Urban public transport network toughness measuring method in extreme rainstorm weather

Abstract

The invention relates to a method for measuring the toughness of an urban public transport network in extreme rainstorm weather. The method comprises the following steps: acquiring station and line data of the urban public transport network, rainstorm disaster information and passenger flow data; a bus-subway double-layer traffic network is constructed; based on the constructed bus-subway double-layer traffic network, establishing a linear relation between rainstorm rainfall intensity and passenger flow change, and calculating disturbance values of the rainstorm to stations and connecting edges in the network; constructing a bus-subway double-layer traffic network cascade failure model considering passenger flow, and representing a dynamic evolution process of an urban public traffic network in extreme rainstorm weather; and determining a network performance measurement index by using the constructed bus-subway double-layer traffic network cascade failure model, and measuring the toughness level of the urban public traffic network in extreme rainstorm weather. According to the method, the urban public transport network toughness can be accurately measured, and the coping capacity of an urban public transport system in extreme rainstorm weather is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of measuring the resilience of urban public transport networks, and particularly relates to a method for measuring the resilience of urban public transport networks under extreme rainstorm weather. Background Art

[0002] At present, in the research on the resilience of urban public transport networks, extreme rainstorm weather is mostly regarded as a qualitative disturbance, lacking the modeling of the quantitative relationship between rainfall intensity and passenger flow changes, resulting in the inability to accurately predict the impact of disasters on stations and lines. Conventional cascading failure models are mostly based on a single network topology or functional parameter, ignoring the spatio-temporal coupling effect of passenger flow redistribution and network load under rainstorm disturbances, and it is difficult to simulate the dynamic characteristics during the evolution process of rainstorm disasters. Therefore, how to establish a cascading failure model for urban public transport networks under extreme rainstorm weather has become a key problem that urgently needs to be solved in measuring the resilience level of its network, and has important practical significance. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for measuring the resilience of urban public transport networks under extreme rainstorm weather, which is conducive to accurately measuring the resilience of urban public transport networks and improving the response ability of urban public transport systems under extreme rainstorm weather.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is: a method for measuring the resilience of urban public transport networks under extreme rainstorm weather, including: Step S1: Obtain urban public transport network station and line data, rainstorm disaster information, and passenger flow data; Step S2: Construct a bus-subway double-layer traffic network; Step S3: Based on the constructed bus-subway double-layer traffic network, establish a linear relationship between rainstorm rainfall intensity and passenger flow changes, and calculate the disturbance values of rainstorms to stations and edges in the network; Step S4: Construct a cascading failure model of the bus-subway double-layer traffic network considering passenger flow to characterize the dynamic evolution process of urban public transport networks under extreme rainstorm weather; Step S5: Use the constructed cascading failure model of the bus-subway double-layer traffic network to determine network performance measurement indicators and measure the resilience level of urban public transport networks under extreme rainstorm weather.

[0005] Further, in step S1, the urban public transport network station and line data includes: the intra-layer station set and intra-layer edge set of buses and subways; The rainstorm disaster information includes: rainstorm rainfall intensity, the impact of extreme rainstorm weather on travel demand, travel mode, vehicle running speed, road traffic capacity, and traffic safety; The passenger flow data includes: the station where passengers swipe their cards, the boarding time, and the starting and ending points of entering and leaving the station.

[0006] Further, step S2 specifically includes the following steps: Step S21: Based on the urban public transportation network station and line data obtained in step S1, use the Space-L method to construct a single-layer bus network L b and a single-layer subway network L s , extract all stations and connecting edges within the range, continuously and incrementally number them, and filter out duplicate stations and duplicate connecting edges between two stations to obtain a set of bus stations N b , a set of subway stations N s , a set of bus connecting edges E b and a set of subway connecting edges E s ; Step S22: Map the bus stations and subway stations to the same layer, create a buffer with a radius of R centered on the subway stations, identify the bus stations with a coupling relationship with them, and generate a set of coupling edges between network layers E t , obtain a set of stations N and a set of connecting edges E , construct a bus-subway double-layer transportation network G = N , E , use ArcGIS for spatial connection to obtain the adjacency matrix of the stations A , define the network connecting edge weight matrix W , and the matrix form is: In the formula, N G is the total number of stations in the double-layer transportation network; a ij is the connection relationship between stations n i and n j in the network. In the matrix A , when there is a connecting edge between stations n i and n j in the network, a ij = 1, otherwise it is 0, i, j ∈ [1, 2,..., NG ; in the matrix W , w ij is the weight of the connecting edge e ij , representing the passenger flow volume between stations n i and n j .

[0007] Furthermore, step S3 specifically includes the following steps: Step S31: Based on the rainstorm disaster information obtained in step S1, calculate the relative rainfall intensity in extreme rainstorm weather. The formula is: In the formula, h is the current rainfall intensity, h 0 is the threshold of the rainstorm rainfall intensity, s is the relative rainfall intensity, with a value range of [0, +∞). s = 0 indicates no rainfall, 0 < s < 1 indicates normal rainfall, and s ≥ 1 indicates rainstorm; Step S32: Determine the failure probability of network stations and connecting edges. The formula is: In the formula, P ( x > 1) is the station failure probability, P ( y > 1) is the connecting edge failure probability; Step S33: According to the bus - subway double - layer traffic network constructed in step S2, fit the linear relationship between the relative rainfall intensity and the traffic volume loss rate. Let the failure probability be equivalent to the traffic volume loss rate, and calculate the perturbation value of stations and connecting edges in the network under extreme rainstorm weather. The formula is: In the formula, l is the traffic volume loss rate, α , β are the weight coefficients, u is an intermediate variable representing the impact of extreme rainstorm weather on stations and connecting edges.

[0008] Furthermore, step S4 specifically includes the following steps: Step S41: According to the perturbation value of stations under extreme rainstorm weather calculated in step S3, construct a station - level cascade failure model of the bus - subway double - layer traffic network, and calculate the stations n iThe state value, with the formula: In the formula, x i ( t + 1) and x i ( t ) are the state variables of the site n i at the (t + 1)-th moment and the t-th moment respectively. 0 ≤ x i ( t ) ≤ 1 indicates that the site is in normal operation, x i ( t ) > 1 indicates that the site fails; ε 1 is the coupling strength of the bus - subway double - layer transportation network between sites, Q ij and Q i are respectively the passenger flows of the connecting edge e ij and the site n i . f ( x ) is the mapping function, f ( x ) = 4 x (1 - x ); Step S42: According to the perturbation value of the extreme rainstorm weather on the connecting edge calculated in Step S3, construct a cascading failure model of the connecting edge of the bus - subway double - layer transportation network, and calculate the state variable of the connecting edge e ij under the influence of extreme rainstorm weather. The formula is: In the formula, x i ( t ) and x j ( t ) are the state variables of the sites n i and n j at the t-th moment respectively, y ij ( t + 1), y ij ( t ) are the state variables of the connecting edge e ij at the (t + 1)-th moment and the t-th moment respectively. 0 ≤ yij ( t )≤1 indicates a connected edge e ij In normal operation, y ij ( t )>1 indicates a connected edge e ij Failure, ε 2 is the edge coupling strength of the bus-subway double-layer transportation network, Q ip , Q jq , Q i , Q j Connecting edges e ip , Lianbian e jq , Site n i , Site n j passenger flow; max{ ,} is the maximum value function; Step S43: Searching for invalid sites in the network n g , remove dead sites n g and the failed edges connected to it e gh , failed site n g Customer flow Q g Will be transferred to all normal sites connected to it n h , determine the site n h Connected edges e hs The passenger flow changes are used to determine whether the passenger flow transfer covers all sites and edges in the network. The formula is: In the formula, Q hs Connecting the front edge for passenger flow transfer e hs of passenger flow, Q * hs To transfer passenger flow and connect the side e hs of passenger flow, Q gh Connecting the front edge for passenger flow transfer e gh passenger flow.

[0009] Furthermore, step S5 specifically includes the following steps: Step S51: Based on the network structure dimension, determine the station loss rate as the network performance measurement index, and the formula is: In the formula, γ(N) is the station loss rate of the bus - subway double - layer traffic network, γ(N) ∈ [0, 1], N * G is the number of stations after the network undergoes cascading failures; Step S52: Based on the passenger dimension, determine the change in network efficiency as the network performance measurement index, and the formula is: In the formula, E is the network efficiency value, t ij is the station n i and the station n j between the shortest travel time, γ(E) is the change in the bus - subway double - layer traffic network efficiency, γ(E) ∈ [0, 1], E 0 is the initial network efficiency value, E T is the network efficiency after the network undergoes cascading failures; Step S53: Based on the network operation dimension, determine the passenger flow loss rate as the network performance measurement index, and the formula is: In the formula, Q is the total passenger flow of the bus - subway double - layer traffic network, Q ij is the passenger flow of the link e ij γ(Q) is the passenger flow loss rate of the bus - subway double - layer traffic network, γ(Q) ∈ [0, 1], Q 0 is the initial total passenger flow of the network, Q T is the total passenger flow after the network undergoes cascading failures; Step S54: Using the network performance measurement indexes determined in steps S51, S52, and S53, assign weights to each index and synthesize to calculate the comprehensive performance of the bus - subway double - layer traffic network, and the formula is: In the formula, PFor the comprehensive performance of the bus - subway double - layer transportation network, λ1, λ2, and λ3 are the weights of γ(N), γ(E), and γ(Q) respectively, where λ1, λ2, λ3 ∈ (0, 1) and λ1 + λ2 + λ3 = 1; Step S55: According to the comprehensive performance of the bus - subway double - layer transportation network calculated in Step S54, the formula for measuring the resistance ability of the network under the interference of extreme rainstorm weather is: In the formula, R 1 is the resistance ability of the network in the interference propagation stage, P ( t ) is the comprehensive performance of the network at time t; Step S56: Measure the absorption ability of the network under the interference of extreme rainstorm weather. The formula is: In the formula, R 2 is the absorption ability of the network in the interference propagation stage, P ( t 0) is the comprehensive performance of the network at t 0 moment, t a is the moment when the interference occurs, t b is the moment when the operation management department starts to resume; Step S57: Measure the recovery ability of the network under the interference of extreme rainstorm weather. The formula is: In the formula, R 3 is the recovery ability of the network in the recovery stage, t c is the moment when the network recovers to the initial level; Step S58: Use the resilience ability characteristics of the bus - subway double - layer transportation network determined in Steps S55, S56, and S57 in different response stages to measure the comprehensive resilience of the network under extreme rainstorm weather. The formula is: In the formula, R G is the comprehensive resilience value of the bus - subway double - layer transportation network during the process of coping with extreme rainstorm weather interference, θ 1, θ 2, θ 3 are the weight coefficients of the resistance ability, absorption ability, and recovery ability respectively, θ 1, θ 2, θ 3 ∈ (0, 1), and θ 1 + θ 2 + θ3 = 1。

[0010] The present invention also provides a resilience measurement system for urban public transportation networks under extreme rainstorm weather, including a memory, a processor, and computer program instructions stored on the memory and executable by the processor. When the processor runs the computer program instructions, the above-mentioned method can be implemented.

[0011] The present invention also provides a computer-readable storage medium with computer program instructions stored thereon. When the computer program instructions are executed by a processor, the above-mentioned method is implemented.

[0012] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention establishes a quantitative linear relationship between rainstorm rainfall intensity and passenger flow changes, dynamically correlates meteorological data with operation data, can effectively characterize the impact of extreme rainstorm weather on urban public transportation networks, and realizes the accurate calculation of disturbance values.

[0013] (2) The present invention simulates the failure propagation process of stations and links through dynamic traffic reallocation, and can reflect the amplification effect of passenger flow on network cascading failures in actual operation.

[0014] (3) The multi-dimensional resilience measurement method for bus-subway double-layer networks under extreme rainstorm weather proposed by the present invention can identify key vulnerable stations in the network, provide a quantitative basis for formulating hierarchical control strategies and optimizing emergency plans, and makes up for the one-sidedness of existing technical solutions in breaking through index evaluation, which is difficult to provide multi-dimensional decision-making support for emergency resource scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a flowchart for implementing the resilience measurement method of urban public transportation networks under extreme rainstorm weather provided by an embodiment of the present invention; Figure 2 is a flowchart for constructing a bus-subway double-layer transportation network in an embodiment of the present invention; Figure 3 is a flowchart for calculating the disturbance values of stations and links in the network under extreme rainstorm weather in an embodiment of the present invention; Figure 4 is a flowchart for constructing a cascading failure model to characterize the dynamic evolution process of the network under extreme rainstorm weather in an embodiment of the present invention; Figure 5 is a schematic flowchart for determining network performance indicators and establishing a resilience measurement model in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0016] The following further describes the present invention with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this application belongs.

[0018] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0019] As Figure 1 shown, this embodiment provides a method for measuring the resilience of urban public transport networks under extreme rainstorm weather, including: Step S1: Obtain urban public transport network station and line data, rainstorm disaster information, and passenger flow data; Step S2: Construct a bus-subway double-layer transport network; Step S3: Based on the constructed bus-subway double-layer transport network, establish a linear relationship between the rainstorm rainfall intensity and the change in passenger flow, and calculate the perturbation values of the stations and connecting edges in the network; Step S4: Construct a cascading failure model of the bus-subway double-layer transport network considering passenger flow to characterize the dynamic evolution process of the urban public transport network under extreme rainstorm weather; Step S5: Use the constructed cascading failure model of the bus-subway double-layer transport network to determine the network performance measurement index and measure the resilience level of the urban public transport network under extreme rainstorm weather.

[0020] In step S1, the urban public transport network station and line data include: the intra-layer station set and intra-layer connecting edge set of buses and subways.

[0021] The rainstorm disaster information includes: the rainstorm rainfall intensity, the impacts of extreme rainstorm weather on travel demand, travel mode, vehicle running speed, road traffic capacity, and traffic safety.

[0022] The passenger flow data includes: the stations where passengers swipe their cards, the boarding time, and the inbound and outbound OD (origin-destination) information.

[0023] As Figure 2 shown, step S2 specifically includes the following steps: Step S21: Based on the urban public transport network station and line data obtained in step S1, construct a single-layer bus network using the Space-L method L b and a single-layer subway networkL s , extract all stations and connecting edges within the range, consecutively number them incrementally, and filter out duplicate stations and duplicate connecting edges between two stations to obtain a set of bus stations N b , a set of subway stations N s , a set of bus connecting edges E b and a set of subway connecting edges E s .

[0024] Step S22: Map bus stations and subway stations to the same layer, create a buffer with a radius of R centered on the subway stations, identify bus stations with a coupling relationship with them, and generate a set of coupling edges between network layers E t , obtain a set of stations N and a set of connecting edges E , and construct a bus-subway two-layer transportation network G =< N , E >, use ArcGIS for spatial join to obtain the adjacency matrix of the stations A , define the network connecting edge weight matrix W , the matrix form is: In the formula, N G is the total number of stations in the two-layer transportation network; a ij is the connection relationship between stations n i and n j in the matrix A , when there is a connecting edge between stations n i and n j in the network, a ij = 1, otherwise it is 0, i, j ∈ [1, 2,..., N G ; in the matrix W , w ij is the weight of the connecting edge e ij , indicating the passenger flow between stations n i and n j .

[0025] As Figure 3 shown, step S3 specifically includes the following steps: Step S31: Based on the rainstorm disaster information obtained in step S1, calculate the relative rainfall intensity of extreme rainstorm weather. The formula is: In the formula, h is the current rainfall intensity, h 0 is the threshold of rainstorm rainfall intensity, s is the relative rainfall intensity, and its value range is [0, +∞). s = 0 indicates no rainfall, 0 < s < 1 indicates normal rainfall, and s ≥ 1 indicates rainstorm.

[0026] Step S32: Determine the failure probability of network sites and edges. The formula is: In the formula, P ( x > 1) is the site failure probability, P ( y > 1) is the edge failure probability.

[0027] Step S33: According to the bus - subway double - layer traffic network constructed in step S2, fit the linear relationship between the relative rainfall intensity and the traffic volume loss rate. Let the failure probability be equivalent to the traffic volume loss rate, and calculate the perturbation value of extreme rainstorm weather on sites and edges in the network. The formula is: In the formula, l is the traffic volume loss rate, α , β are the weight coefficients, u is an intermediate variable representing the impact of extreme rainstorm weather on sites and edges.

[0028] As Figure 4 shown, step S4 specifically includes the following steps: Step S41: According to the perturbation value of extreme rainstorm weather on sites calculated in step S3, construct a site - cascade failure model of the bus - subway double - layer traffic network, and calculate the state value of site n i under the influence of extreme rainstorm weather. The formula is: In the formula, x i ( t + 1) and xi ( t ) are the state variables of the site at the (t + 1)-th moment and the t-th moment, 0 ≤ n i x i (( t ) ≤ 1 indicates that the site is in normal operation, x i ( t ) > 1 indicates that the site fails; ε 1 is the coupling strength of the bus - subway double - layer transportation network sites, Q ij and Q i are respectively the passenger flows of the connecting edge e ij and the site n i , f ( x ) is the mapping function, f ( x ) = 4 x (1 - x ).

[0029] Step S42: According to the perturbation value of the extreme rainstorm weather on the connecting edge calculated in Step S3, construct a cascading failure model of the connecting edge of the bus - subway double - layer transportation network, and calculate the state variable of the connecting edge e ij under the influence of extreme rainstorm weather. The formula is: In the formula, x i ( t ) and x j ( t ) are respectively the state variables of the sites n i and n j at the t-th moment, y ij ( t + 1) and y ij ( t ) are respectively the state variables of the connecting edge e ij at the (t + 1)-th moment and the t-th moment, 0 ≤ y ij ( t ) ≤ 1 indicates that the connecting edge e ij is in normal operation, y ij (t ) > 1 indicates an edge connection e ij Failure ε 2 is the coupling strength of the edge connection in the bus - subway double - layer transportation network Q ip 、 Q jq 、 Q i 、 Q j are respectively the edge connections e ip 、the edge connection e jq 、the passenger flow of the station n i 、the station n j ; max{,} is the maximum - value function;.

[0030] Step S43: Search for failed stations in the network n g , remove the failed stations n g and the failed edge connections connected to them e gh , the passenger flow of the failed station n g will be transferred to all normal stations connected to it Q g , determine the change in the passenger flow of the edge connection n h connected to the station n h , and judge whether the passenger flow transfer spreads to all stations and edge connections in the network. The formula is: e hs In the formula, where Q hs is the passenger flow of the edge connection e hs before the passenger flow transfer, Q * hs is the passenger flow of the edge connection e hs after the passenger flow transfer, Q gh is the passenger flow of the edge connection e gh before the passenger flow transfer.

[0031] As Figure 5 shown, step S5 specifically includes the following steps: Step S51: Based on the network structure dimension, determine the station loss rate as the network performance measure index, and the formula is: In the formula, γ(N) is the station loss rate of the bus - subway double - layer traffic network, γ(N) ∈ [0, 1], N * G is the number of stations after the network undergoes cascading failures.

[0032] Step S52: Based on the passenger dimension, determine the change in network efficiency as the network performance measure index, and the formula is: In the formula, E is the network efficiency value, t ij is the station n i and the station n j the shortest travel time between them, γ(E) is the change in the bus - subway double - layer traffic network efficiency, γ(E) ∈ [0, 1], E 0 is the initial network efficiency value, E T is the network efficiency after the network undergoes cascading failures.

[0033] Step S53: Based on the network operation dimension, determine the passenger flow loss rate as the network performance measure index, and the formula is: In the formula, Q is the total passenger flow of the bus - subway double - layer traffic network, Q ij is the passenger flow of the link e ij γ(Q) is the passenger flow loss rate of the bus - subway double - layer traffic network, γ(Q) ∈ [0, 1], Q 0 is the initial total passenger flow of the network, Q T is the total passenger flow after the network undergoes cascading failures.

[0034] Step S54: Use the network performance measure indexes determined in Steps S51, S52, and S53 to assign weights to each index and synthesize to calculate the comprehensive performance of the bus - subway double - layer traffic network, and the formula is: In the formula, PFor the comprehensive performance of the bus - subway double - layer transportation network, λ1, λ2, and λ3 are the weights of γ(N), γ(E), and γ(Q) respectively, where λ1, λ2, λ3 ∈ (0, 1) and λ1 + λ2 + λ3 = 1.

[0035] Step S55: According to the comprehensive performance of the bus - subway double - layer transportation network calculated in Step S54, considering the network's ability to effectively resist the impact caused by interference after being disturbed and avoid the network completely collapsing and losing its service function, the formula for measuring the resistance ability of the network under extreme rainstorm weather interference is: In the formula, R 1 is the resistance ability of the network in the interference propagation stage, P ( t ) is the comprehensive performance of the network at time t.

[0036] Step S56: Considering the network's ability to continuously adapt to the propagation and diffusion of interference and maintain safe operation, the formula for measuring the absorption ability of the network under extreme rainstorm weather interference is: In the formula, R 2 is the absorption ability of the network in the interference propagation stage, P ( t 0) is the comprehensive performance of the network at t 0 moment, t a is the interference occurrence moment, t b is the start time of the operation management department's restoration.

[0037] Step S57: Considering the network's ability to quickly recover to the initial level through appropriate restoration measures after being disturbed and meet the normal travel demand, the formula for measuring the recovery ability of the network under extreme rainstorm weather interference is: In the formula, R 3 is the recovery ability of the network in the recovery stage, t c is the moment when the network recovers to the initial level.

[0038] Step S58: Using the resilience ability characteristics of the bus - subway double - layer transportation network determined in Steps S55, S56, and S57 in different response stages, the formula for measuring the comprehensive resilience of the network under extreme rainstorm weather is: In the formula, R G is the comprehensive resilience value of the bus - subway double - layer transportation network during the process of coping with extreme rainstorm weather interference.θ 1、 θ 2、 θ 3 are the weight coefficients of the resistance ability, absorption ability, and recovery ability, respectively, θ 1, θ 2, θ 3 ∈ (0, 1), and θ 1 + θ 2 + θ 3 = 1.

[0039] In summary, the present invention provides a method for measuring the resilience of urban public transportation networks under extreme rainstorm weather. The method for measuring the resilience of urban public transportation networks under extreme rainstorm weather in the present invention constructs a bus-subway double-layer transportation network, establishes a linear relationship between the rainstorm rainfall intensity and the passenger flow change, calculates the disturbance values of the stations and links in the network during the rainstorm, constructs a coupled mapping lattice cascade failure model considering the passenger flow, characterizes the dynamic evolution process of the urban public transportation network under extreme rainstorm weather, determines the network performance indicators based on multiple dimensions, and measures the resilience level of the urban public transportation network under extreme rainstorm weather; through the present invention, the disturbance influence value of extreme rainstorm weather can be accurately quantified, the resilience of the urban public transportation network can be effectively measured, a reference basis can be provided for urban traffic emergency management, and it helps to improve the disaster resistance ability and operation reliability of the urban public transportation system in response to extreme rainstorm weather.

[0040] This embodiment also provides a system for measuring the resilience of urban public transportation networks under extreme rainstorm weather, including a memory, a processor, and computer program instructions stored on the memory and capable of being run by the processor. When the processor runs the computer program instructions, the above method can be implemented.

[0041] This embodiment also provides a computer-readable storage medium, on which computer program instructions are stored. When the computer program instructions are executed by the processor, the above method is implemented.

[0042] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0043] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing device generate means for implementing the functions specified in one or more flows and / or blocks in the flowchart. Figure 1 in one or more flows and / or blocks Figure 1 in one or more blocks.

[0044] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one or more flows and / or blocks in the flowchart. Figure 1 in one or more flows and / or blocks Figure 1 in one or more blocks.

[0045] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more flows and / or blocks in the flowchart. Figure 1 in one or more flows and / or blocks Figure 1 in one or more blocks.

[0046] As described above, it is only a preferred embodiment of the present invention and not a limitation in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for measuring the resilience of urban public transport networks under extreme rainstorm weather, characterized in that, Including: Step S1: Obtain the data of urban public transportation network stations and lines, rainstorm disaster information, and passenger flow data; Step S2: Construct a bus-subway double-layer transportation network; Step S3: Based on the constructed bus-subway double-layer transportation network, establish a linear relationship between the rainstorm rainfall intensity and the passenger flow change, and calculate the disturbance values of the stations and connecting edges in the network; Step S4: Construct a cascading failure model of the bus-subway double-layer transportation network considering passenger flow to characterize the dynamic evolution process of the urban public transportation network under extreme rainstorm weather; Step S5: Use the constructed cascading failure model of the bus-subway double-layer transportation network to determine the network performance measurement indicators and measure the resilience level of the urban public transportation network under extreme rainstorm weather.

2. The method for measuring the resilience of urban public transport networks under extreme rainstorm weather according to claim 1, wherein In step S1, the data of urban public transportation network stations and lines includes: the intra-layer station set and intra-layer connecting edge set of buses and subways; The rainstorm disaster information includes: the rainstorm rainfall intensity, the impacts of extreme rainstorm weather on travel demand, travel mode, vehicle running speed, road traffic capacity, and traffic safety; The passenger flow data includes: the stations where passengers swipe cards, the boarding time, and the origin and destination information of getting on and off the vehicle.

3. The method for measuring the resilience of urban public transportation networks under extreme rainstorm weather according to claim 1, wherein Step S2 specifically includes the following steps: Step S21: Based on the urban public transportation network station and line data obtained in Step S1, construct a single-layer bus network and a single-layer subway network using the Space-L method, extract all stations and connecting edges within the range, continuously and incrementally number them, and filter out duplicate stations and duplicate connecting edges between two stations to obtain a bus station set, a subway station set, a bus connecting edge set, and a subway connecting edge set; L b and a single-layer subway network L s , extract all stations and connecting edges within the range, continuously and incrementally number them, and filter out duplicate stations and duplicate connecting edges between two stations to obtain a bus station set N b , a subway station set N s , a bus connecting edge set E b and a subway connecting edge set E s ; Step S22: Map bus stops and subway stops to the same layer, create a buffer with a radius of R centered on the subway stop, identify the bus stops that have a coupling relationship with it, and generate a set of coupling edges between network layers E t , to obtain a set of stops N and a set of connecting edges E , and construct a bus-subway two-layer transportation network G = < N , E >, use ArcGIS for spatial join to obtain the adjacency matrix of the stops A , define the network connection weight matrix W , and the matrix form is: In the formula, N G is the total number of stations in the double - layer traffic network; a ij is the connection relationship between stations n i and n j in the matrix. In the matrix A when there is an edge between stations n i and n j , a ij = 1; otherwise, it is 0, where i, j ∈ [1, 2,..., N G ; in the matrix W , w ij is the weight of the edge e ij , representing the passenger flow between stations n i and n j .

4. The method for measuring the resilience of urban public transport network under extreme rainstorm weather according to claim 1, wherein Step S3 specifically includes the following steps: Step S31: Based on the rainstorm disaster information obtained in step S1, calculate the relative rainfall intensity in extreme rainstorm weather. The formula is: In the formula, h is the current rainfall intensity, h 0 is the threshold of heavy rain rainfall intensity, s is the relative rainfall intensity, and its value range is [0, +∞). s = 0 indicates no rainfall, 0 < s < 1 indicates normal rainfall, and s ≥ 1 indicates heavy rain; Step S32: Determine the failure probability of network stations and connecting edges. The formula is: In the formula, P ( x > 1) is the site failure probability, P ( y > 1) is the edge failure probability; Step S33: According to the bus-subway double-layer transportation network constructed in step S2, fit the linear relationship between the relative rainfall intensity and the traffic volume loss rate, make the failure probability equivalent to the traffic volume loss rate, and calculate the disturbance values of the stations and connecting edges in the network. The formula is: In the formula, l is the traffic volume loss rate, α , β are the weight coefficients, u is an intermediate variable, representing the impact of extreme rainstorm weather on stations and connecting edges.

5. The method for measuring the resilience of urban public transport networks under extreme rainstorm weather according to claim 1, wherein Step S4 specifically includes the following steps: Step S41: Based on the disturbance values of extreme rainstorm weather on stations calculated in Step S3, construct a cascading failure model of stations in the bus-subway double-layer transportation network, and calculate the state values of stations under the influence of extreme rainstorm weather. The formula is as follows: n i The state value of a station is calculated using the following formula: wherein, x i ( t +1) and x i ( t ) are the state variables of the site n i at the (t + 1)-th moment and the t-th moment respectively, 0 ≤ x i ( t ) ≤ 1 indicates that the site is in normal operation, x i ( t ) > 1 indicates that the site fails; ε 1 is the site coupling strength of the bus - subway double - layer transportation network, Q ij and Q i are respectively the passenger flows of the connecting edge e ij and the site n i , f ( x ) is a mapping function, f ( x ) = 4 x (1 - x ); Step S42: Based on the perturbation value of the extreme rainstorm weather to the links calculated in Step S3, construct a cascading failure model of the links in the bus-subway double-layer transportation network, and calculate the link e ij state variables. The formula is as follows: wherein, x i ( t )、 x j ( t ) are the state variables of the station n i and n j at the t-th moment, y ij ( t +1), y ij ( t ) are the state variables of the link e ij at the (t + 1)-th moment and the t-th moment, 0 ≤ y ij ( t ) ≤ 1 indicates that the link e ij is in normal operation, y ij ( t ) > 1 indicates that the link e ij fails, ε 2 is the coupling strength of the links in the bus - subway double - layer traffic network, Q ip 、 Q jq 、 Q i 、 Q j are the passenger flows of the link e ip , the link e jq , the station n i , and the station n j respectively; max{,} is the maximum value function; Step S43: Search for failed sites in the network n g , remove the failed sites n g and the failed edges connected to them e gh , the passenger flow of the failed sites n g will be transferred to all normal sites connected to them Q g , determine the change in the passenger flow of the edges n h connected to the site n h , and judge whether the passenger flow transfer covers all sites and edges in the network. The formula is: e hs ​ In the formula, Q hs is the passenger flow of the edge before passenger flow transfer, e hs is the passenger flow volume, Q * hs is the passenger flow of the edge after passenger flow transfer, e hs is the passenger flow volume, Q gh is the passenger flow of the edge before passenger flow transfer, e gh is the passenger flow volume.

6. The method for measuring the resilience of the urban public transport network under extreme rainstorm weather according to claim 1, wherein Step S5 specifically includes the following steps: Step S51: Based on the network structure dimension, determine the station loss rate as the network performance measurement indicator. The formula is: where γ(N) is the station loss rate of the bus - subway double - layer transportation network, γ(N) ∈ [0, 1], N * G is the number of stations after the network undergoes cascading failures; Step S52: Based on the passenger dimension, determine the change in network efficiency as the network performance measurement indicator. The formula is: In the formula, E is the network efficiency value, t ij is the site n i and the site n j The shortest travel time between them. γ(E) is the change in the efficiency of the bus-subway double-decker transportation network, and γ(E) ∈ [0, 1]. E 0 is the initial network efficiency value. E T is the network efficiency after the network undergoes cascading failures; Step S53: Based on the network operation dimension, determine the passenger flow loss rate as the network performance measurement indicator. The formula is: wherein, Q is the total passenger flow of the bus - subway double - layer transportation network, Q ij is the passenger flow of the connecting edge e ij , γ(Q) is the passenger flow loss rate of the bus - subway double - layer transportation network, γ(Q) ∈ [0, 1], Q 0 is the initial total passenger flow of the network, Q T is the total passenger flow of the network after cascade failure; Step S54: Use the network performance measurement indicators determined in steps S51, S52, and S53 to assign weights to each indicator and synthesize to calculate the comprehensive performance of the bus-subway double-layer transportation network. The formula is: In the formula, P is the comprehensive performance of the bus-subway double-deck transportation network. λ1, λ2, and λ3 are the weights of γ(N), γ(E), and γ(Q) respectively. λ1, λ2, λ3 ∈ (0, 1), and λ1 + λ2 + λ3 = 1; Step S55: According to the comprehensive performance of the bus-subway double-layer transportation network calculated in step S54, measure the resistance ability of the network under extreme rainstorm weather interference. The formula is: In the formula, R 1 is the resistance of the network during the interference propagation stage, P ( t ) is the comprehensive performance of the network at time t; Step S56: Measure the absorption ability of the network under extreme rainstorm weather interference. The formula is: Wherein, R 2 is the absorption capacity of the network during the interference propagation stage, P ( t 0) is the comprehensive performance of the network at t time 0, t a is the moment when the interference occurs, t b is the moment when the operation and management department starts to resume; Step S57: Measure the recovery ability of the network under extreme rainstorm weather interference. The formula is: In the formula, R 3 is the recovery ability of the network during the recovery phase, t c is the moment when the network recovers to the initial level; Step S58: Use the resilience ability characteristics of the bus-subway double-layer transportation network in different response stages determined in steps S55, S56, and S57 to measure the comprehensive resilience of the network under extreme rainstorm weather. The formula is: wherein, R G is the comprehensive resilience value during the process of the bus - subway double - layer transportation network coping with extreme rainstorm weather interference, θ 1, θ 2, θ 3 are the weight coefficients of the resistance ability, absorption ability and recovery ability respectively, θ 1, θ 2, θ 3 ∈ (0, 1), and θ 1 + θ 2 + θ 3 = 1.

7. A resilience measurement system for urban public transportation networks under extreme rainstorm weather, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the method described in any one of claims 1-6.

8. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, it implements the method described in any one of claims 1-6.

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