A method for calculating a key node of a sewer network

Abstract

The application relates to a kind of calculation methods of drainage pipe network key nodes, belonging to the field of drainage pipe network calculation. By obtaining the drainage pipe network graph to be analyzed and processed, the drainage pipe network graph is converted into an undirected network graph, and the nodes are calculated using the theory of network graph, the node betweenness centrality of the undirected network graph and the degree of the nodes of the undirected network graph are calculated, then different threshold values are determined according to the amount of traceable capital investment to perform a segmentation operation, whether using weak threshold segmentation or strong threshold segmentation, finally the network graph with labeled key nodes can be obtained, and then the drainage pipe network graph with labeled key nodes can be obtained. The calculation method disclosed in the application is not limited by pipe network data and does not depend on the working experience of pipe network calculation personnel. In the case of limited budget, the key nodes of the drainage pipe network can be efficiently and reasonably calculated, thereby improving the efficiency and accuracy of pipe network design, reducing the cost of pipe network design, and laying a reliable foundation for pipe network design and pipe network tracing.

Description

Technical Field

[0001] This invention belongs to the field of drainage network calculation, and specifically relates to a calculation method for key nodes of a drainage network. Background Technology

[0002] Urban drainage pipe network systems generally include discharge sources, drainage pipe networks, storage tanks, booster pumping stations, sewage treatment plants, and the final receiving water body. As a crucial component, drainage pipe networks mainly include combined sewer systems (common in older urban areas) and separate sewer systems (common in newly built urban areas). Separate sewer systems primarily consist of sewage pipe networks and stormwater pipe networks. In principle, combined sewer systems can handle the mixed discharge of sewage and stormwater, sewage pipe networks handle only domestic sewage or industrial wastewater, and stormwater pipe networks handle only rainfall or snowmelt discharge. In actual drainage pipe network tracing scenarios, incidents of illegal discharge, leakage, indiscriminate discharge, and scattered discharge into these different types of pipe networks are frequently observed.

[0003] In practice, tracing the source of pollution in drainage pipe networks often requires the deployment of sensors such as water quality, flow rate, and liquid level at key nodes of the network. The collected data is then analyzed and processed, and combined with known sewage discharge point information to infer the location of the pollution source.

[0004] If sensors such as those for water quality, flow rate, and liquid level are installed in the inspection wells corresponding to all nodes of the drainage network and monitored online, the operational status of the drainage network can be comprehensively grasped. However, it is obvious that too many nodes will lead to excessively high monitoring costs and a huge workload for maintenance. How to rationally calculate as few nodes as possible as possible as the critical nodes under limited funding, and how to use the data collected by sensors deployed at the critical nodes to ultimately reflect the operational status of the drainage network as comprehensively as possible, is a topic worthy of continued in-depth research.

[0005] Existing patents for tracing drainage pipe networks often select inspection wells where secondary and branch pipes merge into the main and trunk pipes as key nodes. While this node selection method is reasonable, its implementation relies heavily on comprehensive pipe survey data. In practice, even with such data, tracing often requires experienced technicians who can deduce catchment areas and network hierarchy based on limited network data and design experience. Given the complexity of actual drainage networks and their potential for multiple renovations, even meticulous sorting of secondary, branch, main, and trunk pipes by technicians often requires significant time and effort. Furthermore, if there is no pipe survey data or the data has become significantly less accurate over time, re-surveying or supplementing the network becomes even more costly, time-consuming, and labor-intensive. Summary of the Invention

[0006] In view of the deficiencies in the existing technology, the purpose of this invention is to provide a method for calculating key nodes of drainage pipe networks. Even when complete basic data such as pipe diameter, slope, material, and flow direction of the drainage pipe network are not available, the key nodes of the drainage pipe network can be calculated quickly and efficiently by converting the drainage pipe network diagram into an undirected network diagram and using the calculation method of the network diagram.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is: a calculation method for key nodes of a drainage pipe network, the method comprising the following steps:

[0008] S1. Obtain the drainage network diagram to be analyzed and processed;

[0009] S2. Convert the drainage network diagram to be analyzed into an undirected network diagram;

[0010] S3. Calculate the betweenness centrality of the nodes in the undirected network graph and the degree of the nodes in the undirected network graph;

[0011] S4. Make a judgment based on the amount of funds invested in traceability;

[0012] S5. If it is determined that the funding for traceability is not restricted, use weak threshold segmentation to filter the nodes to be retained.

[0013] S6. If it is determined that the funding for traceability is limited, then use strong threshold segmentation to filter the nodes to be retained.

[0014] S7. Obtain the network graph with labeled key nodes;

[0015] S8. The network diagram with marked key nodes is transformed to obtain the pipeline diagram with marked key nodes.

[0016] Furthermore, the drainage network diagram to be analyzed in step S1 includes any type of drainage network diagram, ranging from a simplified drainage network diagram to a complete drainage network diagram.

[0017] Furthermore, the undirected network graph described in step S2 has the same spatial topology as the drainage network graph before the conversion.

[0018] Furthermore, in step S2, the numbers in the undirected network graph represent the node numbers, which include the numbers of inspection wells and relay pump stations. The non-numeric numbers represent pipeline terminals, which include sewage treatment plants.

[0019] Furthermore, in step S3, the betweenness centrality of the nodes in the undirected network graph and the degree of the nodes in the undirected network graph are calculated using the network graph method.

[0020] Furthermore, in step S7, the key nodes are those with larger betweenness centrality values, and process nodes with high betweenness centrality are excluded by using the degree of the nodes.

[0021] Furthermore, the segmentation mentioned in steps S5 and S6 refers to logical comparison operations, including "greater than" or "greater than or equal to" logical operations.

[0022] Furthermore, the weak threshold mentioned in step S5 is the first statistical parameter in the node betweenness centrality of the undirected network graph, and the first statistical parameter includes the mean, median and 30th percentile.

[0023] Furthermore, the strong threshold mentioned in step S6 is the second statistical parameter in the node betweenness centrality of the undirected network graph, and the second statistical parameter includes the upper quartile and the 80th percentile.

[0024] The beneficial technical effects of this invention are as follows: By acquiring the drainage network diagram to be analyzed and processing, converting it into an undirected network graph, and then using network graph theory to calculate the nodes, the betweenness centrality and degree of the nodes in the undirected network graph are calculated. Then, different thresholds are determined based on the amount of traceability funding invested to perform segmentation operations. Regardless of whether weak or strong threshold segmentation is used, a network graph with labeled key nodes can be obtained, thus obtaining a drainage network diagram with labeled key nodes. The calculation method disclosed in this invention is not limited by network data or relies on the work experience of network calculation personnel. It can efficiently and reasonably calculate the key nodes of the drainage network even with limited budget, thereby improving the efficiency and accuracy of network design, reducing network design costs, and laying a reliable foundation for network design and traceability. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating a calculation method for key nodes in a drainage network according to an embodiment of the present invention;

[0026] Figure 2 This is an undirected network diagram corresponding to the transformed drainage pipe network diagram of a certain project shown in an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the critical nodes calculated using the mean value greater than the betweenness centrality and after removing process nodes, as shown in an embodiment of the present invention.

[0028] Figure 4 This is a schematic diagram of the critical nodes calculated using the upper quartile (greater than betweenness centrality) and after removing process nodes, as shown in an embodiment of the present invention.

[0029] Figure 5This is a schematic diagram of the critical nodes calculated using the upper quartiles with a degree greater than or equal to betweenness centrality and after removing process nodes, as shown in an embodiment of the present invention. Detailed Implementation

[0030] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0031] Example 1

[0032] Before explaining the content of this invention, it is necessary to first explain the basic theory of network graphs.

[0033] Vertex (Node): A point in a network graph that represents an abstraction of something or an object (also known as a node or endpoint).

[0034] Edge: A line connecting points in a network diagram, representing the relationship between things.

[0035] Undirected Graph and Directed Graph: An undirected graph consists of vertices and edges; adding pointing arrows to the edges of an undirected graph creates a directed graph.

[0036] Weight: An additional numerical information on the edges of a graph that reflects certain characteristics of the edges.

[0037] Number of nodes: The number of nodes.

[0038] Edges: The number of edges.

[0039] Degree: In an undirected graph, the number of edges connected to vertex V is called the degree of vertex V; in a directed graph, the number of edges with vertex V as the tail is called the out-degree of vertex V, and the number of edges with vertex V as the head is called the in-degree of vertex V. Therefore, the degree of vertex V = out-degree + in-degree.

[0040] Average Network Distance: The average distance between any two nodes, reflecting the degree of separation between nodes in the network. The smaller the value, the more closely the nodes in the network are connected.

[0041] Closeness Centrality of a Node: The closeness centrality of a node is the reciprocal of the average distance from that node to all other nodes.

[0042] Betweenness centrality: For a given node, the betweenness centrality reflects the number of times that node is found in the shortest paths between all vertices of a network graph. It is sometimes translated as the betweenness centrality of a node.

[0043] Of the metrics mentioned above for measuring the importance of nodes in a network graph, degree only considers the number of neighboring nodes, but ignores the importance of those neighboring nodes. Average path length can be applied to the division of catchment areas in drainage networks. Proximity centrality reflects the closeness of a node to other nodes and is classically used in the site selection problem of shopping malls. Compared to degree, which reflects local characteristics of the network graph, betweenness centrality of a node provides a better view of the global network graph.

[0044] For a node Vi, its betweenness centrality is defined as:

[0045]

[0046] Pst represents the number of shortest paths from node Vs to node Vt;

[0047] Pst(Vi) represents the number of paths that pass through node Vi.

[0048] Since betweenness centrality requires summing over all possible node pairs, its value increases with the size of the graph. Therefore, normalization is needed to make the betweenness centrality of different graphs comparable.

[0049] Applying the betweenness centrality of nodes in network graph theory to drainage network graphs, we can conclude that if many paths between nodes in a network graph pass through a certain node, then that node occupies an important position in the drainage network. The importance of a node is positively correlated with the number of shortest paths passing through that node.

[0050] like Figure 1 As shown in the figure, this embodiment of the invention provides a method for calculating key nodes of a drainage pipe network, the method comprising the following steps:

[0051] S1. Obtain the drainage network diagram to be analyzed. The drainage network diagram to be analyzed can be any type, ranging from a simplified diagram to a complete diagram. There is no limitation on the completeness (network labeling information) of the drainage network diagram, which can be obtained from the project construction party.

[0052] In this embodiment, the project initially lacked complete drainage network data and was located in an old urban area. The network-related data were managed by different departments, so only some old network data were collected. Basic pipeline survey information was lacking, and only the layout plan of the inspection wells and the front-end pumping station of the sewage treatment plant was available. The owner required that the drainage network of the urban area be equipped with sewage monitoring and source tracing functions.

[0053] S2. Convert the drainage network diagram to be analyzed into an undirected network diagram. The layout of the undirected network diagram may not be the same as the network diagram before the conversion, but the spatial topology of the undirected network diagram is the same as that of the network diagram before the conversion.

[0054] In step S2, converting the drainage network diagram to be analyzed into an undirected network diagram requires AutoCAD, ArcGIS software, and software to extract node elements and line segment elements from vector data and generate an undirected network diagram.

[0055] like Figure 2 As shown, the converted undirected network graph in this embodiment includes 35 nodes and 34 edges. The numbers represent the numbers of each inspection well, and node P corresponds to the end point of the pipeline network. In reality, node P can represent a terminal pumping station or a sewage treatment plant.

[0056] S3. Calculate the betweenness centrality and degree of the nodes in the undirected network graph using the network graph method.

[0057] Following the previous example, the results of the node betweenness centrality calculation for this undirected network graph, sorted from smallest to largest, are shown in Table 1.

[0058] Table 1. Ranking of Node Betweenness Centrality in Undirected Network Graphs

[0059] C 0 0 0 0 0 0 0 0 0 0 0 0 33 33 33 33 33 33 V 33 1 28 11 10 27 13 6 15 14 12 8 5 4 7 9 26 C 33 64 64 65 93 93 95 124 124 145 149 173 240 243 253 264 413

[0060] The odd-numbered rows "V" represent nodes, and the even-numbered rows "C" represent the calculated betweenness centrality of the nodes. For ease of explanation, the betweenness centrality mentioned below refers to the betweenness centrality of the nodes.

[0061] Based on the basic concept of betweenness centrality, the key nodes should first be selected from those nodes with larger betweenness centrality values ​​in Table 1, that is, those nodes that are ranked later.

[0062] Observe nodes 5 and 7 in the betweenness centrality ranking table. Both have relatively high betweenness centrality values, 240 and 253 respectively. Although these two nodes are ranked low in the betweenness centrality ranking table and should rightfully be selected as key nodes, they correspond to process nodes in the drainage network. In actual network tracing, following the assumption of water quality balance or flow balance, process nodes are often ignored in the first round of tracing screening.

[0063] Therefore, in the calculation of key nodes, in addition to sorting the betweenness centrality and selecting the nodes with larger values, the degree of the nodes also needs to be considered. The degree calculation results of the nodes in this undirected network graph are shown in Table 2.

[0064] Table 2 Degrees of nodes in an undirected network

[0065] D 2 1 2 3 2 3 2 1 3 3 2 3 3 3 2 3 1 1 1 2 V 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 D 1 1 2 2 2 1 4 2 2 2 1 1 1 2 1

[0066] In this diagram, the odd-numbered rows "V" represent nodes, and the even-numbered rows "D" represent the calculated degree of each node. The degree of a node can be used to eliminate process nodes with high betweenness centrality.

[0067] S4. Make a judgment based on the amount of funds invested in traceability.

[0068] While betweenness centrality and node degree can efficiently calculate critical nodes in a network graph, the question of how many critical nodes to retain becomes crucial and must be considered within the project budget. When the budget is ample, more nodes can be selected; clearly, we tend to retain more critical nodes because this translates to more monitoring data and less manual investigation. Conversely, when the budget is limited, we tend to retain fewer critical nodes.

[0069] S5. If it is determined that the traceability funding is not restricted, then it is "many", and weak threshold segmentation is used to filter the retained nodes.

[0070] The weak threshold can be selected from the first statistical parameter in Table 1, which includes the mean, median, and 30th percentile. For example, the mean of the betweenness centrality of this undirected network graph, rounded to two decimal places, is 80.94.

[0071] The partitioning operation refers to a logical comparison operation, which can choose between "greater than" or "greater than or equal to" logical operations. For example... Figure 3 As shown, in one alternative implementation, key nodes are calculated by taking a value greater than the mean betweenness centrality of the undirected network graph and combining it with the process nodes to be removed.

[0072] S6. If it is determined that the funding for traceability is limited, i.e. "insufficient", then a strong threshold segmentation is used to select the nodes to be retained.

[0073] The strong threshold can be selected from the second statistical parameters in Table 1, which include the upper quartile and the 80th percentile. For example, the upper quartile of the betweenness centrality of this undirected network graph is calculated to be 124.

[0074] Similarly, the partitioning operation refers to a logical comparison operation, which can choose either "greater than" or "greater than or equal to" logical operations. For example... Figure 4 As shown, in one alternative implementation, key nodes are calculated by taking the upper quartile of the betweenness centrality of the undirected network graph as a factor and combining it with the process nodes to be removed.

[0075] like Figure 5 As shown, note that if the selected strong threshold is the upper quartile, but the segmentation operation uses a "greater than or equal to" logical comparison, then... Figure 1 Nodes "6" and "15" will be preserved. Compared to... Figure 3 , Figure 5 Node 13 is missing from the retained key nodes. This is reasonable because the upper quartile of the betweenness centrality of the network graph, 124, is larger than its mean of 80.94, and the number of key nodes calculated using the upper quartile as the splitting threshold would be less.

[0076] S7. Obtain the network graph with labeled key nodes.

[0077] The key nodes actually determined in this project and Figure 3 The results shown are consistent.

[0078] S8. Transform the network diagram with marked key nodes to obtain the pipeline diagram with marked key nodes. Since the network diagram and the pipeline diagram have the same topology, the calculated key nodes will not be missed when converting the network diagram back to the pipeline diagram.

[0079] As can be seen from the above embodiments, the method for calculating key nodes in drainage pipe networks disclosed in this invention can be applied to drainage pipe networks lacking basic data such as pipe survey data. With limited funding, the key nodes of such drainage pipe networks can be calculated quickly and efficiently by utilizing the betweenness centrality of nodes in combination with their degree. At the calculated key nodes, corresponding sensors are precisely deployed to facilitate wastewater source tracing within the drainage pipe network. The number of key nodes to retain can be flexibly selected based on budget constraints, using appropriate statistical indicators (such as the mean or quantiles) as the threshold for retaining key nodes.

[0080] The method described in this invention is not limited to the embodiments described in the specific implementation. Other implementation methods derived by those skilled in the art based on the technical solution of this invention also fall within the scope of technical innovation of this invention.

Claims

1. A method for calculating key nodes in a drainage pipe network, the method comprising the following steps: S1. Obtain the drainage network diagram to be analyzed and processed; S2. Convert the drainage network diagram to be analyzed into an undirected network diagram; S3. Calculate the betweenness centrality of the nodes in the undirected network graph and the degree of the nodes in the undirected network graph. Select the nodes with large betweenness centrality values ​​and use the characteristics of node degree to exclude process nodes with high betweenness centrality. S4. Make a judgment based on the amount of funds invested in traceability; S5. If it is determined that the funding for traceability is not restricted, use weak threshold segmentation to filter the nodes to be retained. S6. If it is determined that the funding for traceability is limited, then use strong threshold segmentation to filter the nodes to be retained. S7. Obtain the network graph with labeled key nodes; S8. Transform the network diagram with marked key nodes to obtain a pipeline diagram with marked key nodes; The segmentation mentioned in steps S5 and S6 refers to logical comparison operations, including greater than or greater than equal to logical operations; The weak threshold mentioned in step S5 is the first statistical parameter in the betweenness centrality of the nodes in the undirected network graph, where the first statistical parameter is the mean, median, or 30th percentile. The strong threshold mentioned in step S6 is the second statistical parameter in the node betweenness centrality of the undirected network graph, where the second statistical parameter is the upper quartile or the 80th percentile.

2. The calculation method for key nodes of a drainage pipe network as described in claim 1, characterized in that: The drainage network diagram to be analyzed in step S1 includes any type of drainage network diagram, from simplified to complete.

3. The calculation method for key nodes of a drainage pipe network as described in claim 2, characterized in that: The undirected network graph described in step S2 has the same spatial topology as the drainage network graph before the transformation.

4. The calculation method for key nodes of a drainage pipe network as described in claim 3, characterized in that: In step S2, the numbers in the undirected network graph represent the node numbers, which include the numbers of inspection wells and relay pump stations. The non-numeric numbers represent pipeline terminals, which include sewage treatment plants.

5. The calculation method for key nodes of a drainage pipe network as described in claim 4, characterized in that: In step S3, the betweenness centrality of the nodes in the undirected network graph and the degree of the nodes in the undirected network graph are calculated using the network graph method.

6. The calculation method for key nodes of a drainage pipe network as described in claim 5, characterized in that: In step S7, the key nodes are those with large betweenness centrality values, and process nodes with high betweenness centrality are excluded by using the degree of the nodes.

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