A method for measuring the resilience of urban public transportation networks under extreme rainstorms

Abstract

The present invention relates to a method for measuring the resilience of an urban public transportation network under extreme rainstorms, comprising: obtaining data on urban public transportation network sites and routes, rainstorm disaster information, and passenger flow data; constructing a bus-subway double-decker transportation network; establishing a linear relationship between rainstorm intensity and passenger flow changes based on the constructed bus-subway double-decker transportation network, and calculating the disturbance value of rainstorms on sites and edges in the network; constructing a bus-subway double-decker transportation network cascading failure model that takes passenger flow into consideration to characterize the dynamic evolution process of the urban public transportation network under extreme rainstorms; and using the constructed bus-subway double-decker transportation network cascading failure model to determine network performance measurement indicators and measure the resilience level of the urban public transportation network under extreme rainstorms. This method is conducive to accurately measuring the resilience of the urban public transportation network and improving the response capability of the urban public transportation system under extreme rainstorms.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban public transportation network resilience measurement, and in particular relates to a method for measuring the resilience of an urban public transportation network under extreme rainstorm weather. Background Art

[0002] Currently, research on the resilience of urban public transportation networks often treats extreme rainstorms as qualitative disturbances, lacking modeling of the quantitative relationship between rainfall intensity and passenger flow variations. This results in an inability to accurately predict the impact of disasters on stations and routes. Conventional cascading failure models are often based on a single network topology or functional parameter, ignoring the spatiotemporal coupling effects of passenger flow redistribution and network load under rainstorm disturbances, making it difficult to simulate the dynamic characteristics of rainstorm disasters during their evolution. Therefore, establishing a cascading failure model for urban public transportation networks under extreme rainstorms has become a key issue that urgently needs to be addressed in measuring their resilience, and it has important practical implications. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for measuring the resilience of urban public transportation networks under extreme rainstorms. This method is conducive to accurately measuring the resilience of urban public transportation networks and improving the response capabilities of urban public transportation systems under extreme rainstorms.

[0004] To achieve the above objectives, the present invention adopts a technical solution: a method for measuring the resilience of urban public transportation networks under extreme rainstorm conditions, comprising:

[0005] Step S1: Obtaining urban public transportation network station and route data, rainstorm disaster information, and passenger flow data;

[0006] Step S2: Construct a bus-subway double-layer transportation network;

[0007] Step S3: Based on the constructed bus-subway double-layer transportation network, a linear relationship between rainstorm intensity and passenger flow changes is established, and the disturbance value of rainstorm on the stations and edges in the network is calculated;

[0008] Step S4: Construct a bus-subway double-layer transportation network cascading failure model considering passenger flow to characterize the dynamic evolution process of the urban public transportation network under extreme rainstorm weather;

[0009] Step S5: Using the constructed bus-subway double-layer transportation network cascading failure model, determine the network performance measurement index and measure the resilience level of the urban public transportation network under extreme rainstorm weather.

[0010] Furthermore, in step S1, the urban public transportation network station and line data includes: a set of intra-layer stations and an intra-layer edge set of buses and subways;

[0011] The rainstorm disaster information includes: rainstorm intensity, and the impact of extreme rainstorm weather on travel demand, travel mode, vehicle speed, road capacity, and traffic safety;

[0012] The passenger flow data includes: the station where passengers swipe their cards, the boarding time, and the entry and exit starting and ending points.

[0013] Furthermore, step S2 specifically includes the following steps:

[0014] Step S21: Based on the urban public transportation network station and route data obtained in step S1, a single-layer bus network is constructed using the Space-L method. L b and a single-deck subway network L s , extract all stations and edges within the range, number them consecutively and incrementally, and filter out duplicate stations and duplicate edges between two stations to obtain the bus station set N b , meet at the subway station N s , bus connection and gathering E b Meet at the subway station E s ;

[0015] Step S22: Map the bus stops and subway stations to the same layer, create a buffer zone with a radius of R with the subway station as the center, identify the bus stops that have a coupling relationship with it, and generate a set of coupling edges between network layers. E t , get the site collection N and edge sets E , building a bus-subway double-layer transportation network G =< N , E >, use ArcGIS to perform spatial connection to obtain the adjacency matrix of the site A , define the network edge weight matrix W , the matrix form is:

[0016]

[0017]

[0018] Where, N G is the total number of stations in the two-tier transportation network; a ij For sites in the network n i and n j The connection relationship between them is in the matrixA Among them, when there is an edge connection between stations in the network n i and n j when there is an edge connection, a ij = 1, otherwise it is 0, where i, j ∈ [1, 2,..., N G ; in the matrix W Among them, w ij is the weight of the edge connection e ij , representing the passenger flow volume between stations n i and n j .

[0019] Furthermore, step S3 specifically includes the following steps:

[0020] Step S31: Based on the rainstorm disaster information obtained in step S1, calculate the relative rainfall intensity in extreme rainstorm weather. The formula is:

[0021]

[0022] 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, and its value range is [0, +∞). s = 0 indicates no rainfall, 0 < s < 1 indicates normal rainfall, and s ≥ 1 indicates rainstorm;

[0023] Step S32: Determine the failure probability of network stations and edge connections. The formula is:

[0024]

[0025] In the formula, P ( x > 1) is the station failure probability, P ( y > 1) is the edge connection failure probability;

[0026] 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. Let the failure probability be equivalent to the traffic volume loss rate, and calculate the perturbation value of stations and edge connections in the network in extreme rainstorm weather. The formula is:

[0027]

[0028]

[0029]

[0030] Where, l is the traffic loss rate, α 、 β is the weight coefficient, u It is an intermediate variable, indicating the impact of extreme rainstorm weather on the site and its edges.

[0031] Furthermore, step S4 specifically includes the following steps:

[0032] Step S41: Based on the disturbance value of the extreme rainstorm on the station calculated in step S3, a station cascade failure model of the bus-subway double-layer transportation network is constructed to calculate the station cascade failure value under the influence of extreme rainstorm. n i The status value of is:

[0033]

[0034] Where, x i ( t +1) and x i ( t ) are sites n i The state variables at time t+1 and time t, 0≤ x i ( t )≤1 means the site is in normal operation. x i ( t )>1 indicates that the site is invalid; ε 1 is the station coupling strength of the bus-subway double-deck transportation network, Q ij and Q i Connecting edges e ij and sites n i passenger flow, f ( x ) is the mapping function, f ( x )=4 x (1- x );

[0035] Step S42: Based on the disturbance value of the extreme rainstorm on the connection calculated in step S3, a connection cascade failure model of the bus-subway double-layer transportation network is constructed to calculate the connection under the influence of extreme rainstorm. e ij State variable, the formula is:

[0036]

[0037] Where, x i ( t ), x j ( t ) are sites n i and n j The state variable at time t is y ij ( t +1), y ij ( t ) are connected edges e ij The state variables at time t+1 and time t, 0≤ y ij ( t )≤1 indicates a connected edge e ij In normal operating condition, 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 、Connect the edges e jq , Site n i , Site n j passenger flow; max{ ,} is the maximum value function;

[0038] Step S43: Search for invalid sites in the network n g , remove dead sites n g and its connected failed edges e gh , failed site n g Passenger flow Q gWill 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 stations and edges in the network. The formula is:

[0039]

[0040] Where, Q hs Connecting the front edge for passenger flow transfer e hs passenger flow, Q * hs To connect the side after passenger flow transfer e hs passenger flow, Q gh Connecting the front edge for passenger flow transfer e gh passenger flow.

[0041] Furthermore, step S5 specifically includes the following steps:

[0042] Step S51: Based on the network structure dimension, determine the site loss rate as a network performance measurement indicator, the formula is:

[0043]

[0044] Where γ(N) is the station loss rate of the bus-subway double-deck transportation network, γ(N)∈[0,1], N * G is the number of sites in the network after cascading failure;

[0045] Step S52: Based on the passenger dimension, determine the network efficiency change as a network performance measurement indicator, the formula is:

[0046]

[0047]

[0048] Where, E is the network efficiency value, t ij For site n i With site n j The shortest travel time between them, γ(E) is the efficiency change of the bus-subway double-deck transportation network, γ(E)∈[0,1], E0 is the initial network efficiency value, E T is the network efficiency after cascading failures;

[0049] Step S53: Based on the network operation dimension, determine the passenger flow loss rate as a network performance measurement indicator, the formula is:

[0050]

[0051]

[0052] Where, Q is the total passenger flow of the bus-subway double-deck transportation network, Q ij For connecting edges e ij passenger flow, γ(Q) is the passenger flow loss rate of the bus-subway double-deck transportation network, γ(Q)∈[0,1], Q 0 is the total passenger flow at the beginning of the network, Q T is the total passenger flow of the network after cascading failure;

[0053] Step S54: Using the network performance measurement indicators determined in steps S51, S52, and S53, weight each indicator and synthesize and calculate the comprehensive performance of the bus-subway double-deck transportation network. The formula is:

[0054]

[0055] Where, 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;

[0056] Step S55: Based on the comprehensive performance of the bus-subway double-deck transportation network calculated in step S54, the formula for measuring the network's resistance to extreme rainstorm interference is:

[0057]

[0058] Where, R 1 is the network's resistance to interference propagation, P ( t ) is the comprehensive performance of the network at time t;

[0059] Step S56: Measure the network's absorption capacity under extreme rainstorm interference. The formula is:

[0060]

[0061] Where, R 2 is the network's absorption capacity during the interference propagation phase, P ( t 0) For the network t Comprehensive performance at time 0, t a is the time when the interference occurs, t b Start recovery moments for operations management;

[0062] Step S57: Measure the network's recovery capability under extreme rainstorm disturbances. The formula is:

[0063]

[0064] Where, R 3 is the network's recovery capability during the recovery phase, t c The moment when the network recovers to its initial level;

[0065] Step S58: Using the resilience characteristics of the bus-subway double-deck transportation network at different response stages determined in steps S55, S56, and S57, measure the comprehensive resilience of the network under extreme rainstorm weather. The formula is:

[0066]

[0067] Where, R G The comprehensive resilience value of the bus-subway double-deck transportation network in response to extreme rainstorm weather disturbances, θ 1. θ 2. θ 3 are the weight coefficients of resistance, absorption and recovery respectively. θ 1, θ 2, θ 3∈(0,1), and θ 1+ θ 2+ θ 3=1.

[0068] The present invention also provides a system for measuring the resilience of urban public transportation networks under extreme rainstorm weather, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the above-mentioned method can be implemented.

[0069] The present invention also provides a computer-readable storage medium having computer program instructions stored thereon, which implement the above method when the computer program instructions are executed by a processor.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] (1) The present invention establishes a quantitative linear relationship between rainstorm intensity and passenger flow changes, dynamically associates meteorological data with operational data, and can effectively characterize the impact of extreme rainstorm weather on urban public transportation networks, thereby achieving accurate calculation of disturbance values.

[0072] (2) The present invention simulates the failure propagation process of sites and edges through dynamic traffic redistribution, which can reflect the amplification effect of passenger flow on network cascading failure in actual operation.

[0073] (3) The multi-dimensional resilience measurement method of the bus-subway double-layer network under extreme rainstorm weather proposed in this invention can identify key vulnerable sites in the network, provide a quantitative basis for formulating hierarchical management and control strategies and optimizing emergency plans, and make up for the one-sidedness of existing technical solutions in breakthrough indicator evaluation and the difficulty in providing multi-dimensional decision support for emergency resource scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 This is a flowchart of an implementation method for measuring the resilience of an urban public transportation network under extreme rainstorm weather provided by an embodiment of the present invention;

[0075] Figure 2 This is a flow chart of constructing a bus-subway double-layer transportation network in an embodiment of the present invention;

[0076] Figure 3 This is a flow chart of calculating the disturbance value of extreme rainstorm weather on sites and edges in a network according to an embodiment of the present invention;

[0077] Figure 4 This is a flowchart of constructing a cascading failure model to characterize the dynamic evolution of a network under extreme rainstorm weather in an embodiment of the present invention;

[0078] Figure 5 It is a flowchart of determining network performance indicators and establishing a resilience measurement model in an embodiment of the present invention. DETAILED DESCRIPTION

[0079] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0080] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0081] 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 "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0082] like Figure 1 As shown, this embodiment provides a method for measuring the resilience of urban public transportation networks under extreme rainstorm weather, including:

[0083] Step S1: Obtaining urban public transportation network station and route data, rainstorm disaster information, and passenger flow data;

[0084] Step S2: Construct a bus-subway double-layer transportation network;

[0085] Step S3: Based on the constructed bus-subway double-layer transportation network, a linear relationship between rainstorm intensity and passenger flow changes is established, and the disturbance value of rainstorm on the stations and edges in the network is calculated;

[0086] Step S4: Construct a bus-subway double-layer transportation network cascading failure model considering passenger flow to characterize the dynamic evolution process of the urban public transportation network under extreme rainstorm weather;

[0087] Step S5: Using the constructed bus-subway double-layer transportation network cascading failure model, determine the network performance measurement index and measure the resilience level of the urban public transportation network under extreme rainstorm weather.

[0088] In step S1, the urban public transportation network station and line data includes: a set of intra-layer stations and a set of intra-layer edges of buses and subways.

[0089] The rainstorm disaster information includes: rainstorm intensity, and the impact of extreme rainstorm weather on travel demand, travel mode, vehicle speed, road capacity, and traffic safety.

[0090] The passenger flow data includes: the station where passengers swipe their cards, the boarding time, and the entry and exit OD (origin and destination) information.

[0091] like Figure 2 As shown, step S2 specifically includes the following steps:

[0092] Step S21: Based on the urban public transportation network station and route data obtained in step S1, a single-layer bus network is constructed using the Space-L method. L b and a single-deck subway network L s, extract all stations and edges within the range, number them consecutively and incrementally, and filter out duplicate stations and duplicate edges between two stations to obtain the bus station set N b , meet at the subway station N s , bus connection and gathering E b Meet at the subway station E s .

[0093] Step S22: Map the bus stops and subway stations to the same layer, create a buffer zone with a radius of R with the subway station as the center, identify the bus stops that have a coupling relationship with it, and generate a set of coupling edges between network layers. E t , get the site collection N and edge sets E , building a bus-subway double-layer transportation network G =< N , E >, use ArcGIS to perform spatial connection to obtain the adjacency matrix of the site A , define the network edge weight matrix W , the matrix form is:

[0094]

[0095]

[0096] Where, N G is the total number of stations in the two-tier transportation network; a ij For sites in the network n i and n j The connection relationship between them is in the matrix A When the site in the network n i and n j When there are edges between them, a ij =1, otherwise it is 0, i, j∈[1, 2, ..., N G ]; in the matrix W middle, w ij For connecting edges e ij The weight of the site n i and n jThe passenger flow between them.

[0097] As Figure 3 shown, step S3 specifically includes the following steps:

[0098] Step S31: Based on the rainstorm disaster information obtained in step S1, calculate the relative rainfall intensity in extreme rainstorm weather. The formula is:

[0099]

[0100] 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, and its value range is [0, +∞). s = 0 indicates no rainfall, 0 < s < 1 indicates normal rainfall, and s ≥ 1 indicates rainstorm.

[0101] Step S32: Determine the failure probability of network sites and edges. The formula is:

[0102]

[0103] In the formula, P ( x > 1) is the site failure probability, P ( y > 1) is the edge failure probability.

[0104] 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 the sites and edges in the network in extreme rainstorm weather. The formula is:

[0105]

[0106]

[0107]

[0108] In the formula, l is the traffic volume loss rate, α 、 β are the weight coefficients, u is an intermediate variable, indicating the impact of extreme rainstorm weather on sites and edges.

[0109] As Figure 4 shown, step S4 specifically includes the following steps:

[0110] Step S41: Based on the disturbance value of the extreme rainstorm on the station calculated in step S3, a station cascade failure model of the bus-subway double-layer transportation network is constructed to calculate the station cascade failure value under the influence of extreme rainstorm. n i The status value of is:

[0111]

[0112] Where, x i ( t +1) and x i ( t ) are sites n i The state variables at time t+1 and time t, 0≤ x i ( t )≤1 means the site is in normal operation. x i ( t )>1 indicates that the site is invalid; ε 1 is the station coupling strength of the bus-subway double-deck transportation network, Q ij and Q i Connecting edges e ij and sites n i passenger flow, f ( x ) is the mapping function, f ( x )=4 x (1- x ).

[0113] Step S42: Based on the disturbance value of the extreme rainstorm on the connection calculated in step S3, a connection cascade failure model of the bus-subway double-layer transportation network is constructed to calculate the connection under the influence of extreme rainstorm. e ij State variable, the formula is:

[0114]

[0115] Where, x i ( t ), x j ( t ) are sites n i and n jThe state variable at time t is y ij ( t +1), y ij ( t ) are connected edges e ij The state variables at time t+1 and time t, 0≤ y ij ( t )≤1 indicates a connected edge e ij In normal operating condition, 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 、Connect the edges e jq , Site n i , Site n j passenger flow; max{ ,} is the maximum value function;.

[0116] Step S43: Search for invalid sites in the network n g , remove dead sites n g and its connected invalid edges e gh , failed site n g Passenger 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 stations and edges in the network. The formula is:

[0117]

[0118] Where, Qhs Connecting the front edge for passenger flow transfer e hs passenger flow, Q * hs To connect the side after passenger flow transfer e hs passenger flow, Q gh Connecting the front edge for passenger flow transfer e gh passenger flow.

[0119] like Figure 5 As shown, step S5 specifically includes the following steps:

[0120] Step S51: Based on the network structure dimension, determine the site loss rate as a network performance measurement indicator, the formula is:

[0121]

[0122] Where γ(N) is the station loss rate of the bus-subway double-deck transportation network, γ(N)∈[0,1], N * G is the number of sites in the network after cascading failure.

[0123] Step S52: Based on the passenger dimension, determine the network efficiency change as a network performance measurement indicator, the formula is:

[0124]

[0125]

[0126] Where, E is the network efficiency value, t ij For site n i With site n j The shortest travel time between them, γ(E) is the efficiency change of the bus-subway double-deck transportation network, γ(E)∈[0,1], E 0 is the initial network efficiency value, E T is the network efficiency after cascading failure.

[0127] Step S53: Based on the network operation dimension, determine the passenger flow loss rate as a network performance measurement indicator, the formula is:

[0128]

[0129]

[0130] Where, Q is the total passenger flow of the bus-subway double-deck transportation network, Q ij For connecting edges e ij passenger flow, γ(Q) is the passenger flow loss rate of the bus-subway double-deck transportation network, γ(Q)∈[0,1], Q 0 is the total passenger flow at the beginning of the network, Q T is the total passenger flow of the network after cascading failure.

[0131] Step S54: Using the network performance measurement indicators determined in steps S51, S52, and S53, weight each indicator and synthesize and calculate the comprehensive performance of the bus-subway double-deck transportation network. The formula is:

[0132]

[0133] Where, P is the comprehensive performance of the bus-subway double-decker 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.

[0134] Step S55: Based on the comprehensive performance of the bus-subway double-deck transportation network calculated in step S54, the network's ability to effectively resist the impact of interference after being disturbed, and to avoid complete network collapse and loss of service functions, is considered. The formula for measuring the network's resistance to extreme rainstorm interference is:

[0135]

[0136] Where, R 1 is the network's resistance to interference propagation, P ( t ) is the comprehensive performance of the network at time t.

[0137] Step S56: Considering the network's ability to continuously adapt to the propagation and diffusion of interference and maintain safe operation, the network's absorption capacity under extreme rainstorm interference is measured. The formula is:

[0138]

[0139] Where, R 2 is the network's absorption capacity during the interference propagation phase, P ( t 0) For the network t Comprehensive performance at time 0, t a is the time when the interference occurs, tb Start recovery time for operations management.

[0140] Step S57: Considering the network's ability to quickly recover to its initial level through appropriate recovery measures after being disturbed and meet normal travel needs, the network's recovery capability under extreme rainstorm disturbances is measured. The formula is:

[0141]

[0142] Where, R 3 is the network's recovery capability during the recovery phase, t c The moment when the network returns to its initial level.

[0143] Step S58: Using the resilience characteristics of the bus-subway double-deck transportation network at different response stages determined in steps S55, S56, and S57, measure the comprehensive resilience of the network under extreme rainstorm weather. The formula is:

[0144]

[0145] Where, R G The comprehensive resilience value of the bus-subway double-deck transportation network in response to extreme rainstorm weather disturbances, θ 1. θ 2. θ 3 are the weight coefficients of resistance, absorption and recovery respectively. θ 1, θ 2, θ 3∈(0,1), and θ 1+ θ 2+ θ 3=1.

[0146] In summary, the present invention provides a method for measuring the resilience of urban public transportation networks under extreme rainstorms. The method for measuring the resilience of urban public transportation networks under extreme rainstorms of the present invention constructs a bus-subway double-layer transportation network, establishes a linear relationship between rainstorm intensity and passenger flow changes, calculates the disturbance value of rainstorms on stations and edges in the network, constructs a coupled mapping lattice cascade failure model considering passenger flow, characterizes the dynamic evolution process of urban public transportation networks under extreme rainstorms, determines network performance indicators based on multiple dimensions, and measures the resilience level of urban public transportation networks under extreme rainstorms. The present invention can accurately quantify the disturbance impact value of extreme rainstorms, effectively measure the resilience of urban public transportation networks, provide a reference basis for urban transportation emergency management, and help improve the disaster resistance and operational reliability of urban public transportation systems in response to extreme rainstorms.

[0147] 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 in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the above-mentioned method can be implemented.

[0148] This embodiment further provides a computer-readable storage medium having computer program instructions stored thereon, which implements the above method when the computer program instructions are executed by a processor.

[0149] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0150] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes 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 a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0151] These computer program instructions may 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, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0152] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0153] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for measuring the resilience of urban public transportation networks under extreme rainstorm conditions, characterized by: 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 perturbation values of the stations and 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; 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, h0 is the threshold of the rainstorm rainfall intensity, s is the relative rainfall intensity, and the value range is [0, +∞). s = 0 means no rainfall, 0 < s < 1 means normal rainfall, and s ≥ 1 means rainstorm; Step S32: Determine the failure probabilities of the network stations and edges. The formula is: In the formula, P(x>1) is the station failure probability, and 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 perturbation values of the stations and edges in the network under extreme rainstorm weather. The formula is: In the formula, l is the traffic volume loss rate, α and β are weight coefficients, and u is an intermediate variable representing the impact of extreme rainstorm weather on the stations and edges; Step S4 specifically includes the following steps: Step S41: Based on the disturbance value of the extreme rainstorm on the station calculated in step S3, a station cascade failure model of the bus-subway double-layer transportation network is constructed to calculate the station n under the influence of extreme rainstorm. i The status value of is: Where x i (t+1) and x i (t) are station n i The state variables at time t+1 and time t, 0≤x i (t)≤1 means the station is in normal operation, x i (t)>1 indicates station failure; ε1 is the station coupling strength of the bus-subway double-layer transportation network, Q ij With Q i They are connected edge e ij and site n i passenger flow, f(x) is the mapping function, f(x)=4x(1-x); Step S42: Based on the disturbance value of the extreme rainstorm on the edge calculated in step S3, a cascading failure model of the bus-subway double-layer transportation network is constructed to calculate the edge e under the influence of extreme rainstorm. ij State variable, the formula is: Where x i (t), x j (t) are station n i and n j The state variable at time t, y ij (t+1),y ij (t) are connected to the edge e ij The state variables at time t+1 and time t, 0≤y ij (t)≤1 means the edge e ij In normal operation, y ij (t)>1 indicates that the edge e ij failure, ε2 is the edge coupling strength of the bus-subway double-layer transportation network, Q ip , Q jq , Q i , Q j They are connected edge e ip 、E jq 、Site n i 、Site n j passenger flow; max{ ,} is the maximum value function; Step S43: Search for failed site n in the network g , remove failed site n g and the failed edge e connected to it gh , failed site n g Passenger flow Q g Will be transferred to all normal sites connected to it 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 stations and edges in the network. The formula is: Where Q hs For passenger flow transfer front edge e hs Passenger flow, Q * hs For passenger flow transfer and side connection hs Passenger flow, Q gh For passenger flow transfer front edge e gh passenger flow.

2. The method for measuring the resilience of urban public transportation networks under extreme rainstorm conditions according to claim 1 is characterized in that: In Step S1, the urban public transportation network station and line data include: the intra-layer station set and intra-layer 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 starting and ending points of entering and leaving the station.

3. The method for measuring the resilience of urban public transportation networks under extreme rainstorm conditions according to claim 1 is characterized in that: Step S2 specifically includes the following steps: Step S21: Based on the urban public transportation network station and route data obtained in step S1, a single-layer bus network L is constructed using the Space-L method. b and single-deck subway network L s , extract all stations and edges within the range, number them consecutively and incrementally, and filter out duplicate stations and duplicate edges between two stations to obtain the bus station set N b , Gather at subway station N s 、Bus connection set E b and subway side set E s ; Step S22: Map the bus stops and subway stations to the same layer, create a buffer zone with a radius of R with the subway station as the center, identify the bus stops that have a coupling relationship with it, and generate the network layer coupling edge set E t , get the site set N and the edge set E, and build a bus-subway double-layer transportation network G =<N, E> , use ArcGIS to perform spatial connection to obtain the site adjacency matrix A, and define the network edge weight matrix W, the matrix form is: Where N G is the total number of stations in the double-layer transportation network; a ij is site n in the network i With n j The connection relationship between them, in the matrix A, when the site n in the network i With n j When there is an edge between them, a ij =1, otherwise it is 0, i, j∈[1, 2, ..., N G ]; in the matrix W, w ij For the edge e ij The weight of site n i With n j passenger flow between them.

4. The method for measuring the resilience of urban public transportation networks under extreme rainstorm conditions according to claim 1 is characterized in that: 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 site loss rate of the bus-subway double-deck transportation network, γ(N)∈[0,1], N * G is the number of sites in the network after cascading failure; Step S52: Based on the passenger dimension, determine the change in network efficiency as the network performance measurement indicator. The formula is: Where E is the network efficiency value, t ij For site n i With site n j The shortest travel time between them, γ(E) is the change in efficiency of the bus-subway double-deck transportation network, γ(E)∈[0,1], E0 is the initial network efficiency value, E T is the network efficiency after the cascade failure; Step S53: Based on the network operation dimension, determine the passenger flow loss rate as the network performance measurement indicator. The formula is: Where Q is the total passenger flow of the bus-subway double-deck transportation network, Q ij For the edge e ij passenger flow, γ(Q) is the passenger flow loss rate of the bus-subway double-deck transportation network, γ(Q)∈[0,1], Q0 is the total passenger flow at the beginning of the network, Q T is the total passenger flow of the network after cascading 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-layer 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: Based on the comprehensive performance of the bus-subway double-deck transportation network calculated in step S54, the formula for measuring the network's resistance to extreme rainstorm interference is: Where R1 is the network's resistance to interference propagation, and P(t) is the network's comprehensive performance at time t. Step S56: Measure the network's absorption capacity under extreme rainstorm interference. The formula is: Where R2 is the absorption capacity of the network during the interference propagation phase, P(t0) is the comprehensive performance of the network at time t0, and t a is the time when the interference occurs, t b Start recovery moments for operations management; Step S57: Measure the network's ability to recover under extreme rainstorm conditions. The formula is: Where R3 is the network's recovery capability during the recovery phase, t c The moment when the network recovers to its initial level; Step S58: Using the resilience characteristics of the bus-subway double-deck transportation network at different response stages determined in steps S55, S56, and S57, measure the comprehensive resilience of the network under extreme rainstorm weather. The formula is: Where R G is the comprehensive resilience value of the bus-subway double-deck transportation network in response to extreme rainstorm weather disturbances. θ1, θ2, and θ3 are the weight coefficients of resistance, absorption, and recovery capabilities, respectively. θ1, θ2, θ3∈(0,1), and θ1+θ2+θ3=1.

5. A system for measuring the resilience of urban public transportation networks under extreme rainstorm conditions, characterized by: The method comprises a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method according to any one of claims 1 to 4 can be implemented.

6. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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