An analytical method for the impact of subway power supply system failures on passenger travel under extreme scenarios.

Abstract

The present invention relates to the technical field of subway power supply systems, and specifically to a method for analyzing the impact of subway power supply system failures on passenger travel in extreme scenarios, including the following steps: S1, subway power supply system and passenger travel modeling: constructing a power supply system model of an urban subway network, defining a collection of subway stations and tracks, and establishing a passenger flow model; S2, modeling of indicators affected by fault conduction and passenger travel: constructing a fault model and a passenger flow transfer model, and proposing indicators for evaluating the impact of faults on passenger travel. The present invention realizes accurate simulation of the specific transfer steps and operation procedures of passenger flow on the fault path. These models and methods can comprehensively and systematically reflect the distribution and transfer of passenger flow after the fault occurs; it provides an important reference for subway operation management departments to formulate emergency plans and optimization plans, and significantly improves the safety and reliability of the subway system.

Description

Technical Field

[0001] The present invention relates to the technical field of subway power supply systems, and in particular to a method for analyzing the impact of subway power supply system failures on passenger travel in extreme scenarios. Background Art

[0002] With the development of rail transit, the subway has become the most important public transportation tool in urbanization. Since subway lines and stations are closely interconnected, a failure at a single station will spread rapidly throughout the network, causing large-scale congestion and even paralyzing the entire city's traffic. Studying the impact of subway power supply system failures on passenger travel in extreme scenarios is of great significance for ensuring the efficient operation of urban transportation.

[0003] In existing technologies, complex network theory is widely used in the study of transportation networks. By constructing a transportation topology network, network performance is evaluated using indicators such as average shortest path length, average clustering coefficient, network efficiency, and relative size of the largest connected subgraph. Network damage is simulated through random or intentional attacks to assess the extent of the network impact. However, such methods do not fully consider the passengers on the network and fail to fully reflect the adverse effects of network transportation disruptions on passengers.

[0004] Existing research has shortcomings in modeling the impact of subway power supply system failures on passenger travel. Subway power supply system failures not only cause subway tracks and stations to stop operating, but also seriously affect passengers' travel. Existing research is relatively fragmented and does not consider the impact of passengers choosing other routes to transfer to other routes. It also does not comprehensively consider the impact of subway power supply system failures on subway passenger flow loss and congestion. Therefore, an analysis method that comprehensively considers these factors is urgently needed.

[0005] The purpose of this invention is to establish a subway network and passenger travel model, as well as a fault conduction model for the impact of subway power supply system failures on passenger travel, and propose passenger travel impact indicators. The purpose is to analyze the impact of subway power supply system failures on passenger travel in extreme scenarios. Through this method, we can more comprehensively understand and evaluate the comprehensive impact of subway power supply system failures on passenger travel, and provide more effective response measures and optimization solutions. Summary of the Invention

[0006] Based on the above objectives, the present invention provides a method for analyzing the impact of subway power supply system failure on passenger travel in extreme scenarios.

[0007] A method for analyzing the impact of a subway power supply system failure on passenger travel in extreme scenarios includes the following steps:

[0008] S1, subway power supply system and passenger travel modeling: Construct a power supply system model for the urban subway network, define the set of subway stations and tracks, and establish a passenger flow model to describe the starting point, end point, and path flow of passenger travel;

[0009] S2, Modeling of Fault Transmission and Passenger Travel Impact Indicators: Construct a fault model and a passenger flow transfer model, and propose indicators to evaluate the impact of faults on passenger travel, including:

[0010] S21, Initial Fault Modeling: Taking the scenario where the overhead network node of the subway track power supply is attacked as the starting fault event, an initial fault model is constructed;

[0011] S22, Fault Conduction Modeling: Simulates the impact of subway power supply system failures on the functional status of subway tracks and stations under extreme scenarios, and describes the state changes of the tracks and stations;

[0012] S23, Post-fault passenger flow redistribution model construction: After a track or station failure, simulate the redistribution of passenger flow in the subway network, describe the path traffic status and flow transfer, and establish a subway fault load redistribution model based on passenger flow transfer;

[0013] S24, evaluation of passenger travel impact indicators: Through a subway fault load redistribution model based on passenger flow transfer, the impact indicators of subway power supply system failure scenarios on passenger travel are evaluated.

[0014] Furthermore, the subway power supply system and passenger travel modeling in S1 includes:

[0015] S11, subway power supply system model construction: abstract the urban subway network into an unweighted and phase-free graph, define the set of subway stations and tracks, and construct the subway power supply system model;

[0016] S12, passenger flow model construction: abstract passenger travel behavior into flow, define the starting point and end point of passenger travel as the starting point and end point of the OD (Origin to Destination) pair, and establish a passenger flow model to describe the passenger travel path and flow distribution in the subway network.

[0017] Furthermore, the calculation formula of the subway power supply system model in S11 is:

[0018]

[0019] Among them, V m It is the subway station meeting point, E m is the set of subway tracks, n m and m m are the number of subway stations and subway tracks respectively.

[0020] Furthermore, the calculation formula of the passenger flow model in S12 is:

[0021]

[0022]

[0023] in, is the flow of the rth path in the dth OD pair, F d is the sum of the flows through the OD pair, and They are the flow through edge e ij , inflow and outflow nodes v i of traffic, and They are path r and edge e respectively ij , node v i The correlation between inflow and outflow, γ ij is the track capacity redundancy factor, C ij and C ij (0) are track capacity and free capacity, V m,o and V m,d are the sets of OD pairs’ starting and ending points respectively.

[0024] Furthermore, the calculation formula of the initial fault model in S21 is:

[0025]

[0026] Among them, V pa and K are the set and sum of the number of attacked contact network nodes in the fault scenario, respectively.

[0027] Furthermore, the fault conduction modeling in S22 includes:

[0028] S221, define the functional state of the subway track: In the extreme scenario, if the traction network failure of the subway power supply system causes the subway track to fail, the functional state of each subway track k is The calculation formula is:

[0029]

[0030] S222, define the functional status of subway stations: the functional status of subway stations Depends on the status of all its adjacent tracks Functional status of subway stations The calculation formula is:

[0031]

[0032] Among them, Eij represents the set of tracks between subway stations i and j.

[0033] Furthermore, the post-fault passenger flow redistribution model construction in S23 includes:

[0034] S231, the path traffic status expression: after the subway track or station fails, the path r fault Interruption, affected traffic If the route is to be transferred in the subway network, the traffic status of the route is determined by the status of all tracks and stations in the route;

[0035] S232, fault path traffic transfer classification: After the original path is interrupted, consider the decision of passenger travel behavior and select other paths r with the same OD pair d or adjacent OD pair d near The path r near , classify the transfer of traffic on the fault path, including:

[0036] Prioritize alternative routes with the same OD pair: To save travel costs, passengers prioritize alternative routes with the same OD pair;

[0037] Selecting paths with adjacent OD pairs: When paths with the same OD pair are all faulty or have insufficient capacity, passengers will select paths with adjacent OD pairs;

[0038] Determine the passenger flow loss: If the flow on the faulty path still has a margin after the backup path that prioritizes the same OD pair and the path that prioritizes the adjacent OD pair is transferred, the margin is considered the passenger flow loss on the faulty path;

[0039] S233, define fault path passenger flow transfer: set the fault path set and quantity, calculate and update the transferable flow, check the remaining flow, and calculate the passenger flow loss.

[0040] Furthermore, the calculation formula of the traffic status of the path in S231 is:

[0041]

[0042] Furthermore, the definition of passenger flow transfer on the fault path in S233 includes:

[0043] Set the fault path set and number: Set the fault path set R fault and the number of fault paths Let i = 1;

[0044] Calculate the flow transferred to the same OD pair path: take R fault The i-th fault path r in fault , calculate the flow transferred to the same OD pair path The calculation formula is:

[0045]

[0046] in, represents the flow rate of the fault path, is the traffic status of path r, represents the maximum throughput of path r;

[0047] Update path and track flow: For each path assigned to the same OD pair, update the flow of each path and track at the next moment. The calculation formula is:

[0048]

[0049] in, is the flow of path r at the next moment, represents the congestion level of path r;

[0050] Check the remaining traffic after the first step of transfer: Check the remaining traffic on the fault path after the first step of transfer and perform corresponding operations;

[0051] Traffic diverted to adjacent OD pairs: diverts the remaining fault path traffic to the adjacent OD pairs. The calculation formula is:

[0052]

[0053] Update adjacent paths and track traffic: Assign to each path and update the flow of each path and track at the next moment. The calculation formula is:

[0054]

[0055] in, is the flow of path r in the adjacent OD pair at the next moment;

[0056] Check the remaining traffic after the second transfer: Check the remaining traffic on the fault path after two transfers and perform corresponding operations;

[0057] Calculation of passenger flow loss: Calculate the fault path r fault The passenger flow loss is calculated as follows:

[0058]

[0059] Check the completion of all paths: If If all fault paths have completed passenger flow transfer, proceed to the next step. Otherwise, set i = i + 1, return to calculate the flow transferred to the same OD pair path, and transfer the flow of the next fault path;

[0060] Calculate the total passenger flow loss of the fault path: fault path set R fault The undiverted flow is considered as the total passenger flow loss Δflow sum , the calculation formula is:

[0061]

[0062] Furthermore, the calculation formula for evaluating the passenger travel impact index in S24 is:

[0063]

[0064] in, represents the failure rate of subway stations, U flow represents the proportion of passenger flow loss in the subway network, Indicates the congestion of the subway network. represents the congestion of path r, R nor A set representing normal paths.

[0065] Beneficial effects of the present invention:

[0066] The present invention constructs a subway power supply system model and a passenger flow model to simulate the impact of a subway power supply system failure on the functional status of subway tracks and stations under extreme scenarios. It also describes in detail the state change process of the tracks and stations. The subway fault load redistribution model based on passenger flow transfer sets and calculates and updates the transferable flow, checks the remaining flow, and calculates the passenger flow loss, thereby accurately simulating the specific transfer steps and operational processes of the passenger flow on the fault path. These models and methods can comprehensively and systematically reflect the passenger flow distribution and transfer situation after a fault occurs.

[0067] By evaluating indicators affecting passenger travel, the present invention can effectively assess the impact of subway power supply system failures on passenger travel in extreme scenarios. By constructing an initial fault model, simulating fault transmission, and redistributing passenger load, key indicators such as the failure rate of subway stations, the passenger loss rate of the subway network, and the congestion of the subway network are quantified. These indicators help analyze and understand the specific impact of failures on passenger travel, provide a reliable basis and data support, and serve as an important reference for subway operation management departments to formulate emergency plans and optimization plans, significantly improving the safety and reliability of the subway system. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only for the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0069] Figure 1 Schematic diagram of the analysis method according to an embodiment of the present invention;

[0070] Figure 2 Schematic diagram of modeling of fault transmission and passenger travel impact indicators according to an embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to specific embodiments.

[0072] It should be noted that, unless otherwise defined, the technical or scientific terms used in the present invention should have the usual meanings understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0073] like Figure 1-Figure 2 As shown in FIG, a method for analyzing the impact of a subway power supply system failure on passenger travel in an extreme scenario includes the following steps:

[0074] 1. Metro power supply system and passenger travel modeling:

[0075] 1.1. Subway power supply system model:

[0076] The urban subway network is a mesh network consisting of subway stations and subway tracks. In this paper, the subway network is abstracted as a network consisting of nodes V m and edge E m The unweighted phase-free graph G m , the model is as follows:

[0077]

[0078] Where: V m Gather at the subway station; E m For subway track collection; n m and m m Represent the number of subway stations and subway tracks respectively.

[0079] 1.2. Passenger flow model:

[0080] This paper abstracts subway passengers as traffic, defines the starting and ending points of passenger trips as the starting and ending points of an OD (Origin to Destination) pair, and establishes a subway network passenger flow model based on each OD pair containing multiple paths:

[0081]

[0082]

[0083] Where: represents the flow of the rth path in the dth OD pair; F d is the sum of the flows through the OD pair; and are the flows through edge e ij and inflow and outflow nodes v i Traffic volume; and are path r and edge e respectively ij and node v i The relationship between inflow and outflow; γ ij is the track capacity redundancy factor; C ij and C ij (0) are track capacity and free capacity respectively; V m,o and V m,d are the sets of OD pairs of starting points and ending points respectively; Equation (7) is the flow conservation constraint of OD pairs; Equations (8) to (10) are the flow conservation constraints of OD pairs of starting nodes, ending nodes and intermediate nodes respectively.

[0084] 2. Modeling of fault transmission and passenger travel impact indicators:

[0085] 2.1. Initial fault modeling:

[0086] This paper takes the scenario where the overhead network node supplying power to the subway track is attacked as the initial fault event, and its expression is:

[0087]

[0088] Where: V pa and K are the set and sum of the number of attacked contact network nodes in the fault scenario, respectively.

[0089] 2.2 Fault conduction modeling:

[0090] In extreme scenarios, the failure of the traction network of the subway power supply system will cause the subway track to fail. Then the functional state of each subway track k is The expression is:

[0091]

[0092] Functional status of subway stations Depends on the status of all its adjacent tracks Its expression is:

[0093]

[0094] Where: e k =e ij , E ij =E ji , E ij represents the set of tracks between subway stations i and j.

[0095] 2.3 Subway Fault Load Redistribution Model Based on Passenger Flow Transfer:

[0096] When a subway track or station fails, it is considered that the path r fault Interruption, affected traffic Will transfer in the subway network. The path's traffic status expression is:

[0097]

[0098] Formula (15) indicates that the traffic status of a path is determined by the status of all tracks and stations in the path.

[0099] After the original path is interrupted, considering the decision of passenger travel behavior, it is necessary to choose another path r with the same OD pair d or an adjacent OD pair d near The path r near , the transfer of traffic on the fault path can be divided into the following three cases:

[0100] 1) To save travel costs, passengers give priority to other routes with the same OD pair.

[0101] 2) When the paths of the same OD pair are all faulty or have insufficient capacity, passengers will choose the paths of the adjacent OD pair.

[0102] 3) If there is still a margin in the flow of the fault path after the transfer of 1) and 2), this margin is considered as the passenger flow loss of the fault path.

[0103] The process of transferring passenger flow on the fault path is as follows:

[0104] 1) Set the fault path set R fault and the number of fault paths N Rfault , let i=1.

[0105] 2) Take R fault The i-th fault path r in fault , calculate the flow that can be transferred to the same OD pair path

[0106]

[0107] Where: Indicates the flow rate of the fault path; is the traffic status of path r; The maximum throughput of path r is determined by the path flow and pathway tracks ij The capacity and flow rate are jointly determined.

[0108] 3) For each path assigned to the same OD pair, update the flow of each path and track at the next moment:

[0109]

[0110] Where: is the flow of path r at the next moment; It indicates the congestion level of path r. The smaller the value, the greater the flow it can carry.

[0111] Update subway track traffic The calculation is the same as formula (2) to (10).

[0112] 4) If there is still enough traffic on the fault path after the first step of transfer, that is, Then proceed to step 5); otherwise, Proceed to step 9).

[0113] 5) The remaining fault path traffic can be transferred to the traffic of the adjacent OD pair for:

[0114]

[0115] 6) Distribute to each path and update the flow of each path and track at the next moment:

[0116]

[0117] Where: is the flow of path r among the adjacent OD pairs at the next moment.

[0118] Update subway track traffic The calculation is the same as formula (2) to (10).

[0119] 7) If the fault path traffic still has a margin after two transfers, that is Then proceed to step 8); otherwise, Proceed to step 9).

[0120] 8) Calculate the fault path r fault Passenger flow loss:

[0121]

[0122] 9) If If all faulty paths have completed passenger flow transfer, proceed to step 10); otherwise, set i=i+1, return to step 2), and transfer the flow of the next faulty path.

[0123] 10) Fault path set R fault The undiverted flow is considered as the total passenger flow loss Δflow sum , the calculation formula is:

[0124]

[0125] 2.4、Indicators of impact on passenger travel:

[0126] Based on the subway fault load redistribution model for passenger flow transfer, this paper proposes the impact indicators on passenger travel under the subway power supply system failure scenario:

[0127]

[0128] Where: represents the failure rate of subway stations; U flow It represents the proportion of passenger flow loss in the subway network; Indicates the congestion of the subway network. represents the congestion of path r, R nor Represents a collection of normal paths.

[0129] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present invention is limited to these examples. Within the scope of the present invention, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the present invention as described above, which are not provided in detail for the sake of simplicity.

[0130] The present invention is intended to cover all such substitutions, modifications and variations that fall within the broad scope of the claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing the impact of subway power supply system failure on passenger travel in extreme scenarios, characterized in that: The following steps are involved: S1, subway power supply system and passenger travel modeling: construct a power supply system model of the urban subway network, define the set of subway stations and tracks, and establish a passenger flow model to describe the starting point, end point and path flow of passenger travel; S2, Modeling of fault transmission and passenger travel impact indicators: Construct fault models and passenger flow transfer models, and propose indicators to evaluate the impact of faults on passenger travel, including: S21, initial fault modeling: taking the scenario where the overhead network node of the subway track power supply is attacked as the starting fault event, the initial fault model is constructed; S22, Fault conduction modeling: simulate the impact of subway power supply system failure on the functional status of subway tracks and stations in extreme scenarios, and describe the state change process of tracks and stations; S23, construction of passenger flow redistribution model after fault: after a track or station fault, simulate the redistribution process of passenger flow in the subway network, describe the path traffic status and flow transfer, and establish a subway fault load redistribution model based on passenger flow transfer; S24, evaluation of passenger travel impact indicators: through the subway fault load redistribution model based on passenger flow transfer, the impact indicators on passenger travel under the subway power supply system failure scenario are evaluated; The subway power supply system and passenger travel modeling in S1 include: S11, construction of subway power supply system model: abstract the urban subway network into an unweighted and phase-free graph, define the set of subway stations and tracks, and construct the subway power supply system model; S12, passenger flow model construction: abstract passenger travel behavior into flow, define the starting point and end point of passenger travel as the starting point and end point of OD pair respectively, establish passenger flow model, and describe the travel path and flow distribution of passengers in the subway network; The calculation formula of the subway power supply system model in S11 is: Among them, V m It is the subway station gathering point, E m is the set of subway tracks, n m and m m They are the number of subway stations and subway tracks; The calculation formula of the passenger flow model in S12 is: in, is the flow of the rth path in the dth OD pair, F d is the sum of the flows through the OD pair, and They are respectively the flow through edge e ij , inflow and outflow nodes v i of traffic, and are path r and edge e respectively ij , node v i The correlation between inflow and outflow, γ ij is the track capacity redundancy factor, C ij and C ij (0) are the track capacity and free capacity, V m,o and V m,d are the sets of starting and ending points of OD pairs respectively; The calculation formula of the initial fault model in S21 is: Among them, V pa and K are respectively the set and sum of the number of attacked contact network nodes in the fault scenario; The fault conduction modeling in S22 includes: S221, define the functional status of the subway track: In the extreme scenario, if the traction network failure of the subway power supply system causes the subway track to fail, then the functional status of each subway track k The calculation formula is: S222, define the functional status of subway stations: the functional status of subway stations Depends on the status of all its adjacent tracks Functional status of subway stations The calculation formula is: Among them, E ij represents the set of tracks between subway stations i and j; The post-fault passenger flow redistribution model construction in S23 includes: S231, the path traffic status expression: after the subway track or station fails, the path r fault Interruption, affected traffic If the route is to be transferred in the subway network, the traffic status of the path is determined by the status of all tracks and stations in the path; S232, transfer classification of fault path traffic: after the original path is interrupted, consider the decision of passenger travel behavior and select other paths r of the same OD pair d or adjacent OD pair d near The path r near , classify the transfer of traffic on the fault path, including: Prioritize alternate routes with the same OD pair: To save travel costs, passengers give priority to alternate routes with the same OD pair; Choose the path of the adjacent OD pair: When the paths of the same OD pair are all faulty or have insufficient capacity, passengers will choose the path of the adjacent OD pair; Determine the passenger flow loss: If the flow of the faulty path still has a margin after the transfer of the backup path that preferentially selects the same OD pair and the path that selects the adjacent OD pair, the margin is considered to be the passenger flow loss of the faulty path; S233, define fault path passenger flow transfer: set the fault path set and quantity, calculate and update the transfer flow, check the remaining flow, and calculate the passenger flow loss; The calculation formula of the traffic status of the path in S231 is: The definition of fault path passenger flow transfer in S233 includes: Set the fault path set and quantity: Set the fault path set R fault and the number of fault paths Let i = 1; Calculate the flow transferred to the same OD pair path: take R fault The i-th fault path r in fault , calculate the flow transferred to the same OD pair path The calculation formula is: in, represents the flow rate of the fault path, is the traffic status of path r, represents the maximum throughput of path r; Update path and track flow: For each path assigned to the same OD pair, update the flow of each path and track at the next moment. The calculation formula is: in, is the flow of path r at the next moment, represents the congestion degree of path r; Check the remaining traffic after the first-step transfer: Check the remaining traffic on the fault path after the first-step transfer and perform corresponding operations; Traffic diverted to the adjacent OD pair: divert the remaining fault path traffic to the adjacent OD pair. The calculation formula is: Update adjacent paths and track traffic: Distribute to each path, update the flow of each path and track at the next moment, the calculation formula is: in, is the flow of path r in the adjacent OD pair at the next moment; Check the remaining traffic after the second transfer: Check the remaining traffic on the fault path after two transfers and perform corresponding operations; Calculation of passenger flow loss: Calculate the fault path r fault The passenger flow loss is calculated as follows: Check the completion of all paths: If If all faulty paths have completed passenger flow transfer, proceed to the next step. Otherwise, set i = i + 1, return to calculate the flow transferred to the same OD pair path, and transfer the flow of the next faulty path; Calculate the total passenger flow loss of the fault path: Fault path set R fault The undiverted flow is considered as the total passenger flow loss Δflow sum , the calculation formula is: The calculation formula for evaluating the passenger travel impact index in S24 is: in, represents the failure rate of subway stations, U flow represents the passenger flow loss ratio of the subway network, Indicates the congestion of the subway network. represents the congestion of path r, R nor A set representing normal paths.

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