A method for optimizing layout of water level gauges based on sewer network overflow risk early warning

Abstract

The application discloses a kind of water level gauge optimization layout based on drainage pipe network overflow risk early warning method, using dynamic rainfall-runoff simulation model to carry out multiple scene hydrodynamic simulation rainfall event, select effective overflow event therein, and further filter out overflow risk node;Using time lag mutual information to quantify the time lag relationship of hydraulic response between nodes, obtain the time lag step parameter when mutual information reaches maximum;Build the bipartite graph of drainage pipe network, solve the minimum sensor set required to cover all risk nodes by maximum matching algorithm;Based on candidate node setting early warning water level threshold, evaluate the early warning time, average early warning time, overflow perception rate and false alarm rate of each node, eliminate redundant nodes, select the final retained water level gauge layout site.The method can quantify the hydraulic time lag relationship between nodes, significantly improve the advance time of overflow early warning, reduce monitoring cost, have strong robustness and practical application value.

Description

Technical Field

[0001] This invention belongs to the field of pipeline layout optimization technology, and in particular relates to a method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipeline networks. Background Technology

[0002] Urban drainage systems are mainly divided into combined sewer systems and separate sewer systems. Combined sewer systems collect domestic sewage, industrial wastewater, and rainwater through the same pipe network, transporting them to a wastewater treatment plant for treatment before discharge. Due to historical investment constraints and technical standards, many older urban areas in my country were built using combined sewer systems in their early stages. Subsequent renovations often continued to use combined sewer systems as a foundation, upgrading them to interceptor-type combined sewer systems by adding interceptor trunk lines. Even after such renovations, these systems are still prone to overflow during rainfall due to surges in runoff, causing localized urban flooding and pollution of receiving water bodies.

[0003] With the development of IoT sensor monitoring equipment, real-time monitoring of water level changes in pipe networks using water level gauges and early warning of overflow nodes based on early water level fluctuation signals has become an effective means of reducing overflow risk. However, the complex topology and numerous nodes of drainage pipe networks make it too costly and impractical to install water level gauges at each node. Existing optimization layout methods mostly focus on post-event monitoring or state estimation, lacking specialized research aimed at early warning; while directly monitoring the water level at the overflow outlet can only record the overflow event itself and cannot provide valuable early warning time. Specifically, current hydraulic monitoring layout methods for drainage pipe network overflows mainly include unsupervised clustering analysis and evaluation based on information entropy indicators. These methods focus on dimensionality reduction and compression of data features, failing to quantify the time lag relationship of hydraulic response between nodes, and therefore cannot answer the core question of "how long in advance can an early warning be given," making it difficult to guarantee sufficient emergency response time. For example, invention patent CN122022072A discloses a data processing method for risk prediction of urban drainage pipe networks, including the following steps: Step S5, Multi-hazard Coupled Risk Assessment: Based on the risk probabilities of each node obtained in Step S4, combined with a pre-constructed urban flooding model, the multi-hazard coupled risk index is calculated to generate a dynamic distribution map of urban drainage pipe network risks; Step S6, Emergency Knowledge and Intelligent Resource Scheduling: Based on the urban pipe network emergency knowledge graph, a path optimization algorithm is used to generate the optimal scheduling path from emergency resource points to risk points, and an emergency decision-making scheme is output. This method mainly relies on the construction of a predictive risk model for state assessment and belongs to a typical unsupervised clustering analysis.

[0004] Therefore, there is an urgent need for an optimized layout method that can quantify the hydraulic time delay relationship between drainage network nodes, maximize the early warning time, and make all overflow risk nodes observable with the fewest water level gauges. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a method for optimizing the layout of water level gauges based on the early warning of overflow risk in drainage pipe networks. This method can maximize the early warning efficiency of overflow without the need for comprehensive deployment of water level gauges, while taking into account the detection rate and false alarm rate, and determining the optimal deployment location and number of water level gauges.

[0006] Therefore, the present invention is implemented using the following technical solution: A method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks includes the following steps: S1, Hydrodynamic simulation rainfall data: Multi-scenario hydrodynamic simulation rainfall events are carried out using a dynamic rainfall-runoff simulation model. Valid overflow events are selected, and nodes that have experienced at least one overflow are screened as overflow risk nodes. S2, Calculate the time-delay mutual information between nodes: Use time-delay mutual information to calculate the mutual information value between the water level time series of any two nodes as the delay time changes, and obtain the time-delay step parameter corresponding to the maximum value of the mutual information. The time-delay step parameter is used to quantify the time lag relationship of the hydraulic response between the two nodes. S3, Determine the minimum candidate set of sensors: Construct a bipartite graph of the drainage network, flip all directed edges in the network to obtain the corresponding bipartite graph structure, and perform the maximum matching algorithm iteratively to solve the problem. In each iteration, add the unmatched right node to the sensor set and use the matched left node as the new target node set to continue iterating until the target node set is empty or equal to the current sensor set. Due to the non-uniqueness of maximum matching, the above process yields multiple sets of sensor nodes that satisfy the target observability. Further combining the time delay step size parameter, the maximum early warning time is introduced as a constraint condition, and finally a unique minimum candidate set of sensor nodes is obtained. S4, Final site selection for water level gauge deployment: Based on the candidate nodes in step S3, set the warning water level threshold, evaluate the warning time of the candidate node set under different warning water levels, the average warning time of the monitoring system, the overflow detection rate and the false alarm rate. If the warning signal issued by a node can be replaced by other nodes that issue a longer warning time, then the redundant node is eliminated, and the final site selection for water level gauge deployment is selected.

[0007] Furthermore, in step S1, five types of return periods, seven types of continuous rainfall duration, and four types of rain peak location coefficients are selected, and a total of 140 rainfall events are generated based on the above combinations.

[0008] Furthermore, the effective overflow event is defined as node overflow rate > 0, duration > 10 minutes, and interval between adjacent effective overflow events > 20 minutes.

[0009] Furthermore, in step S2, the formula for calculating the mutual information value is: in, For X= Y= The joint probability distribution, The time delay step size parameter is determined when the mutual information reaches its peak value. The time-delay mutual information of the water level time series of node X and node Y; the calculation formula for the time-delay step size parameter is: in, The time-delay mutual information of the water level time series of node X and node Y. Let be the time delay step size parameter; when When, it indicates that the water level change at node X leads that at node Y; when When, it indicates that the water level change at node X lags behind that at node Y.

[0010] Furthermore, in step (3), each edge of the bipartite graph is assigned a new weight: in, The time delay step between nodes is denoted as K, which is obtained in step S2; K is a constant.

[0011] Furthermore, in step S4, the warning water level threshold is set within the range of 20% to 80% of the maximum water depth of the node; the warning time for the overflow event is defined as the time difference between the moment when the node begins to overflow and the moment when the earliest warning is issued in the monitoring system; the average warning time is the average of the warning times of all overflow events sensed by the monitoring system under the same rainfall scenario; the overflow perception rate is the proportion of the overflow events sensed to all overflow events; the missed alarm rate is 1 - overflow perception rate; and the false alarm rate is the proportion of warning events that occur within a set window period but are not matched with any overflow events.

[0012] Furthermore, the formula for calculating the warning time of the overflow event is as follows: ; The formula for calculating the average warning time is: ; The formula for calculating the overflow sensing rate is: ; The formula for calculating the false alarm rate is: ; in, The number of overflow events during rainfall. For the first The moment when the overflow event occurs To monitor the number of early warning events generated by the system, F represents the set of overflow events that successfully triggered an early warning, and F is the number of false alarm events.

[0013] The beneficial effects of adopting the above technical solution are as follows: 1. This invention quantifies the time lag relationship of hydraulic response between drainage network nodes through time-delay mutual information, and for the first time uses maximizing the early warning time as a constraint condition for sensor layout, directly answering the core question of "how long in advance can an early warning be given", providing sufficient emergency response time for overflow risk management.

[0014] 2. Based on network observability theory, the minimum number of water level gauges required to cover all overflow risk nodes is solved using the maximum matching algorithm, which significantly reduces monitoring costs and achieves optimal allocation of monitoring resources.

[0015] 3. A multi-dimensional evaluation system was established, including average warning time, overflow detection rate, missed alarm rate, and false alarm rate. The optimal warning water level range was determined through simulation. The system can provide an average warning time of more than 120 minutes for overflow events under various rainfall scenarios, while covering more than 84.2% of overflow events, thus achieving an effective balance between warning timeliness and false alarm risk.

[0016] 4. Through rigorous verification with simulated rainfall and real rainfall data, it is proven that the method of the present invention can provide significant early warning time under both long-duration multi-peak rainfall and short-duration heavy rainfall, with high overflow perception rate and strong robustness. It is significantly better than traditional methods and engineering experience methods based on complex network theory and has practical application value. Attached Figure Description

[0017] The present invention includes the following figures: Figure 1 This is a flowchart of the invention method.

[0018] Figure 2 This is a risk distribution diagram of overflow probability at nodes in a drainage pipe network.

[0019] Figure 3 This is a distribution diagram of standardized time-delay mutual information between nodes.

[0020] Figure 4 This is a distribution diagram of overflow risk nodes and candidate water level gauge nodes.

[0021] Figure 5 This is a graph showing the relationship between overflow detection rate, missed alarm rate, false alarm rate and average warning time under different warning water levels in the first embodiment.

[0022] Figure 6A bar chart showing the number of warnings and the number of overflows that were correctly covered by the candidate nodes of the water level gauge.

[0023] Figure 7 This is a schematic diagram of the final water level gauge location for the scheme proposed in the first embodiment.

[0024] Figure 8 This is a map showing the actual rainfall data for April 30, 2024 (top) in the second embodiment.

[0025] Figure 9 This is a map showing the actual rainfall data for June 28, 2024 (below) in the second embodiment.

[0026] Figure 10 The diagram shows the distribution of overflow nodes based on actual rainfall data from the second embodiment.

[0027] Figure 11 This is a comparison of various indicators of the optimized layout scheme under real rainfall data in the second embodiment.

[0028] Figure 12 This is a spatial distribution map of the node centrality index of a drainage network based on complex network theory.

[0029] Figure 13 This is a schematic diagram comparing the site selection distribution of water level gauges based on complex network theory.

[0030] Figure 14 This is an indicator for optimizing the location of layout schemes based on complex network theory.

[0031] Figure 15 This is a schematic diagram comparing the site selection distribution of water level gauges based on engineering experience.

[0032] Figure 16 This is a comparison chart of various indicators for different scenarios simulating rainfall.

[0033] Figure 17 This is a comparison chart of various indicators for different scenarios under a real rainfall scenario from 04:04 to 14:00 on April 30, 2024.

[0034] Figure 18 This is a comparison chart of various indicators for different scenarios under a real rainfall scenario from 06:25 to 12:00 on June 28, 2024. Detailed Implementation

[0035] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0036] like Figure 1As shown, this invention provides a method for optimizing the layout of water level gauges based on early warning of overflow risks in drainage pipe networks, specifically including the following steps: S1, Hydrodynamic simulation rainfall data: Multi-scenario hydrodynamic simulation rainfall events are carried out using a dynamic rainfall-runoff simulation model. Valid overflow events are selected, and nodes that have experienced at least one overflow are screened as overflow risk nodes. S2, Calculate the time-delay mutual information between nodes: Use time-delay mutual information to calculate the mutual information value between the water level time series of any two nodes as the delay time changes, and obtain the time-delay step parameter corresponding to the maximum value of the mutual information. The time-delay step parameter is used to quantify the time lag relationship of the hydraulic response between the two nodes. S3, Determine the minimum candidate set of sensors: Construct a bipartite graph of the drainage network, flip all directed edges in the network to obtain the corresponding bipartite graph structure, and perform the maximum matching algorithm iteratively to solve it. In each iteration, add the unmatched right node to the sensor set, and use the matched left node as the new target node set to continue iterating until the target node set is empty or equal to the current sensor set. Due to the non-uniqueness of maximum matching, the above process yields multiple sets of sensor nodes that satisfy the target observability. Further combining the time delay step size parameter, the maximum early warning time is introduced as a constraint condition, and finally a unique minimum candidate set of sensor nodes is obtained. S4, Final site selection for water level gauge deployment: Based on the candidate nodes in step S3, set the warning water level threshold, evaluate the warning time of the candidate node set under different warning water levels, the average warning time of the monitoring system, the overflow detection rate and the false alarm rate. If the warning signal issued by a node can be replaced by other nodes that issue a longer warning time, then the redundant node is eliminated, and the final site selection for water level gauge deployment is selected.

[0037] I. The present invention will be described in detail below by way of embodiments: Example 1: Case Study of Data Model Validation Based on Simulation 1. Hydrodynamic simulation of rainfall data to identify overflow risk nodes. The area in this example is 2.94 km². 2 First, a dynamic rainfall-runoff simulation model (SWMM) is used to establish a hydraulic model of the drainage network, such as... Figure 2As shown, the model includes 456 pipes and 447 manholes. To comprehensively analyze possible overflow scenarios, Chicago-type rainfall data was generated using different combinations of return periods, rainfall durations, and rainfall peak location coefficients, which were then used as input for hydrodynamic simulations. Specifically, five different return periods (2a, 5a, 20a, 50a, 100a), seven different rainfall durations (60, 120, 180, 240, 360, 720, 1440 minutes), and four different rainfall peak location coefficients (0.2, 0.4, 0.6, 0.8) were selected, generating a total of 140 rainfall events.

[0038] A script was written in Python to generate rainfall data in Excel format, which was then used as input for hydrodynamic simulations using a rain gauge. After the simulation, the overflow frequency at each node in the pipe network was statistically analyzed. The conditions for a valid overflow event were defined: the node overflow volume must be greater than 0 and the duration must be greater than one time step; in this embodiment, the time step was set to 10 minutes. Overflows at the same node with an interval greater than 20 minutes were classified as two overflow events. Under the simulated rainfall scenario, among the 447 nodes in the drainage pipe network of the study area, 41 nodes had an overflow risk, while the other 406 nodes did not experience overflows in any of the simulation scenarios. Figure 2 As can be seen, overflow events are concentrated in some downstream nodes of the pipeline network and inflow outlets into the lake, as well as in low-lying and flood-prone areas along the lake, showing obvious spatial distribution characteristics.

[0039] 2. Calculate the time-delay mutual information between nodes. Let the two nodes be X and Y. For the water level time series of the two nodes X and Y, first, discretize the continuous water level observations into a finite number of state intervals. Since the time delay is not infinitely large, within the set time delay range... Within an inner sliding time window, the mutual information value is calculated for each time delay step. The time step that reaches the maximum value is taken as the optimal time delay. The formula for calculating the mutual information value is: in, For X= Y= The joint probability distribution, The time delay step size parameter is determined when the mutual information reaches its peak value. This represents the time-delay mutual information between the water level time series of node X and node Y.

[0040] Since the time lag distribution is antisymmetric, the absolute value of the lag time is taken to facilitate the construction of undirected networks. As the weight of the edge, it represents the standardized relative delay time for nodes X and Y to reach maximum similarity in their water level responses.

[0041] Among all simulated rainfall scenarios, five rainfall events with different return periods, durations, and peak locations were selected. The average time delay step size parameter between nodes was calculated, and combined with the physical topology connections between nodes, a standardized time delay step size parameter between nodes was used. As weights, a weighted undirected network graph is constructed, such as Figure 3 As shown, there is usually a small time delay step between two adjacent nodes in space. When the increment of the time delay step between adjacent nodes is large, it indicates that the water flow is stagnant at this point. This may be because the downstream pipe slope becomes gentler, the pipe diameter becomes larger, resulting in a decrease in flow velocity, or the distance between the nodes is longer.

[0042] 3. Determine the minimum candidate set of sensors. Based on step S3, the monitoring of overflow risk nodes in the drainage network is defined as a target observability problem. The core objective is to accurately grasp the status of all overflow risk nodes using the minimum number of sensors. Based on the duality between structural observability and structural controllability, this problem is solved by finding the maximum matching network.

[0043] (The pseudocode for finding the minimum number of sensors is shown in Algorithm 1 below:) Initialize S := Ø and a target node set T := C (C is the overflow risk node set); Flipping all the links in the network yields a flipped network G'; Assign weights to each edge u → v in the flip network. ,in ; When T ≠ Ø and T ≠ S, execute: Construct a weighted bipartite graph B(L, R, W) from the flipped network, where: L = V, where V is the set of left nodes (original network nodes). R = V, where V is the set of right nodes (original network nodes). For each directed edge u→v in the flipped network, add an edge u∈L to the bipartite graph connecting v∈R, with weights of . In a weighted bipartite graph, to find the maximum weight maximum matching M, we first ensure that the number of matching edges is maximized, and then... maximum; Let RMS be the set of nodes matched in the right endpoint set, and RMS T, LMS is the set of nodes in the left endpoint set that match RMS; Define the set of unmatched nodes RUS ← T - RMS Update S ← S ∪ RUS, T ← LMS; Finish Return to S.

[0044] Based on the above weight settings, the maximum weight match is found by executing the greedy maximum matching algorithm. Its pseudocode is shown in Algorithm 2 below: Initialize matching M := Ø, RMS := Ø, LMS := Ø, all nodes are in an unmatched state. For each r∈T, execute If r has already been matched, then: continue Starting from r, find an augmenting path among the unmatched left nodes. If an augmenting path is found, then: Update matching along augmenting path otherwise: Find the edge (l | r) with the largest weight among the unmatched left nodes connected to r. If found, then: Add (l | r) to the match M End if End if Finish.) By executing Algorithm 2 above, a unique set of minimum number of candidate sensor nodes was finally determined, containing a total of 10 candidate locations, such as... Figure 4 As shown, it is theoretically possible to monitor and control all overflow risk nodes.

[0045] 4. Final site selection for water level gauge installation: Further optimization based on monitoring benefits. The following rules are established for the correlation and matching between overflows and early warnings: each overflow is associated with the earliest early warning issued by the monitoring system, allowing early warnings from upstream nodes to provide forward-looking information for downstream overflows. A window period W is set: from the start of rainfall to 3 hours after the end of rainfall, considering only overflow and early warning events occurring within this window period. The window periods corresponding to different rainfall durations are shown in Table 1.

[0046] Table 1. Window periods corresponding to different rainfall durations The warning time for the overflow event is defined as the time difference between the moment when the node begins overflowing and the moment when the earliest warning is issued in the monitoring system. The calculation formula is as follows: .

[0047] The average warning time is the average of the warning times of all overflow events sensed by the monitored systems under the same rainfall scenario, and the calculation formula is: .

[0048] The overflow detection rate refers to the proportion of overflow events successfully detected by the water level gauge monitoring system within the window period W, out of the total number of overflow events. It is used to evaluate the overall overflow event detection capability of the monitoring system, and the calculation formula is: .

[0049] The false negative rate refers to the proportion of overflow events that are not detected by the monitoring system, i.e., false negative rate = 1 - overflow detection rate. A lower false negative rate indicates a stronger detection capability of the system. The calculation formula is: .

[0050] By setting different warning water level values ​​(20%, 30%, 40%, 50%, 60%, 70%, and 80% of the maximum water depth at the candidate nodes of the water level gauges), the study investigated the correctness and omission of overflow event warnings. Based on the statistical results of all simulated rainfall scenarios, the changes of each indicator with the warning water level value are as follows: Figure 5 As shown.

[0051] from Figure 5 As the warning water level rises, the overflow detection rate decreases, while the false alarm rate gradually increases. Once the warning water level reaches 50%, the false alarm rate and false alarm rate no longer change. Simultaneously, the average warning time generally shows a downward trend. Within the warning water level range of 20%-50%, the system can provide an average warning time of over 120 minutes while maintaining a high detection rate (≥84.2%), and the false alarm rate is less than 7% different from that at higher water levels. Therefore, 20%-50% is determined to be the optimal warning water level range.

[0052] Final site selection. For example... Figure 6 As shown, the performance of all candidate nodes in the simulated rainfall scenario is further analyzed from the perspective of early warning nodes. By traversing all water level gauge nodes that correctly detected and warned of overflow events under all rainfall scenarios, it was found that although the water level gauges at nodes J279, J206, and Century Avenue issued warnings, these signals were not matched with overflow events (i.e., they were replaced by other nodes providing longer warning times). Removing these three nodes, as shown... Figure 7 As shown, water level gauges were ultimately installed at the remaining 7 locations.

[0053] Example 2: Verification Implementation Case Based on Real Data Model validation based on real-world cases. Two real rainfall events were used for validation: one from 04:04 to 14:00 on April 30, 2024 (multi-peak, long-duration rainfall) and the other from 06:25 to 12:00 on June 28, 2024 (single-peak, short-duration, heavy rainfall). These two rainfall events were used as input values ​​in a simulation within SWMM, and the rainfall intensity distribution is shown below. Figure 8 , Figure 9As shown, all of these factors caused overflows at some nodes in the drainage network. The specific distribution of the overflowing nodes is as follows: Figure 10 As shown.

[0054] The seven selected water level gauges were used to test overflow events under two real-world rainfall scenarios, with the window W set to three hours from the start of rainfall to its end. Figure 11 As shown, under the set warning water level values ​​of 20%-50%, the water level monitoring system achieved a 100% accuracy rate in detecting overflow events, with an average warning time exceeding 120 minutes, and a false alarm rate within an acceptable range for practical engineering. This demonstrates that the layout scheme ultimately selected in this embodiment can effectively achieve early risk warning in practice.

[0055] II. Comparison and verification between the sensor location method based on node importance assessment according to complex network theory and the optimized layout method of this invention: Node importance assessment based on complex network theory can serve as an effective supplementary means for sensor location selection. This embodiment compares it with the aforementioned layout scheme based on time-delay mutual information and observability theory to verify the differences in overflow early warning effects between different methods.

[0056] Calculate the degree centrality, betweenness centrality, and proximity centrality indices for each node in the drainage network. The distributions of each index are as follows: Figure 12 As shown.

[0057] Define the topological centrality index of a node TC i The calculation formula is: TC i =DC i + BC i + CC i in, TC i For the topological centrality of pipeline nodes, DC i For degree centrality; BC i For betweenness centrality; CC i To approximate centrality.

[0058] The top 7 nodes by centrality are selected and compared with the node scheme in Example 2, such as... Figure 13 As shown. From Figure 13As can be seen, the two methods are similar in spatial distribution. Both methods simultaneously identify areas requiring high-density monitoring from the perspectives of topological and hydraulic information, which is basically consistent with the characteristic that the spatial distribution of overflow risk nodes shows a certain regularity.

[0059] The overflow detection rate, missed detection rate, and average warning time were compared and analyzed using simulated rainfall data. Specific results are as follows: Figure 14 As shown: from Figure 14 As can be seen, after the warning water level rises to 60%, the average warning time, false alarm rate, and overflow detection rate of this layout scheme no longer change. Therefore, the optimal warning water level range is 20% - 60%, which is the performance limit of this monitoring system. Further analysis shows that the upper and lower limits of the overflow detection rate of this layout scheme are lower than those of the proposed scheme, and the false alarm rate is also higher. However, the average warning time is about 60 minutes, which is only half that of the proposed scheme. This proves that the optimized layout method based on the theory of network observability enhancement using time delay step parameters can effectively quantify the time lag relationship of hydraulic response between nodes, thus providing more sufficient time for early warning of overflow events, and its effect is better than the layout scheme that does not consider the time delay effect.

[0060] III. Comparative verification of the water level gauge site selection method based on engineering experience with the optimized layout method of this invention and the sensor site selection method based on node importance assessment of complex network theory: This study compares the site selection of water level gauges based on engineering experience with other methods. The local water management department, based on its experience in managing overflow events and practical engineering practices, has proposed a monitoring plan. Considering the historical patterns and distribution characteristics of overflow events, the main locations for installing water level gauges include overflow outlets along the lake and vulnerable areas of hydraulic structures. A total of 10 water level gauges are required, including those in the intelligent diversion wells. The specific distribution locations are as follows: Figure 15 As shown.

[0061] from Figure 15 As can be seen from the actual engineering experience, most of the water level gauges are distributed on the intercepting main pipes along the lake, and are located at the points where overflows frequently occur or at the outlets into the lake, so as to directly monitor the overflow points.

[0062] We set warning water level values ​​between 20% and 50%, and analyzed and compared various indicators under simulated and real rainfall scenarios. The comparison of indicators for different schemes under simulated rainfall scenarios is shown below. Figure 16 As shown; a comparison of various indicators of different scenarios under two real rainfall scenarios that occurred from 04:04 to 14:00 on April 30, 2024 and from 06:25 to 12:00 on June 28, 2024, as shown. Figure 17 and Figure 18 As shown.

[0063] from Figure 16 As can be seen, as the warning water level rises, the overflow detection rate and false alarm rate of the three schemes all show a downward trend, while the missed alarm rate gradually increases and the average warning time continues to shorten. However, the overflow detection rate of the optimized method of this invention is higher than that of the other two methods, while the missed alarm rate and false alarm rate are also lower, which can provide a longer warning time for overflow events and the overall monitoring effect is the best.

[0064] from Figure 17 As can be seen, in the long-duration rainfall scenario from 04:04 to 14:00 on April 30, 2024, the overflow detection rate of the optimized method of this invention is consistently higher than that of other methods, and it can provide the longest warning time window for overflow events. The water level gauge layout based on engineering experience has a much shorter average warning time than other methods, and its false alarm and missed alarm rates are also higher, thus its warning effect for overflow events is not good. Compared with the optimized method of this invention, the layout based on complex network theory has a similar overall performance in terms of overflow detection rate and average warning time, but the false alarm rate of the optimized method of this invention is still better than that of the optimized layout method based on complex network theory.

[0065] from Figure 18 As can be seen, in the short-duration rainfall scenario from 06:25 to 12:00 on June 28, 2024, although the optimized method of this invention has a higher false alarm rate than the other two schemes, it has a higher detection rate of overflow events and provides a longer warning time. The water level gauge layout based on engineering experience has a lower false alarm rate and is relatively stable under different warning water levels, but it can provide the shortest average warning time, and other indicators are lower than the other two schemes. The optimized layout method based on complex network theory performs relatively evenly in various indicators of overflow monitoring, but it is still weaker than the optimized method of this invention overall.

[0066] By comparing various indicators in simulated and real rainfall scenarios, the robustness and reliability of the water level gauge optimization layout method based on the observability theory of time-delay mutual information enhancement network are further verified.

[0067] In summary, 1. A water level gauge optimization layout method based on the observability theory of time-delay mutual information enhancement networks reveals the time-delay effect in water level dynamics by identifying the time-delay coefficient corresponding to the maximum mutual information. This time-delay coefficient is used as a constraint to maximize the early warning time, enabling the selected sensor layout to maximize the early warning time and provide sufficient time for emergency response.

[0068] 2. By using the maximum matching algorithm to solve for the minimum set of sensor nodes, the deployment and maintenance costs of equipment can be significantly reduced while ensuring that all risk nodes can be monitored.

[0069] 3. Using overflow detection rate, missed alarm rate, false alarm rate, and warning time as evaluation indicators, the optimal warning water level range suitable for the monitoring system was determined through a large number of simulated rainfall scenarios. While ensuring a high detection rate of overflow events, the system also balances the missed alarm rate and false alarm rate in actual engineering, and provides sufficient time for early warning of overflow risks.

[0070] 4. The water level gauge optimization layout method based on the time-delay mutual information enhanced network observability theory can prioritize retaining nodes that can provide the longest early warning time and eliminate redundant points whose early warning signals can be replaced by other nodes, thereby achieving optimized allocation of monitoring resources and maximizing early warning effectiveness.

[0071] 5. By comparing simulated and real rainfall data, the optimization method of this invention was comprehensively compared with optimization layout methods based on complex network theory and water level gauge layout based on engineering experience. It can be concluded that the optimization method of this invention performs better in terms of overflow detection rate, average warning time, missed alarm rate, and false alarm rate. Furthermore, the spatial distribution of water level gauges basically conforms to the distribution pattern of overflow risk nodes, indicating that the optimization method of this invention provides a superior solution for overflow risk monitoring in drainage pipe networks.

[0072] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks, characterized in that: Includes the following steps, S1, Hydrodynamic simulation rainfall data: Multi-scenario hydrodynamic simulation rainfall events were conducted using a dynamic rainfall-runoff simulation model. Valid overflow events were selected, and nodes that had experienced at least one overflow were identified as overflow risk nodes. S2, Calculate the time-delay mutual information between nodes: Use time-delay mutual information to calculate the mutual information value between the water level time series of any two nodes as the delay time changes, and obtain the time-delay step parameter corresponding to the maximum value of the mutual information. The time-delay step parameter is used to quantify the time lag relationship of the hydraulic response between the two nodes. S3, Determine the minimum candidate set of sensors: Construct a bipartite graph of the drainage network, flip all directed edges in the network to obtain the corresponding bipartite graph structure, and perform the maximum matching algorithm iteratively to solve it. In each iteration, add the unmatched right node to the sensor set, and use the matched left node as the new target node set to continue iterating until the target node set is empty or equal to the current sensor set. Due to the non-uniqueness of maximum matching, the above process yields multiple sets of sensor nodes that satisfy the target observability. Further combining the time delay step size parameter, the maximum early warning time is introduced as a constraint condition, and finally a unique minimum candidate set of sensor nodes is obtained. S4, Final site selection for water level gauge deployment: Based on the candidate nodes in step S3, set the warning water level threshold, evaluate the warning time of the candidate node set under different warning water levels, the average warning time of the monitoring system, the overflow detection rate and the false alarm rate. If the warning signal issued by a node can be replaced by other nodes that issue a longer warning time, then the redundant node is eliminated, and the final site selection for water level gauge deployment is selected.

2. The method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks according to claim 1, characterized in that: In step S1, five types of return periods, seven types of continuous rainfall duration, and four types of rain peak location coefficients are selected. Based on the above combinations, a total of 140 rainfall events are generated.

3. The method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks according to claim 2, characterized in that: The valid overflow event is defined as node overflow rate > 0, duration > 10 minutes, and interval between adjacent valid overflow events > 20 minutes.

4. The method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks according to claim 1, characterized in that: In step S2, the formula for calculating the mutual information value is: in, For X= Y= The joint probability distribution, The time delay step size parameter is determined when the mutual information reaches its peak value. The time-delay mutual information of the water level time series of node X and node Y; the time-delay step size parameter The calculation formula is: in, The time-delay mutual information of the water level time series of node X and node Y. Let be the time delay step size parameter; when When, it indicates that the water level change at node X leads that at node Y; when When, it indicates that the water level change at node X lags behind that at node Y.

5. The method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks according to claim 1, characterized in that: In step S3, each edge of the bipartite graph is assigned a new weight: in, The time delay step between nodes is denoted as K, which is obtained in step S2; K is a constant.

6. The method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks according to claim 1, characterized in that: In step S4, the warning water level threshold is set within the range of 20% to 80% of the maximum water depth of the node; the warning time of the overflow event is defined as the time difference between the moment when the node begins to overflow and the moment when the earliest warning is issued in the monitoring system; the average warning time is the average of the warning times of all overflow events sensed by the monitoring system under the same rainfall scenario. The overflow perception rate is the proportion of perceived overflow events out of all overflow events; The false alarm rate = 1 - overflow perception rate, and the false alarm rate is the proportion of warning events that occur within a set window period but are not matched with any overflow events.

7. A method for optimizing the layout of water level gauges based on early warning of overflow risk in drainage pipe networks, as described in claim 6, is characterized in that: The formula for calculating the warning time of the overflow event is: ； The formula for calculating the average warning time is: ； The formula for calculating the overflow sensing rate is: ； The formula for calculating the false alarm rate is: ； in, The number of overflow events during rainfall. For the first The moment when the overflow event occurs To monitor the number of early warning events generated by the system, F represents the set of overflow events that successfully triggered an early warning, and F is the number of false alarm events.

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