A method for evaluating vulnerability of urban rail system considering time-varying demand

Abstract

The application discloses a kind of urban rail system vulnerability assessment methods considering time-varying demand, which comprises: collecting urban rail system site and line data, and AFC system card data;Complex network theory is used to model urban rail system;According to travel time and passenger tolerance, determine the sensitive time demarcation point of passenger to urban rail system operation delay;According to the operation delay time and sensitive time demarcation point, select model to calculate vulnerability index, assess the vulnerability of urban rail system.The application example is based on the traditional vulnerability index based on topological structure, from the angle of different degree operation delay, the vulnerability index model considering dynamic travel demand is established, and the dynamic assessment of urban rail system vulnerability is realized.So it can provide support for daily maintenance, management of urban rail system and post-disaster resource allocation.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit system technology, and in particular to a vulnerability assessment method for urban rail transit systems that takes into account time-varying demand. Background Technology

[0002] Traffic vulnerability refers to the abnormal sensitivity of a traffic system to internal or external risk scenarios. When risk scenarios occur, the system capacity may be significantly reduced and the service quality of the traffic system may be significantly reduced (including reduced accessibility and increased travel costs).

[0003] Urban rail transit systems are crucial for residents' daily lives and the normal operation of cities. However, these systems are also vulnerable to disruptions caused by unforeseen events such as fires, floods, construction, and signal malfunctions. Timely and accurate assessment of the vulnerabilities of urban rail transit systems is essential for operators in their daily maintenance and resource allocation.

[0004] Currently, there are many evaluation indicators for measuring the vulnerability of urban rail transit systems, mainly divided into vulnerability indicators based on topology and vulnerability indicators considering passenger flow characteristics. However, these indicators are all static and cannot truly reflect the impact of dynamic travel demand on system performance. Furthermore, different abnormal events have varying degrees of interference on the system, but few studies have considered the different interference effects. Therefore, this invention, based on traditional vulnerability indicators based on topology, establishes a vulnerability indicator model that considers dynamic travel demand from the perspective of different degrees of operational delays, thus realizing the dynamic assessment of the vulnerability of urban rail transit systems. Summary of the Invention

[0005] To address the issues of existing vulnerability assessment indicators for urban rail systems being non-dynamic and failing to consider the degree of event interference, this invention provides a vulnerability assessment method for urban rail systems that considers time-varying demand. Building upon traditional vulnerability indicators based on topology, a vulnerability indicator model considering dynamic travel demand is established from the perspective of different levels of operational delays, thus achieving dynamic assessment of the vulnerability of urban rail systems.

[0006] To address the aforementioned technical problems, this invention provides a vulnerability assessment method for urban rail transit systems that considers time-varying demand. Starting from the perspective of different levels of operational delays, a vulnerability index model considering dynamic travel demand is established, enabling dynamic assessment of the vulnerability of urban rail transit systems. This method helps support the daily maintenance and management of urban rail transit systems, as well as post-disaster resource allocation. To achieve the above objectives, the technical solutions provided in this application are as follows:

[0007] Step 1: Collect data, including urban rail system station and line data, as well as AFC system card swipe data, including passenger entry and exit times, and entry and exit times;

[0008] Step 2: Model the urban rail system using complex network theory;

[0009] Step 3: Determine the sensitive time threshold for passengers' perception of delays in urban rail system operations based on travel time and passenger tolerance.

[0010] Step 4: Based on the operational delay time T and the sensitive time boundary point Select a model to calculate vulnerability indicators and assess the vulnerability of the urban rail system.

[0011] Furthermore, in step 2, the specific rules for modeling the urban rail system using complex network theory are as follows: the urban rail system is represented by an undirected weighted graph G = {N, E, W}. In graph G, the node set N = {1, 2, 3, ..., N} consists of transfer stations and non-transfer stations of the urban rail system; the edge set E = {e ij |e ij =<i,j> The condition `i ≠ j` is determined by whether the nodes are directly connected. When there is a direct edge connecting two nodes `i` and `j`, `e`... ij =1, otherwise, e ij =0, i, j∈N; weight set W = {w ij |w ij ≥0} represents the weight of the corresponding edge, which refers to the actual travel time, actual distance, or passenger flow between stations during a certain period.

[0012] Furthermore, the sensitive time boundary point in step 3 It is usually taken for 60 minutes.

[0013] Furthermore, in step 4, when At that time, the vulnerability index calculation model is as follows:

[0014]

[0015]

[0016] Among them, f ij (t) represents the delayed passenger flow between any two stations i and j at time t within a delay time period T. If there is no delay between stations i and j, then it represents the passenger flow at that time. ij (t,τ disr Let t represent the actual travel time between any two stations i and j during the delay period. The specific calculation method is as follows:

[0017] τij (t,τ disr )=τ ij +θ ij (t)τ disr

[0018] Where, τ ij θ represents the normal travel time between stations i and j when no delay occurs. ij (t) is a binary decision variable (0-1). When an disturbance occurs at time t, causing a delay in the urban rail system, θ ij When θ(t) = 1 and there is no interference, ij (t) = 0.

[0019] Furthermore, in step 4, when At this time, passengers typically do not choose to travel from this location, and the travel demand is 0. Assuming that the node or edge in the undirected weighted graph G is invalid, the node or edge needs to be deleted from the original graph G and a new undirected weighted graph G′={N′,E′,W′} needs to be reconstructed. In this case, the vulnerability index calculation model is:

[0020]

[0021] Where, τ′ ij For the normal travel time between two stations i and j in the new undirected weighted graph G′; f′ ij (t) represents the passenger flow on the reasonable path between two stations i and j within a time period t; N′ represents the number of nodes in the new undirected weighted graph G′.

[0022] Furthermore, the reasonable path refers to at least one path among all shortest paths to any OD node in a fully connected urban rail network (i.e., an undirected weighted graph obtained through modeling) that minimizes both travel time and transfer count. The method for obtaining this path is as follows: Train travel time between stations is used as edge weights. Based on this, a network topology graph with virtual transfer arcs is constructed according to the urban rail route map. The number of transfer arcs and edge weights represent the transfer count and transfer time at transfer stations, and Dijkstra's algorithm is used to solve for the shortest path between any nodes. Based on minimizing travel time, one or more paths with the minimum transfer time and transfer count are considered as reasonable paths.

[0023] This invention provides a vulnerability assessment method for urban rail systems that considers time-varying demand, which has the following advantages:

[0024] Highly practical and computationally simple, this invention establishes a vulnerability index model that considers dynamic travel demand from the perspective of operational delays of varying degrees, enabling dynamic assessment of the vulnerability of urban rail transit systems. It can distinguish the impact of different levels of disruption events on system vulnerability and capture vulnerability changes under different dynamic travel demands. This provides support for the daily maintenance and management of urban rail transit systems, as well as post-disaster resource allocation. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A flowchart illustrating a vulnerability assessment method for urban rail systems that considers time-varying demands, provided as an embodiment of this application.

[0027] Figure 2 An undirected weighted graph obtained by modeling the Beijing rail transit system, provided for embodiments of this application.

[0028] Figure 3 This is a graph showing the changes in system vulnerability indicators under different delay times, as provided in the embodiments of this application. The time corresponding to each line in the graph decreases sequentially from top to bottom.

[0029] Figure 4 A graph showing the change of system vulnerability indicators when the delay time exceeds the sensitive time threshold, as provided in the embodiments of this application. Detailed Implementation

[0030] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0031] See Figure 1 The figure is a flowchart of a vulnerability assessment method for urban rail systems that takes into account time-varying demand, provided in an embodiment of this application.

[0032] like Figure 1 As shown in the embodiment of this application, a vulnerability assessment method for urban rail systems considering time-varying demand is provided, comprising the following steps:

[0033] Step 1: Collect data, including urban rail system station and line data, as well as AFC system card swipe data, including passenger entry and exit times, and entry and exit times;

[0034] Step 2: Model the urban rail system using complex network theory;

[0035] Step 3: Determine the sensitive time threshold for passengers' perception of delays in urban rail system operations based on travel time and passenger tolerance.

[0036] Step 4: Based on the operational delay time T and the sensitive time boundary point Select a model to calculate vulnerability indicators and assess the vulnerability of the urban rail system.

[0037] As one possible implementation, the specific rules for modeling urban rail transit systems using complex network theory in this application embodiment are as follows: The urban rail transit system is represented by an undirected weighted graph G = {N, E, W}. In graph G, the node set N = {1, 2, 3, ..., N} consists of transfer stations and non-transfer stations of the urban rail transit system; the edge set E = {e ij |e ij =<i,j> The condition `i ≠ j` is determined by whether the nodes are directly connected. When there is a direct edge connecting two nodes `i` and `j`, `e`... ij =1, otherwise, e ij =0, i, j∈N; weight set W = {w ij |w ij ≥0} represents the weight of the corresponding edge, which refers to the actual travel time, actual distance, or passenger flow between stations during a certain period.

[0038] As one possible implementation method, the sensitive time boundary point in the embodiments of this application Take 60 minutes.

[0039] As one possible implementation method, in the embodiments of this application, when At that time, the vulnerability index calculation model is as follows:

[0040]

[0041]

[0042] Among them, f ij (t) represents the delayed passenger flow between any two stations i and j at time t within a delay time period T. If there is no delay between stations i and j, then it represents the passenger flow at that time. ij (t,τ disr Let t represent the actual travel time between any two stations i and j during the delay period. The specific calculation method is as follows:

[0043] τ ij (t,τ disr )=τ ij +θ ij (t)τ disr

[0044] Where, τ ij θ represents the normal travel time between stations i and j when no delay occurs. ij (t) is a binary decision variable (0-1). When an disturbance occurs at time t, causing a delay in the urban rail system, θ ij When θ(t) = 1 and there is no interference, ij (t) = 0.

[0045] As one possible implementation method, in the embodiments of this application, when At this time, passengers typically do not choose to travel from this location, and the travel demand is 0. Assuming that the node or edge in the undirected weighted graph G is invalid, the node or edge needs to be deleted from the original graph G and a new undirected weighted graph G′={N′,E′,W′} needs to be reconstructed. In this case, the vulnerability index calculation model is:

[0046]

[0047] Where, τ′ ij For the normal travel time between two stations i and j in the new undirected weighted graph G′; f′ ij (t) represents the passenger flow on the reasonable path between two stations i and j within a time period t; N′ represents the number of nodes in the new undirected weighted graph G′.

[0048] As one possible implementation, in this embodiment, a reasonable path refers to at least one path with the shortest travel time and the fewest transfers among all shortest paths to any OD node in a fully connected urban rail network, i.e., an undirected weighted graph obtained through modeling. The method for obtaining this path is as follows: Train travel time between stations is used as edge weights. Based on this, a network topology graph with virtual transfer arcs is constructed according to the urban rail route map. The number of transfer arcs and edge weights represent the number of transfers and transfer time at transfer stations, and Dijkstra's algorithm is used to solve for the shortest path between any nodes. Based on minimizing travel time, one or more paths with the shortest transfer time and the fewest transfers are considered as reasonable paths.

[0049] To better understand the vulnerability assessment method for urban rail systems that considers time-varying demands provided in the embodiments of this application, the method will be described below with reference to the accompanying drawings through several specific embodiments.

[0050] See Table 1, which contains the collected AFC system data.

[0051] See Figure 2 This figure is an undirected weighted graph obtained by modeling the Beijing rail transit system, as provided in an embodiment of this application. Figure 2 As shown, an undirected weighted graph consists of stations and edges.

[0052] See Figure 3 This figure shows the changes in system vulnerability indicators under different delay times provided in the embodiments of this application. The delay times are 5, 10, 20, 40, and 60 minutes, and the vulnerability metrics are as follows:

[0053]

[0054]

[0055] See Figure 4 This figure shows the change of system vulnerability indicators when the delay time exceeds the sensitive time threshold, as provided in the embodiments of this application. The vulnerability measurement indicators are:

[0056]

[0057] In summary, this application's embodiments establish a vulnerability index model that considers dynamic travel demand from the perspective of operational delays of varying degrees, enabling dynamic assessment of the vulnerability of urban rail transit systems. This model can distinguish the impact of different levels of disruption events on system vulnerability and capture vulnerability changes under varying dynamic travel demands. It helps provide support for the daily maintenance and management of urban rail transit systems, as well as post-disaster resource allocation.

[0058] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that all or part of the steps in the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network communication device such as a media gateway, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0059] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Regarding the methods disclosed in the embodiments, since they correspond to the systems disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the system section description.

[0060] It should also be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0061] The above description of the disclosed embodiments will enable those skilled in the art to make or use various modifications to these embodiments. It will be readily apparent to those skilled in the art that the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0062] Table 1 Partial AFC System Data

[0063]

Claims

1. A vulnerability assessment method for urban rail transit systems considering time-varying demand, characterized in that, The method includes the following steps: Step 1: Collect data, including urban rail system station and line data, as well as AFC system card swipe data, including passenger entry and exit times, and entry and exit times; Step 2: Model the urban rail system using complex network theory; Step 3: Determine the sensitive time threshold for passengers' perception of delays in urban rail system operations based on travel time and passenger tolerance. Step 4: Based on the operational delay time T and the sensitive time boundary point Select a model to calculate vulnerability indicators and assess the vulnerability of the urban rail system; The specific rules for modeling the urban rail system using complex network theory in step 2 are as follows: The urban rail system is represented by an undirected weighted graph G = {N, E, W}; in graph G, the node set N = {1, 2, 3, ..., N} consists of transfer stations and non-transfer stations of the urban rail system; the edge set E = {e ij |e ij =<i,j> The condition e is determined by whether the nodes i ≠ j. When there is a direct edge connecting two nodes i and j, e ij =1, otherwise, e ij =0, i,j∈N; weight set W={w ij |w ij ≥0} represents the weight of the corresponding edge, which refers to the actual travel time, actual distance, or passenger flow between stations during a certain period. In step 4, when At that time, the vulnerability index calculation model is as follows: Among them, f ij (t) represents the delayed passenger flow between any two stations i and j at time t within a delay time period T. If there is no delay between stations i and j, then it represents the passenger flow at that time. ij (t,τ disr Let t represent the actual travel time between any two stations i and j during the delay period. The specific calculation method is as follows: t ij (t,τ disr )=τ ij +θ ij (t)t disr Where, τ ij θ represents the normal travel time between stations i and j when no delay occurs. ij (t) is a binary decision variable (0-1). When an disturbance occurs at time t, causing a delay in the urban rail system, θ ij When θ(t) = 1 and there is no interference, ij (t) = 0.

2. The method according to claim 1, characterized in that: Sensitive time boundary point in step 3 Take 60 minutes.

3. The method according to claim 1, characterized in that: In step 4, when At this point, passengers will not choose to travel, and the travel demand is 0. Assuming that the node or edge in the undirected weighted graph G is invalid, the node or edge needs to be deleted from the original graph G and a new undirected weighted graph G′={N′,E′,W′} needs to be reconstructed. In this case, the vulnerability index calculation model is: Where, τ′ ij For the normal travel time between two stations i and j in the new undirected weighted graph G′; f′ ij (t) represents the passenger flow on the reasonable path between two stations i and j within a time period t; N′ represents the number of nodes in the new undirected weighted graph G′.

4. The method according to claim 3, characterized in that, A reasonable path refers to at least one path in a fully connected urban rail network, specifically among all shortest paths to any OD node in the undirected weighted graph obtained through modeling, that has the shortest travel time and the fewest transfers. The method for obtaining this path is as follows: Train travel time between stations is used as edge weights; based on this, a network topology graph with virtual transfer arcs is constructed according to the urban rail route map; the number of transfer arcs and edge weights represent the number of transfers and transfer time at transfer stations, and Dijkstra's algorithm is used to solve for the shortest path between any nodes; based on minimizing travel time, one or more paths with the shortest transfer time and the fewest transfers are considered as reasonable paths.

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