Drainage pipe network sensor layout optimization method based on topological space information fusion

Abstract

This invention discloses a method for optimizing the layout of sensors in drainage pipe networks based on topological spatial information fusion. The method includes: acquiring the topology, flow information, and sensor distribution of the drainage pipe network in the target area; constructing a monitoring matrix; and performing derivation inference based on flow quality conservation to obtain the individual monitoring flow of each sensor; calculating the cumulative infiltration monitoring threshold for sensors on each pipe segment, considering the propagation of uncertainty variations, based on the topology and flow information of the drainage pipe network and the individual monitoring flow; calculating the average measurable threshold minimization evaluation index according to the cumulative infiltration monitoring threshold; iterating using a sequential backward selection algorithm to generate several sensor layout subsets; and obtaining the sensor number-performance curve to determine the sensor layout scheme. This invention can quickly solve for a high-performance, low-cost, stable sensor layout, accurately predict low infiltration flow events in drainage pipe networks, and has good interpretability and engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of urban drainage network safety, and particularly relates to a method for optimizing the layout of drainage network sensors based on topological spatial information fusion. Background Technology

[0002] As a critical infrastructure, urban drainage networks bear the heavy responsibility of transporting sewage to wastewater treatment facilities, playing a vital role in protecting public health and the environment. However, their operational efficiency is often negatively impacted by infiltration and inflow (I&I) issues. Infiltration and inflow are generally defined as the abnormal intrusion of external water bodies into the drainage network system, leading to significant risks such as increased network load, decreased transport capacity, and a heightened risk of sewage overflow. Therefore, accurate and timely monitoring of infiltration and inflow events has become a core objective of drainage network system management. Traditional monitoring methods are mainly divided into two categories: the first relies on macroscopic estimation methods, such as flow analysis or pollutant mass balance; the second involves local physical monitoring, including smoke testing and closed-circuit television inspections. However, macroscopic estimation methods often lack spatial resolution, making it difficult to accurately locate specific infiltration and inflow points. In contrast, while local physical monitoring can accurately locate infiltration and inflow points, its high cost and massive workload make it difficult to achieve large-scale infiltration and inflow monitoring and assessment of drainage networks.

[0003] In recent years, advancements in Internet of Things (IoT) technology have enabled the widespread deployment of sensors for monitoring infiltration flows. These sensors typically collect high-resolution hydraulic data (e.g., flow rate or water level), making data-driven techniques more effective than traditional monitoring methods at identifying infiltration events. However, the high costs of sensor procurement, installation, and maintenance make comprehensive sensor system coverage economically impractical. Therefore, maximizing the performance of sensor placement strategies within a limited budget has become a pressing task. This involves two interrelated objectives: (1) maximizing the sensor system's sensitivity to small-scale infiltration events; and (2) optimizing sensor placement for optimal overall monitoring performance. Given that pipe flow rate is the most direct indicator of infiltration flows, this invention focuses on flow sensors to address these dual objectives.

[0004] More specifically, a traditional data-driven approach to infiltration monitoring relies on analyzing historical flow data to establish reasonable ranges of flow variation, such as monitoring thresholds (DTs), which are then triggered when new data exceeds these limits. While effective for coarse identification, this traditional approach suffers from a key drawback: it depends on static thresholds (e.g., a fixed 15% coefficient of variation) calculated individually for each sensor. This approach fails to incorporate uncertainty information from associated flow sensors, inherently limiting its sensitivity to small-scale infiltration events in drainage networks. Crucially, drainage networks typically have a tree-like topology, resulting in deterministic flow quality conservation relationships that allow for estimation of downstream flow based on the sum of upstream tributaries. Furthermore, fusing data uncertainties based on these topological constraints and flow quality conservation can yield lower, more refined monitoring thresholds, thereby enhancing sensitivity to small-scale infiltration events. However, despite this apparent potential, no work has yet integrated topology-derived flow-uncertainty inferences into sensor data calculations to refine the monitoring threshold calculation rules.

[0005] Furthermore, sensor placement optimization is guided by performance evaluation metrics, as they define how to quantify infiltration flow monitoring capabilities. Existing metrics broadly fall into two categories. The first is information-theoretic metrics, designed to maximize the information gain of the sensor system. Representative examples include entropy-based methods. The second is infiltration flow event monitoring reliability metrics, which are based on predefined event scenarios and threshold evaluation systems, such as event detection rate (EDR). However, a key limitation of information-theoretic metrics is that they typically operate as data-driven "black box" tools, prioritizing statistical patterns while neglecting the inherent flow physical relationships within the drainage network topology. Similarly, event monitoring reliability metrics rely on binary monitoring logic, making the results highly sensitive to assumed event parameters. Therefore, neither of these approaches systematically utilizes the inherent topology of the drainage network to guide sensor placement, potentially leading to suboptimal sensor placement strategies.

[0006] It is worth mentioning that in the field of infiltration flow monitoring in urban drainage pipe networks, intelligent optimization algorithms (such as differential evolution (DE) and genetic algorithm (GA) are commonly used to optimize sensor layout for efficient sensing of drainage pipe network status and anomaly early warning, in order to balance monitoring performance and construction cost. These algorithms search for optimal solutions in the solution space based on preset objective functions (such as minimizing the number of monitoring points and maximizing the monitoring probability), and have been applied in drainage pipe network monitoring. However, engineering practice shows that they have two shortcomings: First, the running speed is slow—facing complex pipe networks with numerous nodes and pipe segments, a large number of iterations and evaluations are required in a large-scale solution space, which is time-consuming and difficult to meet the needs of rapid on-site deployment and real-time optimization; second, the results are unstable—affected by random initialization, operator parameters, and search strategies, they are prone to getting trapped in local optima or producing significantly different Pareto front solution sets, resulting in large fluctuations in layout performance of the same pipe network in different runs, increasing the uncertainty of engineering decisions. Summary of the Invention

[0007] The purpose of this application is to overcome the above-mentioned shortcomings of the prior art and provide a method for optimizing the layout of drainage network sensors based on topological spatial information fusion, thereby reducing the lower limit of the monitoring threshold of the sensor system and enabling more accurate early warning of events with smaller infiltration flow in the drainage network.

[0008] According to a first aspect of the embodiments of this application, a method for optimizing the layout of sensors in a drainage network based on topological spatial information fusion is provided, comprising: (1) Obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area, construct a monitoring matrix, and make derivation inferences based on the flow quality conservation to obtain the individual monitoring flow of each sensor; (2) Based on the topology and flow information of the drainage network, and combined with the individual monitoring flow of each sensor, the cumulative infiltration monitoring threshold of the sensors on each section of the pipeline is calculated considering the propagation of uncertain variations. (3) Based on the cumulative infiltration monitoring threshold of each sensor, calculate the evaluation index of minimizing the average monitorable threshold, and use the sequential backward selection algorithm to iterate and generate several sensor layout subsets, and obtain the sensor number-performance curve, thereby determining the sensor layout scheme.

[0009] Further, step (1) includes: (1.1) Obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area; (1.2) Based on the topology of the drainage network, a monitoring matrix is ​​constructed, wherein the monitoring matrix is ​​a binary matrix used to describe whether the downstream sensors of each numbered pipe can detect the infiltration flow rate when infiltration events occur at nodes with different numbers. The row index of the monitoring matrix is ​​the node number, and the column index of the monitoring matrix is ​​the pipe number. (1.3) Based on the monitoring matrix and the flow information of the drainage pipe network in the target area and the sensor distribution, the individual monitoring flow of the sensor is obtained by derivation based on the flow quality conservation.

[0010] Furthermore, the derivation inference in step (1.3) specifically includes: Subtracting the upstream sensor flow rate from the downstream sensor flow rate yields the individual monitoring flow rate of the downstream sensor.

[0011] Further, step (2) includes: (2.1) Based on the topology and flow information of the drainage network, identify the set of pipes monitored by each sensor and its corresponding total flow; (2.2) Apply the predetermined variation tolerance coefficient to the total flow of each pipeline and calculate the individual monitoring threshold of the sensor on each pipeline section; (2.3) The root mean square combination method is used to propagate uncertainty variation for the individual monitoring thresholds of the sensors on each section of the pipeline, thereby calculating the cumulative infiltration monitoring threshold of each sensor.

[0012] Furthermore, the evaluation index for minimizing the average monitoring threshold in step (3) is: , in, This indicates the length of each pipe segment, in meters (m). The infiltration monitoring threshold for each pipe segment calculated in step (2), m 3 / s This represents the number of pipe sections.

[0013] Furthermore, in step (3), the sequential backward selection algorithm is used for iteration, specifically as follows: (3.1) The iteration starts with one sensor installed on each pipe segment; (3.2) Calculate the average monitoring threshold minimization evaluation index corresponding to the sensor layout after removing each sensor, and remove the sensor corresponding to the minimum value among all average monitoring threshold minimization evaluation indices; (3.3) Repeat (3.2) until the predetermined minimum number of sensors is reached.

[0014] According to a second aspect of the embodiments of this application, a drainage network sensor layout optimization device based on topological spatial information fusion is provided, comprising: The derivation and inference module is used to obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area, construct a monitoring matrix, and perform derivation and inference based on the flow quality conservation to obtain the individual monitoring flow of each sensor. The cumulative threshold calculation module is used to calculate the cumulative infiltration monitoring threshold for sensors on each section of the pipeline, taking into account the propagation of uncertainties, based on the topology and flow information of the drainage network and the individual monitoring flow of each sensor. The iterative optimization module is used to calculate the average monitorable threshold minimization evaluation index based on the cumulative infiltration monitoring threshold of each sensor, and to use the sequential backward selection algorithm to iterate and generate several sensor layout subsets, and obtain the sensor number-performance curve, thereby determining the sensor layout scheme.

[0015] According to a third aspect of the embodiments of this application, a computer program product is provided, including a computer program / instructions that, when executed by a processor, implement the method described in the first aspect.

[0016] According to a fourth aspect of the embodiments of this application, an electronic device is provided, comprising: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors perform the method as described in the first aspect.

[0017] According to a fifth aspect of the embodiments of this application, a computer-readable storage medium is provided that stores computer instructions thereon, which, when executed by a processor, implement the steps of the method as described in the first aspect.

[0018] The technical solutions provided by the embodiments of this application may include the following beneficial effects: (1) This invention innovatively uses the flow quality conservation and topology of pipe segments to solve the monitoring matrix, extract the upstream and downstream relationship and topology information, and use the upstream sensor flow to derive the flow of unmonitored sections and its uncertainty, which significantly improves the sensitivity of the sensor system to detect anomalies, provides a key basis for optimizing sensor layout, and achieves more efficient monitoring.

[0019] (2) This invention innovatively introduces the principle of uncertainty variation propagation to optimize the calculation of infiltration monitoring threshold, proposes the Individual Monitoring Threshold (IPDT) rule, integrates topological flow inference and variation accumulation, and uses the root mean square (RSS) method to handle uncertainty variation propagation, avoids the overestimation problem of simple arithmetic accumulation, effectively reduces the infiltration monitoring threshold of downstream pipe sections, and greatly enhances the performance of the monitoring system.

[0020] (3) This invention innovatively embeds the evaluation index of minimizing the average weighted infiltration monitoring threshold into the Sequential Backward Selection (SBS) algorithm. Through iterative elimination of sensors with the least impact, nested subsets and their corresponding sensor number-performance curves are generated to adapt to different budget requirements. With its deterministic characteristics and high computational efficiency, this invention can quickly solve for a stable, low-cost sensor layout with low threshold and strong performance, and accurately predict low infiltration flow events.

[0021] In summary, this invention transforms topological relationships into quantifiable inference criteria and, based on the conservation of flow quality and topological structure of pipe segments, uses the difference between upstream and downstream flow to derive and infer the flow in unmonitored sections. This significantly compensates for the data gaps in existing sensor systems for individual flow indicators, increases the reliability of sensor system monitoring data, and provides support for optimizing sensor layout. Simultaneously, it introduces the uncertainty propagation principle to propose the Individual Monitoring Threshold (IPDT) rule. First, the threshold is defined as 0.15 times the flow in the monitored pipe segment. Combining the same branch determination and root mean square (RSS) variation synthesis, it integrates topological flow derivation inference with uncertainty variation accumulation. The above process comprehensively considers the uncertainty loss caused by hydraulic path transmission in the drainage pipe network topology, effectively reducing the downstream infiltration monitoring threshold and enhancing the monitoring capability for low flow anomalies. In addition, the Sequential Backward Selection (SBS) algorithm is used to optimize the evaluation index of minimizing the average weighted infiltration monitoring threshold. The algorithm only weights the pipe segment length to avoid the concentration of sensors downstream, iteratively eliminates the sensors with the least impact, and generates nested subsets and their corresponding sensor number-performance curves to adapt to different budgets. This allows for the rapid solution of a stable, low-cost sensor layout with low threshold and strong performance, enabling accurate early warning of low infiltration flow.

[0022] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0024] Figure 1 This is a flowchart illustrating a method for optimizing the layout of sensors in a drainage network based on topological spatial information fusion, according to an exemplary embodiment.

[0025] Figure 2 This is a schematic diagram of topology-based flow derivation inference and monitoring enhancement, where (a) is the pipeline topology of two flow sensors (A and B), (b) is the daily flow measurement data of the two flow sensors, (c) is the time series and fluctuation range generated by the differential signal (AB), and (d) is a schematic diagram of the difference between the original flow and the topology-derived flow inferred flow.

[0026] Figure 3 These are schematic diagrams of IPDT calculation in single-sensor and dual-sensor scenarios, where (a) is a schematic diagram of a single-sensor scenario and (b) is a schematic diagram of a dual-sensor scenario.

[0027] Figure 4 This is a schematic diagram of the IPDT calculation process in a multi-sensor system in a complex drainage network.

[0028] Figure 5 This is a schematic diagram of the complete drainage pipe network system of Example 1.

[0029] Figure 6 This is a schematic diagram of the implementation results of the present invention in Example 1, where (a) is the 30 sensor layout schemes obtained by the SBS method; (b) is the iterative elimination process based on the SBS method and the ADT minimization evaluation index; and (c) is the sensor number-ADT performance curve of the sensor layout obtained by the SBS method.

[0030] Figure 7 This is a schematic diagram of the complete drainage pipe network system in Example 2.

[0031] Figure 8 The present invention compares the topology-derived flow-monitoring threshold inference method with the isolated threshold method in the engineering solution of sensor layout, wherein (a) is a comparison of the monitoring threshold distribution of all pipes; and (b) is a comparison of the correlation between threshold reduction and spatial distribution.

[0032] Figure 9 This invention compares the sensor layout obtained by the sequential backward selection method and the engineering solution, where (a) is a comparison of the monitoring threshold distribution of all pipelines; and (b) is a comparison of the correlation between the threshold reduction and the spatial distribution.

[0033] Figure 10 This is a block diagram illustrating a drainage network sensor layout optimization device based on topological spatial information fusion, according to an exemplary embodiment.

[0034] Figure 11 This is a schematic diagram of an electronic device according to an exemplary embodiment. Detailed Implementation

[0035] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0036] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0037] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0038] Figure 1 This is a flowchart illustrating a method for optimizing the layout of sensors in a drainage network based on topological spatial information fusion, according to an exemplary embodiment. Figure 1 As shown, this method, when applied to a terminal, may include the following steps: (1) Obtain parameterized data information of the drainage network in the target area from the engineering design department, and make derivation inferences based on the parameterized data information according to the flow quality conservation to obtain the flow rate of the unmonitored section, wherein the parameterized data information includes parameterized data information of topology, flow rate and sensor location; Specifically, this step may include the following sub-steps: (1.1) Collect basic data on the drainage network from engineering design units or departments, including topology (number of nodes and pipe segments, length of each pipe segment, pipe direction and upstream and downstream node information), node flow, pipe segment flow, sensor location and other parametric data. This sub-step aims to visualize the topology of the drainage network and the spatial distribution of sensors.

[0039] The node is located at the intersection of the pipelines and the manhole at the beginning of the pipeline, and the pipe section is the part of the pipeline between the two manholes.

[0040] (1.2) Based on the drainage network topology in the above basic data, a monitoring matrix is ​​constructed. The monitoring matrix is ​​a binary matrix used to describe whether the downstream sensors of each pipe can detect the infiltration flow rate when infiltration events occur at nodes with different numbers. Among them, the node number is the row index of the monitoring matrix, with smaller node numbers located downstream, and the pipe number is the column index of the monitoring matrix.

[0041] Furthermore, the specific meaning of the monitoring matrix can be illustrated with an example. For instance, if an infiltration inflow event occurs at node i, and the infiltration flow rate can be monitored in pipe j, then the element at the index of row i and column j in the monitoring matrix will be 1. This means that when an infiltration inflow event occurs at node i, a sensor placed downstream of pipe j can detect the infiltration inflow event.

[0042] Conversely, if an infiltration inflow event occurs at node i, and no infiltration flow can be detected in pipe j, then the element at the index of row i and column j in the monitoring matrix will be 0. This means that when an infiltration inflow event occurs at node i, a sensor placed downstream of pipe j will not be able to detect the infiltration inflow event.

[0043] Therefore, the monitoring matrix contains data on the upstream and downstream topology of the drainage pipeline, which can be used in the subsequent step (1.3) to determine the upstream and downstream relationships of the pipelines where the sensors are located, so as to identify the set of pipelines monitored by the sensors individually and their corresponding total flow. Furthermore, after calculating the individual monitoring threshold of each sensor, the root mean square (RSS) combination method is reasonably used to propagate the uncertainty changes of the upstream monitoring threshold based on the determined upstream and downstream relationship information.

[0044] (1.3) Based on the monitoring matrix and the flow information and sensor distribution information of the drainage network in the target area, the flow rate monitored by each sensor is derived and inferred according to the flow quality conservation principle. The inference method is to subtract the flow rate of the upstream sensor from the flow rate of the downstream sensor to estimate the flow rate monitored by the downstream sensor. This sub-step requires the use of sensor location information. More precisely, this utilizes upstream sensor data to compensate for the data gaps in the existing sensor system for individual flow rate indicators, increases the reliability of the sensor system's monitoring data, provides a basis for optimizing sensor layout strategies, and thus achieves more efficient monitoring.

[0045] Figure 2 This demonstrates the application of this principle in improving sensor monitoring capabilities. Figure 2 Figure (a) shows the topology of a drainage network equipped with two flow sensors (A and B). Its daily flow measurement data is as follows: Figure 2 As shown in (b) above, the solid line represents the measured value, and the surrounding semi-transparent band represents the normal fluctuation range; measurements exceeding these ranges indicate abnormal inflow. Based on Figure 2 The pipeline topology shown in (a) is as follows: Figure 2 (c) shows the flow time series and fluctuation range generated by the differential signal (AB). Finally, Figure 2 (d) in the figure visually demonstrates the significantly improved sensor monitoring sensitivity of the topology-derived flow inference technology by comparing the wider flow fluctuation range of the original sensor A with the narrower range of the inferred signal (AB).

[0046] (2) Based on the topology and flow information of the drainage network, and combined with the individual monitoring flow of each sensor, the cumulative infiltration monitoring threshold of the sensors on each section of the pipeline is calculated considering the propagation of uncertain variations. Specifically, the calculation rule for the Individual Infiltration Threshold (IPDT) is as follows: Based on commonly used experience in engineering practice, the initial IPDT is defined as 0.15 times the flow rate of the pipe section under normal operating conditions monitored by the sensor alone (where 0.15 is the tolerance coefficient, and the flow rate under normal operating conditions monitored by the sensor alone is the sensor-monitored flow rate inferred from sub-step (1.3)). As a criterion for determining whether an infiltration event has occurred, when the flow rate data monitored by the sensor exceeds 1.15 times the sensor-monitored flow rate under normal operating conditions, that is, the sensor-monitored flow rate under normal operating conditions plus the defined initial IPDT, then it can be determined that an infiltration event has occurred in the sensor's monitoring area.

[0047] IPDT Calculation Update Utilizing Upstream Flow Information and Quantifying its Cumulative Variation: Based on drainage network topology data from the monitoring matrix, and combining the effective utilization of upstream sensor flow information with consideration of cumulative variation in flow data, a rule integrating network topology-derived flow inference and the uncertainty of cumulative variation is proposed for calculating IPDT. This rule is demonstrated through two example cases: ① A basic case study of a three-pipe drainage network demonstrates the detailed process of IPDT calculation from single sensor to dual sensor. Figure 3 ); First, construct the monitoring matrix D for this three-pipe drainage network. ij As shown below: (1) The monitoring matrix revealed the following topological information: Pipe 3 is located downstream, while pipes 1 and 2 are both branches upstream of pipe 3. Water flows into pipe 3 from pipes 1 and 2 respectively.

[0048] Furthermore, regarding such Figure 3 In (a), only sensor A is shown. Since there are no sensors upstream of sensor a, the IPDT of pipes 1 to 3 is 120L / s × 15% = 18L / s. For example Figure 3In the dual-sensor scenario shown in (b), based on the IPDT identification results of topology-inferred flow in the monitoring matrix, the combined flow of pipes 1 and 3 is inferred from the flow difference between sensor A and sensor B (120 L / s – 40 L / s = 80 L / s) using the pipe network topology of pipes 1 and 2 converging into pipe 3. After applying a 15% tolerance factor, the threshold for this inferred flow is found to be 80 L / s × 15% = 12 L / s.

[0049] Next, in Figure 3 In (b) of this paper, we continue to consider the cumulative IPDT identification due to the propagation of uncertainty variations: the derivation of the inferred flow rate (80 L / s) depends on the data from sensor B, whose relevant variations propagate into the overall estimate. We assume that the variations in the baseline flow rates of each pipe are independent. Therefore, the root mean square (RSS) method is used to calculate the combined standard deviation (i.e., the total variation): ≈13.42 L / s. This method avoids the overestimation of monitoring thresholds inherent in simple arithmetic summation.

[0050] ②Based on the aforementioned mechanism, Figure 4 A method for calculating IPDTs in complex multi-sensor systems is demonstrated, facilitating practical applications. IPDT values ​​are quantified using a three-step method: (2.1) Based on the topology and flow information of the drainage network, the set of pipes monitored by each sensor and their corresponding total flow are identified; (2.2) A predetermined tolerance coefficient for variation is applied to the total flow of each pipe to calculate the individual monitoring threshold of the sensor on each pipe segment; (2.3) For the individual monitoring threshold of the sensor on each pipe segment, the root mean square (RSS) combination method is used to propagate uncertainty variation, thereby calculating the cumulative infiltration monitoring threshold of each sensor.

[0051] First, based on the topology and flow information of the drainage network, the system directly identifies the pipes monitored individually by each sensor and aggregates their respective flow rates. For example... Figure 4 As shown, the color coding configuration is as follows: Sensor A (purple) monitors pipe 1 with a flow rate of 10 L / s; Sensor B (red) monitors pipes 2 and 3 with a total flow rate of 20 L / s; Sensor C (blue) monitors pipes 4, 5 and 6 with a total flow rate of 40 L / s.

[0052] Next, the individual monitoring threshold for each sensor is calculated, ignoring the cumulative uncertainty variation from other pipes. This is achieved by applying an assumed 15% variation tolerance factor to the individual monitored flow rate for each sensor: the individual monitoring threshold for sensor A (10 L / s) is 1.5 L / s; the individual monitoring threshold for sensor B (20 L / s) is 3 L / s; and the individual monitoring threshold for sensor C (40 L / s) is 6 L / s.

[0053] The final step calculates the cumulative IPDT, a threshold that accounts for the propagation of uncertainty variations from upstream sensors using the RSS method. Sensor A, having no upstream sensor, maintains an IPDT of 1.5 L / s. Sensor B's IPDT includes the propagation of uncertainty variations from sensor A, and the calculated result is... Sensor C simultaneously considers the propagation of uncertainties from sensors A and B, ultimately accumulating the IPDT to... Therefore, these cumulative IPDTs were assigned to their respective pipe groups: the IPDT for pipe 1 was 1.5 L / s; the IPDTs for pipes 2 and 3 were 3.35 L / s; and the IPDTs for pipes 4, 5, and 6 were 6.87 L / s. These IPDTs represent the infiltration monitoring thresholds for each pipe that were finally updated and determined after considering the cumulative uncertainty variation.

[0054] (3) Evaluation index based on minimizing the average detectable threshold (ADT) of the sequential backward selection algorithm (SBS).

[0055] After defining the calculation method for the IPDT of pipe segment infiltration, the IPDT of pipe segment infiltration is averaged and weighted to construct an evaluation index that minimizes the average monitoring threshold (ADT), which serves as the evaluation index for each iteration of SBS, expressed as: (2) in, This indicates the length of each pipe segment, in meters (m). To utilize the infiltration monitoring threshold for each pipe segment determined in step (2) of this invention, m 3 / s; m is the number of pipe segments.

[0056] Based on the above evaluation criteria of ADT, the iterative process using the sequential backward selection algorithm is as follows: (3.1) Input the actual pipeline case into the calculation program, configure a sensor on each pipeline segment, and take the arrangement of a sensor on all pipeline segments as the starting point for iteration; (3.2) Calculate the ADT minimization evaluation index corresponding to the sensor layout after removing each sensor, and remove the sensor corresponding to the minimum value among all ADT minimization evaluation indices; (3.3) Repeat (3.2) until the predetermined minimum number of sensors is reached (set according to actual needs).

[0057] The specific evaluation process is as follows: The first iteration starts with "one sensor is placed in all pipe segments". It calculates the ADT (Adenoted as ADT1×m, where m is the number of pipe segments) corresponding to all sensor layouts after "removing only one sensor". The smallest ADT in ADT1×m and its corresponding sensor layout are retained as the unique optimal solution for this round and the starting point for the next round of evaluation. Thereafter, following the same principle, each round repeats this process of "removing one sensor and selecting the best" until the number of sensors reaches zero, at which point the evaluation terminates.

[0058] The reverse elimination process based on the sequential backward selection algorithm in sub-step (3.2) generates a series of integrated sensor layout subsets and obtains sensor number-performance curves. This can be used to determine the optimal number and layout of sensors for cost-performance balance, forming a clear solution hierarchy to meet the needs of different budget levels.

[0059] The following description, in conjunction with specific examples, provides further details.

[0060] Example 1 Figure 5 The topology of a real drainage network, namely Example 1, is shown, providing a realistic scenario for verification. This network covers a total area of ​​7 km². 2 It includes approximately 55 kilometers of pipelines with diameters ranging from 0.4 to 1.5 meters, transporting an average daily wastewater flow of 27,202 m³. 3 To improve modeling efficiency, the original pipeline network was reasonably simplified, retaining only 150 nodes and 149 pipes, with a focus on reducing the number of manholes in sparse areas lacking connecting tributaries. Sensitivity analysis showed that this simplification did not affect the sensor layout optimization results, ensuring both computational operability and system reliability.

[0061] In addition, such as Figure 5 As shown by the red rectangle, the upper region exhibits significantly higher building density and wastewater discharge. Although this region accounts for only 16.7% of the total service area, it contributes approximately 32% of the total daily flow—almost twice the average hydraulic load concentration in the drainage network. This uneven distribution is particularly pronounced in economically developed areas, where dense commercial and residential activity leads to a substantial increase in wastewater generation. Consequently, the flow patterns in these areas are more dynamic and variable, complicating the accurate and timely monitoring of infiltration events. Therefore, the primary objective of this embodiment is to explore how heterogeneous wastewater discharge affects the optimization of drainage network sensor layout, a crucial issue not addressed in previous studies.

[0062] As a specific application demonstration, Case 1 illustrates the process of sequential backward selection iteratively eliminating the sensor with the least impact, and finally generating nested subsets and their corresponding sensor number-performance curves, as shown below. Figure 6 As shown. Specifically, Figure 6 (a) and (b) in the figure show the iterative elimination process based on the SBS method and the ADT minimization of the evaluation index, and (c) shows the sensor number-performance curve.

[0063] from Figure 6 As shown in (a), the distribution of the 30 sensors (this number is set for clarity in demonstrating the implementation of the invention, not the actual number deployed) indicates that the invention prioritizes sensor deployment in hydraulically critical areas. Specifically, nearly half of the sensors (14 out of 30) are concentrated in the upper part of the red rectangular area, which accounts for less than 20% of the entire monitoring area. This targeted sensor deployment stems from the higher building density and larger wastewater discharge in this area, conditions that lead to increased flow volatility. Therefore, a denser sensor deployment is needed in this area to maintain a lower monitoring threshold. Thus, the invention demonstrates robust adaptability to key hydraulic characteristics of drainage networks. This method effectively allocates more sensor resources to areas with high flow uncertainty, which is crucial for maintaining the robustness of the overall monitoring performance of the system.

[0064] Figure 6 As shown in (b), the elimination of 11 sensors followed a systematic process, fully demonstrating the practical application value of this invention. Specifically, the eliminated sensors were distributed throughout the drainage network, with most located at the terminal branches (such as sensors 2-9 and 11), having a negligible impact on overall monitoring performance. This directly reflects the reverse elimination mechanism employed in this invention—gradually eliminating non-critical sensors through an iterative approach. Furthermore, the generated sensor priority table forms a strict subset hierarchy, a feature that not only simplifies the priority ranking of sensor placement but also provides an economical and efficient solution for sensor system expansion.

[0065] Figure 6 Figure (c) shows the sensor number-performance curve obtained using the SBS method of this invention. This reflects the variation of monitoring performance (ADT) with the number of sensors, which helps guide engineers in selecting a sensor layout scheme that balances economy and superior monitoring performance.

[0066] Example 2 The second real drainage network ( Figure 7 It is significantly larger in scale and more complex in structure, covering an area of ​​approximately 15 km². 2 It includes approximately 60 kilometers of pipeline (with diameters ranging from 0.3 to 1.5 meters) with a daily transport capacity of approximately 43,400 m³. 3Its hydraulic model comprises 820 nodes and 819 pipes. This vast scale creates a large solution space, making this drainage network a highly challenging test platform for evaluating the performance of the method described in this invention. Notably, this invention employs a rigorous comparison between its sensor layout (planned to install 20 flow meters) and an engineering solution developed based on experience by a local water authority, thereby comprehensively assessing the potential superiority of this invention.

[0067] This embodiment verifies the applicability of the topology flow-monitoring threshold inference method in this invention to large-scale drainage pipe networks through two key comparisons. First, by analyzing the IPDT distribution in the engineering solution sensor layout ( Figure 8 The sensitivity gain of the topology flow-monitoring threshold inference method in this invention is evaluated compared to the monitoring threshold method alone.

[0068] from Figure 8 As can be seen in (a), compared to the standalone monitoring threshold method, this invention utilizes topology-derived flow-monitoring threshold inference to achieve a significantly lower and more concentrated IPDT distribution. The ADT of this invention is 17.33 L / s, only 40.3% of the 42.90 L / s of the standalone monitoring threshold method, confirming the significant improvement in monitoring sensitivity. This improvement stems from the invention's ability to utilize flow information from multiple upstream sensors, thereby effectively constraining flow uncertainty. Furthermore, Figure 8 (b) reveals a distinct sensor spatial layout pattern in the sensor performance gain. The most significant reduction in IPDT (ΔDT > 50 L / s) consistently occurs in the downstream main pipe section. This trend is attributed to the gradual convergence of sensor data along the flow direction, which imposes stronger constraints on the flow state in the downstream river section, resulting in a greater reduction in IPDT.

[0069] Secondly, by comparing the sensor layout and engineering layout obtained by this invention, we will focus on examining its competitiveness in terms of spatial layout and IPDT distribution. Figure 9 ).

[0070] Figure 9 Figure (a) shows that, compared to the engineered solution's sensor layout, the sensor layout based on the sequential backward selection method of this invention achieves a level of comparable or even superior overall system monitoring sensitivity. This result is confirmed by the high-density low monitoring thresholds shown in its individual monitoring threshold distribution curves relative to the engineered solution's sensor curves. Quantitative analysis shows that the ADT generated by the sensor layout based on the sequential backward selection method of this invention is 10.41 L / s, significantly lower than the 17.33 L / s of the engineered solution's sensor layout.

[0071] Figure 9(b) further demonstrates the superior performance of the sensor layout based on the sequential backward selection method of this invention compared to the engineered solution sensor layout. By focusing on monitoring branches with high flow rates, the sensor layout obtained by this invention significantly improves the monitoring threshold (as indicated by the red line) compared to the engineered solution sensor layout. This further strongly confirms the effectiveness of the sensor layout obtained under this invention in monitoring low infiltration inflow events.

[0072] In summary, the method of this invention employs a sensor-based flow monitoring and uncertainty inference method derived from the drainage network topology and flow quality conservation; an infiltration monitoring threshold calculation rule based on uncertainty variation propagation; an evaluation index for minimizing the average monitorable threshold based on the sequential backward selection algorithm; and inputs actual network cases into the calculation program to obtain sensor number-performance curves to determine the optimal number and layout of sensors with cost-performance balance. In different embodiments, it can quickly solve for high-performance, low-cost, and stable sensor layouts, accurately predict low infiltration flow events in drainage networks, and significantly improve the excellent monitoring capability for low infiltration flow events in drainage networks, providing strong protection for the safe operation of drainage network systems. It has good interpretability and engineering applicability.

[0073] Corresponding to the aforementioned embodiments of the drainage network sensor layout optimization method based on topological spatial information fusion, this application also provides embodiments of the drainage network sensor layout optimization device based on topological spatial information fusion.

[0074] Figure 10 This is a block diagram illustrating a drainage network sensor layout optimization device based on topological spatial information fusion, according to an exemplary embodiment. (Refer to...) Figure 10 The device may include: The derivation inference module 21 is used to obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area, construct a monitoring matrix, and perform derivation inference based on the flow quality conservation to obtain the individual monitoring flow of each sensor. The cumulative threshold calculation module 22 is used to calculate the cumulative infiltration monitoring threshold for each section of the pipeline based on the topology and flow information of the drainage network and the individual monitoring flow of each sensor, taking into account the propagation of uncertainty variations. The iterative optimization module 23 is used to calculate the average monitorable threshold minimization evaluation index based on the cumulative infiltration monitoring threshold of each sensor, and to use the sequential backward selection algorithm to iterate and generate several sensor layout subsets, and obtain the sensor number-performance curve, thereby determining the sensor layout scheme.

[0075] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0076] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0077] Accordingly, this application also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the above-described method for optimizing the layout of drainage network sensors based on topological spatial information fusion.

[0078] Accordingly, this application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-described method for optimizing the layout of drainage network sensors based on topological spatial information fusion. Figure 11 The diagram shown is a hardware structure diagram of any device with data processing capabilities, which is an optimization device for the layout of drainage pipe networks based on topological spatial information fusion, according to an embodiment of the present invention. Except for... Figure 11 In addition to the processor, memory, and network interface shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0079] Accordingly, this application also provides a computer-readable storage medium storing computer instructions, which, when executed by a processor, implement the aforementioned method for optimizing the layout of drainage network sensors based on topological spatial information fusion. The computer-readable storage medium can be an internal storage unit of any data-processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data-processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data-processing device, and can also be used to temporarily store data that has been output or will be output.

[0080] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A method for optimizing the layout of sensors in drainage pipe networks based on topological spatial information fusion, characterized in that, include: (1) Obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area, construct a monitoring matrix, and make derivation inferences based on the flow quality conservation to obtain the individual monitoring flow of each sensor; (2) Based on the topology and flow information of the drainage network, and combined with the individual monitoring flow of each sensor, the cumulative infiltration monitoring threshold of the sensors on each section of the pipeline is calculated considering the propagation of uncertain variations. (3) Based on the cumulative infiltration monitoring threshold of each sensor, calculate the evaluation index of minimizing the average monitorable threshold, and use the sequential backward selection algorithm to iterate and generate several sensor layout subsets, and obtain the sensor number-performance curve, thereby determining the sensor layout scheme.

2. The method according to claim 1, characterized in that, Step (1) includes: (1.1) Obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area; (1.2) Based on the topology of the drainage network, a monitoring matrix is ​​constructed, wherein the monitoring matrix is ​​a binary matrix used to describe whether the downstream sensors of each numbered pipe can detect the infiltration flow rate when infiltration events occur at nodes with different numbers. The row index of the monitoring matrix is ​​the node number, and the column index of the monitoring matrix is ​​the pipe number. (1.3) Based on the monitoring matrix and the flow information of the drainage pipe network in the target area and the sensor distribution, the individual monitoring flow of the sensor is obtained by derivation based on the flow quality conservation.

3. The method according to claim 2, characterized in that, The derivation inference in step (1.3) is as follows: Subtracting the upstream sensor flow rate from the downstream sensor flow rate yields the individual monitoring flow rate of the downstream sensor.

4. The method according to claim 1, characterized in that, Step (2) includes: (2.1) Based on the topology and flow information of the drainage network, identify the set of pipes monitored by each sensor and its corresponding total flow; (2.2) Apply the predetermined variation tolerance coefficient to the total flow of each pipeline and calculate the individual monitoring threshold of the sensor on each pipeline section; (2.3) The root mean square combination method is used to propagate uncertainty variation for the individual monitoring thresholds of the sensors on each section of the pipeline, thereby calculating the cumulative infiltration monitoring threshold of each sensor.

5. The method according to claim 1, characterized in that, The evaluation index for minimizing the average monitoring threshold in step (3) is: ， in, This indicates the length of each pipe segment, in meters (m). The infiltration monitoring threshold for each pipe segment calculated in step (2), m 3 / s This represents the number of pipe sections.

6. The method according to claim 1, characterized in that, In step (3), the sequential backward selection algorithm is used for iteration, specifically as follows: (3.1) The iteration starts with one sensor installed on each pipe segment; (3.2) Calculate the average monitoring threshold minimization evaluation index corresponding to the sensor layout after removing each sensor, and remove the sensor corresponding to the minimum value among all average monitoring threshold minimization evaluation indices; (3.3) Repeat (3.2) until the predetermined minimum number of sensors is reached.

7. A drainage pipe network sensor layout optimization device based on topological spatial information fusion, characterized in that, include: The derivation and inference module is used to obtain the topology, flow information and sensor distribution of the drainage pipe network in the target area, construct a monitoring matrix, and perform derivation and inference based on the flow quality conservation to obtain the individual monitoring flow of each sensor. The cumulative threshold calculation module is used to calculate the cumulative infiltration monitoring threshold for sensors on each section of the pipeline, taking into account the propagation of uncertainties, based on the topology and flow information of the drainage network and the individual monitoring flow of each sensor. The iterative optimization module is used to calculate the average monitorable threshold minimization evaluation index based on the cumulative infiltration monitoring threshold of each sensor, and to use the sequential backward selection algorithm to iterate and generate several sensor layout subsets, and obtain the sensor number-performance curve, thereby determining the sensor layout scheme.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the method as described in any one of claims 1-6.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-6.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the method as described in any one of claims 1-6.

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