value, select a node from each of the top NS classes with high ADR values ​​to arrange the sensors, and take the combination with the largest multivariate joint entropy as the final optimal arrangement solution.

2. The method for optimizing the arrangement of inflow and infiltration detection sensors for sewage pipe networks based on information entropy according to claim 1 is characterized in that: 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 that there are N nodes in the sewage network, the total number of abnormal events is M, and each node i in the network is considered as a potential location for sensor placement; (12) For node i, use formula (1-1) to calculate its information content based on abnormal event m Determine whether an abnormal event m is detected by node i by the change of the considered flow, water depth or water quality parameter exceeding 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 ; 3. The method for optimizing the arrangement of inflow and infiltration detection sensors for sewage pipe networks based on information entropy according to claim 1 is characterized in that: The specific process of step (2) is as follows: (21) After obtaining the information content vector of each node i, the information matrix IM of the entire sewage network is calculated: The information matrix IM is used to calculate the joint entropy H(NI i ,NI j ): Among them, R(NI i ,s) and R(NI j ,k) are NI i and NI j Different records in ; S and K are NI i and NI j The number of different records in , given the information content S and K, is 2; p(R(NI i ,s),R(NI j ,k)) is R(NI i ,s) and R(NI j ,k) probability of simultaneous occurrence; (22) According to the joint entropy between every two nodes, the joint entropy matrix EM is constructed. Here, EM is a diagonal matrix containing the joint entropy between every pair of nodes in the sewage network.

4. The method for optimizing the arrangement of inflow and infiltration detection sensors for sewage pipe networks based on information entropy according to 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 clustering, and transform the information content vector NI of each node i into i is regarded as a point in space; then the similarity w between node i and node j is estimated ij : (32) Construct the 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 minimization loss function as the result of cutting the undirected graph G into different classes C, as shown in formula (3-3); min L(C1,C2,...,C g )=min∑ (i,j)∈CT In ij (3-3) Among them, L(C1,C2,...,C g ) is the loss function for cutting out a total number of g clusters from the original undirected graph G, where the total number g is equal to the number of sensors NS to be arranged, and CT is the set removed by the cutting graph; (34) After the first stage of clustering, some nodes located in different branches are classified into one category. Then, based on the topological structure of the sewage pipe network, the second stage of clustering is performed to separate such nodes. Specifically, each category is traversed. If there are nodes located in different branches, they are divided into two categories, which further increases the number of clusters in the first stage. The number of clusters becomes NC categories, where NC>NS, ensuring that the nodes in each category have a lower joint entropy when detecting abnormal events.

5. The method for optimizing the arrangement of inflow and infiltration detection sensors for sewage pipe networks based on information entropy according to 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 NS clusters 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 values ​​are; Among them, Ω k is the set of nodes in the kth class, S(Ω k ) is the total number of nodes in the kth class; (42) Sort the classes in descending order according to the average detection rate values, and select a node from each of the first few NS classes with high average detection rate values ​​to place the sensor; (43) Under the condition of a certain NS class, the joint entropy of each candidate sensor placement scheme for a single sensor in each class is enumerated, and the combination with the largest multivariate joint entropy is taken as the final optimal placement scheme.

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