Cross-border transportation network key node identification method

Abstract

The invention relates to a cross-border transportation network key node identification method, which comprises the following steps: constructing a multimodal transportation network by adopting a three-layer network modeling method, and carrying out cost quantification on the multimodal transportation network; carrying out vulnerability evaluation and node importance correction on the multimodal transport network; determining the weight of the important evaluation index of each node by adopting a machine learning model; determining the weight of an important evaluation index of each node by adopting a machine learning model; evaluating the comprehensive score of the network node by adopting a TOPSIS model; a node overload and load redistribution process is simulated through a cascade failure model, and the criticality of nodes in dynamic risk propagation is evaluated. According to the scheme provided by the invention, the key problem that the cross-border hub is underestimated due to the scale difference of domestic and overseas networks is effectively solved, the toughness of the cross-border transportation network is improved, the resource layout is optimized, and the stability and management efficiency of the network in response to emergencies are enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of transportation network, in particular to a method for identifying key nodes of cross-border transportation network. BACKGROUND

[0002] With the continuous prosperity and development of economy, transnational economic and trade cooperation is deepening, and transnational transportation is the artery of globalized economy, and its development and efficiency directly determine the scope and efficiency of economic activities.

[0003] The current transnational transportation channel is a complex intermodal network composed of highways, railways and sea transportation. Precise identification of key nodes of cross-border transportation network is the core to ensure its efficient and stable operation. However, when the intermodal network faces local conflicts, port closures and other emergencies, it shows significant vulnerability, and failure of key nodes will lead to systematic risks such as transportation time surge and cost rise.

[0004] At present, the key node identification method based on complex network theory has been widely applied. This kind of method usually abstracts the transportation system as a network topology structure, and uses single or multi-index fusion (such as entropy weight-TOPSIS model) such as degree centrality and betweenness centrality to evaluate.

[0005] However, the traditional key node identification method focuses on the global contribution of nodes in the whole network, and fails to adapt to the core function of "cross-border". When the scale of domestic and foreign networks is different, the real importance of ports and other cross-border hubs will be systematically underestimated. In the process of multi-index fusion, the determination of the weight of key nodes often depends on expert experience or data dispersion, and lacks the internal mapping and reverse learning mechanism from network function to node characteristics, which limits the objectivity and accuracy of the identification results.

[0006] Therefore, there is a need for a transportation network key node identification method that can accurately quantify the cross-border function contribution of nodes and establish an objective weight relationship between node characteristics and network performance, to improve the resilience and risk response ability of cross-border transportation network. SUMMARY

[0007] To solve or partially solve the problems in the related art, the present application provides a method for identifying key nodes of cross-border transportation network, aiming to solve the problem of accurate identification of key nodes of cross-border transportation network.

[0008] The present application provides a method for identifying key nodes of cross-border transportation network, comprising:

[0009] Obtaining all cities and transportation related data of three types of transportation modes of highway, railway and sea transportation between the source of goods, the port and the destination;

[0010] A three-layer network modeling method is adopted, which sets the three types of transportation modes as three-layer sub-networks. Different sub-network layers are connected through nodes to construct a multimodal transport network and quantify the cost of the multimodal transport network.

[0011] Vulnerability assessment and node importance correction are performed on the multimodal transport network; network vulnerability assessment is performed on the multimodal transport network using cross-border network efficiency and cross-border network connectivity as basic indicators; and betweenness centrality correction, proximity centrality correction, Katz centrality correction, eigenvector centrality correction, and PageRank value correction are performed on the nodes of the multimodal transport network.

[0012] Machine learning models are used to determine the weights of important evaluation indicators for each node. By employing four heterogeneous models with different calculation methods—lightweight gradient boosting machine, support vector machine, resilient network regression, and least squares boosting—diffusion and vulnerability are integrated to quantify the mapping relationship between node features and network features from different perspectives, thereby determining the weights of important evaluation indicators for each node.

[0013] Based on the weights of key evaluation indicators for each node, the TOPSIS model is used to evaluate the comprehensive score of network nodes and determine the importance of multimodal transport network nodes.

[0014] By simulating node overload and load redistribution processes using a cascading failure model, the criticality of nodes in dynamic risk propagation is assessed, and the dynamic impact mechanism of critical node failure on the network is determined.

[0015] Optionally, in some implementations, a multimodal transport network is constructed, including:

[0016] The selection and layer copying of physical nodes involves selecting N cities between the source, port, and destination as physical nodes, and then numbering these physical nodes. Each physical node is replicated in three modes of transportation: road, rail, and sea, forming three layers of virtual nodes, resulting in a multi-layer network with 3N nodes. The index of the i-th physical node of the layer is ;

[0017] Calculate the intra-layer adjacency weights using the total transportation cost between adjacent nodes as the edge weights. Based on the three transportation modes, construct three weighted adjacency matrices for road, rail, and sea transport respectively. Place these three weighted adjacency matrices in the three diagonal blocks of the Sup hybrid matrix to ensure that intra-layer connections occur only within the same transportation mode.

[0018] (1)

[0019] In the formula, Represents a mixed weighted matrix. Represents the highway weighted matrix. denotes the railway weighted matrix, denotes the sea shipping weighted matrix;

[0020] The inter-layer coupling edge determination, i.e., the transit route determination, is determined at the hub node by the vector denotes the transit cost of highway ↔ railway, railway ↔ sea shipping, and highway ↔ sea shipping, respectively;

[0021] The complete The mixed matrix, outside the corresponding diagonal block, constructs three sparse transit diagonal matrices, only in the transport node position is replaced by the corresponding transit cost, and the rest is zero. The intra-layer and inter-layer weights are combined to obtain:

[0022] (2).

[0023] Optionally, in some embodiments, the cost quantification of the multimodal transport network includes:

[0024] The total transportation cost includes transportation cost, transit cost, carbon emission cost, and time cost;

[0025] Transportation cost:

[0026] (3)

[0027] wherein, , denotes the base price and the transportation base price per kilometer using transportation mode m, respectively, denotes whether transportation mode m is used from node i to j, if used, =1, otherwise 0, denotes the transportation mileage of node i to j using transportation mode m, is a variable that determines whether there is a direct connection between node i and j in the transportation network, if there is a direct connection between node i and j, =1, otherwise 0, and M is the set of transportation modes;

[0028] Time cost: The cross-border multimodal transport time is a composite index, which not only includes the in-transit transport time, but also includes the collection time and the customs clearance time. The transport time is converted by the cross-border transport speed, and the calculation method is as follows:

[0029] (4)

[0030] (5)

[0031] (6)

[0032] wherein, denotes the cross-border transportation speed using transportation mode m, 、 denotes the operating mileage and operating time of the transportation line using transportation mode m, respectively, denotes the transportation time of node i to j using transportation mode m, and denotes the transportation time cost and the capital possession cost, respectively, denotes the time devaluation rate of goods a, the annual loan interest rate of the bank, the initial value of a container of goods a;

[0033] carbon emission cost:

[0034] (7)

[0035] wherein, denotes the unit carbon emission cost of goods from node i to j using transportation mode m;

[0036] total edge cost:

[0037] (8)

[0038] wherein, denotes the transit cost.

[0039] Optionally, in some embodiments, the vulnerability of the multimodal transport network is evaluated, including:

[0040] When the port node fails to interwork, the departure and destination are completely disconnected in the multimodal transport network, and the cross-border transportation function of the network should be equal to zero. In order to accurately measure the vulnerability characteristics of the cross-border multi-layer transport network and identify the key nodes, the cross-border network efficiency and the cross-border network connectivity rate are used as basic indexes;

[0041] The cross-border network efficiency is used to measure the comprehensive cost between any node at both ends of the port node. When the cross-border network efficiency decreases, it indicates that the average transportation cost increases. The network vulnerability is measured in the functional dimension:

[0042] (9)

[0043] wherein, denotes the cross-border network efficiency, 、 denote the number of overseas nodes and the number of domestic nodes, respectively, denotes the minimum weight sum of the domestic node s to the overseas node t in any layer network,

[0044] Cross-border network connectivity rate, used to measure the proportion of whether there is a reachable path between any domestic node and any overseas node. If all paths have at least one reachable path, the multimodal transport network is complete in cross-border connectivity. If some levels or node pairs cannot interwork, the cross-border connectivity of the network is weak. The structural dimension measures the vulnerability of the network:

[0045] (10)

[0046] In the formula, represents the cross-border network connectivity rate, is an indicator function, which is 1 if the two nodes are reachable, and 0 if they are not;

[0047] The comprehensive vulnerability of the multimodal transport network is:

[0048] (11)

[0049] In the formula, is the geometric mean of cross-border network efficiency and cross-border network connectivity rate;

[0050] Combining the cross-border efficiency and cross-border connectivity rate into one overall vulnerability measurement overcomes the one-sidedness of a single indicator and simultaneously quantifies the two risks of transport efficiency decline and network connectivity interruption.

[0051] Optionally, in some embodiments, the node importance correction includes:

[0052] Betweenness centrality correction, closeness centrality correction, Katz centrality correction, eigenvector centrality correction, and PageRank value correction;

[0053] Betweenness centrality correction calculates the frequency of a node appearing as an intermediary in cross-border minimum cost paths, eliminates the interference of internal regional node pairs on paths, and highlights the bridge role of the node in transport links. The calculation is as follows:

[0054] (12)

[0055] In the formula, is the modified betweenness centrality of node i, is the total number of all shortest paths from node s to t, is the number of paths passing through physical node i in the layer in all shortest paths from node s to t;

[0056] The modified closeness centrality measures the inverse of the average minimum cost of a node to all nodes in another group. The larger the value, the closer the node is to the core position of another group, reflecting the comprehensive accessibility of the node in the cross-border transport network:

[0057] (13)

[0058] (14)

[0059] (15)

[0060] For the corrected proximity centrality of node i, / This represents the reciprocal of the average minimum cost from node i (domestic or overseas) to all nodes (domestic or overseas). No. The weighted minimum cost from node i in layer m to node t in layer m. Indicates the first The weighted minimum cost from node i in layer m to the s-th node in layer m;

[0061] The modified Katz centrality further distinguishes whether the path connects domestic and foreign routes based on the traditional approach, and strengthens or weakens cross-border propagation by using different attenuation factors. Domestic routes are treated with a smaller attenuation factor, while cross-border routes are treated with a relatively larger attenuation factor, highlighting the importance of cross-border channels and reflecting the potential impact of nodes in cross-border transportation.

[0062] (16)

[0063] (17)

[0064] (18)

[0065] In the formula, Let I be the corrected Katz centrality of node i, where I is the identity matrix and W is the decaying adjacency matrix. , These represent matrices that retain only domestic connections and matrices that retain only cross-border connections, respectively. , Let x represent the attenuation factor for the domestic path and the attenuation factor for the cross-border path, respectively. Let x be the Katz score vector and f be the source vector with a value of 1, which has the same dimension as W.

[0066] Similar to correcting Katz centrality, the corrected eigenvector centrality is calculated by constructing a cross-border preference matrix with different cross-border factors, and then calculating the corrected eigenvector centrality of the nodes as follows:

[0067] (19)

[0068] (20)

[0069] (21)

[0070] wherein, denotes the modified eigenvector centrality of node i, denotes the cross-border preference matrix, , denotes the preference factor of domestic paths and the preference factor of cross-border paths, , are respectively , the cost mapping matrix, wherein the matrix elements are calculated by , y is the characteristic centrality score vector, is the corresponding matrix maximum eigenvalue;

[0071] The modified PageRank value is calculated by setting different cross-border factors, and the calculation is as follows:

[0072] (22)

[0073] (23)

[0074] wherein, denotes the modified PageRank value of node i, denotes the PageRank score vector, denotes the transpose matrix of P, P denotes the transition matrix, which is calculated by , D denotes the diagonal matrix, denotes the damping factor, which is usually 0.85, denotes the personalized vector, which denotes the preference of random jump.

[0075] Optionally, in some embodiments, a machine learning model is used to determine the weight of each node importance evaluation index, including:

[0076] The four machine learning models are used to quantify the complex mapping relationship between node features and network features from different angles by combining diffusion and vulnerability;

[0077] The modified betweenness centrality, the modified closeness centrality, the modified Katz centrality, the modified eigenvector centrality and the modified PageRank are used to construct a node feature matrix as an input variable, and diffusion and vulnerability are used as dual supervision learning labels. The diffusion is based on the improved SIR propagation model to design a cross-border infection simulation with a fixed number of propagation rounds, and the propagation probability is determined by the comprehensive cost of the path between nodes. The simulation takes each domestic / overseas node as an infection source, and statistics the proportion of nodes that can be infected within T rounds.

[0078] The lightweight gradient boosting machine model, support vector machine model, elastic network regression model and least squares boosting model are used to independently learn the feature-label association mechanism of the nodes, and the weights of the important evaluation indexes of the nodes are obtained.

[0079] Optionally, in some embodiments, the comprehensive score of the network node is evaluated by using the TOPSIS model, including:

[0080] According to the weights of the important evaluation indexes of the nodes, the comprehensive score of the network node is evaluated by using the TOPSIS model, and the calculation is as follows:

[0081] (24)

[0082] In the formula, is the comprehensive score of the i-th node, and the value range is [0, 1], and the larger the value is, the higher the importance of the node is; and respectively represent the distance between the importance of the i-th node and the optimal solution and the worst solution.

[0083] Optionally, in some embodiments, the node overload and load redistribution process is simulated by using the cascading failure model, including:

[0084] The node betweenness can reflect the load condition of the site to a great extent, and the node betweenness is used as the initial load quantization index. For a network with a total number of nodes N, the initial load of the node is:

[0085] (25)

[0086] In the formula, represents the initial load of the node;

[0087] It is assumed that the nodes of the multimodal transport network have the ability to bear the load, the maximum capacity of the node is positively correlated with the initial load and related to the standby capacity coefficient, and the maximum capacity of the node is:

[0088] (26)

[0089] In the formula, represents the maximum capacity of the node, represents the capacity redundancy coefficient;

[0090] ​​​Considering the uncertainty and unexpected situations in actual operation, the nodes in the network are designed to have certain overload bearing capacity to deal with peak transport periods and emergency scheduling, so whether a node fails or not is related to the bearing capacity of its node freight transport facility and the degree of congestion, etc. Therefore, the overloaded node does not always stop running immediately, and the node can bear the load exceeding its standard capacity under certain conditions, and the overload failure can be regarded as a risk, and the corresponding failure probability is valued in [0, 1]. The overload capacity coefficient is introduced, which is valued in [0, ∞], and at the same time, considering that the ability of each node to bear the load exceeding its capacity is not the same in reality, the more critical the node is, the more congested it is, and the greater the failure probability is, and the more reasonable measures need to be taken to ensure its freight transport capacity, that is, the node failure probability is not only related to the overload capacity coefficient , but also related to the criticality of the node, therefore, a reasonable critical capacity is set for each node, so that the more the load exceeds, the more likely the node is to fail, which is more in line with the actual situation.

[0091] When the load of the node is less than its maximum capacity , the node will not fail; when the load of the node exceeds its maximum capacity but within a certain allowed range , the node has a certain probability of failure; when the flow load of the node reaches or exceeds the allowed limit , the node is overloaded and fails, and the failure probability is , the overload load with a failure probability of 1 is set as the removal threshold.

[0092] (27)

[0093] In the formula, , represents the failure probability of node i at time t, , represents the overload capacity coefficient, , represents the load of node i at time t, , represents the modified betweenness centrality of node i, , represents the average modified betweenness centrality of the network.

[0094] Cascade failure propagation process, after the failure of the node in the multimodal transport network, considering the effect of the remaining capacity of the adjacent node of the failed node and the criticality of the node on the load redistribution process of the failed node, the remaining capacity coefficient and the node importance coefficient are introduced, and the node load redistribution strategy is proposed:

[0095] ​Node load transfer condition, in the process of cascading failure of multimodal transport network, the load state of the node existing in the network is determined, if the load of the node exceeds the node capacity at this time, the node i is in overload state at this time, at this time, the failure probability of the node is calculated , state determination is carried out, then load redistribution is carried out, the random failure threshold is set as P, P is in the range of [0, 1], if the failure probability of the node at this time is , the load of the node exceeding the capacity is distributed according to the set strategy; if the failure probability of the node i at this time is , the node is regarded as being in overload state and failure, and all loads are distributed according to the set strategy; if the load of the node i at this time is greater than the overload capacity, the node is directly regarded as being in failure state, and all loads are distributed according to the set strategy;

[0096] Node load distribution ratio:

[0097] (28)

[0098] In the formula, , , indicates the remaining capacity coefficient, , indicates the node importance coefficient, indicates the equal consideration of the role of node remaining capacity and node importance in load redistribution, and J indicates the adjacent node set;

[0099] Node load distribution strategy, considering the different settings of node overload state, overload but not failure node and failure node load distribution strategy, the load distribution of overload but not failure node is:

[0100] (29)

[0101] The load distribution of failure node is:

[0102] (30)

[0103] In the formula, , indicates the load amount of node i distributed to node j.

[0104] The technical scheme provided by the application can include the following beneficial effects:

[0105] The three types of transportation modes of highway, railway and sea transportation are constructed as multi-layer sub-networks, and the transportation cost, transfer cost, carbon emission cost and time cost are quantified to comprehensively reflect the complex structure and actual operation characteristics of the cross-border intermodal network, and avoid underestimating the importance of cross-border nodes due to the difference in network scale between domestic and foreign networks; by fusing multiple correction centrality indexes and machine learning models, the mapping relationship between node features and network performance is automatically learned, the weights of each evaluation index are determined, the subjectivity of the weights caused by relying on expert experience or data dispersion is avoided, and the objectivity and accuracy of the identification of key nodes are improved; the cascading failure model is used to simulate the node overload and load redistribution process, the remaining capacity and criticality of the node are comprehensively considered, the influence of the node in the dynamic risk propagation is evaluated, the cascading effect of the key node failure on the network is revealed, a scientific basis is provided for the resilience design and risk prevention and control of the cross-border transportation network, and the stability and recovery ability of the network under the sudden event are improved.

[0106] It should be understood that the foregoing general description and the following detailed description are only exemplary and explanatory and are not restrictive of the application. BRIEF DESCRIPTION OF DRAWINGS

[0107] The above and other objects, features and advantages of the present application will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which like reference characters refer to like parts throughout and in which:

[0108] Figure 1 is a flowchart of a cross-border transportation network key node identification method according to an embodiment of the application;

[0109] Figure 2 is a schematic diagram of an intermodal network structure of a cross-border transportation network key node identification method according to an embodiment of the application. DETAILED DESCRIPTION

[0110] Embodiments of the application will be described in greater detail below with reference to the accompanying drawings. Although embodiments of the application are shown in the drawings, it should be understood that the application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to make the application more thorough and complete, and to fully convey the scope of the application to those skilled in the art.

[0111] The technical solutions of the embodiments of the application are described in detail below with reference to the accompanying drawings.

[0112] Figure 1 is a flowchart of a cross-border transportation network key node identification method according to an embodiment of the application;

[0113] Referring to Figure 1 , a cross-border transportation network key node identification method comprises:

[0114] S101, obtain all cities and transportation related data of highway, railway and sea transportation modes between the origin, port and destination;

[0115] Cross-border transportation can be mainly divided into three transportation modes, the first being international highway train, the second being international railway train, and the third being sea train. Among them, the international train and inland transportation data are derived from the Railway Freight Tariff Rules and the public timetable of the national railway group, and the sea route data integrates the route maps of COSCO Shipping, Maersk and other shipping companies and the official information released by each port, and uses Yandex Maps API to batch obtain and calibrate the distances of various paths.

[0116] The transportation cost adopts the national unified transportation price standard, including the Railway Freight Tariff Rules and the industry guide price of highway and sea transportation, so as to avoid subjective pricing; the time value of goods is classified according to the customs code, and the average value is taken to reflect the comprehensive characteristics of goods flow.

[0117] S102, a three-layer network modeling method is used, three types of transportation modes are set as three layers of sub-networks, different sub-network layers are connected through nodes, a multimodal transport network is constructed, and the cost of the multimodal transport network is quantified;

[0118] Specifically, the multimodal transport network is constructed, including:

[0119] Selection and layer copying of physical nodes, N cities between the origin, port and destination are selected as physical nodes, and the physical nodes are numbered ; each physical node is copied in highway, railway and sea transportation modes respectively to form three layers of virtual nodes, so that there are 3N nodes in the multi-layer network, the index of the i-th physical node in the first layer is .

[0120] Calculate the intra-layer adjacency weight, take the total transportation cost between adjacent nodes as the edge weight, construct three weighted adjacency matrices of highway, railway and sea transportation based on the three transportation modes, place the three weighted adjacency matrices in the three diagonal blocks of the Sup hybrid matrix, and ensure that the intra-layer connection only occurs in the same transportation mode:

[0121] (1)

[0122] In the formula, denotes the hybrid weighted matrix, denotes the highway weighted matrix, denotes the railway weighted matrix, denotes the sea weighted matrix.

[0123] ​The interlayer coupling edge determination, i.e. the transit route determination, is determined by a vector at the hub node respectively represent the transit cost of highway ↔ railway, railway ↔ sea transport, highway ↔ sea transport.

[0124] The complete The mixed matrix, outside the corresponding diagonal block, constructs three sparse transit diagonal matrices, only in the transport node position is replaced by the corresponding transit cost, and the rest is zero. The intra-layer and inter-layer weights are combined to obtain:

[0125] (2).

[0126] Specifically, the cost quantification of the multimodal transport network includes:

[0127] The total transportation cost considered in the present application includes transportation cost, transit cost, carbon emission cost and time cost;

[0128] The transportation cost is calculated as:

[0129] (3)

[0130] In the formula, , respectively represent the base price and the transportation base price per kilometer using transportation mode m, represent whether transportation mode m is used from node i to j, if used, =1, otherwise 0, represent the transportation mileage of node i to j using transportation mode m, is a variable that determines whether there is a direct connection between node i and j in the transportation network, if there is a direct connection between node i and j, =1, otherwise 0, M is the set of transportation modes.

[0131] The time cost, the cross-border multimodal transport time is a composite index, not only including the in-transit transport time, but also including the collection time, i.e. the collection and distribution time of goods at hub nodes, the customs clearance time, i.e. the clearance, inspection and quarantine procedure time. Due to the large geographical span of cross-border land-sea channels and the wide range of countries involved, it is difficult to obtain data such as customs clearance time and goods collection time. The present application converts the transport time by cross-border transport speed, and the calculation method is as follows:

[0132] (4)

[0133] (5)

[0134] (6)

[0135] In the formula, This represents the cross-border transport speed using mode m. , These represent the mileage and travel time of the transportation route using transportation mode m, respectively. This represents the transportation time from node i to j using transportation mode m. and These represent transportation time costs and capital occupation costs, respectively. This represents the time depreciation rate of good A. Bank annual loan interest rate The initial value of cargo A in one container;

[0136] Carbon emission costs:

[0137] (7)

[0138] In the formula, This represents the unit carbon emission cost of goods transported from node i to j using mode m.

[0139] Total cost of connecting edges:

[0140] (8)

[0141] In the formula, This indicates transit costs.

[0142] S103. Conduct vulnerability assessment and node importance correction for the multimodal transport network;

[0143] Specifically, a vulnerability assessment of the multimodal transport network is conducted, including:

[0144] When a port node fails and interoperability is disrupted, the origin and destination in the multimodal transport network are completely disconnected, and the cross-border transport function of the network should be equivalent to zero. In order to accurately measure the vulnerability characteristics of the cross-border multi-level transport network and identify key nodes, cross-border network efficiency and cross-border network connectivity are used as basic indicators.

[0145] Cross-border network efficiency measures the overall cost between any two nodes at a port of entry. Decreased cross-border network efficiency indicates an increase in average transportation costs. Network vulnerability is measured from a functional perspective.

[0146] (9)

[0147] In the formula, Indicates cross-border network efficiency. , These represent the number of overseas nodes and the number of domestic nodes, respectively. Let represent the minimum weight sum from a node s within China to a node t outside China in any layer network.

[0148] Cross-border network connectivity rate, used to measure the proportion of whether there is a reachable path between any domestic node and any overseas node. If all paths have at least one reachable path, the multimodal transport network is complete in cross-border connectivity. If some levels or node pairs cannot interwork, the cross-border connectivity of the network is weak. The structural dimension measures the network vulnerability:

[0149] (10)

[0150] In the formula, Cross-border network connectivity rate, is an indicator function, which is 1 if the two nodes are reachable, and 0 if they are not.

[0151] The comprehensive vulnerability of multimodal transport network is:

[0152] (11)

[0153] In the formula, is the geometric mean of cross-border network efficiency and cross-border network connectivity rate.

[0154] Combining cross-border efficiency and cross-border connectivity into a whole vulnerability measurement overcomes the one-sidedness of a single indicator and simultaneously quantifies the two risks of transport efficiency decline and network connectivity interruption.

[0155] Specifically, node importance correction includes:

[0156] Betweenness centrality correction, closeness centrality correction, Katz centrality correction, eigenvector centrality correction and PageRank value correction;

[0157] Betweenness centrality correction calculates the frequency of a node appearing as an intermediary in cross-border minimum cost paths, eliminates the interference of internal regional node pairs on paths, and highlights the bridge role of the node in transport links. It is calculated as follows:

[0158] (12)

[0159] In the formula, is the modified betweenness centrality of node i, is the total number of all shortest paths from node s to t, is the number of paths passing through physical node i in the layer in all shortest paths from node s to t.

[0160] The modified closeness centrality measures the inverse of the average minimum cost of a node to all nodes in another group. The larger the value, the closer the node is to the core position of another group, reflecting the comprehensive accessibility of the node in the cross-border transport network:

[0161] (13)

[0162] (14)

[0163] (15)

[0164] the modified closeness centrality of node i, / denotes the reciprocal of the average minimum cost from the domestic or foreign node i to all nodes in the domestic or foreign, the weighted minimum cost from the node i in the m-th layer to the t-th node in the m-th layer, denotes the weighted minimum cost from the node i in the m-th layer to the s-th node in the m-th layer. The modified Katz centrality further distinguishes whether the path connects the domestic and foreign on the basis of the traditional, and strengthens or weakens the cross-border transmission through different attenuation factors, and the domestic path is processed with a smaller attenuation factor, while the cross-border path is processed with a relatively larger attenuation factor, highlighting the importance of cross-border channels and reflecting the potential influence of nodes in cross-border transportation;

[0165]

[0166] (16)

[0167] (17)

[0168] (18)

[0169] wherein, the modified Katz centrality of node i, I is the unit matrix, W is the attenuation adjacency matrix, , denote the matrices that only retain domestic connections and only retain cross-border connections, respectively, , denote the attenuation factor of the domestic path, the attenuation factor of the cross-border path, respectively, x is the Katz score vector, and f is a source vector with a value of 1, which has the same dimension as W.

[0170] The modified eigenvector centrality is similar to the modified Katz centrality, and a cross-border preference matrix is constructed by setting different cross-border factors, and the modified eigenvector centrality of the node is calculated based on this, and the calculation is as follows:

[0171] (19)

[0172] (20) ​​

[0173] (21)

[0174] wherein, denotes the modified eigenvector centrality of node i, denotes the cross-border preference matrix, , denotes the preference factor of domestic paths and the preference factor of cross-border paths, , are respectively , the cost mapping matrix of wherein the matrix elements are calculated by , y is the characteristic centrality score vector, is the corresponding matrix maximum eigenvalue.

[0175] The modified PageRank value is calculated by setting different cross-border factors, and the calculation is as follows:

[0176] (22)

[0177] (23)

[0178] wherein, denotes the modified PageRank value of node i, denotes the PageRank score vector, denotes the transpose matrix of P, P denotes the transition matrix, which is calculated by , D denotes the diagonal matrix, denotes the damping factor, usually 0.85, denotes the personalized vector, which denotes the preference of random jump.

[0179] S104, the weight of each node importance evaluation index is determined by using a machine learning model, specifically including:

[0180] The complex mapping relationship between node features and network features is quantified from different angles by four machine learning models to fuse diffusion and vulnerability.

[0181] With the five types of indexes of modified betweenness centrality, modified closeness centrality, modified Katz centrality, modified eigenvector centrality and modified PageRank, the node feature matrix is constructed as an input variable, and diffusion and vulnerability are fused as dual supervision learning labels; wherein, the cross-border infection simulation of fixed propagation round number is designed based on the improved SIR propagation model, and the propagation probability is determined by the comprehensive cost of the path between nodes. The simulation takes each domestic / overseas node as the source of infection, and statistics the proportion of nodes that can be infected within T rounds.

[0182] Four heterogeneous models with different computational methods—lightweight gradient boosting machine, support vector machine, elastic network regression, and least squares boosting—are used to independently learn the feature-label association mechanism and obtain the weights of important evaluation indicators for each node.

[0183] S105. Based on the weights of the important evaluation indicators of each node, the TOPSIS model is used to evaluate the comprehensive score of the network nodes and determine the importance of the multimodal transport network nodes.

[0184] Specifically, the TOPSIS model is used to evaluate the overall score of network nodes, including:

[0185] Based on the weights of key evaluation indicators for each node, the TOPSIS model is used to evaluate the comprehensive score of network nodes, calculated as follows:

[0186] (twenty four)

[0187] In the formula, For the first The overall score of each node, with a value range of [0, 1], where a larger value indicates a higher importance of the node; and They represent the first The importance of each node and the distance between the optimal and worst solutions.

[0188] S106. Simulate node overload and load redistribution processes using a cascading failure model to assess the criticality of nodes in dynamic risk propagation and determine the dynamic impact mechanism of critical node failure on the network.

[0189] Specifically, the cascading failure model simulates the node overload and load redistribution process, including:

[0190] Node betweenness largely reflects the load of a site. Using node betweenness as a quantitative indicator of initial load, for a network with a total of N nodes:

[0191] (25)

[0192] In the formula, This indicates the initial load of the node.

[0193] Assuming that all nodes in the multimodal transport network have the capacity to handle loads, and that the maximum capacity of a node is positively correlated with its initial load and related to its reserve capacity coefficient, the maximum capacity of a node is:

[0194] (26)

[0195] In the formula, Indicates the maximum capacity of the node. This represents the capacity redundancy coefficient.

[0196] Considering the uncertainty and unexpected situations in actual operation, the nodes in the network are designed to have certain overload capacity to deal with peak transport periods and emergency scheduling, so whether a node fails or not is related to the capacity of the node's freight transport facilities and the degree of congestion, etc. Therefore, overloaded nodes do not always stop running immediately, and nodes can bear loads exceeding their standard capacity under certain conditions. The overload failure can be regarded as a risk, and the corresponding failure probability is in the range of [0, 1]. The overload capacity coefficient is introduced, which is in the range of [0, ∞]. At the same time, considering that the ability of each node to bear loads exceeding its capacity is not the same, the more critical the node is, the busier it is, and the greater the failure probability is, and the more reasonable measures need to be taken to ensure its freight transport capacity, that is, the node failure probability is not only related to the overload capacity coefficient , but also related to the criticality of the node. Therefore, a reasonable critical capacity is set for each node, so that the more the load exceeds, the more likely the node is to fail, which is more in line with the actual situation.

[0197] When the load of a node is less than its maximum capacity , the node will not fail. When the load of a node exceeds its maximum capacity but is within a certain allowed range , the node has a certain probability of failure. When the flow load of a node reaches or exceeds the allowed limit , the node is overloaded and fails, and the failure probability is . The overload load with a failure probability of 1 is set as the removal threshold.

[0198] (27)

[0199] In the formula, represents the failure probability of node i at time t, represents the overload capacity coefficient, represents the load of node i at time t, represents the modified betweenness centrality of node i, represents the average modified betweenness centrality of the network.

[0200] Cascade failure propagation process, after the failure of a node in the multimodal transport network, considering the effect of the remaining capacity of the adjacent nodes of the failed node and the criticality of the node on the load redistribution process of the failed node, the remaining capacity coefficient and the node importance coefficient are introduced, and a node load redistribution strategy is proposed:

[0201] ​Node load transfer condition, in the process of cascading failure of multimodal transport network, the load state of the current node in the network is determined, if the node load exceeds the node capacity at this time, the node i is in overload state at this time, the failure probability of the node is calculated , state judgment is carried out, and then load redistribution is carried out, the random failure threshold is set as P, P is in the range of [0, 1], if the failure probability of the node at this time is , the load of the node exceeding the capacity is distributed according to the set strategy; if the failure probability of the node i at this time is , the node is considered to be in overload state and failure, and all loads are distributed according to the set strategy; if the load of the node i at this time is greater than the overload capacity, the node is directly considered to be in failure state, and all loads are distributed according to the set strategy;

[0202] Node load distribution ratio:

[0203] (28)

[0204] In the formula, , , represents the remaining capacity coefficient, , represents the node importance coefficient, represents the equal consideration of the role of node remaining capacity and node importance in load redistribution, and J represents the adjacent node set;

[0205] Node load distribution strategy, considering the different settings of node overload state, overload but not failure node and failure node load distribution strategy, the load distribution of overload but not failure node is:

[0206] (29)

[0207] The load distribution of failure node is:

[0208] (30)

[0209] In the formula, , represents the load amount of node i distributed to node j.

[0210] The above has described the embodiments of the present application, the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes are obvious to those skilled in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles, practical application or improvement of technology in the market of the embodiments, or to enable other ordinary skilled persons in the art to understand the embodiments disclosed herein.

Claims

1. A method for identifying key nodes in a cross-border transportation network, characterized in that, include: Acquire all cities and related transportation data for the three modes of transportation (road, rail, and sea) between the origin, port, and destination of goods; A three-layer network modeling method is adopted, which sets the three types of transportation modes as three-layer sub-networks. Different sub-network layers are connected through nodes to construct a multimodal transport network and quantify the cost of the multimodal transport network. Vulnerability assessment and node importance correction for multimodal transport networks; Using cross-border network efficiency and cross-border network connectivity as basic indicators, we conduct a network vulnerability assessment of multimodal transport networks. The nodes of the multimodal transport network are corrected for betweenness centrality, proximity centrality, Katz centrality, eigenvector centrality, and PageRank value. Machine learning models are used to determine the weights of important evaluation indicators for each node. By employing four heterogeneous models with different calculation methods—lightweight gradient boosting machine, support vector machine, resilient network regression, and least squares boosting—diffusion and vulnerability are integrated to quantify the mapping relationship between node features and network features from different perspectives, thereby determining the weights of important evaluation indicators for each node. Based on the weights of the important evaluation indicators for each node, the TOPSIS model is used to evaluate the comprehensive score of the network nodes and determine the node importance of the multimodal transport network. By simulating node overload and load redistribution processes using a cascading failure model, the criticality of nodes in dynamic risk propagation is assessed, and the dynamic impact mechanism of critical node failure on the network is determined.

2. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The construction of the multimodal transport network includes: The selection and layer copying of physical nodes involves selecting N cities between the source, port, and destination as physical nodes, and then numbering these physical nodes. ; Each physical node is replicated in three modes of transportation: road, rail, and sea, forming a three-layer virtual node network with 3N nodes in the multi-layer network. The index of the i-th physical node of the layer is ; Calculate the intra-layer adjacency weights and construct three weighted adjacency matrices for highways, railways, and sea transport respectively. Place these three weighted adjacency matrices in the three diagonal blocks of the Sup mixture matrix: （1） In the formula, Represents a mixed weighted matrix. Represents the highway weighted matrix. Represents the railway weighted matrix. Represents the weighted matrix for maritime transport; Interlayer coupling edges are determined using vectors at pivot nodes. These represent the transshipment costs for road-rail, rail-sea, and road-sea transport, respectively. Build a complete A hybrid matrix is ​​constructed by creating three sparse transit diagonal matrices, where the transit costs are replaced only at the transport node positions, with the rest set to zero. The intra-layer and inter-layer weights are then merged to obtain: （2）。 3. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The cost quantification of the multimodal transport network includes: Total transportation costs include transportation costs, transshipment costs, carbon emission costs, and time costs; Transportation costs: （3） In the formula, , These represent the base price for delivery and the base price per kilometer using transportation method m, respectively. Indicates whether transportation mode m is used from node i to j. If so, =1, otherwise 0. This represents the transportation distance from node i to j using transportation mode m. This variable determines whether there is a direct connection between node i and node j in the transportation network. If there is a direct connection between node i and node j... =1, otherwise 0, M is the set of transportation modes; Time cost, specifically cross-border multimodal transport time, is a composite indicator that includes not only transit time but also cargo collection and customs clearance time. The calculation is as follows: （4） （5） （6） In the formula, This represents the cross-border transport speed using mode m. , These represent the mileage and travel time of the transportation route using transportation mode m, respectively. This represents the transportation time from node i to j using transportation mode m. and These represent transportation time costs and capital occupation costs, respectively. This represents the time depreciation rate of good A. Bank annual loan interest rate The initial value of cargo A in one container; Carbon emission costs: （7） In the formula, This represents the unit carbon emission cost of goods transported from node i to j using mode m. Total cost of connecting edges: （8） In the formula, This indicates transit costs.

4. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The vulnerability assessment of the multimodal transport network includes: Cross-border network efficiency and cross-border network connectivity are used as basic indicators. Cross-border network efficiency measures the overall cost between any two nodes at a port of entry, measured by functional dimensions: （9） In the formula, Indicates cross-border network efficiency. , These represent the number of overseas nodes and the number of domestic nodes, respectively. Let represent the minimum weight sum from a node s within China to a node t outside China in any layer network; Cross-border network connectivity, measuring the proportion of times a reachable path exists between any domestic node and any overseas node, is measured from a structural dimension: （10） In the formula, Indicates cross-border network connectivity. This is an indicator function; it is 1 if the two nodes are reachable, and 0 if they are not reachable. The overall vulnerability of multimodal transport networks is as follows: （11） In the formula, This is the geometric mean of cross-border network efficiency and cross-border network connectivity.

5. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The node importance correction includes: Betweenness centrality correction, proximity centrality correction, Katz centrality correction, eigenvector centrality correction, and PageRank value correction; Betweenness centrality correction calculates the frequency of a node's appearance as an intermediary in a cross-border minimum cost path, eliminates interference from internal regional nodes on the path, and highlights the bridging role of nodes in the transportation link. Modified proximity centrality measures the reciprocal of the average minimum cost from a node to all nodes in another group. The larger the value, the closer the node is to the core of another group, reflecting the node's overall accessibility in cross-border transportation networks. The Katz centrality is corrected to further distinguish whether the path connects domestic and foreign routes. Different attenuation factors are used to strengthen or weaken cross-border propagation. Domestic routes are treated with a smaller attenuation factor, while cross-border routes are treated with a relatively larger attenuation factor, highlighting the importance of cross-border channels and reflecting the potential impact of nodes in cross-border transportation. The eigenvector centrality is corrected by constructing a cross-border preference matrix by setting different cross-border factors, and the corrected eigenvector centrality of the nodes is calculated based on this matrix. The PageRank value is adjusted by setting different cross-border factors.

6. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The method of using a machine learning model to determine the weights of important evaluation indicators for each node includes: By integrating diffusion and vulnerability through four machine learning models, the complex mapping relationship between node features and network features is quantified from different perspectives; Five metrics—corrected betweenness centrality, corrected proximity centrality, corrected Katz centrality, corrected eigenvector centrality, and corrected PageRank—are used to construct a node feature matrix as input variables, and diffusion and vulnerability are integrated as dual-supervised learning labels. Four heterogeneous models with different computational methods—lightweight gradient boosting machine, support vector machine, elastic network regression, and least squares boosting—are used to independently learn the feature-label association mechanism and obtain the weights of important evaluation indicators for each node.

7. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The evaluation of the comprehensive score of network nodes using the TOPSIS model includes: Based on the weights of key evaluation indicators for each node, the TOPSIS model is used to evaluate the comprehensive score of network nodes, calculated as follows: （24） In the formula, For the first The overall score of each node, with a value range of [0, 1], where a larger value indicates a higher importance of the node; and They represent the first The importance of each node and the distance between the optimal and worst solutions.

8. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The simulation of node overload using a cascaded failure model includes: Node betweenness largely reflects the load of a site. Using node betweenness as a quantitative indicator of initial load, for a network with a total of N nodes: （25） In the formula, Indicates the initial load of the node; Assuming that all nodes in the multimodal transport network have the capacity to handle loads, and that the maximum capacity of a node is positively correlated with its initial load and related to its reserve capacity coefficient, the maximum capacity of a node is: （26） In the formula, Indicates the maximum capacity of the node. Indicates the capacity redundancy coefficient; Due to the uncertainties and unforeseen circumstances in actual operation, each node in the network is designed with a certain overload capacity to cope with peak transportation periods and emergency dispatch situations. Whether a node fails depends on its capacity and workload. Therefore, an overloaded node does not immediately stop operating. Under certain conditions, a node can withstand a load exceeding its standard capacity. Overload failure is considered a risk, and the corresponding failure probability is in the range of [0, 1]. Introducing overload capacity factor The value range is [0, ∞]. Furthermore, considering that the capacity of each node to handle loads exceeding its capacity varies in reality, the more critical the node, the busier it is, and the higher its probability of failure. Therefore, reasonable measures need to be taken to ensure its cargo transportation capacity. In other words, the probability of node failure is not only related to the overload capacity coefficient... It is also related to the criticality of the nodes; therefore, a reasonable critical capacity should be set for each node. This means that the more the load exceeds the limit, the more likely it is to fail, which aligns with reality. When the node's load is less than its maximum capacity When the node's load exceeds its maximum capacity, it will not fail; when the node's load exceeds its maximum capacity, but within a certain allowable range... Within the node, there is a certain probability of failure; when the node's traffic load... Reaching or exceeding the permitted limits When a node is overloaded and fails, its failure probability is: Overload with a failure probability of 1 Set as the removal threshold, the expression is as follows: （27） In the formula, Let represent the failure probability of node i at time t. Indicates the overload capacity factor. This represents the load of node i at time t. Indicates the corrected betweenness centrality of node i. This indicates the network's average corrected betweenness centrality.

9. The method for identifying key nodes in a cross-border transportation network according to claim 1, characterized in that, The load redistribution process includes: In the cascading failure propagation process of a multimodal transport network, after a node fails, the remaining capacity of adjacent nodes and the criticality of the node are considered in relation to the load redistribution process, and a remaining capacity coefficient is introduced. With node importance coefficient A node load redistribution strategy is proposed: Node load transfer conditions: During a cascading failure in a multimodal transport network, the load status of existing nodes in the network is assessed. If the node load exceeds its capacity, then node i is in an overloaded state at that moment. The failure probability of this node is then calculated. The system performs a status determination, then load redistributes the load. A random failure threshold of P is set, where P is in the range [0, 1]. If the failure probability of node i is... If the load exceeding the capacity of node i is then distributed according to the set strategy; if the failure probability of node i is at this time... If the load on node i exceeds the overload capacity, the node is considered to be in an overloaded state and has failed, and all load is distributed according to the set strategy. If the load on node i exceeds the overload capacity, the node is considered to be in a failed state and all load is distributed according to the set strategy. The node load distribution ratio is as follows: （28） In the formula, , Represents the remaining capacity coefficient. denoted by the node importance coefficient, indicating that the remaining capacity and importance of nodes are considered equally in load redistribution, and J represents the set of adjacent nodes; The node load distribution strategy considers different settings for node overload states, and the load distribution strategy for overloaded but not failed nodes versus failed nodes. The load distribution for overloaded but not failed nodes is as follows: （29） The load distribution for the failed node is as follows: （30） In the formula, This represents the load that node i is allocated to node j.

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