Construction method of cascading failure model of multimodal transport network based on hypergraph

Abstract

The application discloses a kind of based on hypergraph multimodal transport network cascading failure model, comprising: step 1, actual transport line and actual capacity in target area are hypergraph modeling;Step 2, the capacity and load of different layer hypergraph network node in target area are calculated;Step 3, simulate the cascading effect caused by site failure in multimodal transport network based on hypergraph.The application based on hypergraph theory, multimodal transport network is abstracted as multilayer hypernetwork, so as to study the propagation process of failure in multimodal transport network, and provide theoretical guidance for the prediction and prevention of multimodal transport cascading failure.

Description

Technical Field

[0001] This invention relates to the field of complex transportation networks, and more specifically to a method for constructing a cascading failure model of a multimodal transport network based on a hypergraph. Background Technology

[0002] With the development of science and technology, research on complex systems increasingly focuses on multi-dimensional and multi-layered network structures. Traditional network models typically only consider simple graphs, where nodes are connected only by edges. However, this simple graph model exhibits significant limitations when dealing with more complex network systems. Hypergraphs, which can better represent multi-dimensional relationships, are one method to address this limitation. Hypergraph theory is an emerging research approach that has been widely applied to analyze and model various complex systems, such as social networks, information networks, and transportation networks.

[0003] Multimodal transport is an important concept in modern transportation systems, referring to the use of multiple modes of transport (such as road, rail, waterway, and air) to transport goods or passengers, thereby improving transport efficiency, reducing costs, and minimizing environmental impact, providing strong support for urban economic and social development. However, despite the numerous conveniences brought by multimodal transport networks, their complexity and vulnerability are increasingly apparent. In reality, the failure of one station in a multimodal transport network can have a cascading effect on the entire network, leading to cascading failures. For example, when a city is hit by a rainstorm, freight, water, and air transport are all affected. Freight transport stops entering the city, and instead, the affected goods are transported to other reachable cities. However, a city's warehouses have limited capacity, resulting in surplus goods needing to be transported to other cities, causing the cascading failure of the multimodal transport network to propagate. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a construction of a cascading failure model for multimodal transport networks based on hypergraphs. The aim is to abstract multimodal transport networks into multi-layered hypernetworks based on hypergraph theory, enabling a deeper analysis and solution to the problem of cascading failures in real-world multimodal transport networks, thereby helping to improve transportation efficiency and network management flexibility.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] The present invention provides a method for constructing a cascading failure model of a multimodal transport network based on a hypergraph, characterized by the following steps:

[0007] Step 1. Based on the transportation methods in the target area, construct a multimodal transport supernetwork H = {H} 1 H 2 H 3}, where H 1 H represents the first-layer railway supernetwork. 2 H represents the second-layer air transport hypernetwork. 3 Let V denote the third-layer water transport hypernetwork; let the set of stations in the target region be denoted as V = {v1, v2, ..., v...}. j ,...,v n}, where v j Let j represent the j-th station, and n represent the total number of stations;

[0008] Step 2. Calculate the capacity and load of nodes in different layers of the hypergraph network in the target region;

[0009] Step 3: Simulate the cascading effect caused by site failure in a hypergraph-based multimodal transport network;

[0010] Step 3.1. Construct the adjacency matrix A of the i-th layer supernetwork at time t+1. i If there exists a j-th station v in the i-th layer hypernetwork j Let A i The element in the j-th row and j-th column Otherwise, let

[0011] Step 3.2. Initialize j to any number between 1 and n;

[0012] Step 3.3. Initialize and define the failed site as the x-th node v in the hypernet. x ;

[0013] Step 3.4. Initialize i = 1;

[0014] Step 3.5. If A i The element in the x-th row and x-th column This indicates that there exists a x-th node v in the i-th layer of the supernetwork. x If i > 3, then execute step 3.6; otherwise, assign i+1 to i. If i > 3, output the multimodal transport hypernetwork at time t and end the process; otherwise, return to execute step 3.5.

[0015] Step 3.6. For the x-th node v x The i-th layer supernetwork performs single-layer failure load redistribution;

[0016] Step 3.7. Iterate through the remaining capacity of each station in all layers of the supernetwork at time t+1. If there is a remaining capacity ≤ 0, it means that there is a failed station in the corresponding layer of the supernetwork, and execute step 3.8. If there is no remaining capacity ≤ 0, output the multimodal transport supernetwork at time t and end the process.

[0017] Step 3.8. Store the layer number, site number, and remaining capacity of all failed sites into the single-layer failed site set V, in order of site number. sin In the process, update the adjacency matrix of the corresponding layer supernetwork;

[0018] Step 3.9. Traverse the single-layer set of failed sites V sin Each failed site in the list:

[0019] Determine the x-th failed station v in the i-th layer supernetwork at time t+1. x Remaining capacity of stations in different layers of hypernetworks If all values ​​are ≤0, then execute the single-layer supernetwork site load redistribution in step 3.6; otherwise, execute the multi-layer supernetwork site load redistribution.

[0020] Step 3.10. For the single-layer failure site set V sin After each failed site is traversed, t+1 is assigned to t, and the process jumps to step 3.7 to execute sequentially.

[0021] The method for constructing a cascading failure model of a multimodal transport network based on a hypergraph, as described in this invention, is also characterized in that step 2 includes the following steps:

[0022] Step 2.1. Define the current time as t, and initialize t = 0;

[0023] Step 2.2. Based on the traffic data of the target area, obtain the load of each station in each layer of the multimodal transport hypernetwork at time t. in, This indicates the existence of the j-th station v in the i-th layer supernetwork. j Load at time t; if the j-th station v does not exist in the i-th layer supernetwork. j Then let

[0024] Step 2.2. Based on the maximum capacity data of the target area, obtain the maximum capacity of each station in each layer of the multimodal transport hypernetwork. in, v represents the j-th station in the i-th layer of the supernetwork. j Maximum capacity; if the j-th station v does not exist in the i-th layer supernetwork. j Then let

[0025] Step 2.3. Calculate the value of the j-th station v in the i-th layer supernetwork using equation (1). j Remaining capacity at time t+1

[0026]

[0027] Step 2.4. Calculate the value of the j-th station v in the i-th layer supernetwork using equation (2). j Load at time t+1

[0028]

[0029] In equation (2), It is assigned to the j-th station v in the i-th layer of the supernetwork. j The load.

[0030] Step 3.6 includes the following steps:

[0031] Step 3.6.1. Let i = 1;

[0032] Step 3.6.2. The hyperedge set E of the i-th layer hypernetwork i Find the x-th node v in x The included superedge set and by superedge set The x-th node v in the i-th layer hypernet consists of all the distinct non-failed nodes contained in each hyperedge. x neighboring site set Neighboring site set The sites in the list are used as load redistribution sites;

[0033] Step 3.6.3. Calculate the set of adjacent nodes using equation (3). The p-th load redistribution site v p The load added at time t+1

[0034]

[0035] In equation (3), v represents the p-th load redistribution station in the i-th layer supernetwork. p The remaining capacity at time t; v represents the x-th station in the i-th layer of the supernetwork. x The load at time t;

[0036] Step 3.6.4. Connect the x-th node v in the i-th layer of the supernetwork. x Load at time t Assigned to the set of neighboring nodes Therefore, the p-th load redistribution site v is calculated using equation (4). p Total load after being allocated to the load at time t+1

[0037]

[0038] Step 3.6.5. Calculate the load redistribution site v using equation (2). p Remaining capacity after being allocated to the load at time t+1

[0039] Step 3.6.6. Assign i+1 to i. If i>3, then execute step 3.7; otherwise, return to execute step 3.6.2.

[0040] The multi-layer hypernetwork site load redistribution in step 3.9 includes the following steps:

[0041] Step a. The hyperedge set E of the i-th layer hypernetwork i Find the xth invalid site v x The included superedge set and by superedge set The x-th failed site v in the i-th layer hypernet consists of all the distinct non-failed nodes contained in each hyperedge. x neighboring node set and adjacent site set The sites in the list are used as load redistribution sites;

[0042] Step b. At time t+1, determine the x-th failed site v in the two supernetworks other than the i-th supernetwork. x Remaining capacity of stations in different layers of hypernetworks Is it greater than 0? If so, then allocate the remaining capacity. The x-th failed site v in other layers of the supernetwork with a value greater than 0 x Add the x-th failed site v to the i-th layer supernetwork x Related node set In, and the relevant node set Sites in the list will be designated as load redistribution sites; otherwise, they will not be added.

[0043] Step c. Calculate the set of adjacent nodes using equation (5). The p-th station v in the i-th layer of the supernetwork p and related node sets The x-th failed site v in the s-th layer supernetwork x The load allocated at time t+1

[0044]

[0045] In equation (5), S represents the layer number of the supernetwork in the load redistribution site, and P represents the sequence number of the load redistribution site. This represents the P-th load redistribution site v assigned to in the S-th layer supernetwork.P The load; Represents the set of adjacent nodes The p-th station v in the i-th layer of the supernetwork p The remaining capacity at time t; Represents the set of related nodes In the s-th layer supernetwork, the x-th load redistribution station v x The remaining capacity at time t;

[0046] Step d. Remove the x-th failed station v from the i-th layer hypernetic network. x The load at time t+1 is distributed to the set of neighboring nodes. and related node sets Therefore, using equation (6), the P-th load redistribution station v in the S-th layer supernetwork is obtained. P Total load after being allocated to the load at time t+1

[0047]

[0048] Step e. Calculate the load redistribution station v in the S-layer supernetwork using equation (2). P Remaining capacity after being allocated to the load at time t+1

[0049] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the construction method, and the processor is configured to execute the program stored in the memory.

[0050] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program is executed by a processor to perform the steps of constructing the method.

[0051] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0052] 1. This invention uses hypergraph theory, which utilizes the characteristics of hypergraphs to not only represent complex relationships between multiple nodes but also to effectively represent hyperedge relationships between multiple nodes to construct a multimodal transport network, making the model more consistent with the complex connections between stations, transport routes, and transport modes in real-world multimodal transport networks.

[0053] 2. This invention, combined with hypergraph theory, can more accurately express the complex interactions and interdependencies between different modes of transport, routes, and stations in real-world multimodal transport systems. The propagation of cascading failures starts from the failed station and spreads along the interactions and dependencies between different modes of transport, routes, and stations, making the cascading failure model more consistent with reality.

[0054] 3. This invention combines hypergraph theory and considers the way failures propagate in multimodal transport networks in reality. It proposes a new cascading failure model in which the load after a station fails is not only transported to adjacent stations, but also to stations of other modes of transport in the same region. This is consistent with reality and can more accurately analyze and predict how failures propagate in multimodal transport networks, which is in line with practical applications.

[0055] 4. After the invention is implemented, the analysis of the images after failure can identify the key stations of the multimodal transport network, explore the robustness of the multimodal transport network, help design a more robust multimodal transport network, and provide reference for the planning of multimodal transport networks. Attached Figure Description

[0056] Figure 1 Schematic diagrams of a single layer and the overall network of the multimodal transport hypernetwork of this invention;

[0057] Figure 2 A schematic diagram of the site failure cascading failure model of this invention. Detailed Implementation

[0058] In this embodiment, a method for constructing a cascading failure model of a multimodal transport network based on hypergraphs is proposed. This model, based on hypergraph theory, abstracts the multimodal transport network into a multi-layered hypernetwork, enabling a deeper analysis and resolution of cascading failure problems in real-world multimodal transport networks. It also helps improve transport efficiency and network management flexibility, providing theoretical support and practical guidance for the design and optimization of real-world multimodal transport networks. Specifically, the method includes the following steps:

[0059] Step 1. Based on the transportation methods in the target area, construct a multimodal transport supernetwork H = {H} 1 H 2 H 3}, where H 1 H represents the first-layer railway supernetwork. 2 H represents the second-layer air transport hypernetwork. 3 Let V denote the third-layer water transport hypernetwork; let the set of stations in the target region be denoted as V = {v1, v2, ..., v...}. j ,...,v n}, where v j Let j represent the j-th station, and n represent the total number of stations. The diagrams for a single-layer hypernetwork and a full-layer hypernetwork are shown below. Figure 1 As shown, Figure 1 The first three images are schematic diagrams of a single transportation mode hypergraph network, and the last image is a schematic diagram of the hypergraph network of all layers. Each circle in the image is a hyperedge, representing a transportation route in a certain transportation mode.

[0060] Step 2. Calculate the capacity and load of nodes in different layers of the hypergraph network in the target region;

[0061] Step 2.1. Define the current time as t, and initialize t = 0;

[0062] Step 2.2. Based on the traffic data of the target area, obtain the load of each station in each layer of the multimodal transport hypernetwork at time t. in, This indicates the existence of the j-th station v in the i-th layer supernetwork. j Load at time t; if the j-th station v does not exist in the i-th layer supernetwork. j Then let

[0063] Step 2.2. Based on the maximum capacity data of the target area, obtain the maximum capacity of each station in each layer of the multimodal transport hypernetwork. in, v represents the j-th station in the i-th layer of the supernetwork. j Maximum capacity; if the j-th station v does not exist in the i-th layer supernetwork. j Then let

[0064] Step 2.3. Calculate the value of the j-th station v in the i-th layer supernetwork using equation (1). j Remaining capacity at time t+1

[0065]

[0066] Step 2.4. Calculate the value of the j-th station v in the i-th layer supernetwork using equation (2). j Load at time t+1

[0067]

[0068] In equation (2), It is assigned to the j-th station v in the i-th layer of the supernetwork. j The load.

[0069] Step 3, as follows Figure 2 As shown, the cascading effect caused by station failure in a hypergraph-based multimodal transport network is simulated.

[0070] Step 3.1. Construct the adjacency matrix A of the i-th layer supernetwork at time t+1. i If there exists a j-th station v in the i-th layer hypernetwork j Let A i The element in the j-th row and j-th column Otherwise, let

[0071] Step 3.2. Initialize j to any number between 1 and n;

[0072] Step 3.3. Initialize and define the failed site as the x-th node v in the hypernet. x ;

[0073] Step 3.4. Initialize i = 1;

[0074] Step 3.5. If The element in the x-th row and x-th column This indicates that there exists a x-th node v in the i-th layer of the supernetwork. x If there is a possibility of cascading failure, proceed to step 3.6. Otherwise, assign i+1 to i. If i>3, output the multimodal transport hypernetwork at time t and end the process. Otherwise, return to step 3.5.

[0075] Step 3.6. For the x-th node v x The i-th layer supernetwork performs single-layer failure load redistribution;

[0076] Step 3.6.1. Let i = 1;

[0077] Step 3.6.2. The hyperedge set E of the i-th layer hypernetwork i Find the x-th node v in x The included superedge set and by superedge set The x-th node v in the i-th layer hypernet consists of all the distinct non-failed nodes contained in each hyperedge. x neighboring site set Neighboring site set The site in the middle is used as a load redistribution site, because the first round of site v x Failure occurs in a three-layer hypernetwork as long as it contains station v x All of them fail, and failures cannot propagate between layers, so it is equivalent to affecting the entire site v. x Each layer of the hypernetwork performs a site v operation once. x Load redistribution after failure.

[0078] Step 3.6.3. Calculate the set of adjacent nodes using equation (3). The p-th load redistribution site v p The load added at time t+1

[0079]

[0080] In equation (3), v represents the p-th load redistribution station in the i-th layer supernetwork. p The remaining capacity at time t;

[0081] Step 3.6.4. Connect the x-th node v in the i-th layer of the supernetwork. x Load at time t Assigned to the set of neighboring nodes Therefore, the p-th load redistribution site v is calculated using equation (4). p Total load after being allocated to the load at time t+1

[0082]

[0083] Step 3.6.5. Calculate the load redistribution site v using equation (2). p Remaining capacity after being allocated to the load at time t+1

[0084] Step 3.6.6. Assign i+1 to i. If i>3, then execute step 3.7; otherwise, return to execute step 3.6.2.

[0085] Step 3.7. Iterate through the remaining capacity of each station in all layers of the supernetwork at time t+1. If there is a remaining capacity ≤ 0, it means that there is a failed station in the corresponding layer of the supernetwork, and execute step 3.8. If there is no remaining capacity ≤ 0, it means that there is no failed station in the corresponding layer of the supernetwork, the failure has not propagated, output the multimodal transport supernetwork at time t, and end the process.

[0086] Step 3.8. Store the layer number, site number, and remaining capacity of all failed sites into the single-layer failed site set V, in order of site number. sin In the process, update the adjacency matrix of the corresponding layer supernetwork;

[0087] Step 3.9. Traverse the single-layer set of failed sites V sin Each failed site in the list:

[0088] Determine the x-th failed station v in the i-th layer supernetwork at time t+1. x Remaining capacity of stations in different layers of hypernetworks If all values ​​are ≤0, then execute step 3.6 for single-layer supernetwork site load redistribution; otherwise, execute steps 3.10-3.14 for multi-layer supernetwork site load redistribution. Here, i represents other layers of the supernetwork besides layer i. This step is to determine the single-layer failed site V during this round of failure propagation. sin Can the failure of sites in the set propagate between layers?

[0089] Step 3.10. The hyperedge set E of the i-th layer hypernetwork i Find the xth invalid site v x The included superedge set and by superedge set The x-th failed site v in the i-th layer hypernet consists of all the distinct non-failed nodes contained in each hyperedge. x neighboring node set and adjacent site set The sites in the list are used as load redistribution sites;

[0090] Step 3.11. At time t+1, determine the x-th failed station v in the two supernetworks other than the i-th supernetwork. x Remaining capacity of stations in different layers of hypernetworks Is it greater than 0? If so, then allocate the remaining capacity. The x-th failed site v in other layers of the supernetwork with a value greater than 0 x Add the x-th failed site v to the i-th layer supernetwork x Related node set In, and the relevant node set Sites in the list will be designated as load redistribution sites; otherwise, they will not be added.

[0091] Step 3.12. Calculate the set of adjacent nodes using equation (5). The p-th v in the i-th layer of the supernetwork p and related node sets The x-th failed site v in the s-th layer supernetwork x The load allocated at time t+1

[0092]

[0093] In equation (5), S represents the layer number of the supernetwork in the load redistribution site, and P represents the sequence number of the load redistribution site. This represents the P-th load redistribution site v assigned to in the S-th layer supernetwork. P The load; Represents the set of adjacent nodes The p-th station v in the i-th layer of the supernetwork p The remaining capacity at time t; Represents the set of related nodes In the s-th layer supernetwork, the x-th load redistribution station v x The remaining capacity at time t;

[0094] In equation (5), S represents the set of adjacent sites. and related node sets In a hypernetwork, the layer number of different layers is P, which represents the set of adjacent sites. and related node sets The serial numbers of different stations in China This indicates that it is assigned to the set of adjacent sites. and related node sets In the S-th layer supernetwork, the P-th station v p The load.

[0095] Step 3.13. Remove the x-th failed station v from the i-th layer supernetwork. x The load at time t+1 is distributed to the set of neighboring nodes. and related node sets Therefore, using equation (6), the P-th load redistribution station v in the S-th layer supernetwork is obtained. P Total load after being allocated to the load at time t+1

[0096]

[0097] Step 3.14. Calculate the load redistribution station v in the S-layer supernetwork using equation (2). P Remaining capacity after being allocated to the load at time t+1

[0098] Step 3.15. For the single-layer failure site set V sin After each failed site is traversed, t+1 is assigned to t, and the process jumps to step 3.7 to execute sequentially.

[0099] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0100] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0101] In summary, to study the propagation of cascading failures in multimodal transport networks, this invention utilizes hypergraph theory. In a hypergraph, an edge connecting multiple nodes is called a "hyperedge." Hyperedges can represent complex relationships between multiple nodes, a characteristic that allows hypergraphs to more accurately reflect many-to-many relationships in complex systems. Therefore, hypergraph-based models can more accurately capture the connections between different stations and different transport modes in multimodal transport networks, thereby better analyzing and predicting the occurrence and propagation of cascading failures.

[0102] This model not only provides a new solution to the cascading failure problem in multimodal transport networks, but also offers managers a fresh perspective, helping them better understand and manage the operation of multimodal transport networks. By studying the propagation patterns of cascading failures in multi-layered hypernetworks, managers can formulate timely response strategies, improving transport efficiency and network management flexibility, thereby ensuring the safe and stable operation of multimodal transport networks.

Claims

1. A method for constructing a cascading failure model of a multimodal transport network based on a hypergraph, characterized in that, Includes the following steps: Step 1. Based on the transportation methods in the target area, construct a multimodal transport supernetwork H = {H} 1 H 2 H 3 }, where H 1 H represents the first-layer railway supernetwork. 2 H represents the second-layer air transport hypernetwork. 3 Let V denote the third-layer water transport hypernetwork; let the set of stations in the target region be denoted as V = {v1, v2, ..., v...}. j ,...,v n }, where v j Let j represent the j-th station, and n represent the total number of stations; Step 2. Calculate the capacity and load of nodes in different layers of the hypergraph network in the target region; Step 3: Simulate the cascading effect caused by site failure in a hypergraph-based multimodal transport network; Step 3.

1. Construct the adjacency matrix A of the i-th layer supernetwork at time t+1. i If there exists a j-th station v in the i-th layer hypernetwork j Let A i The element in the j-th row and j-th column Otherwise, let Step 3.

2. Initialize j to any number between 1 and n; Step 3.

3. Initialize and define the failed site as the x-th node v in the hypernet. x ; Step 3.

4. Initialize i = 1; Step 3.

5. If A i The element in the x-th row and x-th column This indicates that there exists a x-th node v in the i-th layer of the supernetwork. x If i > 3, then execute step 3.6; otherwise, assign i+1 to i. If i > 3, output the multimodal transport hypernetwork at time t and end the process; otherwise, return to execute step 3.

5. Step 3.

6. For the x-th node v x The i-th layer supernetwork performs single-layer failure load redistribution; Step 3.

7. Iterate through the remaining capacity of each station in all layers of the supernetwork at time t+1. If there is a remaining capacity ≤ 0, it means that there is a failed station in the corresponding layer of the supernetwork, and execute step 3.

8. If there is no remaining capacity ≤ 0, output the multimodal transport supernetwork at time t and end the process. Step 3.

8. Store the layer number, site number, and remaining capacity of all failed sites into the single-layer failed site set V, in order of site number. sin In the process, update the adjacency matrix of the corresponding layer supernetwork; Step 3.

9. Traverse the single-layer set of failed sites V sin Each failed site in the list: Determine the x-th failed station v in the i-th layer supernetwork at time t+1. x Remaining capacity of stations in different layers of hypernetworks If all values ​​are ≤0, then execute the single-layer supernetwork site load redistribution in step 3.6; otherwise, execute the multi-layer supernetwork site load redistribution. Step 3.

10. For the single-layer failure site set V sin After each failed site is traversed, t+1 is assigned to t, and the process jumps to step 3.7 to execute sequentially.

2. The method for constructing a cascading failure model of a multimodal transport network based on a hypergraph, as described in claim 1, is characterized in that... Step 2 includes the following steps: Step 2.

1. Define the current time as t, and initialize t = 0; Step 2.

2. Based on the traffic data of the target area, obtain the load of each station in each layer of the multimodal transport hypernetwork at time t. in, This indicates the existence of the j-th station v in the i-th layer of the supernetwork. j Load at time t; if the j-th station v does not exist in the i-th layer supernetwork. j Then let Step 2.

2. Based on the maximum capacity data of the target area, obtain the maximum capacity of each station in each layer of the multimodal transport hypernetwork. in, v represents the j-th station in the i-th layer of the supernetwork. j Maximum capacity; if the j-th station v does not exist in the i-th layer supernetwork. j Then let Step 2.

3. Calculate the value of the j-th station v in the i-th layer supernetwork using equation (1). j Remaining capacity at time t+1 Step 2.

4. Calculate the value of the j-th station v in the i-th layer supernetwork using equation (2). j Load at time t+1 In equation (2), It is assigned to the j-th station v in the i-th layer of the supernetwork. j The load.

3. The method for constructing a cascading failure model of a multimodal transport network based on a hypergraph, as described in claim 2, is characterized in that... Step 3.6 includes the following steps: Step 3.6.

1. Let i = 1; Step 3.6.

2. The hyperedge set E of the i-th layer hypernetwork i Find the x-th node v in x The included superedge set and by superedge set The x-th node v in the i-th layer hypernet consists of all the distinct non-failed nodes contained in each hyperedge. x neighboring site set Neighboring site set The sites in the list are used as load redistribution sites; Step 3.6.

3. Calculate the set of adjacent nodes using equation (3). The p-th load redistribution site v p The load added at time t+1 In equation (3), v represents the p-th load redistribution station in the i-th layer supernetwork. p The remaining capacity at time t; v represents the x-th station in the i-th layer of the supernetwork. x The load at time t; Step 3.6.

4. Connect the x-th node v in the i-th layer of the supernetwork. x Load at time t Assigned to the set of neighboring nodes Therefore, the p-th load redistribution site v is calculated using equation (4). p Total load after being allocated to the load at time t+1 Step 3.6.

5. Calculate the load redistribution site v using equation (2). p Remaining capacity after being allocated to the load at time t+1 Step 3.6.

6. Assign i+1 to i. If i>3, then execute step 3.7; otherwise, return to execute step 3.6.

2.

4. The method for constructing a cascading failure model of a multimodal transport network based on a hypergraph according to claim 3, characterized in that, The multi-layer hypernetwork site load redistribution in step 3.9 includes the following steps: Step a. The hyperedge set E of the i-th layer hypernetwork i Find the xth broken site v x The included superedge set and by superedge set The x-th failed site v in the i-th layer hypernet consists of all the distinct non-failed nodes contained in each hyperedge. x neighboring node set and adjacent site set The sites in the list are used as load redistribution sites; Step b. At time t+1, determine the x-th failed site v in the two supernetworks other than the i-th supernetwork. x Remaining capacity of stations in different layers of hypernetworks Is it greater than 0? If so, then allocate the remaining capacity. The x-th failed site v in other layers of the supernetwork with a value greater than 0 x Add the x-th failed site v to the i-th layer supernetwork x Related node set In, and the relevant node set Sites in the list will be designated as load redistribution sites; otherwise, they will not be added. Step c. Calculate the set of adjacent nodes using equation (5). The p-th station v in the i-th layer of the supernetwork p and related node sets The x-th failed site v in the s-th layer supernetwork x The load allocated at time t+1 In equation (5), S represents the layer number of the supernetwork in the load redistribution site, and P represents the sequence number of the load redistribution site. This represents the P-th load redistribution site v assigned to in the S-th layer supernetwork. P The load; Represents the set of adjacent nodes The p-th station v in the i-th layer of the supernetwork p The remaining capacity at time t; Represents the set of related nodes In the s-th layer supernetwork, the x-th load redistribution station v x The remaining capacity at time t; Step d. Remove the x-th failed station v from the i-th layer supernetwork. x The load at time t+1 is distributed to the set of neighboring nodes. and related node sets Therefore, using equation (6), the P-th load redistribution station v in the S-th layer supernetwork is obtained. P Total load after being allocated to the load at time t+1 Step e. Calculate the load redistribution station v in the S-layer supernetwork using equation (2). P Remaining capacity after being allocated to the load at time t+1 5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing any of the construction methods described in claims 1-4, the processor being configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of any of the construction methods described in claims 1-4.

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