Subway key station identification and vulnerability evaluation method

Abstract

The invention relates to the technical field of metro key station identification and vulnerability evaluation methods, in particular to a metro key station identification and vulnerability evaluation method, which specifically comprises the following steps: step 1, metro network construction: establishing a weighted metro network model by adopting a Space-L space method according to a topological relation between metro stations and intervals, taking stations as nodes, intervals as edges and passenger flow as edge weights to form a weighted graph structure reflecting passenger travel rules, constructing an OD passenger flow matrix based on subway passenger flow card swiping data, and quantifying passenger flow connection strength between different stations; according to the method, the time-varying importance evaluation of the dynamic Domiank is combined with the feature learning ability of the graph convolutional network, and meanwhile, the structural complexity and passenger flow dynamic features of the subway network are described, so that the high-precision identification of the key stations and the comprehensive evaluation of the network vulnerability are realized.

Description

Technical Field

[0001] This invention relates to the technical field of methods for identifying and assessing the vulnerability of key subway stations, and in particular to a method for identifying and assessing the vulnerability of key subway stations. Background Technology

[0002] As a vital mode of transportation in modern cities, subways play an irreplaceable role in alleviating traffic congestion and improving travel efficiency and safety. With the continuous expansion of subway networks, the safety and stability of their operation face higher demands. Due to the enclosed operating environment of subway systems, emergencies such as equipment failures, fires, floods, and human sabotage can all damage network operations or even cause widespread paralysis. Therefore, identifying critical stations and conducting vulnerability analysis of subway networks is of great significance for mitigating risks and ensuring system operation.

[0003] In existing technologies, key nodes are identified based on network topology, but most are limited to static analysis and cannot reflect the dynamic changes in network structure after node failure. At the same time, some methods consider functional factors such as passenger flow, but lack integration with structural features, resulting in insufficient accuracy of the results. Summary of the Invention

[0004] In response to the technical problems mentioned in the background art, the present invention provides a method for identifying and assessing the vulnerability of key subway stations.

[0005] The technical solution adopted in this invention is: a method for identifying and assessing the vulnerability of key subway stations, specifically including the following steps: Step 1, Metro Network Construction: Based on the topological relationship between metro stations and sections, a weighted metro network model is established using the Space-L spatial method. Stations are regarded as nodes and sections as edges, and passenger flow is used as edge weights to form a weighted graph structure that reflects the travel patterns of passengers. Based on metro passenger flow card swiping data, an OD passenger flow matrix is ​​constructed to quantify the passenger flow connection strength between different stations. Step 2, Dynamic DomiRank Node Importance Calculation: The dynamic DomiRank algorithm is used to evaluate the importance of nodes in a time-varying manner, simulating the change in importance of nodes under gradual failure or attack scenarios; Step 3, Passenger flow DomiGCN model construction and key station identification: First, a second-order subgraph network is constructed. The second-order subgraph network is constructed by breadth-first search and the symmetric normalized Laplacian matrix is ​​calculated to capture deep information and suppress the oversmoothing problem in the traditional model. Step 4, Vulnerability Assessment: Assess and make a comprehensive judgment on the vulnerability of the subway network from both structural and functional perspectives.

[0006] In one embodiment, in step 1, the mathematical expression for the OD passenger flow matrix is: in: This represents the daily OD (Original Departure) passenger flow matrix. This represents the total passenger flow from station i to station j on a certain day, where n is the total number of stations; the diagonal elements of the matrix... The value is 0; Meanwhile, a comprehensive clustering algorithm was used to analyze the OD passenger flow matrix for different dates, dividing the dates into three categories: weekdays, weekends, and holidays, to adapt to the differences in passenger flow characteristics under different scenarios.

[0007] In one embodiment, step 2 specifically includes the following steps: Step 2.1, calculate the node importance values ​​of the initial network, using the following formula: ; in: This represents the importance value of the initial network node at time t. This represents the initial adjacency matrix of the network. A scaling factor representing the intensity of competition between nodes; the larger the value, the more intense the competition. This represents the scaling factor for the natural decay of nodes; the larger the value, the faster the node decays. It is a unit vector; Step 2.2: In each iteration, delete the node with the highest score and update the network as a subnetwork. The relevant formula is: in: This represents the node with the highest score in the k-th iteration. This represents the node set at the k-th iteration. Represents the node in the k-th iteration Importance score Indicates the first The node set for the k-th iteration is obtained by removing the node with the highest score from the node set for the k-th iteration. Step 2.3, recalculate the scores of the remaining nodes using the following formula: ; in: This represents the importance score of a node in the (k+1)th iteration. This represents the adjacency matrix of the network after iterative updates. Let f represent the importance score of a node in the k-th iteration, where f is the corresponding calculation function. Step 2.4, repeat steps 2.2 and 2.3 until all nodes have been removed.

[0008] In one embodiment, step 3 is specifically as follows: Feature extraction: Improved dynamic DomiRank centrality is used as one of the input features, with the following formula: ; in: This represents the improved node importance feature. These are the node importance values ​​obtained from the dynamic DomiRank algorithm. This represents a weighting coefficient that controls the impact of transfer stations. It is a one-dimensional vector, and the node is a transfer station. ,otherwise ; The formula for calculating passenger flow is: ; in: Indicates site Total passenger flow This indicates the total number of stations in the subway network. Indicates from the site to station The number of passengers; PageRank value is calculated using the following formula: ; in: Represents a node PageRank value, Indicates the damping factor. Represents a node Neighborhood set, This indicates the number of neighboring nodes.

[0009] The clustering coefficient is calculated using the following formula: ; in: Represents a node Clustering coefficient, Represents a node The actual number of connected edges between neighbors. Represents a node Degree (number of neighboring nodes). Represents a node The maximum possible number of edges connecting the neighbors; Node embedding: The node2vec method is used to map node information to a low-dimensional vector space. First, multiple types of information are encoded into information vectors through one-hot encoding, and then multiplied with the embedding matrix to obtain the node embedding vector, thereby mining the hidden features of the nodes. Passenger Flow DomiGCN Model Construction and Training: The mathematical expression of the model is: ; in: Let be the symmetric normalized Laplacian matrix of a second-order subgraph network. Features of the first-level nodes and For trainable parameters, Corresponding parameters of the skip connection layer For ELU activation function; Using the ELU activation function, the mathematical expression is: ; Where: x is the input value, and λ is a hyperparameter that controls the saturation of negative input; In terms of model structure, the GCN layer is followed by three fully connected layers: the first fully connected layer uses dropout based on a degenerate learning rate to reduce the risk of overfitting, and the latter two fully connected layers use the ELU activation function to speed up training and improve accuracy. The node criticality score is obtained through the model output, the nodes are ranked, and key sites with significant functional influence are identified.

[0010] In one embodiment, step 4 is specifically as follows: At the structural level: two indicators, network efficiency and maximum connected subgraph, are used to quantitatively evaluate the changes in network topology connectivity and transmission efficiency under node failure or attack conditions, reflecting the robustness of the network structure.

[0011] Functional level: Functional failure simulation based on the susceptible-infection-recovery model is introduced to simulate the failure propagation process of key stations under different failure scenarios, and the network’s ability to maintain passenger flow after damage is quantitatively measured by calculating the remaining passenger flow, thus quantifying the vulnerability of network functions.

[0012] The beneficial effects of this invention are as follows: Compared with the prior art, this invention combines the time-varying importance assessment of dynamic DomiRank with the feature learning capability of graph convolutional networks, simultaneously characterizing the structural complexity and dynamic passenger flow features of the subway network, achieving high-precision identification of key stations and comprehensive assessment of network vulnerability; by using a comprehensive clustering algorithm to divide the scenarios into three categories—weekdays, weekends, and holidays—the key station identification results are more closely aligned with the passenger flow characteristics of different periods. Key stations on weekdays are mainly transfer hubs and commercial centers, on weekends they are mainly leisure and entertainment stations, and on holidays they are concentrated in intercity transportation hubs, improving the scientific rigor and practicality of the identification results; at the structural level, the dynamic DomiRank algorithm significantly improves network efficiency and the maximum connected subgraph size compared to traditional algorithms, effectively reflecting network changes after node dynamic failures; at the functional level, the passenger flow DomiGCN model, relying on the advantages of deep learning in handling complex passenger flow patterns and nonlinear relationships between features, identifies key stations whose damage to the overall network during attacks is significantly higher than that of existing methods; it can provide operators with a basis for key station maintenance, daily capacity optimization, and transfer management, while also providing scientific decision support for improving the resilience of the subway network and disaster response. Attached Figure Description

[0013] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a flowchart of the passenger flow DomiGCN model in this invention; Figure 3 This is a flowchart of the feature extraction process in this invention; Figure 4 This is the Shanghai Metro network topology diagram used in this invention; Figure 5 This is the optimal clustering graph in this invention; Figure 6 This is a diagram illustrating the comprehensive impact of the dynamic DomiRank algorithm on network efficiency in this invention. Figure 7 This is the comprehensive influence diagram of the dynamic DomiRank algorithm on the maximum connected subgraph in this invention; Figure 8 These are experimental results of the SIR model on different dates in this invention; Figure 9 This is a chart showing the remaining passenger flow categorized by different dates in this invention. Detailed Implementation

[0014] In the description of this invention, it should be noted that the terms "front", "up", "down", "left", "right", "vertical", "horizontal", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0015] To address the problems existing in the background technology, this application proposes the following technical solution: a method for identifying and assessing the vulnerability of key subway stations, specifically including the following steps: First, a hierarchical analysis of urban rail transit is conducted. To comprehensively consider the structural and functional characteristics of the network, this invention divides the urban rail transit network into a structural layer and a functional layer. The structural layer is described by network topology information, reflecting the connectivity between stations; the functional layer is described by origin-destination (OD) passenger flow information and the functional attributes of subway stations, reflecting the passenger travel intensity between stations.

[0016] Based on this, this invention proposes a dynamic DomiRank algorithm (for identifying key sites in the structural layer) and a passenger flow DomiGCN model (for identifying key sites in the functional layer). The overall flowchart is as follows. Figure 1 As shown.

[0017] Secondly, network construction is performed. The subway network is a typical example of a complex network, consisting of interconnected subway stations and lines. In this framework, stations correspond to nodes in the network, while lines correspond to the edges connecting nodes. Each station exists as a node, and the lines connecting two stations act as edges, reflecting their topological relationships. Therefore, methods from complex network theory can be used to model the subway network.

[0018] Step 1, Metro Network Construction: Based on the topological relationship between metro stations and sections, a weighted metro network model is established using the Space-L spatial method. Stations are regarded as nodes, sections are regarded as edges, and passenger flow is used as edge weights to form a weighted graph structure that reflects the travel patterns of passengers.

[0019] Based on subway passenger card swiping data, an OD (origin and destination) passenger flow matrix is ​​constructed to quantify the passenger flow connection strength between different stations, providing basic data support for subsequent analysis.

[0020] The mathematical expression for the OD passenger flow matrix is: In the above technical solution, the intensity of passenger flow connections between different stations is quantified, providing a data foundation for subsequent node importance calculation and key station identification.

[0021] in: This represents the daily OD (Original Departure) passenger flow matrix. This represents the total passenger flow from station i to station j on a certain day, where n is the total number of stations; the diagonal elements of the matrix have a value of 0, because the journeys to and from the same station have no practical significance in passenger flow analysis.

[0022] Meanwhile, a comprehensive clustering algorithm was used to analyze the OD passenger flow matrix for different dates, dividing the dates into three categories: weekdays, weekends, and holidays, to adapt to the differences in passenger flow characteristics under different scenarios.

[0023] Step 2, Dynamic DomiRank Node Importance Calculation: The dynamic DomiRank algorithm is used to evaluate the importance of nodes in a time-varying manner, simulating the changes in the importance of nodes under gradual failure or attack scenarios. The specific steps are as follows: Step 2.1, calculate the node importance values ​​of the initial network, using the following formula: ; In the above technical solution: the initial importance value of each node in the initial network is calculated to provide a benchmark for subsequent dynamic iterative updates.

[0024] in: This represents the importance value of the initial network node at time t. This represents the initial adjacency matrix of the network. A scaling factor representing the intensity of competition between nodes; the larger the value, the more intense the competition. This represents the scaling factor for the natural decay of nodes; the larger the value, the faster the node decays. Let be a unit vector. The steady-state solution of this formula can be obtained by solving the differential equation.

[0025] Step 2.2: In each iteration, delete the node with the highest score and update the network as a subnetwork. The relevant formula is:

[0026] The above technical solution enables dynamic removal of nodes and network updates, simulating scenarios where nodes fail or are attacked.

[0027] in: This represents the node with the highest score in the k-th iteration. This represents the node set at the k-th iteration. Represents the node in the k-th iteration Importance score Indicates the first The node set for the k-th iteration is obtained by removing the node with the highest score from the node set for the k-th iteration.

[0028] Step 2.3, recalculate the scores of the remaining nodes using the following formula: ; In the above technical solution: in the sub-network after a node is removed, the importance of the remaining nodes is reassessed to achieve dynamic updates of node importance.

[0029] in: This represents the importance score of a node in the (k+1)th iteration. This represents the adjacency matrix of the network after iterative updates. Let f represent the importance score of a node in the k-th iteration, and f be the corresponding calculation function.

[0030] Step 2.4, repeat steps 2.2 and 2.3 until all nodes are removed, finally obtaining the node importance sequence considering the effects of dynamic propagation.

[0031] Step 3, Passenger Flow DomiGCN Model Construction and Key Station Identification: Constructing a Second-Order Subgraph Network: A second-order subgraph network is constructed using a breadth-first search method, and a symmetric normalized Laplacian matrix is ​​calculated to capture deep information and suppress the oversmoothing problem in traditional models.

[0032] Next, the DomiGCN passenger flow model is introduced, and its method is as follows: This invention combines the dynamic DomiRank algorithm with the topological and passenger flow attributes of a metro network to construct a passenger flow DomiGCN model. By constructing a second-order subgraph and employing a skip connection layer, this model can comprehensively capture both local and global network information, overcoming the limitations of static topology methods. Furthermore, this model comprehensively considers passenger flow characteristics and transfer station attributes, providing an innovative framework for identifying key stations and analyzing network vulnerabilities. The model consists of three parts: second-order subgraph network construction, feature extraction, and key node identification. The model flowchart is shown below. Figure 2 As shown.

[0033] Feature extraction: Improved dynamic DomiRank centrality is used as one of the input features, and the formula is: ; In the above technical solution, the attributes of transfer stations are integrated into the node importance features to improve the comprehensiveness of the features.

[0034] in: This represents the improved node importance feature. These are the node importance values ​​obtained from the dynamic DomiRank algorithm. This represents a weighting coefficient that controls the impact of transfer stations. It is a one-dimensional vector, and the node is a transfer station. ,otherwise .

[0035] The formula for calculating passenger flow is: ; In the above technical solution: quantifying the total passenger flow of a single site is used as one of the functional characteristics of the node.

[0036] in: Indicates site Total passenger flow This indicates the total number of stations in the subway network. Indicates from the site to station The number of passengers.

[0037] PageRank value is calculated using the following formula: ; In the above technical solution: the propagation influence of the evaluation node in the network is used as a supplement to the structural features.

[0038] in: Represents a node PageRank value, Indicates the damping factor. Represents a node Neighborhood set, This indicates the number of neighboring nodes.

[0039] The clustering coefficient is calculated using the following formula: ; The above technical solution describes the local connectivity of nodes and the closeness between stations, reflecting the local structural characteristics of the network.

[0040] in: Represents a node Clustering coefficient, Represents a node The actual number of connected edges between neighbors. Represents a node Degree (number of neighboring nodes). Represents a node The maximum possible number of edges connecting the neighbors.

[0041] Node embedding: The node2vec method is used to map node information to a low-dimensional vector space. First, multiple types of information are encoded into information vectors through one-hot encoding, and then multiplied with the embedding matrix to obtain the node embedding vector, thereby mining the hidden features of the nodes.

[0042] To further explore node features, this invention also employs node embedding technology to extract other hidden features of nodes, thereby improving the accuracy of key site identification. This invention uses the node2vec method to map node information to a low-dimensional vector space. First, multiple pieces of information are encoded into information vectors using one-hot encoding. Then, this information vector is multiplied by the embedding matrix to finally obtain the node's embedding vector.

[0043] Passenger Flow DomiGCN Model Construction and Training: The mathematical expression of the model is: ; The above technical solution achieves deep fusion and nonlinear mapping of node features to extract the potential influence of nodes.

[0044] in: Let be the symmetric normalized Laplacian matrix of a second-order subgraph network. Features of the first-level nodes and For trainable parameters, Corresponding parameters of the skip connection layer The activation function is ELU. This method uses the ELU activation function, mathematically represented as: ; Where x is the input value, and λ is a hyperparameter controlling the negative input saturation. Structurally, the GCN layer is followed by three fully connected layers: the first fully connected layer uses dropout based on a degenerate learning rate to reduce overfitting risk, and the latter two fully connected layers use the ELU activation function to accelerate training and improve accuracy. The model output yields node criticality scores, which are then used to rank the nodes and identify key sites with significant functional influence.

[0045] In the DomiGCN passenger flow model, the GCN layer is followed by three fully connected layers for classification. The first fully connected layer uses dropout based on a degenerate learning rate to reduce the risk of overfitting, while the other two fully connected layers use exponential linear units (ELU) as activation functions to speed up training and improve accuracy. Finally, the model output yields node keyness scores, and nodes with high scores are identified as key nodes. The node feature extraction process of the DomiGCN passenger flow model is as follows: Figure 3 As shown.

[0046] Step 4, vulnerability assessment; The vulnerability of the subway network is assessed and comprehensively judged from both structural and functional perspectives: At the structural level: two indicators, network efficiency and maximum connected subgraph, are used to quantitatively evaluate the changes in network topology connectivity and transmission efficiency under node failure or attack conditions, reflecting the robustness of the network structure.

[0047] Functional level: Functional failure simulation based on the susceptible-infected-recovery (SIR) model is introduced to simulate the failure propagation process of critical stations under different failure scenarios, and the network’s ability to maintain passenger flow after damage is quantitatively measured by calculating the remaining passenger flow (RPF), thus quantifying the network’s functional vulnerability.

[0048] Example Verification: This invention is verified using the Shanghai Metro as an example. In 2015, the Shanghai Metro network comprised 288 stations, 14 lines, and 352 edges, as shown in the topology diagram below. Figure 4 As shown.

[0049] Based on card swipe data from April 2015, an OD passenger flow matrix was constructed. This invention first uses a comprehensive classification algorithm to classify subway passenger flow on different dates. The optimal date clustering diagram is shown below. Figure 4 The figure shows that when the number of clusters is 2, the sum of squared errors within each cluster decreases significantly, indicating a substantial increase in the density of each cluster. Simultaneously, the silhouette coefficient reaches its maximum value when the number of clusters is 2, indicating a clear separation between the two clusters. Therefore, OD passenger flow on different dates can be initially divided into weekdays and non-weekdays. Further analysis revealed differences between non-weekday OD passenger flow and holiday passenger flow, with significant variations observed during holidays. Intercity transportation hubs experience a surge in passenger flow during holidays; therefore, non-weekdays can be further divided into weekends and holidays. Ultimately, this invention classifies subway network OD passenger flow into weekdays, weekends, and holidays for a more accurate analysis of passenger flow characteristics.

[0050] At the structural level, for critical sites obtained by the dynamic Domirank algorithm, this invention uses two metrics—network efficiency and maximum connected subgraph—to evaluate network vulnerability, such as... Figure 6 and Figure 7 The proposed dynamic DomiRank algorithm demonstrates superior performance across both of the aforementioned structural metrics, effectively maintaining overall network connectivity and transmission efficiency even in the event of node failure or attacks. Compared to the traditional DomiRank algorithm, the dynamic DomiRank algorithm achieves significant improvements in both network efficiency and maximum connected subgraph size, validating the effectiveness and superiority of the algorithm in network structural robustness assessment.

[0051] At the functional level, for key stations identified by the DomiGCN passenger flow model, this invention introduces the SIR model and the RPF metric to assess the functional vulnerability of the metro network. The SIR model simulates the functional propagation process of the metro network under node failure or attack conditions to characterize the diffusion characteristics of service failures within the network. Simultaneously, the RPF metric is used to measure the network's ability to maintain passenger flow under different attack scenarios. Figure 8 and Figure 9 As shown. Figure 8 The change in the number of infected sites over time is shown; due to the randomness of the simulation, the model underwent 500 independent trials. Figure 8 We observed that, across three different date categories—weekdays, weekends, and holidays—the DomiGCN passenger flow model of this invention generates more infection sites, spreads the virus faster, and outperforms other methods.

[0052] Figure 9 This demonstrates the changes in RPF (Recovery Point Validation) of the Shanghai Metro under different attack strategies. Figure 9 As can be seen, the RPF decreases rapidly with the increase in the node removal rate, indicating that the Shanghai Metro network is highly vulnerable to attacks on critical stations. Furthermore, among the four methods, the passenger flow DomiGCN model proposed in this invention has the lowest RPF, demonstrating its effectiveness in identifying critical stations.

[0053] The final experimental results show that key stations on weekdays are mainly transfer hubs and commercial centers (such as Century Avenue, People's Square, and Xujiahui); key stations on weekends exhibit leisure characteristics (such as Shanghai Stadium); and key stations on holidays are concentrated in intercity transportation hubs (such as Shanghai Railway Station and Hongqiao Railway Station). These results verify the effective differentiation and accurate identification of passenger flow characteristics under different date classifications, and demonstrate high stability and accuracy at both structural and functional levels, showing significant advantages over traditional centrality index methods.

[0054] The methods described above enable efficient identification and in-depth analysis of critical stations in complex subway networks, thereby achieving comprehensive optimization at both the network structure and functional levels. The application of this method not only improves the operational efficiency and service quality of the subway system and enhances the passenger travel experience, but also provides a scientific basis for network planning and scheduling management. Furthermore, through quantitative assessment of network vulnerability, critical stations that significantly impact overall operation under abnormal events or node failures can be accurately identified, providing crucial support for improving the subway network's resilience and safety.

[0055] Although embodiments of the invention have been shown and described, the scope of the invention will be defined by the appended claims and their equivalents by those skilled in the art.

Claims

1. A method for identifying and assessing the vulnerability of critical subway stations, characterized in that, Specifically, the following steps are included: Step 1, Metro Network Construction: Based on the topological relationship between metro stations and sections, a weighted metro network model is established using the Space-L spatial method. Stations are regarded as nodes and sections as edges, and passenger flow is used as edge weights to form a weighted graph structure that reflects the travel patterns of passengers. Based on metro passenger flow card swiping data, an OD passenger flow matrix is ​​constructed to quantify the passenger flow connection strength between different stations. Step 2, Dynamic DomiRank Node Importance Calculation: The dynamic DomiRank algorithm is used to evaluate the importance of nodes in a time-varying manner, simulating the change in importance of nodes under gradual failure or attack scenarios; Step 3, Passenger flow DomiGCN model construction and key station identification: First, a second-order subgraph network is constructed. The second-order subgraph network is constructed by breadth-first search and the symmetric normalized Laplacian matrix is ​​calculated to capture deep information and suppress the oversmoothing problem in the traditional model. Step 4, Vulnerability Assessment: Assess and make a comprehensive judgment on the vulnerability of the subway network from both structural and functional perspectives.

2. The method for identifying and assessing the vulnerability of key subway stations according to claim 1, characterized in that, In step 1, the mathematical expression for the OD passenger flow matrix is: in: This represents the daily OD (Original Departure) passenger flow matrix. This represents the total passenger flow from station i to station j on a certain day, where n is the total number of stations; the diagonal elements of the matrix... The value is 0; Meanwhile, a comprehensive clustering algorithm was used to analyze the OD passenger flow matrix for different dates, dividing the dates into three categories: weekdays, weekends, and holidays, to adapt to the differences in passenger flow characteristics under different scenarios.

3. The method for identifying and assessing the vulnerability of key subway stations according to claim 2, characterized in that, Step 2 involves the following specific steps: Step 2.1, calculate the node importance values ​​of the initial network, using the following formula: in: This represents the importance value of the initial network node at time t. This represents the initial adjacency matrix of the network. A scaling factor representing the intensity of competition between nodes; the larger the value, the more intense the competition. This represents the scaling factor for the natural decay of nodes; the larger the value, the faster the node decays. It is a unit vector; Step 2.2: In each iteration, delete the node with the highest score and update the network as a subnetwork. The relevant formula is: in: This represents the node with the highest score in the k-th iteration. This represents the node set at the k-th iteration. Represents the node in the k-th iteration Importance score Indicates the first The node set for the k-th iteration is obtained by removing the node with the highest score from the node set for the k-th iteration. Step 2.3, recalculate the scores of the remaining nodes using the following formula: ； in: This represents the importance score of a node in the (k+1)th iteration. This represents the adjacency matrix of the network after iterative updates. Let f represent the importance score of a node in the k-th iteration, where f is the corresponding calculation function. Step 2.4, repeat steps 2.2 and 2.3 until all nodes have been removed.

4. The method for identifying and assessing the vulnerability of key subway stations according to claim 3, characterized in that, Step 3 is detailed as follows: Feature extraction: Improved dynamic DomiRank centrality is used as one of the input features, with the following formula: ； in: This represents the improved node importance feature. These are the node importance values ​​obtained from the dynamic DomiRank algorithm. This represents a weighting coefficient that controls the impact of transfer stations. It is a one-dimensional vector, and the node is a transfer station. ,otherwise ; The formula for calculating passenger flow is: ； in: Indicates site Total passenger flow This indicates the total number of stations in the subway network. Indicates from the site to station The number of passengers; PageRank value is calculated using the following formula: ； in: Represents a node PageRank value, Indicates the damping factor. Represents a node Neighborhood set, Indicates the number of neighboring nodes; The clustering coefficient is calculated using the following formula: ； in: Represents a node Clustering coefficient, Represents a node The actual number of connected edges between neighbors. Represents a node Degree (number of neighboring nodes). Represents a node The maximum possible number of edges connecting the neighbors; Node embedding: The node2vec method is used to map node information to a low-dimensional vector space. First, multiple types of information are encoded into information vectors through one-hot encoding, and then multiplied with the embedding matrix to obtain the node embedding vector, thereby mining the hidden features of the nodes. Passenger Flow DomiGCN Model Construction and Training: The mathematical expression of the model is: ； in: Let be the symmetric normalized Laplacian matrix of a second-order subgraph network. Features of the first-level nodes and For trainable parameters, Corresponding parameters of the skip connection layer For ELU activation function; Using the ELU activation function, the mathematical expression is: ； Where: x is the input value, and λ is a hyperparameter that controls the saturation of negative input; In terms of model structure, the GCN layer is followed by three fully connected layers: the first fully connected layer uses dropout based on a degenerate learning rate to reduce the risk of overfitting, and the latter two fully connected layers use the ELU activation function to speed up training and improve accuracy. The node criticality score is obtained through the model output, the nodes are ranked, and key sites with significant functional influence are identified.

5. The method for identifying and assessing the vulnerability of key subway stations according to claim 4, characterized in that, Step 4 is detailed as follows: At the structural level: two indicators, network efficiency and maximum connected subgraph, are used to quantitatively evaluate the changes in network topology connectivity and transmission efficiency under node failure or attack conditions, reflecting the robustness of the network structure. Functional level: Functional failure simulation based on the susceptible-infection-recovery model is introduced to simulate the failure propagation process of key stations under different failure scenarios, and the network’s ability to maintain passenger flow after damage is quantitatively measured by calculating the remaining passenger flow, thus quantifying the vulnerability of network functions.

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