A method for establishing a cascading failure model of a rail transit network

Abstract

This invention discloses a method for establishing a cascading failure model for rail transit networks, belonging to the technical field of calculation, estimation, or counting. The method includes the following steps: acquiring data and constructing a rail transit network model; removing faulty nodes and generating a new rail transit network model; simulating node states considering demand changes and time delays; and calculating cascading failure impact indicators. The cascading failure model established by this invention can simultaneously consider demand changes and time delays under cascading failure states in rail transit networks, revealing the cascading failure mechanism in the real world.

Description

Technical Field

[0001] This invention relates to transportation engineering and intelligent transportation technology, specifically to a method for establishing a cascading failure model for rail transit networks, belonging to the technical field of calculation, estimation, or counting. Background Technology

[0002] Cascading failure refers to the phenomenon where a fault in one node of a network propagates through the network topology, causing further faults in other nodes and ultimately leading to widespread network failures or even complete network paralysis. In real-world scenarios, rail transit stations are susceptible to faults caused by extreme weather and congestion. Although these faults often only affect individual stations or lines, their failure can result in significant commuting delays and substantial economic losses for the rail transit network. To assess the robustness of rail transit networks and accurately analyze the impact of station failures, it is necessary to study the cascading failure propagation mechanism. In recent years, cascading failure models for rail transit networks have made some progress. Most studies focus on traffic flow redistribution, revealing the importance of traffic flow in cascading failure propagation. Some models consider time delay effects, describing the propagation and impact of cascading failures over time. Due to factors such as the time required for passenger transfers, the impact of a faulty station cannot immediately affect adjacent stations; time delay is evident in cascading failures. Previous studies have relied on static traffic demand modeling, failing to reflect the dynamic characteristics of cascading failure propagation.

[0003] As is well known, traffic demand in rail transit networks is constantly changing. The impact of station failures occurring during off-peak hours on the entire rail transit network may increase significantly with the surge in traffic volume during peak hours; conversely, the impact of station failures occurring during peak hours may decrease as the peak period ends. The impact of cascading failures occurring during peak and off-peak hours differs significantly, thus requiring careful consideration of traffic demand changes in the propagation of cascading failures. However, while existing models can preliminarily explain the propagation mechanism of cascading failures, they do not simultaneously consider the time delay and demand changes associated with cascading failures in the transportation network. Therefore, they cannot objectively reflect the mechanism of cascading failures in actual rail transit networks and are difficult to assess their impact. This invention aims to propose a method for establishing a cascading failure model for rail transit networks that simultaneously considers demand changes and time delays to reflect the cascading failure situation in real-world rail transit. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing a method for establishing a cascading failure model for rail transit networks. This method can simultaneously consider demand changes and time delay effects under cascading failure states in rail transit networks, thereby objectively revealing the cascading failure mechanism in the real world and solving the technical problem that existing cascading failure models for rail transit networks are unable to assess the impact of cascading failures.

[0005] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0006] The present invention provides a method for establishing a cascading failure model of a rail transit network that considers the effects of demand changes and time delays, comprising steps S1 to S4.

[0007] S1. Obtain data on rail transit stations, routes, operating hours, and passenger travel demand within a specified time and space range, and construct a rail transit network model.

[0008] S2. Remove faulty nodes from the rail transit network model and generate a new rail transit network model.

[0009] S3. Based on the newly generated rail transit network model, simulate the node states considering demand changes and time delays, specifically including the following steps:

[0010] S31. Based on the obtained passenger travel demand data, filter passengers with the same origin and destination.

[0011] S32. Define passengers with the same origin and destination as a data packet in the rail transit network model. Set the initial movement path of the data packet as the shortest time path between the origin and destination. The shortest time path is calculated using Dijkstra's algorithm.

[0012] S33. At time zero, all data packets simultaneously begin moving from the starting point to the destination.

[0013] S34, Time step (min) determines the node's running status. The unit is min, and the specific steps include the following:

[0014] S34a. Calculate node load: For all nodes in the new rail transit network model, based on... Time to reach node Data packet set ,get Time Node The total number of passengers received , ,in, It is a data packet The corresponding number of passengers;

[0015] S34b, Identify and remove failed nodes: If Then the corresponding node The node is considered to be in a failed state and will be... Removed from the new rail transit network model, where, It is a node The maximum number of passengers that the corresponding rail transit station can accommodate under normal operating conditions;

[0016] S34c, Update the movement path of the data packet: for Time reaches node i The data packets, in The time to reach the next node, i.e., the j-th node. If in The next node at any moment If it is invalid, set the node. The shortest path to the destination is the new path; if there is no feasible route to the destination, the data packet is deleted.

[0017] S34d, Node Data Packet Update: Generate new data packets at nodes with passenger travel needs that are not expired; remove data packets that have reached their destination from the rail transit network model;

[0018] S35. Repeat step S34 until the system is stable.

[0019] S4. Calculate the impact index of cascade failure. .draw The time-varying curve visualizes the characteristics of how the effects of cascading failure change over time.

[0020] As a further improvement to the method for establishing a cascading failure model of a rail transit network that considers demand changes and time delays, in step S1, the acquired rail transit stations are defined as nodes in the rail transit network model. This indicates that the acquired route data is used to determine whether node locations are adjacent, and adjacent nodes... and The path between them is defined as an edge in the rail transit network model, with Indicates; edge travel time Calculated using the following formula:

[0021]

[0022] in, Pointer node and The distance between rail transit lines, Rail transit in the node Corresponding site and number node The corresponding speed of operation between sites It can be obtained from the acquired rail transit operating schedule data.

[0023] As a further improvement to the method for establishing a cascade failure model of a rail transit network that considers demand changes and time delays in this invention, in step S2, the method for removing faulty nodes is as follows: the nodes in the model corresponding to the faulty rail transit station are regarded as faulty nodes, and the faulty nodes and the edges connected to them are removed from the network.

[0024] As a further improvement to the method for establishing a cascading failure model of a rail transit network that considers demand changes and time delays in this invention, in step S4, the cascading failure impact index... The calculation formula is as follows:

[0025]

[0026] in, This represents the number of failed nodes. This represents the total number of nodes in the rail transit network.

[0027] As a further improvement to the method for establishing a cascading failure model of a rail transit network that considers demand changes and time delays in this invention, in step S35, the method for determining system stability is: if If no node fails or all nodes fail within a given time period, the system is considered stable; where, It is the time threshold, which represents the observation time for judging the stability of the system within the error range.

[0028] The present invention adopts the above-mentioned technical solution and has the following beneficial effects: The present invention utilizes graph theory and computer traffic simulation technology, taking a set of passengers with the same travel demand as the simulation object of traffic flow, to simulate the delay and demand changes of traffic flow at each node in the rail transit network model, and establishes a rail transit network cascading failure model that takes into account the effects of demand changes and time delay. The established cascading failure model not only considers the difference in the impact of cascading failures occurring during peak and off-peak periods, but also objectively reflects the dynamic characteristics of cascading failure propagation caused by time delay. It can scientifically and rationally analyze the impact of cascading failures in rail transit networks and provide technical support for traffic planning. Attached Figure Description

[0029] Figure 1 The flowchart illustrates the cascading failure model of the rail transit network for this invention.

[0030] Figure 2 This is an example scenario diagram of a rail transit network in a specific embodiment of the present invention.

[0031] Figure 3 A schematic diagram illustrating the update of the data packet movement path in step S34c.

[0032] Figures 4-6 The graphs show the changes of the cascading failure impact index I over time under the specific examples of the present invention: the failure of Medieval Avenue Station, Jing'an Temple Station, and People's Square Station. Detailed Implementation

[0033] The technical solution of the invention will now be described in detail with reference to the accompanying drawings.

[0034] like Figure 1 As shown, the present invention provides a cascading failure model for a rail transit network that considers demand changes and time delays, comprising the following steps: S1, acquiring data and constructing a rail transit network model; S2, removing faulty nodes and generating a new rail transit network model; S3, simulating node states considering demand changes and time delays; S4, calculating cascading failure impact indicators.

[0035] S1. Obtain rail transit station data, route data, operating schedule data, and passenger travel demand data within a specified time and space range, and construct a rail transit network model:

[0036] This example uses the Shanghai rail transit network at 8:00 AM for modeling. Figure 2 As shown. The obtained subway stations are defined as nodes in the Shanghai Rail Transit Network Model, with... This indicates that the acquired subway route data is used to determine whether node locations are adjacent; adjacent nodes... and The path between them is defined as an edge in the rail transit network model, with express.

[0037] The edge is calculated using the following formula. travel time :

[0038]

[0039] in, The distance between subway lines refers to the distance between nodes. The subway is in the node Corresponding site and number node The operating speed between corresponding stations can be obtained from the Shanghai Metro operation data.

[0040] S2. Remove faulty nodes from the rail transit network model and generate a new rail transit network model:

[0041] This example sequentially sets Century Avenue Station, Jing'an Temple Station, and People's Square Station as faulty subway stations to study the impact of cascading failures. Nodes in the rail transit network corresponding to the faulty subway stations are considered faulty nodes, and the faulty nodes and their connected edges are removed from the network.

[0042] S3. Based on the newly generated rail transit network model, simulate the node states considering demand changes and time delays, specifically including the following steps:

[0043] S31. Based on the obtained passenger travel demand data, filter passengers with the same origin and destination.

[0044] S32. Define passengers with the same origin and destination as a data packet in the subway network model, and set the initial movement path of the data packet as the shortest time path between the origin and destination; wherein, the shortest time path is calculated using Dijkstra's algorithm;

[0045] S33. At time zero, all data packets simultaneously begin moving from the starting point to the destination.

[0046] S34. At regular time steps (min), determine the node's running status, specifically including the following steps:

[0047] S34a. Calculate node load: For all nodes in the network, according to... Time to reach node Data packet set ,get Time Node The total number of passengers received , ;in, It is a data packet The corresponding number of passengers;

[0048] S34b, Identify and remove failed nodes: If Then the corresponding node The node is considered to be in a failed state and will be... Removed from the new rail transit network model, where, It is a node The maximum number of passengers that a subway station can accommodate under normal operating conditions;

[0049] S34c, Update the movement path of the data packet: such as Figure 3 As shown, Time to reach node The data packets, in Time to reach the next node If in The next node at any moment If it is invalid, set the node. The shortest path to the destination is the new path; if there is no feasible route to the destination, the data packet is deleted.

[0050] S34d, Node Data Packet Update: Generate new data packets at nodes with passenger travel needs that are not expired; remove data packets that have reached their destination from the rail transit network model.

[0051] S35. Repeat step S34 until the system is stable. The method for determining system stability is: if... If no node fails or all nodes fail within a given time period, the system is considered stable; where, It is the time threshold, which represents the observation time for judging the stability of the system within the error range.

[0052] S4. Calculate the impact indicators of cascade failure:

[0053] The cascading failure impact index is calculated using the following formula. :

[0054]

[0055] in, This represents the number of failed nodes. This represents the total number of nodes in the Shanghai Metro network.

[0056] Curves depicting the cascading failure impact index I over time were plotted for the following scenarios: failures at Century Avenue Station, Jing'an Temple Station, and People's Square Station. The curves for the cascading failure impact index over time at the three stations are shown below. Figure 4 , Figure 5 , Figure 6 As shown.

[0057] The above descriptions are merely preferred embodiments of this application, and the present invention is not limited to the above embodiments. It is understood that other improvements and variations directly derived or conceived by those skilled in the art without departing from the spirit and concept of the present invention should be considered to be included within the protection scope of the present invention.

Claims

1. A method for establishing a cascading failure model for a rail transit network, characterized in that, Includes the following steps: Step 1: Obtain data on rail transit stations, routes, operating hours, and passenger travel demand within a specified time and space range, and construct a rail transit network model; Step 2: Remove faulty nodes from the rail transit network model and update the rail transit network model; Step 3: For the updated rail transit network model, perform state simulation for each node, taking into account demand changes and time delays. Step 4: Calculate the cascading failure impact index based on the traffic network model after state simulation in Step 3; The specific method for simulating the state of each node in step 3, considering changes in demand and time delays, is as follows: Step 31: Based on the passenger travel demand data obtained in Step 1, filter passengers with the same origin and destination. Step 32: Define passengers with the same origin and destination as a data packet in the rail transit network model, and set the initial movement path of the data packet to the shortest time path between the origin and destination. Step 33: Initialize all data packets to move from their respective origin nodes to their respective destination nodes starting at time zero. Step 34: Determine the node's running status at regular time intervals, specifically including steps 34a to 34d: Step 34a: Calculate the load of all nodes in the updated rail transit network model. , for Time i node The total number of passengers received. for Time reaches node i The set of data packets, It is a data packet The corresponding number of passengers Step 34b: Determine and remove failed nodes based on the load of each node in the updated rail transit network model. The criterion for determining failed nodes based on the load of each node in the updated rail transit network model is as follows: , It is the i-th node The corresponding rail transit station has the maximum number of passengers it can accommodate under normal operating conditions. Step 34c: Update the data packet movement path based on the rail transit network model after removing the failed node: For in Time reaches node i exist Time reaches node j If the data packet is in Time j node If it is invalid, then set the i-th node. The shortest path to the destination is the new path. If there is no feasible route to the destination, the data packet is deleted. Step 34d: Update data packets at each node: Generate new data packets at nodes with passenger travel needs that are not expired, and remove data packets that have already reached their destinations from the rail transit network model. Step 35: Repeat step 34 until the system is stable.

2. The method for establishing a cascading failure model for a rail transit network according to claim 1, characterized in that, The specific method for constructing the rail transit network model in step 1 is as follows: Nodes of the rail transit network model are generated based on the acquired rail transit station data; whether two nodes are adjacent is determined based on the acquired route data; the i-th node... and the j-th node The edges of the rail transit network model that determine the path between these two adjacent nodes The edges of the rail transit network model travel time for , For the i-th node With the j-th node The distance between rail transit lines, Rail transit at node i Corresponding site and j-th node The speed of operation between corresponding sites.

3. The method for establishing a cascading failure model for a rail transit network according to claim 2, characterized in that, The specific method for removing faulty nodes in the rail transit network model in step 2 is as follows: the nodes in the rail transit network model corresponding to the faulty rail transit station are regarded as faulty nodes, and the faulty nodes and the edges connected to them are removed from the rail transit network model.

4. The method for establishing a cascading failure model for a rail transit network according to claim 1, characterized in that, Step 32 uses Dijkstra's algorithm to calculate the shortest path in time.

5. The method for establishing a cascading failure model for a rail transit network according to claim 1, characterized in that, The criterion for system stability in step 35 is: if No failed nodes or all nodes failed within the specified time. The time threshold for observing system stability.

6. The method for establishing a cascading failure model for a rail transit network according to claim 5, characterized in that, The expression for calculating the cascading failure impact index in step 4, based on the traffic network model after state simulation in step 3, is as follows: , As an indicator of the impact of cascading failures, This represents the number of failed nodes. This represents the total number of nodes in the rail transit network.

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