A method for evaluating the resilience of a multimodal transport network based on cascading failures of multiple layers of networks

Abstract

The application discloses a kind of based on multilayer network cascading failure multimodal transport network resilience evaluation method, belong to multimodal transport network operation and resilience evaluation technical field.First, according to multimodal transport network multilayer structure and freight flow transfer characteristics, ML-space method is used to construct highway and water weighted undirected multilayer network model;On this basis, fusion network topology and freight attribute double perspective, calculate node multilayer centrality and freight level to determine node importance, combined with the heterogeneity of subnetwork to build load-capacity cascading failure model containing initial load, node capacity and differential load redistribution strategy;Then based on the resilience triangle theory, build the whole stage resilience evaluation system covering resistance, absorption capacity and recovery capacity, through MATLAB software numerical simulation, compare the network resilience under different cascading failure and recovery strategy, reveal the influence law of node capacity coefficient on resilience.The application starts from the actual operation scene of multimodal transport network, considers multilayer characteristics and cascading failure propagation law, proposes the precise evaluation method of multimodal transport network resilience under cascading failure scenario, provides scientific reference for the planning construction, risk prevention and control and resilience improvement of multimodal transport network.

Description

Technical Field

[0001] This invention relates to the field of multimodal transport network operation and resilience assessment technology, and in particular to a multimodal transport network resilience assessment method based on a multi-layer network perspective and cascading failure scenarios. Background Technology

[0002] Multimodal transport, by integrating road, rail, and waterway transportation modes, enables efficient cargo flow, reducing logistics costs and becoming a crucial infrastructure supporting regional economic development. This aligns with the development requirements of the "Outline for Building a Powerful Transportation Nation," which calls for "building a high-quality, comprehensive, and three-dimensional transportation network and enhancing system resilience." However, multimodal transport networks typically have a complex, multi-layered structure with strong inter-node connections. When faced with disturbances such as natural disasters or pandemic control measures, the risk of node failure can easily propagate within and between layers, triggering cargo diversion and cascading failures. In severe cases, this can lead to network paralysis, threatening the stable operation of the transport network. Therefore, conducting resilience assessments of multimodal transport networks that consider cascading failures, accurately revealing the evolutionary patterns of network resilience, and providing support for network planning, construction, and risk prevention are of significant practical importance.

[0003] Existing research on the resilience of multimodal transport networks still has the following shortcomings:

[0004] (1) The evaluation of node importance relies on single-layer network topology indicators, ignoring the multi-layer characteristics and freight attributes of multimodal transport networks. This makes it difficult to fully reflect the actual impact of nodes on the network and to accurately identify key risk nodes.

[0005] (2) In the construction of the cascading failure model, the differences in freight load and the heterogeneity of sub-networks in the multimodal transport network were not fully considered. The load redistribution strategy did not closely match the actual freight flow transfer pattern, making it difficult to realistically simulate the cascading failure propagation process.

[0006] (3) Resilience assessments often focus on single-layer transportation networks or single performance indicators (such as vulnerability and robustness), lacking a comprehensive resilience assessment system that takes into account the characteristics of multimodal transport multi-layer structures and covers the entire process of resistance-absorption-recovery, and rarely incorporates cascading failure scenarios into the assessment.

[0007] Therefore, those skilled in the art urgently need to combine the multi-layered characteristics and freight attributes of multimodal transport networks to construct a realistic cascading failure model and a full-stage resilience assessment method to solve the technical problem of accurate assessment of the resilience of multimodal transport networks under cascading failure scenarios. Summary of the Invention

[0008] The purpose of this invention is to overcome the limitations of existing multimodal transport network performance evaluation methods, such as ignoring multi-layer characteristics and freight attributes, cascading failure simulations that are not realistic, and single evaluation dimensions. It provides an evaluation method that covers accurate node evaluation, failure propagation simulation, and full-stage resilience quantification, providing theoretical support and practical guidance for the planning, construction, and resilience improvement of multimodal transport networks.

[0009] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0010] This invention provides a method for assessing the resilience of multimodal transport networks based on multi-layer network cascading failures, characterized in that the method includes the following steps:

[0011] Step 1: Obtain basic data on multimodal transport network routes and transport nodes, and construct a road-rail-water multimodal transport network topology model using the ML-space method;

[0012] Step 2: Based on the dual perspectives of network topology and node freight attributes, calculate the multi-level centrality and freight level of each node in the multimodal transport network, and determine the node importance ranking.

[0013] Step 3: Establish a load-capacity cascading failure model based on node importance, and define the initial load of nodes, node capacity, and load redistribution strategy for failed nodes;

[0014] Step 4: Based on the resilience triangle theory, construct a multimodal transport network resilience assessment model that includes resistance, absorption and recovery capabilities, and calculate the network resilience value;

[0015] Step 5: Use MATLAB software to perform numerical simulations on the multi-layer network model, cascading failure model, and resilience assessment model. Compare the network resilience under different cascading failure strategies and recovery strategies to complete the multimodal transport network resilience assessment.

[0016] 2. Step 1, constructing the multimodal transport network topology model, specifically includes:

[0017] This patent abstracts freight terminals for each mode of transport in a multimodal transport network as nodes, and the shortest transport route between adjacent terminals as edges. Edges within the same mode of transport network are intra-layer edges, and transfer routes between nodes of different modes of transport within the same city are inter-layer edges, constructing a weighted undirected multi-layer network. The multi-layer network is defined as D = (G h G r G w C);

[0018] Among them, G h G r G wThese represent the highway transport network layer, the railway transport network layer, and the waterway transport network layer, respectively; G h ={V h E h Let G be the adjacency matrix of the highway layer network. r ={V r E r Let G be the adjacency matrix of the railway layer network. w ={V w E w} represents the adjacency matrix of the waterway layer network; E represents the set of nodes in the highway, railway, and waterway networks, respectively. h E r E w These are represented as matrices formed by the internal edges of the highway, railway, and waterway network layers, respectively. Let i be the i-th node in the highway network layer. For nodes within the highway network layer With nodes The edges between layers are consistent with the representation of the railway network layer and the waterway network layer. C represents the coupling matrix of the inter-layer relationships. E (h，r) E (h,w) E (r，w) This represents the matrix composed of the weight values ​​of the inter-layer connections between different network nodes. From this, we can obtain the three coupling matrices C1, C2, and C3 between each pair of the three-layer network.

[0019] Express the undirected nature of the network using symmetric matrices. Let C1, C2, and C3 be the transpose matrices, respectively. Based on this, the mathematical model of the three-layer multimodal transport network in this paper is specifically represented as follows:

[0020]

[0021] 3. The node importance calculation method in step 2 specifically includes:

[0022] Step 2.1: Calculate the overall centrality value of a node in the entire multi-layer network, i.e., multi-layer centrality, using the following formula:

[0023]

[0024] in, α-layer node Multilevel centrality values; For nodes The structural entropy value of layer α; L is the total number of layers in the multilayer network.

[0025] Step 2.1: Calculate the structural entropy and local connectivity strength of nodes and each layer of the network, using the following formula:

[0026]

[0027] in, for Its neighboring nodes at the same level The local connectivity strength; n α C represents the total number of nodes in layer α. α (j) represents a node Initial multilayer centrality value in layer α; D egree (j) is same-level neighbor nodes The degree value;

[0028] Step 2.2: Calculate the structural entropy and local connectivity strength of nodes and each layer of the network, using the following formula:

[0029]

[0030] Among them, C α (i) represents a node Initial multilayer centrality values ​​in layer α; B α (i) represents a node Betweenness centrality value in the α layer; B β (j) is Other network layer nodes among the neighboring nodes The betweenness centrality value; For decision variables, if the node For inter-layer nodes, The value is 1 if α is the highest and 0 otherwise; 1 ≤ α ≠ β ≤ L; s and t are any two nodes in the α-layer network. and This represents the number of shortest paths in the α-layer network. For nodes in the α-layer network The number of shortest paths;

[0031] Step 2.3: Calculate the overall centrality value of a node in the entire multi-layer network, i.e., multi-layer centrality, using the following formula:

[0032]

[0033] in, α-layer node Multilevel centrality values; For nodes The structural entropy value of layer α; L is the total number of layers in the multilayer network;

[0034] Step 2.4: Calculate the total freight volume of each transportation node in the city to characterize the freight level of each node. Standardize the deviation to a dimensionless value of 0-100, as shown in the following formula:

[0035]

[0036] Among them, Z i Represents a node The raw value of the node importance index, (Z i ) max and (Z) i ) max These are the maximum and minimum values ​​of the original index, Z′. i The index values ​​are standardized; This represents the standardized value of the freight volume at each node, signifying the value of a node in the α-layer network. The freight level value is calculated. Finally, the multi-level centrality and freight level value of the nodes are calculated and sorted.

[0037] 4. Step 3, based on the dynamic load-capacity model of nodes, specifically includes:

[0038] Step 3.1: Calculate the initial load of the node, using the following formula:

[0039]

[0040] Among them, L i Represents a node The initial load; Nodes after deviation standardization Multilevel centrality values; σ and These are the weight values ​​for the two parameters: node multi-level centrality and node freight level. Considering that both are of equal importance, they are set as follows:

[0041] Step 3.2: Define node capacity as a nonlinear function of the initial load, as shown in the following formula:

[0042] C i =L i +γ·L i ρ

[0043] Among them, C i Let γ be the initial capacity of network node i; γ and ρ are node capacity redundancy coefficients, and γ > 0 and ρ > 0. By changing the values ​​of γ and ρ, the capacity of each node can be adjusted. When the node load exceeds the node capacity, the node fails and the node load needs to be transferred.

[0044] Step 3.3: Develop a load redistribution strategy for failed network nodes: After an inter-layer node fails, the load is redistributed across layers according to the average transport speed ratio of each layer (road 80km / h, railway 70km / h, waterway 30km / h, i.e., the speed ratio is 8:7:3; therefore, the load distribution ratio for a three-layer road-rail-water network is 8:7:3, for a two-layer road-rail network it is 8:7, for a two-layer rail-water network it is 7:3, and for a two-layer road-water network it is 8:3). The calculation formula for cross-layer redistribution of nodes is as follows:

[0045]

[0046] in, When the inter-layer nodes of a coupled subnetwork fail, the failed node in layer α is represented as... The amount of load transferred to the β layer; This refers to the proportional coefficient allocated based on the average transport speed of different levels. Failed node The total amount of transferred load generated.

[0047] Then, a secondary allocation is performed according to the intra-layer strategy. That is, when an intra-layer node within the same network fails, its load is distributed based on the proportion of its neighboring nodes' tight centrality. The corresponding calculation formula is as follows:

[0048]

[0049] Where, ΔL ij Indicates nodes within the layer After failure, it is assigned to a neighboring node. The load capacity; For nodes neighboring nodes Close centrality Represents a node The set of neighboring nodes; For nodes The close centrality; For other nodes and nodes in this layer of the network The length of the shortest path between them; Let be the set of all points in the α-layer network.

[0050] 5. Step 4, constructing a multimodal transport network resilience assessment model, specifically includes:

[0051] Step 4.1: Calculate the resilience, characterized by the average efficiency of the initial network, as shown in the following formula:

[0052]

[0053] Where N is the total number of nodes in the multi-layer network; d ijLet d be the shortest path length between any two distinct nodes in the current network. When there is no path between the two nodes, d ij It is infinitely large;

[0054] Step 4.2: The node ranked first in importance is removed, thus becoming invalid. The cascading failure model from Step 3 is applied to trigger cascading failures, obtaining the failure order of all failed nodes. From the first to the last failed node, the average network efficiency is calculated after each removal to determine the absorption capacity. The absorption capacity is the integral of the average network efficiency over time during the disturbance phase (node ​​failure process). The specific calculation formula is as follows:

[0055]

[0056] Step 4.3: Using the node importance calculated from the two indicators of multi-level centrality and freight level, restore the nodes and their corresponding edges in descending order of importance. Calculate the average network efficiency for each restored node to determine the recovery capability. The recovery capability is the integral of the average network efficiency over time during the recovery phase (node ​​recovery process). The specific calculation formula is as follows:

[0057]

[0058] Step 4.4: Calculate the network resilience value, which is the sum of resistance, absorption, and recovery capabilities. The specific calculation formula is as follows:

[0059] R = E1 + A + R e

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] To address the shortcomings of existing multimodal transport network resilience assessment techniques, such as neglecting multi-layer characteristics and freight attributes, failing to accurately simulate cascading failures, and having incomplete assessment systems, this paper proposes a multimodal transport network resilience assessment method based on a multi-layer network perspective and cascading failure. Based on the construction of a realistic multimodal transport network model (road-rail-water) using the ML-space method, this method accurately evaluates node importance by integrating multi-layer centrality and freight level indicators. It also designs load redistribution strategies based on sub-network heterogeneity, constructing a load-capacity cascading failure model. Furthermore, based on the resilience triangle theory, a resilience assessment system covering the entire process of resistance, absorption, and recovery is established. MATLAB software simulations are used to compare network resilience under different cascading failure and recovery strategies, revealing the influence of node capacity coefficients on resilience. This provides a scientific theoretical reference for the planning, construction, risk prevention, and resilience improvement of multimodal transport networks, ensuring their stable and efficient operation. Attached Figure Description

[0062] Figure 1This is a flowchart of the multimodal transport network resilience assessment based on multi-layer network cascading failure as described in this invention.

[0063] Figure 2 This is a schematic diagram of the multimodal transport network model of road, rail and water as described in this invention.

[0064] Figure 3 This is a flowchart of the load-capacity cascading failure model for multimodal transport networks described in this invention.

[0065] Figure 4 This is a schematic diagram of the multimodal transport network resilience formation process described in this invention.

[0066] Figure 5 This is a topology diagram of a regional road-rail-water intermodal transport network in an embodiment of the present invention.

[0067] Figure 6 This is a network performance diagram of different cascading failure and recovery strategies in the embodiments of the present invention. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0069] Example 1:

[0070] like Figure 1 As shown, Embodiment 1 of the present invention provides a method for assessing the resilience of multimodal transport networks based on a multi-layer network perspective and cascading failure scenarios, comprising the following steps:

[0071] Step 1: Obtain basic data on multimodal transport network routes and transport nodes, and construct a road-rail-water multimodal transport network topology model using the ML-space method;

[0072] Step 2: Based on the dual perspectives of network topology and node freight attributes, calculate the multi-level centrality and freight level of each node in the multimodal transport network, and determine the node importance ranking.

[0073] Step 3: Establish a load-capacity cascading failure model based on node importance, and define the initial load of nodes, node capacity, and load redistribution strategy for failed nodes;

[0074] Step 4: Based on the resilience triangle theory, construct a multimodal transport network resilience assessment model that includes resistance, absorption and recovery capabilities, and calculate the network resilience value;

[0075] Step 5: Use MATLAB software to perform numerical simulations on the multi-layer network model, cascading failure model, and resilience assessment model. Compare the network resilience under different cascading failure strategies and recovery strategies to complete the multimodal transport network resilience assessment.

[0076] 2. Step 1, constructing the multimodal transport network topology model, specifically includes:

[0077] This patent abstracts freight terminals for each mode of transport in a multimodal transport network as nodes, and the shortest transport route between adjacent terminals as edges. Edges within the same mode of transport network are intra-layer edges, and transfer routes between nodes of different modes of transport within the same city are inter-layer edges, constructing a weighted undirected multi-layer network. The multi-layer network is defined as D = (G h G r G w C);

[0078] Among them, G h G r G w These represent the highway transport network layer, the railway transport network layer, and the waterway transport network layer, respectively; G h ={V h E h} represents the adjacency matrix of the highway layer network, Gr={V r E r Let G be the adjacency matrix of the railway layer network. w ={V w E w} represents the adjacency matrix of the waterway layer network; E represents the set of nodes in the highway, railway, and waterway networks, respectively. h E r E w These are represented as matrices formed by the internal edges of the highway, railway, and waterway network layers, respectively. Let i be the i-th node in the highway network layer. For nodes within the highway network layer With nodes The edges between layers are consistent with the representation of the railway network layer and the waterway network layer. C represents the coupling matrix of the inter-layer relationships. E (h，r) E (h,w) E (r，w) This represents the matrix composed of the weight values ​​of the inter-layer connections between different network nodes. From this, we can obtain the three coupling matrices C1, C2, and C3 between each pair of the three-layer network.

[0079] Express the undirected nature of the network using symmetric matrices. These are the transpose matrices of C1, C2, and C3, respectively. Based on this, the mathematical model of the three-layer multimodal transport network in this patent is specifically represented as follows:

[0080]

[0081] 3. The node importance calculation method in step 2 specifically includes:

[0082] Step 2.1: Calculate the overall centrality value of a node in the entire multi-layer network, i.e., multi-layer centrality, using the following formula:

[0083]

[0084] in, α-layer node Multilevel centrality values; For nodes The structural entropy value of layer α; L is the total number of layers in the multilayer network.

[0085] Step 2.1: Calculate the structural entropy and local connectivity strength of nodes and each layer of the network, using the following formula:

[0086]

[0087] in, for Its neighboring nodes at the same level The local connectivity strength; n α C represents the total number of nodes in layer α. α (j) represents a node Initial multilayer centrality value in layer α; D egree (j) is same-level neighbor nodes The degree value;

[0088] Step 2.2: Calculate the structural entropy and local connectivity strength of nodes and each layer of the network, using the following formula:

[0089]

[0090] Among them, C α (i) represents a node Initial multilayer centrality values ​​in layer α; B α (i) represents a node Betweenness centrality value in the α layer; B β (j) is Other network layer nodes among the neighboring nodes The betweenness centrality value; For decision variables, if the node For inter-layer nodes, The value is 1 if α is the highest and 0 otherwise; 1 ≤ α ≠ β ≤ L; s and t are any two nodes in the α-layer network. and This represents the number of shortest paths in the α-layer network. For nodes in the α-layer network The number of shortest paths;

[0091] Step 2.3: Calculate the overall centrality value of a node in the entire multi-layer network, i.e., multi-layer centrality, using the following formula:

[0092]

[0093] in, α-layer node Multilevel centrality values; For nodes The structural entropy value of layer α; L is the total number of layers in the multilayer network;

[0094] Step 2.4: Calculate the total freight volume of each transportation node in the city to characterize the freight level of each node. Standardize the deviation to a dimensionless value of 0-100, as shown in the following formula:

[0095]

[0096] Among them, Z i Represents a node The raw value of the node importance index, (Z i ) max and (Z) i ) max These are the maximum and minimum values ​​of the original index values, respectively. The index values ​​are standardized; This represents the standardized value of the freight volume at each node, signifying the value of a node in the α-layer network. The freight level value is calculated. Finally, the multi-level centrality and freight level value of the nodes are calculated and sorted.

[0097] 4. Step 3, based on the dynamic load-capacity model of nodes, specifically includes:

[0098] Step 3.1: Calculate the initial load of the node, using the following formula:

[0099]

[0100] Among them, L i Represents a node The initial load; Nodes after deviation standardization Multilevel centrality values; σ and These are the weight values ​​for the two parameters: node multi-level centrality and node freight level. Considering that both are of equal importance, they are set as follows:

[0101] Step 3.2: Define node capacity as a nonlinear function of the initial load, as shown in the following formula:

[0102] C i =L i +γ·L i ρ

[0103] Among them, C i Let γ be the initial capacity of network node i; γ and ρ are node capacity redundancy coefficients, and γ > 0 and ρ > 0. By changing the values ​​of γ and ρ, the capacity of each node can be adjusted. When the node load exceeds the node capacity, the node fails and the node load needs to be transferred.

[0104] Step 3.3: Develop a load redistribution strategy for failed network nodes: After an inter-layer node fails, the load is redistributed across layers according to the average transport speed ratio of each layer (road 80km / h, railway 70km / h, waterway 30km / h, i.e., the speed ratio is 8:7:3; therefore, the load distribution ratio for a three-layer road-rail-water network is 8:7:3, for a two-layer road-rail network it is 8:7, for a two-layer rail-water network it is 7:3, and for a two-layer road-water network it is 8:3). The calculation formula for cross-layer redistribution of nodes is as follows:

[0105]

[0106] in, When the inter-layer nodes of a coupled subnetwork fail, the failed node in layer α is represented as... The amount of load transferred to the β layer; This refers to the proportional coefficient allocated based on the average transport speed of different levels. Failed node The total amount of transferred load generated.

[0107] Then, a secondary allocation is performed according to the intra-layer strategy. That is, when an intra-layer node within the same network fails, its load is distributed based on the proportion of its neighboring nodes' tight centrality. The corresponding calculation formula is as follows:

[0108]

[0109] Where, ΔL ij Indicates nodes within the layer After failure, it is assigned to a neighboring node. The load capacity; For nodes neighboring nodes Close centrality Represents a node The set of neighboring nodes; For nodes The close centrality; For other nodes and nodes in this layer of the network The length of the shortest path between them; Let be the set of all points in the α-layer network.

[0110] 5. Step 4, constructing a multimodal transport network resilience assessment model, specifically includes:

[0111] Step 4.1: Calculate the resilience, characterized by the average efficiency of the initial network, as shown in the following formula:

[0112]

[0113] Where N is the total number of nodes in the multi-layer network; d ij Let d be the shortest path length between any two distinct nodes in the current network. When there is no path between the two nodes, d ij It is infinitely large;

[0114] Step 4.2: The node ranked first in importance is removed, thus becoming invalid. The cascading failure model from Step 3 is applied to trigger cascading failures, obtaining the failure order of all failed nodes. From the first to the last failed node, the average network efficiency is calculated after each removal to determine the absorption capacity. The absorption capacity is the integral of the average network efficiency over time during the disturbance phase (node ​​failure process). The specific calculation formula is as follows:

[0115]

[0116] Step 4.3: Using the node importance calculated from the two indicators of multi-level centrality and freight level, restore the nodes and their corresponding edges in descending order of importance. Calculate the average network efficiency for each restored node to determine the recovery capability. The recovery capability is the integral of the average network efficiency over time during the recovery phase (node ​​recovery process). The specific calculation formula is as follows:

[0117]

[0118] Step 4.4: Calculate the network resilience value, which is the sum of resistance, absorption, and recovery capabilities. The specific calculation formula is as follows:

[0119] R=E1+A+R e

[0120] Example 2:

[0121] This embodiment 2 describes the specific application of a multimodal transport network resilience assessment method based on a multi-layer network perspective and cascading failure scenarios to a multimodal transport network in a certain region, and the process of assessing the network resilience.

[0122] Step 1: Obtain multimodal transport network node data for a certain region up to September 2024, construct a multimodal transport network model, and obtain freight volume data for each node based on data from national or provincial statistical yearbooks to provide conditions for subsequent node importance ranking calculations.

[0123] The multimodal transport network node data for a certain region includes the following two attributes: city name and multimodal transport network node name, each assigned a corresponding number for ease of implementation. A specific data example is shown in Table 1. In the multimodal transport network node name, 1 represents the city's road node, 2 represents the city's railway node, and 3 represents the city's waterway node.

[0124] Table 1. Example of multimodal transport network node data in a certain region.

[0125]

[0126] Based on the above node data, we continue to collect the connection data of the multimodal transport network in this region. The connection length is taken as the length of the shortest actual transport route between nodes. The data is recorded in the form of an OD table for subsequent matrix data input. An example of OD data is shown in Table 2.

[0127] Table 2. Example of connection length between nodes in a multimodal transport network in a certain region (unit: km)

[0128]

[0129]

[0130] Based on the above data and combined with complex network theory, the ML-space method is used to construct a road-rail-water intermodal transport network model for a certain region's central area.

[0131] For the network D = (G, C), there are 187 edges, and the number of valid nodes with at least one edge is 73; the highway network layer G h The set of nodes V h It contains 27 valid nodes, and the set of intra-layer edges E h Contains 64 edges; Railway network layer G r The set of nodes V r It contains 26 valid nodes, and the set of intra-layer edges E r Contains 35 edges; Waterway Network Layer G w The set of nodes V w It contains 20 valid nodes, and the set of intra-layer edges E wIt contains 22 edges; there are a total of 66 inter-layer connections coupling the various network layers, including the inter-layer connection E between the highway layer and the railway layer. (h,r) There are 25, E, the interlayer connection between the highway layer and the waterway layer. (h,w) There are 20 connecting edges between the railway level and the waterway level, E. (r，w) There are 21 items.

[0132] Step 2: Based on the node importance evaluation method of this patent, calculate and rank the multi-level centrality and freight level values ​​of 81 nodes in the intermodal transport network of a certain central area. To select the most important nodes in the network, list the top 5 nodes and their relevant values. Specific data examples are shown in Table 3.

[0133] Table 3. Ranking of the top 5 most important nodes in a region's multimodal transport network.

[0134]

[0135] This embodiment considers the worst-case scenario and conducts initial network attacks on the two most important nodes, "Nantong 1" and "Shanghai 3", to induce cascading failures and explore the network resilience of a certain region's multimodal transport network under cascading failures.

[0136] Step 3: To compare and analyze the impact of four strategies—multi-level centrality cascade failure, freight level cascade failure, multi-level centrality recovery, and freight level recovery—on the resilience of the Yangtze River Delta central area's multimodal transport network, it is necessary to calculate the initial average network efficiency and the corresponding network absorption and recovery capabilities under each of the four strategies. The recovery order is based on the importance ranking of multi-level centrality and freight level, proceeding from highest to lowest. Simultaneously, considering the unfavorable situation of relatively congested freight nodes (i.e., node capacity saturation), the node capacity coefficients are set to fixed values ​​γ = 0.1 and ρ = 0.1. The average network efficiency is then calculated, and the network's resistance, absorption, and recovery capabilities under different conditions are further statistically analyzed to obtain the network resilience value, as shown in Table 4.

[0137] Table 4. Network Capability and Resilience Values ​​under Different Failure and Recovery Conditions

[0138]

[0139] Table 4 compares the network capacity values ​​of the multimodal transport network under different failure and recovery strategies. It reveals that compared to cascading failures based on freight level, cascading failures based on multi-level centrality have the lowest network absorption capacity, decreasing by approximately 29.7%. Recovery capacity based on multi-level centrality increases by approximately 21.3% compared to recovery based on freight level. However, scenario 2, which involves cascading failures based on multi-level centrality followed by recovery based on freight level, has the lowest network resilience value, decreasing by approximately 18.4% compared to scenario 3, which has the highest resilience value. This indicates that node multi-level centrality has a greater impact on network performance than node freight level, resulting in the worst network resilience. Therefore, to improve the overall resilience of the multimodal transport network in this region, enhance its ability to resist interference, and ensure normal network operation, it is recommended to maintain and construct transport nodes according to their multi-level centrality. Furthermore, after a large-scale failure propagation of transport nodes, recovery work can be carried out sequentially based on the multi-level centrality to quickly improve the performance of the multimodal transport network in this region.

[0140] In summary, the multimodal transport network resilience assessment method based on multi-layer networks and cascading failures described in this patent embodiment starts from the actual characteristics of the multi-layer structure and freight attributes of multimodal transport networks. It uses the ML-space method to construct a weighted undirected multi-layer network model of road-rail-water transport, analyzes the propagation laws of cascading failures within and between layers, combines network topology and freight perspectives, integrates multi-layer centrality and freight level indicators to accurately evaluate node importance, and constructs a load-capacity cascading failure model that includes initial node load, capacity, and differentiated load redistribution strategies. Furthermore, based on the resilience triangle theory, it establishes a resilience assessment system covering the entire stages of resistance, absorption, and recovery. The effectiveness of the model is verified through numerical simulation using MATLAB software, revealing the impact of different failure and recovery strategies and node capacity coefficients on network resilience. This allows for an accurate assessment of multimodal transport network resilience, providing a scientific reference for the planning, construction, risk prevention, and resilience enhancement of multimodal transport networks. Ultimately, this enhances the anti-interference capability of multimodal transport networks, ensures the stable and efficient operation of transport networks, and supports high-quality regional economic development.

[0141] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can make several improvements and modifications within the scope of the technology disclosed in the present invention, and these improvements and modifications are similarly covered within the scope of protection of the present invention.

Claims

1. A method for assessing the resilience of multimodal transport networks based on multi-layer network cascading failures, characterized in that, The method includes the following steps: Step 1: Obtain basic data on multimodal transport network routes and transport nodes, and construct a road-rail-water multimodal transport network topology model using the ML-space method; Step 2: Based on the dual perspectives of network topology and node freight attributes, calculate the multi-level centrality and freight level of each node in the multimodal transport network, and determine the node importance ranking. Step 3: Establish a load-capacity cascading failure model based on node importance, and define the initial load of nodes, node capacity, and load redistribution strategy for failed nodes; Step 4: Based on the resilience triangle theory, construct a multimodal transport network resilience assessment model that includes resistance, absorption and recovery capabilities, and calculate the network resilience value; Step 5: Use MATLAB software to perform numerical simulations on the multi-layer network model, cascading failure model, and resilience assessment model. Compare the network resilience under different cascading failure strategies and recovery strategies to complete the multimodal transport network resilience assessment.

2. The multimodal transport network resilience assessment method based on multi-layer network cascading failure as described in claim 1, characterized in that, Step 1, constructing the multimodal transport network topology model, specifically includes: This patent abstracts freight terminals for each mode of transport in a multimodal transport network as nodes, and the shortest transport route between adjacent terminals as edges. Edges within the same mode of transport network are intra-layer edges, and transfer routes between nodes of different modes of transport within the same city are inter-layer edges, constructing a weighted undirected multi-layer network. The multi-layer network is defined as D = (G h G r G w C); Among them, G h G r G w These represent the highway transport network layer, the railway transport network layer, and the waterway transport network layer, respectively; G h ={V h E h Let G be the adjacency matrix of the highway layer network. r ={V r E r Let G be the adjacency matrix of the railway layer network. w ={V w E w } represents the adjacency matrix of the waterway layer network; E represents the set of nodes in the highway, railway, and waterway networks, respectively. h E r E w These are represented as matrices formed by the internal edges of the highway, railway, and waterway network layers, respectively. Let i be the i-th node in the highway network layer. For nodes within the highway network layer With nodes The edges between layers are consistent with the representation of the railway network layer and the waterway network layer. C represents the coupling matrix of the inter-layer relationships. E (h，r) E (h,w) E (r，w) This represents the matrix composed of the weight values ​​of the inter-layer connections between different network nodes. From this, we can obtain the three coupling matrices C1, C2, and C3 between each pair of the three-layer network. Express the undirected nature of the network using symmetric matrices. Let C1, C2, and C3 be the transpose matrices, respectively. Based on this, the mathematical model of the three-layer multimodal transport network in this patent is specifically represented as follows:

3. The multimodal transport network resilience assessment method based on multi-layer networks and cascading failures as described in claim 1, characterized in that, The node importance calculation method in step 2 specifically includes: Step 2.1: Calculate the overall centrality value of a node in the entire multi-layer network, i.e., multi-layer centrality, using the following formula: in, α-layer node Multilevel centrality values; For nodes The structural entropy value of layer α; L is the total number of layers in the multilayer network. Step 2.1: Calculate the structural entropy and local connectivity strength of nodes and each layer of the network, using the following formula: in, for Its neighboring nodes at the same level Local connectivity strength; nα is the total number of nodes in layer α; C α (j) represents a node Initial multilayer centrality value in layer α; D egree (j) is same-level neighbor nodes The degree value; Step 2.2: Calculate the structural entropy and local connectivity strength of nodes and each layer of the network, using the following formula: Among them, C α (i) represents a node Initial multilayer centrality values ​​in layer α; B a (i) represents a node Betweenness centrality value in the α layer; B β (j) is Other network layer nodes among the neighboring nodes The betweenness centrality value; For decision variables, if the node For inter-layer nodes, The value is 1 if α is the highest and 0 otherwise; 1 ≤ α ≠ β ≤ L; s and t are any two nodes in the α-layer network. and This represents the number of shortest paths in the α-layer network. For nodes in the α-layer network The number of shortest paths; Step 2.3: Calculate the overall centrality value of a node in the entire multi-layer network, i.e., multi-layer centrality, using the following formula: in, α-layer node Multilevel centrality values; For nodes The structural entropy value of layer α; L is the total number of layers in the multilayer network; Step 2.4: Calculate the total freight volume of each transportation node in the city to characterize the freight level of each node. Standardize the deviation to a dimensionless value of 0-100, as shown in the following formula: Among them, Z i Represents a node The raw value of the node importance index, (Z i ) max and (Z) i ) max These are the maximum and minimum values ​​of the original index, Z′. i The index values ​​are standardized; This represents the standardized value of the freight volume at each node, signifying the value of a node in the α-layer network. The freight level value is calculated. Finally, the multi-level centrality and freight level value of the nodes are calculated and sorted.

4. The multimodal transport network resilience assessment method based on multi-layer networks and cascading failures as described in claim 1, characterized in that, Step 3 is based on a dynamic load-capacity model for nodes, and specifically includes: Step 3.1: Calculate the initial load of the node, using the following formula: Among them, L i Represents a node The initial load; Nodes after deviation standardization Multilevel centrality values; σ and These are the weight values ​​for the two parameters: node multi-level centrality and node freight level. Considering that both are of equal importance, they are set as follows: Step 3.2: Define node capacity as a nonlinear function of the initial load, as shown in the following formula: C i =L i +γ·L i r Among them, C i Let γ be the initial capacity of network node i; γ and ρ are node capacity redundancy coefficients, and γ > 0 and ρ > 0. By changing the values ​​of γ and ρ, the capacity of each node can be adjusted. When the node load exceeds the node capacity, the node fails and the node load needs to be transferred. Step 3.3: Develop a load redistribution strategy for failed network nodes: After an inter-layer node fails, the load is redistributed across layers according to the average transport speed ratio of each layer (road 80km / h, railway 70km / h, waterway 30km / h, i.e., the speed ratio is 8:7:3; therefore, the load distribution ratio for a three-layer road-rail-water network is 8:7:3, for a two-layer road-rail network it is 8:7, for a two-layer rail-water network it is 7:3, and for a two-layer road-water network it is 8:3). The calculation formula for cross-layer redistribution of nodes is as follows: in, When the inter-layer nodes of a coupled subnetwork fail, the failed node in layer α is represented as... The amount of load transferred to the β layer; This refers to the proportional coefficient allocated based on the average transport speed of different levels. Failed node The total amount of transferred load generated. Then, a secondary allocation is performed according to the intra-layer strategy. That is, when an intra-layer node within the same network fails, its load is distributed based on the proportion of its neighboring nodes' tight centrality. The corresponding calculation formula is as follows: Where, ΔL ij Indicates nodes within the layer After failure, it is assigned to a neighboring node. The load capacity; For nodes neighboring nodes Close centrality Represents a node The set of neighboring nodes; For nodes The close centrality; For other nodes and nodes in this layer of the network The length of the shortest path between them; Let be the set of all points in the α-layer network.

5. The multimodal transport network resilience assessment method based on multi-layer networks and cascading failures as described in claim 1, characterized in that, Step 4, constructing a multimodal transport network resilience assessment model, specifically includes: Step 4.1: Calculate the resilience, characterized by the average efficiency of the initial network, as shown in the following formula: Where N is the total number of nodes in the multi-layer network; d ij Let d be the shortest path length between any two distinct nodes in the current network. When there is no path between the two nodes, d ij It is infinitely large; Step 4.2: The node ranked first in importance is removed, thus becoming invalid. The cascading failure model from Step 3 is applied to trigger cascading failures, obtaining the failure order of all failed nodes. From the first to the last failed node, the average network efficiency is calculated after each removal to determine the absorption capacity. The absorption capacity is the integral of the average network efficiency over time during the disturbance phase (node ​​failure process). The specific calculation formula is as follows: Step 4.3: Using the node importance calculated from the two indicators of multi-level centrality and freight level, restore the nodes and their corresponding edges in descending order of importance. Calculate the average network efficiency for each restored node to determine the recovery capability. The recovery capability is the integral of the average network efficiency over time during the recovery phase (node ​​recovery process). The specific calculation formula is as follows: Step 4.4: Calculate the network resilience value, which is the sum of resistance, absorption, and recovery capabilities. The specific calculation formula is as follows: R=E1+A+R e。

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