Digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks

Abstract

This invention discloses a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks. It integrates GIS, real-time sensor data, meteorological data, and historical hydrological data to construct a dynamic hydraulic-water quality coupling model, outputting hydraulic-water quality parameters and fault probabilities for pipe sections. Based on this, a spectral clustering similarity matrix is ​​generated in real time, fusing dynamic characteristics of pipe sections with fault probability weights to divide functional zones into risk levels. The clustering results are fed back to the digital twin model for verification: if a zone fails to pass extreme conditions, the similarity matrix is ​​recalibrated and clustering is iterated; if it passes, NSGA-II multi-objective optimization is triggered. Combined with the risk level allocation weights for each zone, a sensor deployment scheme is output. The missed detection rate is verified through digital twin simulation, enabling dynamic adjustment of target weights and re-optimization until the final scheme is achieved. This invention forms a closed loop of "simulation-dimensionality reduction-optimization-verification," achieving dynamic adjustment of sensor layout while effectively reducing deployment costs.

Description

Technical Field

[0001] This invention relates to the field of dynamic risk prevention and control technology for critical urban infrastructure, and in particular to an adaptive deployment method for urban water system monitoring networks based on digital twins and multi-objective optimization, applicable to scenarios such as smart city disaster prevention and mitigation, and environmental risk early warning. Background Technology

[0002] Urban drainage systems (UDS) are critical infrastructure responsible for collecting urban runoff in catchment areas, transporting rainwater to receiving water bodies, and diverting wastewater to treatment plants, effectively mitigating urban flooding and regulating water pollution. However, the existing urban water system monitoring network topology optimization process still has the following shortcomings:

[0003] ① Existing methods for optimizing sensor layout in urban water system monitoring network topology mostly rely on manual forward experience or simplified rule-driven methods. These methods cannot dynamically adjust sensor arrangement, cannot adapt to changes under different environments and conditions, lack quantitative analysis of pipeline topology and hydraulic dynamic characteristics, and are subject to subjective bias.

[0004] ② Existing technologies often focus on a single optimization objective, which has fundamental limitations in optimizing the topology of urban water system monitoring networks. Their model design, guided by a single indicator (such as cost or coverage), cannot balance the complex conflicts between multi-dimensional objectives: pursuing maximum coverage may lead to uncontrolled costs, while cost reduction can easily cause the expansion of monitoring blind spots. This single-objective drive disrupts the overall balance of the system, resulting in solutions that are incomplete in practical applications. Furthermore, the operating status of the pipeline network is significantly affected by dynamic factors such as weather and pollution; the single-objective framework lacks the ability to adaptively adjust to multiple operating conditions, making it difficult to meet the differentiated needs of high-frequency monitoring during rainstorms or daily water quality tracking. In addition, multi-dimensional constraints in real-world deployments are often simplified into penalty terms or rigidly truncated, ignoring the coupling effects between constraints, leading to a narrow feasible solution space. Single-objective optimization can only provide a single "optimal" solution, failing to generate a diverse set of solutions that balance the interests of multiple parties, thus limiting decision-making flexibility.

[0005] ③ Most current monitoring network layout algorithms are based on static pipe network models, which are difficult to match the dynamic operating characteristics of drainage systems. Their core flaw lies in simulating system behavior with fixed parameters, ignoring the real-time impact of external disturbances. The spatiotemporal deviation between the model and actual operating conditions leads to sensor layout schemes missing detections during heavy rain and experiencing delayed source tracing in pollution events. Simultaneously, the static framework lacks online coupling capabilities with IoT data, making it impossible to dynamically calibrate the monitoring network through real-time water level and water quality feedback, resulting in expanded monitoring blind spots in extreme scenarios.

[0006] ④ Current multi-objective optimization algorithms face significant challenges in solving the topology optimization problem of large-scale urban water system monitoring networks. First, pipe network systems typically contain thousands of hydraulic functional units, and the massive combination of variables leads to an exponential increase in computational complexity, making it difficult to obtain a reliable solution within a reasonable timeframe. Second, actual deployments must meet complex constraints, such as equipment installation feasibility, regional maintenance cost differences, and communication stability. Traditional algorithms often oversimplify these constraints, resulting in solutions that are either unimplementable or deviate from real-world requirements. Furthermore, the importance of each objective in the drainage network dynamically changes under different operating conditions, but existing methods lack adaptive weight adjustment mechanisms, making it difficult to generate balanced solutions that flexibly adapt to multiple scenarios. These bottlenecks collectively lead to optimization results easily getting trapped in local optima and insufficient solution set diversity, ultimately affecting the overall effectiveness of the monitoring network.

[0007] ⑤ Data-driven technology has not yet fully realized its potential in drainage network monitoring, mainly due to three limitations: First, digital twin models often employ simplified assumptions, leading to significant discrepancies between simulation results and actual operating conditions, affecting the accuracy of sensor placement; second, traditional clustering methods are not optimized for features such as network topology connectivity and hydraulic correlation, resulting in incorrect functional zoning and misleading sensor deployment; third, algorithm design is disconnected from hardware characteristics, failing to consider cost differences among various sensor types, data heterogeneity, and collaborative monitoring requirements, leading to mismatches between optimized solutions and actual engineering conditions.

[0008] Existing technologies suffer from three major drawbacks: "static modeling," "single-objective decision-making," and "data silos," making it impossible to achieve coordinated optimization of "dynamic risk, cost, and efficiency." Especially in large-scale urban water systems, traditional methods face the dual bottlenecks of the curse of dimensionality and scenario mismatch.

[0009] Therefore, how to provide a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks that can dynamically adjust sensor layout while effectively reducing deployment costs is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] In response to the aforementioned research status, this invention provides a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks. Based on the digital twin method, sensors can be dynamically adjusted according to the modeled simulation state. The digital twin model provides dynamic simulation data to drive clustering and multi-objective optimization. Spectral clustering constrains the search space of the NSGA-II algorithm, and the NSGA-II output feedback value is fed back to the digital twin model to achieve closed-loop operation.

[0011] This invention provides a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks, comprising the following steps:

[0012] S1: Based on digital twin modeling, integrate GIS geographic information, real-time water system pipeline sensor data, meteorological data and historical hydrological records to construct a dynamic hydraulic-water quality coupling model of the urban drainage system;

[0013] S2: Through dynamic simulation of the dynamic hydraulic-water quality coupling model, digital twin simulation results are generated, including hydraulic-water quality data of the pipe section and the predicted probability of pipe section failure.

[0014] S3: Based on the digital twin simulation results, the reconstruction of the spectral clustering similarity matrix is ​​triggered in real time to represent the similarity weight between the current pipe segment and adjacent pipe segments; dynamic weighted spectral clustering is performed on the water system network based on the spectral clustering similarity matrix; the water system network is divided into multiple functional zones based on the clustering results, and the risk level of each zone is marked.

[0015] S4: Feed the clustering results back to the dynamic hydraulic-water quality coupling model of the urban drainage system. Based on the digital twin feedback results, trigger the return to S3 to recalibrate the spectral clustering similarity matrix and re-perform dynamic weighted spectral clustering, or trigger the use of the NSGA-II algorithm to optimize the sensor deployment of each functional area, including assigning optimization target weights to each functional area and performing multi-objective sensor optimization deployment for the functional area.

[0016] S5: Import the optimized deployment scheme of S4 into the dynamic hydraulic-water quality coupling model, simulate and verify the monitoring missed detection rate under preset extreme working conditions. If the missed detection rate exceeds the standard, trigger the return to S4 to adjust the weight of the optimization target, and re-execute the NSGA-II algorithm iteration until the verification is passed, and output the final sensor deployment scheme.

[0017] Preferably, the input data for constructing the dynamic hydraulic-water quality coupling model of the urban drainage system in S1 includes integrated GIS geographic information such as: pipeline GIS topology, terrain elevation model, and land use type; dynamic data such as: real-time water system pipeline sensor data, meteorological data, and pump station operating status; and historical hydrological records such as: historical rainfall events, pollution accident records, and equipment maintenance logs.

[0018] Preferably, the system receives real-time data from water system pipeline sensors and dynamically updates the initial conditions of the dynamic hydraulic-water quality coupling model of the drainage system for dynamic simulation to generate digital twin simulation results.

[0019] Preferably, the dynamic hydraulic-water quality coupling model outputs real-time hydraulic-water quality data for the pipe section, including the pipe section's hydraulic sensitivity and pollution risk, through dynamic calibration of model parameters.

[0020] Hydraulic sensitivity is: ;

[0021] in, For the real-time flow rate of the pipeline segment, Design flow rate for the pipeline section, Let i be the slope of the pipe segment at node i in the pipeline network;

[0022] The pollution risk is: ;

[0023] Where C is the pollutant concentration and v is the flow velocity. β is the attenuation factor, β is the first-order attenuation coefficient of pollutants, and T is the simulation period.

[0024] Preferably, the step of reconstructing the spectral clustering similarity matrix in real time based on the digital twin simulation results in S3 includes:

[0025] Construct the spectral clustering similarity matrix:

[0026] ;

[0027] Among them, multidimensional feature vectors , For hydraulic sensitivity Feature weights, For pollution risk Feature weights, Failure probability Feature weights, For topological centrality, Let be the failure probability of pipeline node i. Let be the failure probability of pipeline node j downstream of pipeline node i. The bandwidth parameter of the Gaussian kernel. , is the flow direction penalty factor, used to characterize the dependence of downstream pipeline node j on upstream pipeline node i. The flow direction penalty intensity coefficient;

[0028] The dynamic hydraulic-water quality coupling model updates the failure probability in real time. This triggers the reconstruction of the spectral clustering similarity matrix.

[0029] Preferably, in step S4, the step of triggering a return to step S3 to recalibrate the spectral clustering similarity matrix based on the digital twin feedback result includes: recalibrating the hydraulic sensitivity. Pollution risk and failure probability The feature weights are used to obtain a new spectral clustering similarity matrix, and dynamic weighted spectral clustering is performed again.

[0030] Preferably, in step S3, the step of dynamically weighted spectral clustering of the water system network based on the spectral clustering similarity matrix includes:

[0031] Calculate the normalized Laplacian matrix based on the spectral clustering similarity matrix. Used to describe the pipeline network topology:

[0032] ;

[0033] ;

[0034] ;

[0035] Where n is the total number of pipeline nodes;

[0036] For the normalized Laplace matrix Perform eigenvalue decomposition and solve the equation:

[0037] ;

[0038] Calculate the eigenvalues ​​of the Laplacian matrix And the corresponding eigenvectors V; sorted in ascending order of eigenvalues, the eigenvectors corresponding to the k smallest non-zero eigenvalues ​​are selected to form a low-dimensional embedding matrix. ;

[0039] The K-means algorithm is executed on the low-dimensional embedding matrix V to divide the network nodes into k clusters and determine the optimal number of clusters.

[0040] Preferably, S4 includes:

[0041] The clustering results are fed back into a dynamic hydraulic-water quality coupling model of the urban drainage system to simulate the behavior of each cluster under preset extreme conditions.

[0042] If the cluster simulation of the high-risk functional zone shows that the hydraulic and water quality data of the pipe section exceeds the standard, the NSGA-II algorithm will be used to deploy sensors in each functional zone to increase the sensor density.

[0043] If the cluster simulation of the low-risk functional zone shows that the hydraulic and water quality data of the pipe section does not exceed the standard, then the NSGA-II algorithm is used to deploy sensors in each functional zone to reduce the sensor density.

[0044] If the cluster miss rate corresponding to a functional partition exceeds the standard, it will trigger a return to S3 to recalibrate the spectral clustering similarity matrix and re-perform dynamic weighted spectral clustering, or trigger the use of the NSGA-II algorithm to optimize sensor deployment for each functional partition.

[0045] Preferably, in step S4, the objective function for multi-objective sensor optimization deployment of functional partitions using the NSGA-II algorithm includes:

[0046] Objective function for maximizing coverage utility:

[0047] ;

[0048] ;

[0049] in, For clusters The optimization target weight is determined by the partition risk level. For the corresponding cluster Sensor deployment status;

[0050] Economic cost minimization objective function:

[0051] ;

[0052] in, For clusters The equipment cost, To be with cluster Installation costs related to geographical characteristics;

[0053] Redundancy minimization objective function:

[0054] ;

[0055] in, For inter-cluster data correlation, This represents the physical distance between clusters.

[0056] Preferably, in step S4, the constraints for performing multi-objective sensor optimization deployment for functional partitions using the NSGA-II algorithm include:

[0057] High-risk cluster mandatory coverage constraint: High-risk clusters;

[0058] Connectivity constraint: If cluster and Adjacent and ,but , Maximum allowed communication distance;

[0059] Budget constraints: , For the total budget.

[0060] Preferably, step S5 further includes one or more of the following steps:

[0061] High-risk clusters If the false negative rate exceeds the target, the optimization objective weight of the corresponding cluster will be increased. Hard constraints are added to the NSGA-II algorithm iteration. The sensor deployment in each functional area was re-optimized.

[0062] Clusters corresponding to functional partitions that have been retained across multiple generations. Add hard constraints in subsequent iterations .

[0063] Compared with existing technologies, which suffer from incomplete sensor coverage and blind spots, insufficient adaptability to dynamic scenes, and low efficiency in multi-objective optimization, this invention has the following advantages:

[0064] This invention enhances dynamic simulation capabilities based on digital twin technology: it simulates the hydraulic and water quality behavior of pipeline networks under different operating conditions (such as rainstorms and pollution events) in real time through high-precision models, supporting dynamic scenario prediction and decision-making; data-driven updates: it accesses sensor and meteorological data in real time, dynamically adjusts model parameters (such as Manning coefficient), and improves the consistency between simulation results and actual operating conditions.

[0065] This invention achieves intelligent dimensionality reduction based on spectral clustering: functional partitioning is performed based on the physical characteristics of the pipeline network, such as hydraulic sensitivity, pollution risk, and topology, compressing the complex pipeline network into a small number of functional clusters, significantly reducing the complexity of the optimization problem; dynamic weight fusion introduces dynamic parameters (such as failure probability) from digital twin output, strengthening the clustering density of high-risk areas and improving the scenario adaptability of partitioning; engineering interpretability: the partitioning results are highly matched with the operation and maintenance logic, such as flood-prone sub-basins and pollution-sensitive areas, facilitating the implementation and verification of the solution.

[0066] This invention achieves multi-objective balanced optimization based on the NSGA-II algorithm: it simultaneously optimizes conflicting objectives such as coverage utility, deployment cost, and information redundancy, generating diverse Pareto optimal solution sets to support flexible decision-making; it has efficient search capabilities: through non-dominated sorting and crowding distance calculation, it converges quickly in the dimensionality-reduced search space, taking into account both the quality and diversity of the solution set; and it has dynamic adaptability: combined with real-time scenario requirements such as rainstorm warnings, it dynamically adjusts the target weights to achieve flexible switching of multi-objective priorities.

[0067] The above three aspects work together to significantly improve efficiency: spectral clustering reduces the optimization dimensionality, NSGA-II searches efficiently in low-dimensional space, and computational efficiency is significantly improved; digital twin provides real-time data feedback, avoiding ineffective iterations and further shortening response time. Regarding accuracy and robustness, digital twin provides dynamic simulation support, spectral clustering ensures clear physical meaning of partitions, and NSGA-II generates balanced solution sets, forming a closed loop of "simulation-dimensionality reduction-optimization-verification"; in extreme scenarios, model parameters and target weights are dynamically adjusted to improve the scenario adaptability of the monitoring network; spectral clustering partitions are consistent with operational experience, NSGA-II solution sets provide multi-objective trade-offs, and digital twin visualization assists decision-making, collectively enhancing the feasibility and acceptability of the solution.

[0068] This invention achieves dynamic linkage throughout the entire process from real-time perception and efficient dimensionality reduction to precise optimization through this three-order dynamic coupling mechanism. It fully leverages the advantages of digital twins, spectral clustering, and the NSGA-II algorithm, and organically integrates them to form an efficient, intelligent, and reliable urban water system monitoring network for adaptive deployment. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without creative effort.

[0070] Figure 1 This is a flowchart of a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks, provided in an embodiment of the present invention.

[0071] Figure 2 This is a logical function diagram of the digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks provided in this embodiment of the invention;

[0072] Figure 3 This is a flowchart of spectral clustering dimensionality reduction provided in an embodiment of the present invention;

[0073] Figure 4 This is an optimization principle diagram of the digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks provided in an embodiment of the present invention;

[0074] Figure 5 This is a flowchart of the NSGA-II algorithm provided in an embodiment of the present invention;

[0075] Figure 6 This is a flowchart of the digital twin construction process provided in an embodiment of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] This invention discloses a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks, such as... Figure 1-2 As shown, it includes the following steps:

[0078] S1: Based on digital twin modeling, integrate GIS geographic information, real-time water system pipeline sensor data, meteorological data and historical hydrological records to construct a dynamic hydraulic-water quality coupling model of the urban drainage system, ensuring that the simulation results are consistent with the actual pipeline network behavior;

[0079] S2: Through dynamic simulation of the dynamic hydraulic-water quality coupling model, digital twin simulation results are generated, including hydraulic-water quality data of the pipe section and the predicted probability of pipe section failure.

[0080] S3: Based on the digital twin simulation results, the reconstruction of the spectral clustering similarity matrix is ​​triggered in real time to represent the similarity weight between the current pipe segment and the adjacent pipe segments; dynamic weighted spectral clustering of the water system network is performed based on the spectral clustering similarity matrix; the water system network is divided into multiple functional zones based on the clustering results, and the risk level of each zone is marked.

[0081] S4: Feed the clustering results back to the dynamic hydraulic-water quality coupling model of the urban drainage system. Based on the digital twin feedback results, trigger the return to S3 to recalibrate the spectral clustering similarity matrix and re-perform dynamic weighted spectral clustering, or trigger the use of the NSGA-II algorithm to optimize the sensor deployment of each functional area, including assigning optimization target weights to each functional area and performing multi-objective sensor optimization deployment for the functional area.

[0082] S5: Import the optimized deployment scheme of S4 into the dynamic hydraulic-water quality coupling model to simulate and verify the monitoring missed detection rate under preset extreme working conditions. If the missed detection rate exceeds the standard, it will trigger the return to S4 to adjust the optimization target weights and re-execute the NSGA-II algorithm iteration until the verification is passed, and output the final sensor deployment scheme.

[0083] This invention, through the deep integration of digital twins, spectral clustering, and the NSGA-II algorithm, constructs an intelligent technology system for topology optimization of urban water system monitoring networks. The digital twin simulation method can be dynamically adjusted based on the results fed back from NGSA-II. Adding a spectral clustering algorithm to the digital twin framework integrates the physical characteristics of the pipe network with data-driven methods, reducing optimization complexity while preserving the functional correlation between pipe segments. This provides a physically interpretable dimensionality reduction space for subsequent multi-objective decision-making, avoiding the loss of key information due to dimensionality compression. Combined with the NSGA-II algorithm, which provides a scientific decision-making framework for the layout of drainage pipe network sensors through multi-objective collaborative optimization, high-dimensional space solution set control, and dynamic constraint response, the generated scheme possesses both global optimality and engineering operability, becoming a key technological link between digital twin simulation and physical deployment.

[0084] The spectral clustering algorithm introduces fault probability weights, which cleverly reduces the dimensionality of large-scale monitoring networks. By incorporating fault probability weights into the spectral clustering similarity matrix, it not only considers the physical distance and feature similarity of pipe segments, but also fully integrates the key factor of fault probability. This makes the clustering results more in line with the actual pipeline network operation risk situation and provides more targeted functional partitioning for subsequent optimization deployment.

[0085] In one embodiment, the input data for constructing the dynamic hydraulic-water quality coupling model of the urban drainage system in S1 integrates GIS geographic information including: pipeline GIS topology, terrain elevation model, and land use type; dynamic data including: real-time water system pipeline sensor data, meteorological data, and pump station operating status; and historical hydrological records including: historical rainfall events, pollution accident records, and equipment maintenance logs. The input data is cleaned and fused, including denoising, spatiotemporal alignment, and missing data imputation, before being used in the digital twin modeling step.

[0086] In this embodiment, the digital twin model integrates geographic information systems, real-time sensor data, and meteorological forecast information. Based on a hydraulic simulation engine, it dynamically simulates the pipeline network status under extreme conditions such as heavy rain, drought, and pollution, generating a spatiotemporal evolution dataset containing flow mutations, pollutant diffusion paths, and pipe section siltation rates. To address the dimensionality curse caused by the massive scale of the pipeline network, an improved spectral clustering algorithm extracts multi-dimensional features from the digital twin data, including hydraulic sensitivity, pollution risk, and topological hub-like characteristics of pipe sections. A similarity matrix is ​​constructed using a Gaussian kernel function and dynamic weights to divide the pipeline network into functionally related partitions.

[0087] In one embodiment, the dynamic hydraulic-water quality coupling model enables multi-scenario simulation, including: normal operating conditions, 1-year / 50-year return period rainfall simulation, outputting flow rate, water level, and overflow point; extreme events, such as short-duration heavy rainfall and sudden pollution surges. The dynamic hydraulic-water quality coupling model receives real-time data from water system pipeline sensors, such as receiving sensor data every 5 minutes, and dynamically updates the model's initial conditions (e.g., water level, pump station status). Real-time access to pump station operating status via an IoT interface improves prediction accuracy. The dynamic hydraulic-water quality coupling model of the drainage system dynamically updates its initial conditions for generating digital twin simulation results.

[0088] In one embodiment, the hydraulic model in the dynamic hydraulic-water quality coupling model uses the Storm Water Management Model (SWMM). The Saint-Venant equations are employed to simulate transient flow dynamics. Key parameters include the Manning coefficient and Horton infiltration model parameters. The water quality model uses the Advance-Dispersion equations to simulate pollutant migration and diffusion. Source terms are defined based on industrial wastewater discharge patterns. Parameter calibration employs Shuffled Complex Evolution to optimize the Manning coefficient and pollutant attenuation rate, with a target Nash-Sutcliffe efficiency coefficient (NSE) > 0.7 and peak flow error < 15%.

[0089] The dynamic hydraulic-water quality coupling model obtains dynamic simulations of scenarios such as pollution accidents through real-time output of dynamically calibrated model parameters, generating a spatiotemporal dataset of pollutant diffusion paths. Based on this, the calculated hydraulic-water quality data of the pipe section includes the pipe section's hydraulic sensitivity and pollution risk.

[0090] Flow rate acquired in real time by sensors The hydraulic sensitivity is dynamically updated based on water level H, flow velocity V, and other parameters. ;

[0091] in, For the real-time flow rate of the pipeline segment, Design flow rate for the pipeline section, Let be the slope of the pipe segment at node i in the pipeline network. It should be noted that... The SWMM Saint-Venant equations are obtained by real-time solution. The SWMM Saint-Venant equations are coupled with water level H (flow area A(H)) and flow velocity V (V=Q). 实际 / A(H)). The hydraulic sensitivity calculation formula accurately captures the changes in the hydraulic state of the pipe section in different time periods by calculating the rate of change of flow over time. Especially under extreme weather conditions such as heavy rain, it can promptly reflect the sudden changes in flow of hydraulic functional units, providing real-time hydraulic sensitivity information for subsequent optimization decisions.

[0092] The spatiotemporal distribution of pollutant concentrations output by the Advancement-Dispersion model in digital twins is used to calculate pollution risk as follows: ;

[0093] Where C is the pollutant concentration and v is the flow velocity. It is a decay factor that decreases exponentially over time. The first-order attenuation coefficient of pollutants reflects the natural attenuation or sedimentation of pollutants over time, and T is the simulation period. The pollution risk calculation formula comprehensively considers the cumulative effect of pollutant concentration and water flow velocity over time, which can accurately assess the pollution risk of a pipe section within a specific time period and provide strong support for the prevention and response to pollution incidents.

[0094] Digital twins predict the probability of pipe section failures based on historical fault data and real-time operating conditions, such as sediment thickness and sudden changes in flow velocity. (a·siltation rate + b·flow velocity variation coefficient).

[0095] In one embodiment, the step of reconstructing the spectral clustering similarity matrix in real time based on the digital twin simulation results in S3 includes:

[0096] Construct the spectral clustering similarity matrix:

[0097] ;

[0098] Among them, multidimensional feature vectors , For hydraulic sensitivity Feature weights, For pollution risk Feature weights, Failure probability Feature weights, For topological centrality, Let be the failure probability of pipeline node i. Let be the failure probability of pipeline node j downstream of pipeline node i. The bandwidth parameter of the Gaussian kernel. , is the flow direction penalty factor, used to characterize the dependence of downstream pipeline node j on upstream pipeline node i. The flow direction penalty intensity coefficient;

[0099] The dynamic hydraulic-water quality coupling model updates the failure probability in real time. For example, digital twins are updated every hour. This triggers the reconstruction of the spectral clustering similarity matrix, introduces the fault probability output by the digital twin as the clustering weight, strengthens the cluster density within high-risk areas, and partitions the drainage pipe network. If a certain pipe section... Failure probability A sudden increase in the similarity weight between the high-risk cluster and its adjacent pipe sections ensures that pipe sections within the high-risk cluster are prioritized for monitoring.

[0100] In one embodiment, such as Figure 3 The diagram shown is a flowchart of spectral clustering dimensionality reduction. In S3, the spectral clustering dimensionality reduction process consists of the following steps: updating the Laplacian matrix, and driving the process with real-time digital twin data. Dynamic changes, and then updates ; Eigenvalue decomposition and cluster partitioning, solution A low-dimensional embedding matrix V is generated, and K-means clustering is performed to obtain the network partitions. .

[0101] In this embodiment, the steps for dynamically weighted spectral clustering of the water system network based on the spectral clustering similarity matrix include:

[0102] Calculate the normalized Laplacian matrix based on the spectral clustering similarity matrix. Used to describe the pipeline network topology:

[0103] ;

[0104] ;

[0105] ;

[0106] Where n is the total number of pipeline nodes;

[0107] For the normalized Laplace matrix Perform eigenvalue decomposition and solve the equation:

[0108] ;

[0109] Calculate the eigenvalues ​​of the Laplacian matrix And the corresponding eigenvectors V; sorted by eigenvalues ​​in ascending order, the eigenvectors corresponding to the k smallest non-zero eigenvalues ​​are selected, and the eigenvectors are arranged column-wise to form a low-dimensional embedding matrix. ;

[0110] The low-dimensional embedding matrix V preserves the functional correlation of the pipeline network, facilitating subsequent K-means clustering. The objective function of K-means clustering is:

[0111] ;

[0112] in, For the i-th cluster, For clusters The centroid of the network is V, which is a row vector in the low-dimensional embedding matrix, representing a network node.

[0113] The K-means algorithm is executed on the low-dimensional embedding matrix V to divide the nodes into k clusters; the optimal number of clusters k is determined based on the silhouette coefficient or domain knowledge.

[0114] Clustering results divide the pipeline network into functionally similar areas, such as high-risk pollution zones, guiding the optimal deployment of sensors.

[0115] It should be noted that the special processing for pipeline network zoning includes: dynamic weight fusion, which introduces dynamic parameters such as pipeline segment failure probability from the digital twin output into the similarity matrix. :

[0116] ;

[0117] If a certain pipe section has a high probability of failure, that is... Larger similarity weights between nodes increase the likelihood of clustering high-risk areas; enhanced topological constraints allow for the introduction of directional penalty factors in similarity calculations, such as unidirectional water flow, if the network exhibits directionality.

[0118] ;

[0119] in, The directional weight is set to 1 when the downstream node j has a strong dependence on the upstream node i, and 0.5 otherwise.

[0120] In one embodiment, risk indicators output by the digital twin, such as overflow frequency and contamination concentration, are used for each cluster. Mark the risk level: red / yellow / green.

[0121] In one embodiment, S4 includes:

[0122] The clustering results are fed back to the dynamic hydraulic-water quality coupling model of the urban drainage system to simulate the behavior of each cluster under preset extreme conditions. If the missed detection rate of the cluster corresponding to the functional area exceeds the standard, it triggers a return to S3 to recalibrate the spectral clustering similarity matrix and re-perform dynamic weighted spectral clustering. This belongs to the data preprocessing and clustering modeling stage, and is used to calculate the importance weights of various features (such as pollution risk, hydraulic sensitivity, and topological hub status) of the similarity between pipe segments. The specific steps are as follows:

[0123] Recalibrate hydraulic sensitivity Feature weights Pollution risk Feature weights and failure probability Feature weights This yields a new spectral clustering similarity matrix, and dynamic weighted spectral clustering is performed again. The update rules are as follows:

[0124] Hydraulic sensitivity weight:

[0125] ;

[0126] Pollution risk weights:

[0127] ;

[0128] Failure probability weights:

[0129] ;

[0130] Among them, the digital twin outputs the duration of exceedance for each pipe segment i. Peak concentration Peak traffic , This is an adjustable coefficient, which can be 0.1–0.5.

[0131] The following example illustrates how clustering results can be input into a digital twin to simulate the behavior of each cluster under a rainstorm scenario:

[0132] If the false negative rate of a certain functional area exceeds 5%, it is because the pollution risk is underestimated. The system will increase the weight of the "pollution risk" feature, causing the area to be assigned to a higher-risk cluster during re-clustering, thereby prompting the subsequent optimization phase to strengthen monitoring and deployment in that area.

[0133] When a cluster experiences a false negative rate exceeding the acceptable limit during the validation phase, the process reverts to the spectral clustering phase. This reassessment re-evaluates the impact of each feature on the clustering results. By increasing the weights of features closely related to the false negative issue, the clustering results more accurately reflect the actual risk distribution. This allows for a re-evaluation of cluster boundaries and the application of new clustering methods. After re-performing spectral clustering to obtain new functional partitions, the NSGA-II algorithm is then used to optimize sensor deployment in each functional partition.

[0134] In one embodiment, S4 includes:

[0135] The clustering results are fed back to the dynamic hydraulic-water quality coupling model of the urban drainage system to simulate the behavior of each cluster under preset extreme conditions. Based on the digital twin feedback results, the NSGA-II algorithm is used to optimize the sensor deployment of each functional area. This is part of the optimization decision-making stage, which is used to adjust the weight of high-risk clusters in the optimization objective function, i.e., the cluster priority weight. The specific steps are as follows:

[0136] If the cluster simulation of the high-risk functional zone shows that the hydraulic and water quality data of the pipe section exceeds the standard, the NSGA-II algorithm will be used to deploy sensors in each functional zone to increase the sensor density.

[0137] If the cluster simulation of the low-risk functional zone shows that the hydraulic and water quality data of the pipe section does not exceed the standard, then the NSGA-II algorithm is used to deploy sensors in each functional zone to reduce the sensor density.

[0138] If the cluster miss rate for each functional partition exceeds the standard, the weight of that cluster in the objective function will be directly increased, so that the cluster will be covered first in the next round of optimization, but the cluster boundary division will not be changed.

[0139] The following example illustrates how clustering results can be input into a digital twin to simulate the behavior of each cluster under a rainstorm scenario:

[0140] High-risk clusters (red): If simulation shows that their overflow is greater than 120% of the design value, the "forced sensor deployment" constraint in NSGA-III optimization is triggered; Low-risk clusters (green): If digital twin verification shows stability, such as 10 years without failure, sensor density can be reduced. When only a single cluster k has a false negative rate greater than 5%, the optimization weight coefficient of that cluster in the NSGA-II objective function is directly updated.

[0141] .

[0142] This process forces NSGA-II to deploy sensors in the cluster in the next round of optimization, but does not re-divide the cluster boundaries.

[0143] In one embodiment, such as Figure 4-5 As shown, in S4, optimized deployment is based on clustering results, providing precise deployment guidance for each partition, mainly including the following steps:

[0144] S41: Problem Modeling and Initialization

[0145] First, the population is initialized, and encoding and constraints are performed based on partitioning. The decision variables are defined as k functional clusters generated based on spectral clustering. Each solution is represented as a binary vector. ,in:

[0146] ;

[0147] Each variable It directly corresponds to the deployment status of a cluster, rather than a segment-level variable, reflecting the partition constraints after dimensionality reduction.

[0148] S42: Initialization rules:

[0149] Forced deployment of high-risk clusters: If If a data twin simulation overflow frequency is greater than 5 times per year, then... .

[0150] Minimum coverage constraint: Each cluster must deploy at least one sensor; this is a hard constraint to avoid completely uncovered areas. Example: If spectral clustering divides... (High risk) (Medium risk) (Low risk)

[0151] Forced during initialization And randomly generated The combination, but satisfying .

[0152] S43: Objective Function Design: The objective function design should directly reflect the partitioning results of spectral clustering.

[0153] Objective function for maximizing coverage utility:

[0154] ;

[0155] ;

[0156] in, For clusters The optimization target weight is determined by the partition risk level. For the corresponding cluster The sensor deployment status; the risk-weighted objective function assigns higher weights to the coverage utility of high-risk clusters, ensuring that coverage of high-risk areas is prioritized during the optimization process, thereby improving the overall effectiveness and reliability of the monitoring network.

[0157] Partition correlation: High-risk clusters have higher coverage utility weights, driving the algorithm to prioritize sensor deployment.

[0158] Economic cost minimization objective function:

[0159] ;

[0160] in, For clusters The equipment cost, To be with cluster Installation costs related to geographical characteristics;

[0161] Zonal correlation: Cost parameters are set based on the geographical attributes of the zonals, rather than being uniformly distributed.

[0162] Redundancy minimization objective function:

[0163] ;

[0164] in, For inter-cluster data correlation, This represents the physical distance between clusters.

[0165] Partition correlation: Only the redundancy of adjacent clusters is calculated, and duplicate coverage of functionally similar regions is suppressed.

[0166] S44: Constraints: Explicitly Embedded Partitioning Rules:

[0167] High-risk cluster mandatory coverage constraint: High-risk cluster set; partition association: directly inherit the high-risk labeling results of spectral clustering.

[0168] Connectivity constraint: If cluster and Adjacent and ,but , The maximum allowable communication distance, such as 500 meters, is used to ensure the connectivity of the monitoring network; partition correlation: the relationship between adjacent clusters is defined based on spectral clustering.

[0169] Budget constraints: , The total budget needs to be dynamically adjusted based on the geographical cost characteristics of each zone.

[0170] S45: Evolutionary Operation: Maintaining Partition Constraints

[0171] Crossover operator:

[0172] Single-point crossover: Randomly select a crossover point in the parent chromosome and exchange the deployment state of the offspring clusters.

[0173] Constraint protection: If the high-risk cluster deployment bit in the parent generation is 1, the child generation is forced to inherit this bit (e.g., in parent generation A). Parent B offspring ).

[0174] Mutation operator:

[0175] Non-high-risk cluster mutations: in terms of probability Flip (Only medium and low risk cluster mutations are allowed).

[0176] High-risk cluster lockout: Prohibit changes to the deployment status of high-risk clusters. (Immutable).

[0177] Repair strategy:

[0178] If the solution violates the constraints, such as a cluster without deployed sensors: prioritize randomly selecting undeployed sensors from high-risk clusters. Set to 1; if the budget is insufficient, replace the sensors of the low-weight cluster to the high-priority cluster.

[0179] S46: Elite Selection and Regional Orientation:

[0180] Non-dominated ranking: This method uses a non-dominant ranking algorithm to rank the plans in the population by merit. When comparing plan X0 with plan X1, X0 dominates X1 if and only if X0 is better than X1 on at least one objective and is at least as good as X1 on all other objectives. When ranking multiple plans in the population, each plan is compared with all other plans to identify pairwise dominance relationships. Plans not dominated by any other plan are then placed in the first tier. Plans dominated only by solutions in the first tier are placed in the second tier. This process continues until all plans are placed in the first tier.

[0181] In target space In this process, solutions that cover more high-risk clusters are prioritized for retention.

[0182] Strengthening of dominance relationship: If two solutions have the same other objectives, the one that covers more high-risk clusters takes priority.

[0183] To further differentiate plans within the Firstfront, a crowding distance metric was calculated to promote diversity among plans. After elite ranking, the better half of the population produces the same number of offspring through the evolutionary process, while the other half is eliminated; the relative influence of nodes can be observed over 50 consecutive iterations by considering the number of all other nodes connected to the node through this direct neighbor in the target value. The Firstfront plan in the last generation is considered the Pareto optimal deployment plan. Additional weight is given to the number of high-risk clusters covered in the crowding distance formula:

[0184] ;

[0185] Where α is an adjustment parameter, such as α = 0.5. To solve The number of high-risk clusters covered.

[0186] This embodiment implements the standard NSGA-II algorithm to solve the OSP problem. The NSGA-II algorithm searches in the cluster-level space and, with the help of a risk-weighted objective function and a cluster-guided mutation strategy, achieves accelerated convergence and significantly improves optimization efficiency and effectiveness.

[0187] In the mutation operation of the NSGA-II algorithm, a clustering-guided approach is used to lock the mutation bits corresponding to high-risk clusters, ensuring that the sensor deployment status in these critical areas is not lost due to mutation. This strategy effectively guides the optimization search direction, avoids gaps in monitoring coverage in high-risk areas, and improves the algorithm's convergence speed, making the optimization process more efficient and accurate.

[0188] In this embodiment, under the partitioning constraints after dimensionality reduction, the improved NSGA-II algorithm dynamically balances the conflicts among multiple objectives such as coverage utility, economic cost, and information redundancy through an adaptive reference point generation mechanism. The algorithm introduces a cluster-guided cross-mutation strategy, prioritizing spatial exploration of solutions at functional cluster boundaries, while dynamically adjusting target weights based on real-time data streams from the digital twin. The optimized Pareto solution set is validated through a digital twin closed-loop process, simulating monitoring effectiveness under extreme scenarios. If the threshold is not reached, feedback is sent to the clustering module to adjust feature weights and iterate again until the robustness requirements for multiple scenarios are met.

[0189] This embodiment uses real-time data to drive model parameter updates, forming a closed loop of "perception-simulation-optimization-response". It outputs a Pareto optimal solution set, providing multiple sensor layout schemes for decision-makers to choose from as needed.

[0190] In one embodiment, step S5 further includes one or more of the following steps:

[0191] High-risk clusters If the false negative rate exceeds the target, such as when a high-risk cluster has a false negative rate greater than 5%, the optimization objective weight of the corresponding cluster will be increased. , such as from Hard constraints are added to the NSGA-II algorithm iteration. The sensor deployment in each functional area was re-optimized.

[0192] High-frequency deployment clusters that are retained over 50 consecutive generations are dynamically marked as "critical clusters" and forcibly identified in subsequent iterations. .

[0193] By deeply embedding the results of spectral clustering partitioning into NSGA-II's variable encoding, objective function, constraints, evolutionary operations, and elite selection, the following core correlations were achieved:

[0194] Variable dimensionality compression: Decision variables are reduced from the segment level to the cluster level, significantly reducing computational complexity.

[0195] Physical meaning-driven: forced coverage of high-risk clusters, connectivity constraints of adjacent clusters, etc., to ensure that the optimization scheme is in line with reality.

[0196] Real-time dynamic feature updates: The digital twin model serves as the perception center of the entire system, updating key dynamic feature vectors such as hydraulic sensitivity and pollution risk every 5 minutes to ensure the timeliness and accuracy of monitoring data.

[0197] In one embodiment, ParaView+Unity3D is chosen as the visualization simulation tool to render a real-time heatmap of pipeline network flow, with red indicating overload and pollutant diffusion animations. The interactive features allow users to click on a pipe segment to view real-time data, historical event replays, and risk warning pop-ups. In extreme scenario testing, the optimized scheme is imported into the digital twin to simulate a 50-year rainstorm, verifying the sensor's missed detection rate. If the verification fails, the spectral clustering weights are adjusted or the algorithm parameters are optimized for iterative iteration. Figure 6 The diagram shown is a flowchart for building a digital twin.

[0198] The above provides a detailed description of a digital twin-driven multi-objective optimization method for deploying urban water system monitoring networks. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

[0199] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A digital twin driven multi-objective optimization urban water system monitoring network deployment method, characterized in that, The method comprises the following steps: S1: Based on digital twin modeling, integrate GIS geographic information, real-time water system pipeline sensor data, meteorological data and historical hydrological records to build a dynamic hydraulic-water quality coupling model of the urban drainage system; S2: Through dynamic simulation of the dynamic hydraulic-water quality coupling model, generate digital twin simulation results, including pipe section hydraulic-water quality data and predicted pipe section failure probability; S3: Based on the digital twin simulation results, real-time trigger reconstruction of the spectral clustering similarity matrix for representing the similarity weight of the current pipe section and adjacent pipe sections; Based on the spectral clustering similarity matrix, perform dynamic weighted spectral clustering on the water system pipe network; Based on the clustering results, divide the water system pipe network into multiple functional partitions and label the partition risk level; S4: Feedback the clustering results to the dynamic hydraulic-water quality coupling model of the urban drainage system, based on the digital twin feedback results, trigger the recalibration of the spectral clustering similarity matrix and re-perform dynamic weighted spectral clustering, or trigger the use of the NSGA-II algorithm to optimize sensor deployment for each functional partition, including assigning optimized target weights to each functional partition, and performing multi-objective sensor optimization deployment for the functional partition; S5: Import the optimization deployment scheme of S4 into the dynamic hydraulic-water quality coupling model to simulate and verify the monitoring omission rate under the preset extreme working condition, if the omission rate exceeds the standard, trigger the adjustment of the optimization target weight and re-perform the NSGA-II algorithm iteration until the verification is passed, and output the final sensor deployment scheme.

2. The digital twin driven multi-objective optimization urban water system monitoring network deployment method according to claim 1, wherein, In the input data of the dynamic hydraulic-water quality coupling model of the urban drainage system in S1, the integrated GIS geographic information includes: pipe network GIS topology, terrain elevation model, land use type; dynamic data includes: real-time water system pipeline sensor data, meteorological data, pump station operation status; historical hydrological records include: historical rainfall events, pollution accident records, equipment maintenance logs.

3. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 1, wherein, Real-time receive water system pipeline sensor data, dynamically update the initial conditions of the dynamic hydraulic-water quality coupling model of the drainage system, for dynamic simulation to generate digital twin simulation results.

4. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 1, wherein, The dynamic hydraulic-water quality coupling model outputs pipe section hydraulic-water quality data including pipe section hydraulic sensitivity and pollution risk in real time by dynamically calibrating model parameters: Hydraulic sensitivity is: ; wherein, is the real-time flow of the pipe segment, is the design flow of the pipe segment, is the pipe segment slope of the pipe network node i; Contamination risk is: ; where C is the pollutant concentration, v is the flow rate, is the decay factor, β is the first order decay coefficient of the pollutant, and T is the simulation period.

5. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 4, wherein, The step of real-time triggering reconstruction of the spectral clustering similarity matrix based on the digital twin simulation results in S3 comprises: Construct a spectral clustering similarity matrix: ； wherein the multi-dimensional feature vector , is a characteristic weight of the hydraulic sensitivity , is a characteristic weight of the contamination risk , is a characteristic weight of the failure probability , is a topological centrality, is the failure probability of the pipe network node i, is the failure probability of the pipe network node j downstream of the pipe network node i, is a bandwidth parameter of the Gaussian kernel, is a flow direction penalty factor for characterizing the dependency of a downstream pipe network node j on an upstream pipe network node i, is a flow direction penalty strength coefficient; The dynamic hydraulic-water quality coupling model updates the failure probability in real time , triggering reconstruction of the spectral clustering similarity matrix.

6. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 5, wherein, In S3, the step of performing dynamic weighted spectral clustering on the water system pipe network based on the spectral clustering similarity matrix comprises: calculating a normalized laplacian matrix based on the spectral clustering similarity matrix for describing the topology of the pipe network: ； ； ； Where n is the total number of pipe network nodes; normalizing laplacian matrix performing eigen decomposition, solving the equation: ； Eigenvalues of the Laplacian matrix are computed and the corresponding eigenvectors V; sorted in ascending order of eigenvalues, the eigenvectors corresponding to the k smallest non-zero eigenvalues are selected to form the low-dimensional embedding matrix ; Perform K-means algorithm on the low-dimensional embedding matrix V to divide the pipe network nodes into k clusters and determine the optimal cluster number.

7. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 1, wherein, S4 comprises: Feedback the clustering results to the dynamic hydraulic-water quality coupling model of the urban drainage system to simulate the behavior of each cluster under the preset extreme working condition: If the pipe section hydraulic-water quality data of the high-risk functional partition corresponding cluster simulation shows that it exceeds the standard, trigger the use of the NSGA-II algorithm to increase the sensor density for sensor deployment of each functional partition; If the hydraulic and water quality data of the cluster simulation display pipe section corresponding to the low-risk functional partition does not exceed the standard, triggering the use of the NSGA-II algorithm to reduce the sensor density of each functional partition for sensor deployment; If the cluster miss detection rate corresponding to the functional partition exceeds the standard, triggering returning to S3 to recalibrate the spectral clustering similarity matrix, re-performing dynamic weighted spectral clustering, or triggering the use of the NSGA-II algorithm to optimize the sensor deployment of each functional partition.

8. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 1, wherein, In the S4, the objective function of the multi-objective sensor optimization deployment of the functional partition by the NSGA-II algorithm includes: The maximum coverage utility objective function: ； ； wherein, is the optimization target weight of the cluster is determined by the partition risk level, is the sensor deployment state corresponding to the cluster . The minimum economic cost objective function: ； wherein, is the cost of equipment, is the installation cost associated with the geographical characteristics of the cluster .​ The minimum redundancy objective function: ； wherein, is the inter-cluster data correlation, is the inter-cluster physical distance.

9. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 8, wherein, In the S4, the constraint conditions of the multi-objective sensor optimization deployment of the functional partition by the NSGA-II algorithm include: High risk cluster mandatory coverage constraints: High risk cluster set; Connectivity constraint: if cluster is adjacent to cluster then is the maximum allowed communication distance. , ​ Budget constraints: , are total budgets.

10. The digital twin driven multi-objective optimization urban water system monitoring network deployment method of claim 8, wherein, In the S5, one or more of the following steps are further included: High-risk cluster If the missed detection rate exceeds the standard, the optimization target weight of the corresponding cluster is increased And add hard constraints in the iteration of the NSGA-II algorithm Re-optimize sensor deployment for each functional partition statistical clusters of functional partitions that are retained across multiple generations increasing hard constraints in subsequent iterations .

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