Typhoon disaster under a multi-mode traffic network robustness calculation method

Abstract

The application discloses a kind of typhoon disaster under multi-mode traffic network robustness calculation method, comprising: the construction includes multiple traffic modes of intercity public transport network;In combination with the spatial-time dynamic characteristics of typhoon disaster, pressure attenuation model and typhoon sustained influence model are generated;Based on system vulnerability curve and Monte Carlo simulation method, the failure probability distribution and state of intercity public transport network under typhoon disaster are calculated;According to the failure probability distribution and state of intercity public transport network under typhoon disaster, a traffic network cascading failure model is established to simulate the structure and function loss process of traffic network sites and lines under disaster conditions;Design a traffic network robustness index calculation system to quantify the performance changes of intercity public transport network from both topological structure and service function.The application can accurately quantify the influence of typhoon disaster on the traffic system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of traffic management, in particular to a multi-mode traffic network robustness calculation method under typhoon disaster. BACKGROUND

[0002] Intercity public transportation network has the characteristics of large scale, high spatio-temporal concentration, sparse departure frequency, etc., and is more vulnerable to impact under large-scale and high-intensity extreme meteorological disasters such as typhoon.

[0003] The impact of typhoon disaster on the transportation system has the characteristics of multi-level and multi-type. The direct impact includes infrastructure damage, road closure, railway suspension, etc. caused by extreme weather such as strong wind and heavy rain, which seriously disrupts the traffic operation order. The more complex is the indirect impact, the large-scale transfer of passenger flow caused by the interruption of part of the hub or line will lead to overload of alternative paths, network imbalance and even trigger cascading failure. The patent with publication number CN116090687A "Establishment method of rail transit network cascading failure model" proposes a rail transit network cascading failure model, but it assumes that passengers are completely rational and passenger flow will be transferred to all feasible paths, ignoring the cancellation and delay of passengers' travel intention under typhoon disaster, which is difficult to accurately reflect the actual process of passenger flow redistribution under disaster.

[0004] The prior art discloses a typhoon disaster urban power distribution network resilience evaluation and defense measure research, which uses batts model to evaluate the resilience of urban power distribution network under typhoon disaster. However, the urban power distribution network is different from the transportation network, the network points are relatively fixed, and the passenger flow is not involved. Moreover, the failure probability measurement of power distribution network and transportation network is different, so it is difficult to apply this method to transportation network.

[0005] At present, the typhoon disaster transportation network robustness calculation method mainly focuses on single-mode transportation network, ignores the cascading failure effect caused by passenger flow cross-mode transfer under disaster situation, and does not fully consider the network heterogeneity and functional difference between different modes. In addition, most of the researches use static or simplified attack mode to simulate the typhoon process, which is difficult to reflect the complex evolution characteristics of typhoon disaster, ignores the key characteristics of typhoon moving path, influence range, duration and intensity change, etc. At the same time, the existing robustness calculation method mainly focuses on structural index, lacks functional description of service capacity and transportation efficiency, and is difficult to comprehensively evaluate the robustness of network in disaster process. SUMMARY

[0006] The purpose of the present application is to provide a multi-mode traffic network robustness calculation method under typhoon disaster to measure the influence of specific typhoon disaster on intercity public transportation system and robustness.

[0007] To achieve the above technical purposes, the technical scheme adopted by the present application is:

[0008] A multi-mode traffic network robustness calculation method under typhoon disaster, the method comprising the following steps:

[0009] S1, an intercity public transport network containing various traffic modes including high-speed rail, general rail and highway passenger transport is constructed, and the weight attributes of each traffic mode are loaded;

[0010] S2, a Batts typhoon meteorological model is adopted, combined with the spatial-temporal dynamic characteristics of typhoon disaster, a pressure attenuation model and a typhoon sustained influence model are generated to simulate the spatial and temporal distribution and intensity variation of typhoon intensity;

[0011] S3, combined with the pressure attenuation model and the typhoon sustained influence model, based on the system vulnerability curve and the Monte Carlo simulation method, the failure probability distribution and state of the intercity public transport network under typhoon disaster are calculated;

[0012] S4, according to the failure probability distribution and state of the intercity public transport network under typhoon disaster, a traffic network cascading failure model is established to simulate the structural and functional loss process of the traffic network sites and lines under disaster conditions;

[0013] S5, a traffic network robustness index calculation system is designed to quantify the performance changes of the intercity public transport network from the aspects of topological structure and service function.

[0014] Step S1 further comprises:

[0015] The complex network modeling method Space L is used to map the real network to a topological network, and the generated intercity public transport network contains three elements of nodes, edges and weights, and the representation method is: , wherein, contains a highway subnet and a railway subnet ; is a set of topological nodes, including highway passenger stations and railway stations; is a set of topological edges, which satisfies the connection between adjacent two stations when there is direct transport service between them;

[0016] For transfer between different traffic modes, there is a transport connection between different traffic modes in the same county, and a transfer edge is established to form a complete multi-mode traffic network; in the edge set, the adjacency matrix of the topological network is defined as , if the node is adjacent to the node , then , otherwise weighted adjacency matrix distance Obtained by searching for the shortest path in a real network; Represents a set of other attributes of the edge, where Indicates starting point To the end The average daily passenger volume, is the service frequency, For travel expenses, is the travel time; through the shortest path allocation principle, the passenger flow of all OD pairs will be allocated along their shortest path. Passenger flow weight It is defined as the sum of the passenger flow of the shortest path between all node pairs passing through the edge.

[0017] Step S2 further comprises:

[0018] S21: Calculate the maximum gradient wind speed using the friction-neglecting gradient wind equation , the calculation formula is:

[0019] ;

[0020] ;

[0021] Where, is the maximum gradient wind speed; is the empirical coefficient; is the center pressure difference, the unit is hPa; is the maximum wind speed radius, in m; is the Coriolis force parameter of the Earth's rotation, in s -1 ;

[0022] S22: Definition and The relationship, and The statistical fitting relationship between them is:

[0023] ;

[0024] S23: Calculate the average maximum wind speed at 10m above sea level for 10 minutes for:

[0025] ;

[0026] Where, Indicates the center moving speed;

[0027] S24: calculating the 10-minute average wind speed at 10m height from the typhoon center r; wherein the 10-minute average wind speed at 10m height from the typhoon center r on the direction line OM obtained by rotating 115° clockwise from the typhoon moving direction is:

[0028] ;

[0029] in the formula, is a parameter related to the radial intensity decay of the typhoon;

[0030] S25: calculating the average wind speed at the research point ; wherein the 10-minute average wind speed at 10m height at the research point on the straight line OP with an angle of to the straight line OM is is:

[0031] ;

[0032] S26: defining the air pressure decay model, and the relationship between the central air pressure difference and time is:

[0033] ;

[0034] in the formula, is the time after the typhoon lands, and the unit is ; represents the central air pressure difference corresponding to the time after the typhoon lands; represents the central air pressure difference of the typhoon on the sea before landing; is the angle between the typhoon path and the coastline, and the size range is ;

[0035] S27: calculating the duration of the site affected by the typhoon disaster in the time dimension, defining the typhoon continuous influence model, and representing as:

[0036] ;

[0037] in the formula, is the typhoon moving track distance, is the moving speed of the typhoon after landing.

[0038] Step S3 further comprises:

[0039] S31: the wind speed is characterized as the disaster-causing factor intensity of the typhoon disaster, when the wind speed exceeds the safety threshold, the site is closed, and the corresponding connection line is speed-limited or even shut down, causing the traffic function to be interrupted; ​

[0040] The failure probability model of the intercity public transport network is constructed by using the vulnerability curve, and the failure probability is

[0041]

[0042] wherein, is the cumulative distribution function of the normal distribution; the parameters of the highway transport network are set as =0.157, =20.363; the parameters of the railway network are set as =0.094, =28.836;

[0043] S32: using the Monte Carlo method to generate a random failure scenario of the traffic stations within the influence range of the typhoon; specifically including:

[0044] S321: defining the total iteration number , and setting the iteration number to be equal to 1;

[0045] S322: initializing the state vector of each station ;

[0046] S323: generating a uniformly distributed random number for each station, and comparing and the failure probability of the station , which is calculated by the failure probability model. If , the station fails, and it is set that ;

[0047] S324: calculating the network performance function as the robustness index value after cascading failure;

[0048] S325: increasing the iteration number by 1, repeating steps S323 to S324 until the maximum iteration number is reached or the network performance function reaches the expected value.

[0049] Step S4 further includes:

[0050] S41: defining the initial load of the node in the intercity public transport network as the node passenger flow intensity, that is, the sum of the passenger flow weights on all edges of the node, denoted as :

[0051] ; ​​​

[0052] Where, is a node Its adjacent nodes The weight of the edge, is a node Initial load;

[0053] S42: The capacity of each node in the intercity public transportation network is defined as the maximum passenger flow carrying capacity, and the node capacity is defined as Expressed as:

[0054] ;

[0055] Where, Represents the maximum capacity of nodes in the network, and are tolerance parameters and are all greater than 0;

[0056] S43: Set passenger flow transfer and load redistribution rules. In the initial attack phase, if the initial node attacked by the disaster exceeds the safety threshold, the node enters a failure state, and its passenger flow will be transferred to other adjacent nodes. In the cascading failure phase, if the load of the adjacent node exceeds the maximum capacity, the adjacent node enters an overload failure state, and its passenger flow is transferred again.

[0057] Among them, in the initial failure stage, when the node When a node fails, it is removed from the network and its load According to the proportion Assigned to non-terminal adjacent nodes , non-terminal adjacent nodes The load is updated to :

[0058] ;

[0059] Where, is the flexible travel ratio; is a node The capacity of the node The ratio of the sum of the capacities of all non-terminal adjacent nodes is expressed as:

[0060] ;

[0061] Where, is a node The set of non-terminal adjacent nodes of For nodes Maximum capacity;

[0062] During the cascading failure process, by comparing the nodes Current load and capacity The size of the update determines whether cascading failure will occur: Exceeding the maximum capacity of the node When the node fails and is removed from the network, With non-terminal adjacent nodes, cascading failures may occur again; if the updated load Exceeding the maximum capacity of the node , but the node There is no adjacent node, or its adjacent nodes are all terminal nodes, the node Removed from the network, cascading failures will stop; if the updated load The maximum capacity of the node is not exceeded , then the node Normal operation will continue and the cascading failure will be terminated.

[0063] Step S5 further comprises:

[0064] S51: Computing Network Connectivity , network connectivity It is the ratio of the number of edges that remain connected after the typhoon to the total number of edges before the disturbance. This indicator is used to reflect the overall structural connectivity level of the network. The formula is as follows:

[0065] ;

[0066] Where, Indicates the total number of initial nodes, Indicates the total number of failed nodes;

[0067] S52: Calculate global efficiency , global efficiency It is the average value of the reciprocal of the shortest path length between all pairs of nodes in the network, and is used to reflect the efficiency of transportation between any two nodes in the network. The formula is as follows:

[0068] ;

[0069] Where, Representation node To Node The shortest path;

[0070] S53: Computing Service Capabilities , service capabilities It is the ratio of the total passenger flow actually transported by the network under the influence of the disaster to the total passenger flow that can be transported in the initial state. It is used to reflect the ability of the network to maintain the transportation task after the disturbance. Its formula is as follows:

[0071] ;

[0072] wherein, denotes the node the traffic flow to the node , denotes the total traffic flow after failure, denotes the traffic flow of the initial network;

[0073] S54: Calculate the service efficiency , the service efficiency is the weighted average of the transport efficiency of all OD pairs, and its formula is as follows:

[0074] ;

[0075] ;

[0076] ;

[0077] wherein, , , and respectively represent the service frequency, travel cost, travel time and travel impedance between and , and is the time average value between two nodes, denotes the average traffic flow per unit time between and ;

[0078] S55: Calculate the robustness value , the robustness value is the ratio of the area surrounded by the performance curve of the system under typhoon disaster attack and the coordinate axis to the area surrounded by the performance curve of the system under normal state and the coordinate axis, which represents the size of the robustness, and its formula is as follows:

[0079] ;

[0080] , ;

[0081] , ;

[0082] wherein, denotes the moment of typhoon attack, denotes the moment of attack start, denotes the moment of attack end, denotes the network performance function, which can be the network connectivity ​, global efficiency , service capacity , and service efficiency . and represent the topological robustness value of the network under typhoon disaster, and represent the functional robustness value of the network under typhoon disaster; and represent the area surrounded by the topological performance curve of the network under typhoon disaster and the coordinate axes; and represent the area surrounded by the topological performance curve of the network under normal circumstances and the coordinate axes; and represent the area surrounded by the functional performance curve of the network under typhoon disaster and the coordinate axes; and represent the area surrounded by the functional performance curve of the network under normal circumstances and the coordinate axes.

[0083] Compared with the prior art, the beneficial effects of the present application are as follows:

[0084] The multi-mode traffic network robustness calculation method under typhoon disaster of the present application can accurately quantify the influence of typhoon disaster on the traffic system; by introducing the cascading failure model, the present application can effectively describe the passenger flow transfer and failure propagation process under typhoon disaster, and is more in line with the actual operation situation. The method can provide theoretical basis and technical support for the planning optimization and emergency dispatch of intercity public transportation network under extreme weather. BRIEF DESCRIPTION OF DRAWINGS

[0085] Figure 1 is a flow chart of the multi-mode traffic network robustness calculation method under typhoon disaster of the present application;

[0086] Figure 2 is a schematic diagram of Batts typhoon meteorological model;

[0087] Figure 3 is a schematic diagram of cascading failure passenger flow transfer and load redistribution;

[0088] Figure 4 is a performance curve diagram of intercity public transportation network under different tolerance parameter , values;

[0089] Figure 5 is a performance curve diagram of intercity public transportation network under different elastic travel proportion values;

[0090] Figure 6 is the robustness value of intercity public transportation network under typhoon disaster. DETAILED DESCRIPTION

[0091] The embodiments of the present application are further described in detail below with reference to the accompanying drawings.

[0092] A multi-mode traffic network robustness calculation method under typhoon disaster, specifically comprising the following steps:

[0093] S1: Construct an intercity public transportation network model containing high-speed rail, general rail, highway passenger transport and other transportation modes, and load the weight attributes of each transportation mode.

[0094] The real network is mapped into a topological network using the complex network modeling method Space L. The intercity public transportation network contains three elements: nodes, edges, and weights, and its representation method is: , contains a highway subnetwork and a railway subnetwork , wherein is a set of topological nodes, including highway passenger stations and railway stations, is a set of topological edges, which is connected when there is direct transportation service between two adjacent stations. For transfer between different transportation modes, considering the distance factor, it is considered that there is transportation connection between different transportation modes in the same county, and a transfer edge is established to form a complete multi-mode transportation network.

[0095] In the edge set, the adjacency matrix of the topological network is defined as , if node is adjacent to node , then , otherwise The distance of the weighted adjacency matrix of the edge is obtained by performing shortest path search in the real network. Other attribute sets of the edge , wherein represents the daily passenger volume from the starting point to the ending point , is the service frequency, is the travel cost, is the travel time. Through the shortest path distribution principle, the passenger flow of all OD pairs will be distributed along the shortest path, and the passenger flow weight of the edge is defined as the sum of the passenger flow of all node pairs passing through the edge.

[0096] S2: Adopt the Batts typhoon meteorological model, combine the space-time dynamic characteristics, generate a typhoon disaster scene, and simulate the spatial and temporal distribution and intensity variation of the typhoon disaster.

[0097] S2.1: Calculate the maximum gradient wind speed The Batts wind field model is to superimpose the gradient wind speed and the moving wind speed in the cyclone, and determine the wind speed value of the point through the position relationship between the typhoon center and the research point. The maximum gradient wind speed can be obtained by the gradient wind equation without considering friction, and the calculation formula is:

[0098] (1);

[0099] (2);

[0100] In the formula, is the maximum gradient wind speed; is the empirical coefficient, which is 6.72; is the central pressure difference (hpa); is the maximum wind speed radius (m); is the earth rotation Coriolis force parameter, with the unit of (s -1 ).

[0101] S2.2: Definition The relationship between The average maximum wind speed of the typhoon appears at the maximum wind speed radius , The statistical fitting relationship between

[0102] (3);

[0103] S2.3: Calculate the 10m height, 10min average maximum wind speed at the research point. It can be represented as the superposition of the maximum gradient wind speed and the central moving speed :

[0104] (4);

[0105] S2.4: Calculate the 10m height, 10min average wind speed at r from the typhoon center . The direction line OM obtained by rotating the moving direction of the typhoon clockwise by 115° is:

[0106] (5);

[0107] In the formula, is the parameter related to the radial intensity attenuation of the typhoon, which is between 0.5 and 0.7.

[0108] S2.5: Calculate the average wind speed at the research point​​ The angle between it and the straight line OM is On the straight line OP, the distance to the typhoon center is The 10-minute average wind speed at a height of 10m at the research point for:

[0109] (6);

[0110] S2.6: Define the pressure decay model. The model assumes that the typhoon's direction of movement does not change after it approaches the coast and makes landfall. The decay of the typhoon's intensity over time is caused by the decrease in the central pressure difference, and its relationship with time is:

[0111] (7);

[0112] Where, is the time the typhoon travels after landing, in units of ; Indicates the typhoon landed after The central air pressure difference corresponding to the moment; It is expressed as the central pressure difference over the sea before the typhoon makes landfall; is the angle between the typhoon path and the coastline, and its size range is .

[0113] S2.7: Define the typhoon continuous impact model. When studying the impact of typhoons on the failure rate of transportation stations, it is necessary to consider the duration of the station's impact by the typhoon disaster in the time dimension, which can be expressed as:

[0114] (8);

[0115] Where, is the typhoon's moving track, The moving speed of the typhoon after making landfall.

[0116] S3: Based on the system vulnerability curve and Monte Carlo simulation method, calculate the failure probability distribution and status of the transportation network under typhoon disasters.

[0117] The intensity of typhoon disaster-causing factors is mainly characterized by wind speed. When wind speed exceeds the safety threshold, some stations will be forced to close for safety reasons, or their connecting lines will be forced to limit speed or even stop operating, directly causing traffic function interruption. In addition, different stations have significant differences in wind resistance due to their location, construction specifications and maintenance conditions, resulting in different probabilities of damage in the same typhoon event. The failure probability model of the transportation network can be described by a vulnerability curve, which usually has a lognormal form:

[0118] (9);

[0119] wherein, is the cumulative distribution function of normal distribution. Due to the lack of detailed information of stations, the present application assumes that each station has the same vulnerability curve. According to the requirements of Highway / Railway Traffic Meteorological Condition Grade, the present application sets the parameters of highway traffic network as = 0.157, = 20.363, and sets the parameters of railway network as = 0.094, = 28.836. This function defines the failure probability of stations in the traffic network under a given typhoon wind speed.

[0120] In order to generate a random failure scenario of traffic stations within the typhoon influence range, the Monte Carlo method is used. Specifically, the total number of iterations is defined, and the iteration number is set to be equal to 1. The state vector of each station is initialized. First, a uniformly distributed random number is generated for each station, and then the failure probability of the station is calculated by comparing with the failure probability of the station . If (i.e., the station fails), then is set. The network performance function, which is the network performance curve after cascading failure in the present application, is calculated. Whether the algorithm ends is determined by judging whether the iteration number or the network performance function reaches the expected value.

[0121] S4: Establish a traffic network cascading failure model to simulate the process of structural and functional loss of traffic network stations and lines under disaster conditions.

[0122] In an intercity public transportation network, due to the complex interconnection between stations and lines, the failure of any link can quickly spread to the entire system, leading to the occurrence of cascading failure phenomenon. The nonlinear load capacity model (LC model) is used to describe the cascading failure phenomenon, and the specific model is represented as follows:

[0123] S4.1: Definition of initial load of node. The initial load describes the load state of each node in the system at the initial time, which is usually based on actual data or empirical estimation. The initial load of the node in the intercity public transportation network is defined as the passenger flow intensity of the node, i.e., the sum of passenger flow weights on all edges of the node, denoted as

[0124] (10).

[0125] wherein, is a node and its adjacent nodes the weight on the edge, is a node the initial load of

[0126] S4.2: Node capacity definition. The maximum capacity of a node describes the maximum carrying capacity of each node in the system, which is the maximum amount of load or service demand that the node can handle, and exceeding this capacity will lead to node failure. The capacity of each node in the intercity public transport network is defined as the maximum passenger flow carrying capacity in this invention. At the same time, according to the LC model, the node capacity is expressed as,

[0127] (11);

[0128] wherein, represents the maximum capacity of the node in the network, and are tolerance parameters and are both greater than 0.

[0129] S4.3: Passenger flow transfer and load redistribution rules.

[0130] In the initial attack stage, if the initial node attacked by the disaster exceeds the safety threshold, it will enter the failure state, and its passenger flow will be transferred to other adjacent nodes. In the cascading failure stage, if the load of the adjacent node exceeds the maximum capacity, the node enters the overload failure state, and its passenger flow is transferred again. The process of passenger flow transfer in these two stages is defined as load redistribution.

[0131] S4.3.1: Passenger flow transfer and load redistribution rules in the initial failure stage. When a node fails, the node is removed from the network, and its load will be redistributed to adjacent nodes . It is worth noting that if a neighboring node is only connected to node , this node is called a terminal node in the network. Among all the adjacent nodes of , in addition to these terminal nodes that are only connected to , other nodes are connected to at least two or more nodes, which are called non-terminal nodes. In fact, when passenger flow is allocated, it will not be transferred to terminal nodes. Therefore, it is defined that in the cascading failure process of highway-railway dual-level network, the load of the failed node will only be redistributed to non-terminal adjacent nodes.

[0132] In fact, since stations with larger capacity can provide more service options, higher transportation efficiency and accommodate larger passenger flows, that is, they have strong passenger service capabilities, when a node fails, passenger flows will tend to be transferred to non-terminal adjacent nodes with larger capacity. After failure, the load is set to be proportional to the Assigned to non-terminal adjacent nodes .here, is a node The capacity of the node The ratio of the sum of the capacities of all non-terminal adjacent nodes is expressed as follows:

[0133] (12);

[0134] Where, is a node The set of non-terminal adjacent nodes.

[0135] In addition, considering that some passengers may choose to cancel their trips when faced with factors such as long alternative route time, complex transfers, increased costs, or reduced travel safety in extreme weather, a flexible travel ratio is introduced. To more realistically reflect post-disaster passenger behavior. A certain proportion of the load, then the non-terminal adjacent node The load is updated to ,Right now:

[0136] (13);

[0137] S4.3.2: Passenger flow transfer and load redistribution rules during cascading failure. Current load and capacity The size of the update determines whether cascading failure will occur: Exceeding the maximum capacity of the node When the node fails and is removed from the network, With non-terminal adjacent nodes, cascading failures may occur again; if the updated load Exceeding the maximum capacity of the node , but the node There is no adjacent node, or its adjacent nodes are all terminal nodes, the node Removed from the network, cascading failures will stop; if the updated load The maximum capacity of the node is not exceeded , then the node Normal operation will continue and the cascading failure will be terminated.

[0138] In fact, when passengers try to transfer from a station to an adjacent station, if the station is saturated and cannot operate, the passengers may choose other modes of transportation or temporarily not travel. Therefore, in the definition of cascading failure, the passenger flow will only be transferred once. The passenger flow from the station will be transferred to Departure, if the site If it also fails, the extra passenger flow will be lost, and the station The extra load on the node will be redistributed to its non-end adjacent nodes.

[0139] S5: Design a transportation network robustness index calculation system to quantify the performance changes of the intercity public transportation network from the perspectives of topology and service functions.

[0140] The present invention proposes an index for characterizing network topology: network connectivity ( ) and global efficiency ( ), and indicators used to measure service capabilities: network service capabilities ( ) and network service efficiency ( ).

[0141] S5.1: Calculate network connectivity ( ). It is defined as the ratio of the number of edges that remain connected after the typhoon to the total number of edges before the disturbance. This indicator reflects the overall structural connectivity level of the network. The formula is as follows:

[0142] (14);

[0143] Where, Indicates the total number of initial nodes, Indicates the total number of failed nodes.

[0144] S5.2: Calculate the global efficiency ( ). It is defined as the average of the reciprocal of the shortest path lengths between all pairs of nodes in the network, reflecting the efficiency of transportation between any two nodes in the network. The formula is as follows:

[0145] (15);

[0146] Where, Representation node To Node The shortest path.

[0147] S5.3: Computing service capabilities ( ). It is defined as the ratio between the total passenger flow actually transported by the network under the influence of a disaster and the total passenger flow that can be transported in the initial state. It reflects the ability of the network to maintain transportation tasks after being disturbed. Its formula is as follows:

[0148] (16);

[0149] Where, Representation node To Node passenger flow, Represents the total passenger flow after the failure, represents the passenger flow of the initial network.

[0150] S5.4: Calculate service efficiency ( ). Transport efficiency weight Defined as the frequency of service Proportional to travel impedance Inversely proportional, It is constructed by "travel time" and "fare". It is defined as the weighted average of the transport efficiency of all OD pairs, and its formula is as follows:

[0151] (17);

[0152] (18);

[0153] (19);

[0154] Where, , , and Respectively and service frequency, travel cost (RMB), travel time (min), and travel impedance (min) between is the average time between two nodes (RMB / h). Here, travel cost refers to the ticket price. express arrive The average passenger flow per unit time.

[0155] S5.5: Calculate the robustness value ( ). Take the performance curve of the system under typhoon disaster attack The ratio of the area enclosed by the coordinate axis to the area enclosed by the performance curve of the system under normal conditions and the coordinate axis represents the robustness. The formula is as follows:

[0156] (20);

[0157] , (21);

[0158] , (22);

[0159] In the formula, represents each attack time of the typhoon, represents an attack starting time, represents an attack ending time, represents a system performance curve, which can be represented by network connectivity , global efficiency , service capacity and service efficiency . and represent a topological robustness value of the network under the typhoon disaster, and represent a functional robustness value of the network under the typhoon disaster; and represent an area surrounded by the topological performance curve of the network under the typhoon disaster and coordinate axes; and represent an area surrounded by the topological performance curve of the network under the normal condition and coordinate axes; and represent an area surrounded by the functional performance curve of the network under the typhoon disaster and coordinate axes; and represent an area surrounded by the functional performance curve of the network under the normal condition and coordinate axes.

[0160] Examples

[0161] Taking the intercity public transportation network of Guangdong Province as an example, the calculation method of the application specifically comprises the following steps:

[0162] S1: constructing a Guangdong intercity public transportation network model comprising high-speed rail, general rail, highway passenger transport and other transportation modes, and loading the weight attributes of each transportation mode.

[0163] Specifically, the physical infrastructure data of the highways and railways in Guangdong Province is obtained by using Baidu Map, and a topological network is constructed by using Space L model, wherein the highway subnet has a total of 124 nodes and 273 edges; the railway subnet has a total of 114 nodes, 129 edges and 106 transfer edges.

[0164] The car commuting information is obtained by using Qunar, and the train commuting information is obtained by using Tuniu, so that the network attribute travel cost , travel time Travel impedance The unit time value index calculated based on the income method , which represents the economic value corresponding to the time loss in the travel process, is defined as follows: , wherein, is the per capita annual income of the county where the node is located (the data is from the Seventh National Census and the Guangdong Statistical Yearbook), is the annual effective working time, which is 1992 hours. The intercity passenger demand data is derived from Baidu migration data, which includes 15252 highway and 15252 railway travel OD pair data. The passenger flow of all OD pairs is distributed along the shortest path to obtain the passenger flow weight of the edge .

[0165] S2: Adopt the Batts typhoon meteorological model, combine the spatial-temporal dynamic characteristics of Typhoon Nida, and generate a typhoon disaster scenario to simulate the spatial and temporal distribution and intensity variation of the typhoon disaster, as shown in Figure 2 .

[0166] Specifically, according to the typhoon information released by the China Weather Network, the path of Typhoon Nida moving is 154.74° with the positive direction of the X-axis, the central pressure of the typhoon is 965 hPa when landing, and the typhoon moves along the straight line at a speed of 25 kilometers per hour. In addition, the central latitude and longitude and the moving speed during the moving process can also be obtained. The wind speed value of each research station at each time is calculated by using the Batts typhoon meteorological model .

[0167] S3: Based on the system vulnerability curve and the Monte Carlo simulation method, the failure probability distribution and state of the traffic network under the typhoon disaster are calculated.

[0168] Specifically, the failure probability value of the station under the corresponding wind speed is obtained according to the vulnerability curve , and the stable failure probability of the station is obtained by simulating 100 times by using the Monte Carlo method and judging whether it is in the failure state.

[0169] S4: A cascading failure model of the traffic network is established to simulate the structure and function loss process of the traffic network stations and lines under disaster conditions.

[0170] S4.1: Calculate the initial load of the node .

[0171] S4.2: Calculate the node capacity .

[0172] S4.3: Determine whether the node is failed according to the passenger flow transfer and load redistribution rules.

[0173] S4.3.1: Initial node failure judgment. As shown in the attached Figure 3 figure, if a node fails, the node is removed from the network, and its load will be proportionally reallocated to adjacent non-terminal adjacent nodes , considering the elastic travel proportion , and the final updated load is .

[0174] S4.3.2: Cascading failure node failure judgment. As shown in the attached Figure 3 figure, by comparing the current load of a node with its capacity , it is determined whether cascading failure will occur: when the updated load exceeds the maximum capacity of the node, the node will fail and be removed from the network. And if the node has non-terminal adjacent nodes, it may cause cascading failure to occur again; if the updated load exceeds the maximum capacity of the node, but the node has no adjacent nodes, or all its adjacent nodes are terminal nodes, the node is removed from the network, and cascading failure will stop; if the updated load does not exceed the maximum capacity of the node, the node will continue to operate normally, and the termination of cascading failure.

[0175] S5: Design a traffic network robustness index calculation system to quantify the performance changes of intercity public transportation networks from the aspects of topological structure and service function.

[0176] Specifically, according to the evolution of the network structure at each perturbation time step, the network connectivity and global efficiency at the corresponding time are calculated. According to the actual passenger flow loss and transfer, the service capacity and network service efficiency at the corresponding time are calculated. In addition, by changing the values of the tolerance parameters and and the elastic travel proportion , performance curves under different combinations (as shown in Figure 4 and Figure 5 ) and overall robustness index values (as shown in​Figure 6 The calculation results can be used to quantitatively evaluate the anti-disturbance capability of the transportation network under different scenarios, providing a decision-making basis for transportation planning, capacity allocation, and emergency management during disasters.

[0177] Example results:

[0178] like Figure 4 As shown in Figure 2, as more nodes fail, the network structure and functional performance curves decrease significantly. Figure 6 The robustness value of the network can be seen, the robustness of the network structure and function is related to the network tolerance parameter and As the parameter value increases, the node capacity increases with the initial load, which makes the network have a stronger carrying capacity when facing external disturbances, effectively suppresses the propagation process of cascading failure, and thus enhances the robustness of the system. Figure 5 and Figure 6 As shown in Figure 2, robustness is also positively correlated with the elastic travel ratio γ. A larger elastic travel ratio γ helps reduce the scale of transferred passenger flow per unit time, alleviates the load pressure of adjacent nodes, and reduces the scope and intensity of cascading failure propagation. Functional robustness index Fluctuations occurred in the later period. and The value leads to a too rapid increase in node capacity, which can effectively cope with local failures in the early stage. However, as the network load increases, the capacity growth is overly concentrated in a few key nodes, causing these nodes to be overloaded and triggering cascading failures. In summary, moderately improving node tolerance and guiding reasonable flexible travel behavior are of positive significance for improving the structural stability and functional sustainability of the intercity public transportation network under typhoon disasters. However, we still need to be vigilant about the critical effects that may be induced by certain intermediate capacity values ​​and the loss of passenger flow caused by excessive abandonment of travel.

[0179] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0180] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A method for calculating the robustness of a multimodal transportation network under typhoon disasters, characterized in that: The method comprises the following steps: S1, build an intercity public transportation network that includes multiple modes of transportation, including high-speed rail, conventional rail, and highway passenger transport, and load the weight attributes of each mode of transportation; S2 uses the Batts typhoon meteorological model, combined with the spatial-temporal dynamic characteristics of typhoon disasters, to generate a pressure decay model and a typhoon continuous impact model to simulate the spatial and temporal distribution and intensity changes of typhoon intensity; S3, combining the pressure decay model and the typhoon continuous impact model, based on the system vulnerability curve and Monte Carlo simulation method, calculates the failure probability distribution and status of the intercity public transportation network under typhoon disasters; S4. Based on the failure probability distribution and status of the intercity public transportation network under typhoon disasters, a transportation network cascading failure model is established to simulate the structural and functional loss process of transportation network stations and lines under disaster conditions; S5. Design a transportation network robustness index calculation system to quantify the performance changes of intercity public transportation networks from the perspectives of topology and service functions; Step S4 further comprises: S41: The initial load of a node in an intercity public transportation network is defined as the node passenger flow intensity, which is the sum of the passenger flow weights of all edges connecting the node. express: ； Where, is a node Its adjacent nodes The weight of the edge, is a node Initial load; n is the node The number of adjacent nodes; S42: The capacity of each node in the intercity public transportation network is defined as the maximum passenger flow carrying capacity, and the node capacity is defined as Expressed as: ； Where, Represents a node in the network The maximum capacity, and are tolerance parameters and are all greater than 0; S43: Set passenger flow transfer and load redistribution rules. In the initial attack phase, if the initial node attacked by the disaster exceeds the safety threshold, the node enters a failure state, and its passenger flow will be transferred to other adjacent nodes. In the cascading failure phase, if the load of the adjacent node exceeds the maximum capacity, the adjacent node enters an overload failure state, and its passenger flow is transferred again. Among them, in the initial failure stage, when the node When a node fails, it is removed from the network and its load According to the proportion Assigned to non-terminal adjacent nodes , non-terminal adjacent nodes The load is updated to : ； Where, is the flexible travel ratio; is a node The capacity of the node The ratio of the sum of the capacities of all non-terminal adjacent nodes is expressed as: ； Where, is a node The set of non-terminal adjacent nodes of For nodes Maximum capacity; In the cascading failure phase, by comparing nodes Current load and capacity The size of the update determines whether cascading failure will occur: Exceeding the maximum capacity of the node When the node fails and is removed from the network, With non-terminal adjacent nodes, cascading failures will occur again; if the updated load Exceeding the maximum capacity of the node , but the node There is no adjacent node or its adjacent nodes are all terminal nodes, then the node Removed from the network, cascading failures stop; if the updated load The maximum capacity of the node is not exceeded , then the node Normal operation will continue and the cascading failure will be terminated.

2. The method for calculating the robustness of a multimodal transportation network under typhoon disasters according to claim 1 is characterized in that: Step S1 further comprises: The complex network modeling method Space L is used to map the real network into a topological network. The generated intercity public transportation network contains three elements: nodes, edges, and weights. Its representation method is as follows: , where Contains road subnetwork and railway subnet ; is a set of topological nodes, including highway passenger stations and railway stations; It is a set of topological edges that connects two adjacent sites when there is direct transportation service between them. For transfers between different modes of transportation, based on districts and counties, there are transport connections between different modes of transportation within the same county, and transfer links are established. To form a complete multimodal transportation network; in the set of edges, the adjacency matrix of the topological network is defined as , if the node With node Adjacent, then ,otherwise , weighted adjacency matrix distance Obtained by searching for the shortest path in a real network; Represents a set of other attributes of the edge, where Represents a slave node To Node The average daily passenger volume, is the service frequency, For travel expenses, is the travel time; through the shortest path allocation principle, the passenger flow of all OD pairs will be allocated along their shortest path. Passenger flow weight It is defined as the sum of the passenger flow of the shortest path between all node pairs passing through the edge.

3. The method for calculating the robustness of a multimodal transportation network under typhoon disasters according to claim 1, characterized in that: Step S2 further comprises: S21: Calculate the maximum gradient wind speed using the friction-neglecting gradient wind equation , the calculation formula is: ； ； Where, is the maximum gradient wind speed; is the empirical coefficient; is the center pressure difference, the unit is hPa; is the maximum wind speed radius, in m; is the Coriolis force parameter of the Earth's rotation, in s -1 ; S22: Definition and The relationship, and The statistical fitting relationship between them is: ； S23: Calculate the average maximum wind speed at 10m above sea level for 10 minutes for: ； Where, Indicates the center moving speed; S24: Calculate the average wind speed at a height of 10m from the typhoon center for 10 minutes; the average wind speed at a height of 10m from the typhoon center for 10 minutes on the direction line OM obtained by rotating the typhoon's moving direction 115 degrees clockwise is for: ； Where, is a parameter related to the radial intensity attenuation of the typhoon; S25: Calculate the average wind speed at the study point ; Among them, the angle with the straight line OM is On the straight line OP, the distance to the typhoon center is The 10-minute average wind speed at a height of 10m at the research point for: ； S26: Define the pressure decay model. The relationship between the central pressure difference and time is: ； Where, is the time the typhoon travels after landing, in units of ; After the typhoon landed The central air pressure difference corresponding to the moment; It indicates the central pressure difference at sea before the typhoon makes landfall; is the angle between the typhoon path and the coastline, and its size range is ; S27: Calculate the duration of the site affected by the typhoon disaster in the time dimension , define the typhoon continuous impact model, expressed as: ； Where, is the typhoon's moving track. The moving speed of the typhoon after making landfall.

4. The method for calculating the robustness of a multimodal transportation network under typhoon disasters according to claim 1, wherein: Step S3 further comprises: S31: The wind speed is represented as the intensity of the typhoon disaster hazard factor. When the wind speed exceeds the safety threshold, the station is closed, and the corresponding connecting line is speed-restricted or even shut down, causing traffic interruption. The fragility curve is used to construct the failure probability model of the intercity public transportation network, and the speed is The failure probability is : ； Where, is the cumulative distribution function of the normal distribution; the corresponding parameters of the highway traffic network are set to =0.157, =20.363; the corresponding parameters for the railway network are set to =0.094, =28.836; S32: Use the Monte Carlo method to generate random failure scenarios for transportation stations within the typhoon impact area; specifically, S321: Define the total number of iterations , the number of iterations Set equal to 1; S322: Initialize the state vector of each station ; S323: For each site Generate a uniformly distributed random number , by comparison and sites Failure probability , Calculated by the failure probability model; if , site Failure, set ; S324: Calculate network performance function ; S325: Iterations Add 1 and repeat steps S323 to S324 until the maximum number of iterations is reached or the network performance function reaches the expected value.

5. The method for calculating the robustness of a multimodal transportation network under typhoon disasters according to claim 1, wherein: Step S5 further comprises: S51: Computing Network Connectivity , network connectivity It is the ratio of the number of edges that remain connected after the typhoon to the total number of edges before the disturbance. This indicator is used to reflect the overall structural connectivity level of the network. The formula is as follows: ； Where, Indicates the total number of initial nodes, Indicates the total number of failed nodes; S52: Calculate global efficiency , global efficiency It is the average value of the reciprocal of the shortest path length between all pairs of nodes in the network, and is used to reflect the efficiency of transportation between any two nodes in the network. The formula is as follows: ； Where, Representation node To Node The shortest path; S53: Computing Service Capabilities , service capabilities It is the ratio of the total passenger flow actually transported by the network under the influence of the disaster to the total passenger flow that can be transported in the initial state. It is used to reflect the ability of the network to maintain the transportation task after the disturbance. Its formula is as follows: ； Where, Representation node To Node passenger flow, Represents the total passenger flow after the failure, represents the passenger flow of the initial network; S54: Calculating service efficiency , service efficiency is the weighted average of the transport efficiency of all OD pairs, and its formula is as follows: ； ； ； Where, 、 、 and Represents nodes respectively and nodes service frequency, travel cost, travel time, and travel impedance between is the average time between two nodes, Representation node To Node Average passenger flow per unit time; S55: Calculate robustness value , robustness value Performance curve of the system under typhoon disaster attack The ratio of the area enclosed by the coordinate axis to the area enclosed by the performance curve of the system under normal conditions and the coordinate axis represents the robustness. The formula is as follows: ； , ； , ； Where, Indicates the time when the typhoon will strike. Indicates the time when the attack starts. Indicates the moment the attack ends; Represents network performance function, using network connectivity , global efficiency , service capabilities and service efficiency express; and represents the topological robustness value of the network under typhoon disaster, and represents the functional robustness value of the network under typhoon disaster; and The area enclosed by the topological performance curve of the network under typhoon disaster and the coordinate axis; and It represents the area enclosed by the topological performance curve of the network and the coordinate axis under normal circumstances; and It represents the area enclosed by the network's functional performance curve and the coordinate axis under typhoon disasters; and It represents the area enclosed by the network's functional performance curve and the coordinate axis under normal circumstances.

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