Multi-mode traffic network robustness calculation method under typhoon disaster

Abstract

The invention discloses a multi-mode traffic network robustness calculation method under typhoon disasters. The multi-mode traffic network robustness calculation method comprises the following steps: constructing an inter-city public traffic network comprising a plurality of traffic modes; combining the space-time dynamic characteristics of the typhoon disaster to generate an air pressure attenuation model and a typhoon continuous influence model; based on a system vulnerability curve and a Monte Carlo simulation method, calculating failure probability distribution and state of the inter-city public transport network under typhoon disasters; establishing a traffic network cascade failure model according to the failure probability distribution and state of the inter-city public traffic network under the typhoon disaster, and simulating the structure and function loss process of traffic network sites and lines under the disaster condition; and designing a traffic network robustness index calculation system, and quantifying the performance change of the inter-city public traffic network from two aspects of a topological structure and a service function. The influence of typhoon disasters on the traffic system can be accurately quantified.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic management, and in particular to a method for calculating the robustness of a multi-mode traffic network under typhoon disasters. Background Art

[0002] The intercity public transportation network is characterized by large scale, high temporal and spatial concentration, and sparse departure frequency. It is more vulnerable to large-scale and high-intensity extreme meteorological disasters such as typhoons.

[0003] The impact of typhoon disasters on the transportation system has multi-level and multi-type characteristics. Its direct impacts include infrastructure damage, road closures, railway suspensions, etc. caused by extreme weather such as strong winds and heavy rains, which seriously disrupt the order of traffic operation. Even more complicated is the indirect impact. The interruption of some hubs or lines will trigger a large-scale transfer of passenger flow, resulting in overload of alternative paths, network imbalance and even triggering cascading failures. The Chinese patent "A Method for Establishing a Cascading Failure Model for Rail Transit Networks" with publication number CN116090687A proposes a cascading failure model for rail transit networks. However, it assumes that passengers are completely rational and that passenger flow will be transferred to feasible paths. It ignores the passengers' willingness to cancel or delay travel under typhoon disasters, and it is difficult to accurately reflect the actual process of passenger flow redistribution under disasters.

[0004] Prior art has disclosed a method for assessing the resilience of urban distribution networks and implementing preventive measures to protect them from typhoons. This method uses the BATTS model to assess the resilience of urban distribution networks under typhoon conditions. However, unlike transportation networks, urban distribution networks have relatively fixed points and lack passenger flow. Furthermore, the failure probability measures for distribution and transportation networks differ, making this method difficult to apply to transportation networks.

[0005] Currently, methods for calculating the robustness of transportation networks during typhoon disasters primarily focus on single-mode transportation networks, ignoring the cascading failure effects caused by cross-modal passenger flow shifts in disaster scenarios and failing to fully consider the network heterogeneity and functional differences between different modes. Furthermore, most studies use static or simplified attack methods to simulate typhoon processes, which makes it difficult to reflect the complex evolution of typhoon disasters and ignores key characteristics such as typhoon movement paths, impact ranges, duration, and intensity variations. Furthermore, existing robustness calculation methods often focus on structural indicators and lack a functional description of service capacity and transportation efficiency, making it difficult to comprehensively assess the robustness of networks during disasters. Summary of the Invention

[0006] The purpose of this invention is to propose a method for calculating the robustness of a multimodal transportation network under typhoon disasters, so as to measure the impact and robustness of a specific typhoon disaster on the intercity public transportation system.

[0007] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0008] A method for calculating the robustness of a multimodal transportation network under typhoon disasters, the method comprising the following steps:

[0009] 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;

[0010] 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;

[0011] 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;

[0012] 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;

[0013] S5. Design a transportation network robustness index calculation system to quantify the performance changes of the intercity public transportation network from the perspectives 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 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.

[0016] 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 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: 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:

[0028] ;

[0029] Where, is a parameter related to the radial attenuation of the typhoon;

[0030] 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:

[0031] ;

[0032] S26: Define the pressure decay model. The relationship between the central pressure difference and time is:

[0033] ;

[0034] 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 ;

[0035] S27: Calculate the duration of the site affected by the typhoon disaster in the time dimension and define the typhoon continuous impact model, which is expressed as:

[0036] ;

[0037] Where, is the typhoon's moving track. The moving speed of the typhoon after making landfall.

[0038] Step S3 further comprises:

[0039] 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.

[0040] The fragility curve is used to construct the failure probability model of the intercity public transportation network, with a speed of The failure probability is :

[0041] ;

[0042] 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;

[0043] S32: Use the Monte Carlo method to generate random failure scenarios for transportation stations within the typhoon impact area; specifically,

[0044] S321: Define the total number of iterations , the number of iterations Set to equal 1;

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

[0046] S323: Generate a uniformly distributed random number for each site , by comparison and sites Failure probability , Calculated by the failure probability model. , site Failure, set ;

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

[0048] 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.

[0049] Step S4 further comprises:

[0050] 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:

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

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

[0074] ;

[0075] ;

[0076] ;

[0077] Where, , , and Respectively and service frequency, travel cost, travel time, and travel impedance between is the average time between two nodes, express arrive The average passenger flow per unit time;

[0078] 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:

[0079] ;

[0080] , ;

[0081] , ;

[0082] Where, Indicates the time when the typhoon hits. Indicates the time when the attack starts. Indicates the time when the attack ends. Represents the network performance function, which can be expressed as 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.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] This method for calculating the robustness of multimodal transportation networks during typhoon disasters accurately quantifies the impact of typhoons on transportation systems. By introducing a cascading failure model, it effectively describes the passenger flow shift and failure propagation processes during typhoon disasters, more accurately reflecting actual operational scenarios. This method can provide theoretical basis and technical support for the planning, optimization, and emergency dispatch of intercity public transportation networks during extreme weather conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 This is a flow chart of a method for calculating the robustness of a multi-modal transportation network under typhoon disasters according to the present invention;

[0086] Figure 2 This is a schematic diagram of the Batts typhoon weather model;

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

[0088] Figure 4 are different tolerance parameters 、 Performance curve of intercity public transportation network under different values;

[0089] Figure 5 The proportion of different flexible travel Performance curve of intercity public transportation network under different values;

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

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

[0092] A method for calculating the robustness of a multimodal transportation network under typhoon disasters specifically includes the following steps:

[0093] S1: Construct an intercity public transportation network model that includes multiple transportation modes such as high-speed rail, conventional rail, and highway passenger transport, and load the weight attributes of each transportation mode.

[0094] The complex network modeling method Space L is used to map the real network into a topological network. The intercity public transportation network consists of three elements: nodes, edges, and weights. Its representation method is as follows: , Contains road subnetwork and railway subnet ,in is a set of topological nodes, including highway passenger stations and railway stations, It is a topological edge set that satisfies the need to establish a connection when there is a direct transportation service between two adjacent stations. For transfers between different modes of transportation, considering the distance factor, it is considered that there are transportation connections between different modes of transportation in the same county, and a transfer edge is established. To form a complete multimodal transportation network.

[0095] In the set of edges, the adjacency matrix of the topological network is defined as , if the node With node Adjacent, then ,otherwise , its weighted adjacency matrix distance It is obtained by searching for the shortest path in a real network. ,in Indicates starting point To the end The average daily passenger volume, is the service frequency, For travel expenses, is the travel time. According to 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.

[0096] S2: The Batts typhoon meteorological model is used in combination with spatial-temporal dynamic characteristics to generate typhoon disaster scenarios to simulate the spatial and temporal distribution and intensity changes of typhoon disasters.

[0097] S2.1: Calculate the maximum gradient wind speed The Batts wind field model superimposes the gradient wind speed and moving wind speed in the cyclone, and determines the wind speed value at the point through the positional 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. The calculation formula is:

[0098] (1);

[0099] (2);

[0100] Where, is the maximum gradient wind speed; is the empirical coefficient, with a value of 6.72; is the center pressure difference (hPa); is the maximum wind speed radius (m); is the Coriolis force parameter of the Earth's rotation, unit is (s -1 ).

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

[0102] (3);

[0103] S2.3: Calculate the 10-minute average maximum wind speed at a height of 10 m above sea level. Can be expressed as the maximum gradient wind speed and center moving speed The superposition of:

[0104] (4);

[0105] S2.4: Calculate the average wind speed at a height of 10 m from the typhoon center over 10 minutes. The direction line OM obtained by rotating the typhoon's moving direction 115° clockwise is the distance from the typhoon center r. for:

[0106] (5);

[0107] Where, It is a parameter related to the radial attenuation of the typhoon's intensity, and its value ranges from 0.5 to 0.7.

[0108] S2.5: Calculate the average wind speed at the study 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] Where, is the cumulative distribution function of the normal distribution. Due to the lack of detailed information on the site, the present invention assumes that each site has the same vulnerability curve. According to the requirements of the "Highway / Railway Traffic Meteorological Condition Level", the present invention sets the parameters of the highway traffic network to =0.157, =20.363, set the parameters of the railway network to =0.094, =28.836. This function specifies the failure probability of a station in the transportation network under a given typhoon wind speed.

[0120] In order to generate random failure scenarios of traffic stations within the typhoon impact area, the Monte Carlo method is used. Specifically, it includes: defining the total number of iterations , the number of iterations Set to 1. Initialize the state vector of each station First, generate a uniformly distributed random number for each site , and secondly, by comparing and sites Failure probability , Calculated by the failure probability model. (i.e. site Failure), then set Calculate the network performance function, which in this invention is the network performance curve after cascade failure. Determine whether the algorithm ends by judging whether the number of iterations or the network performance function reaches the expected value.

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

[0122] In intercity public transportation networks, due to the complex interconnectedness of stations and lines, a failure in any link can quickly spread to the entire system, leading to cascading failures. The nonlinear load-capacity model (LC model) is used to describe cascading failures. The specific model is expressed as follows:

[0123] S4.1: Definition of initial node load. The initial load describes the load status of each node in the system at the initial moment, which is usually estimated based on actual data or experience. This paper defines the initial load of a node in an intercity public transportation network as the node passenger flow intensity, that is, the sum of the passenger flow weights of all the edges connecting the node, and uses express:

[0124] (10);

[0125] Where, is a node Its adjacent nodes The weight of the edge, is a node initial load.

[0126] S4.2: Node capacity definition. The maximum capacity of a node describes the maximum carrying capacity of each node in the system. This is the maximum load or service demand that the node can handle. Exceeding this capacity will cause the node to fail. This invention defines the capacity of each node in the intercity public transportation network as the maximum passenger flow carrying capacity. At the same time, according to the LC model, the node capacity Expressed as,

[0127] (11);

[0128] Where, Represents the maximum capacity of nodes in the network, and are tolerance parameters and are all greater than 0.

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

[0130] In the initial attack phase, if the initial node under attack exceeds the safety threshold, it enters a failure state, and its passenger flow is transferred to other adjacent nodes. In the cascading failure phase, if the load of adjacent nodes exceeds the maximum capacity, the node enters an overload failure state, and its passenger flow is again transferred. The process of passenger flow transfer in these two phases is defined as load redistribution.

[0131] S4.3.1: Passenger flow transfer and load redistribution rules during the initial failure phase. When a node fails, it is removed from the network and its load will be reallocated to adjacent nodes It is worth noting that if an adjacent node is only connected to node If the node is connected to the other node, it is called the end node in the network. Among all the adjacent nodes, except for those that are only connected to Aside from the connected terminal nodes, all other nodes are connected to at least two or more nodes; these nodes are called non-terminal nodes. In practice, passenger flow is not transferred to terminal nodes during passenger flow redistribution. Therefore, in a cascading failure process defined in a road-rail dual-layer network, the load of a failed node is redistributed only to adjacent non-terminal 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 a certain ratio 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] , (twenty one);

[0158] , (twenty two);

[0159] Where, Indicates every attack moment of the typhoon, Indicates the time when the attack starts. Indicates the time when the attack ends. To represent the system performance curve, network connectivity can be used , 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 shows 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.

[0160] Examples

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

[0162] S1: Construct an intercity public transportation network model for Guangdong Province that includes multiple transportation modes such as high-speed rail, conventional rail, and highway passenger transport, and load the weight attributes of each transportation mode.

[0163] Specifically, Baidu Maps was used to obtain the physical infrastructure data of roads and railways in Guangdong Province, and the Space L model was used to construct a topological network. The road 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] Use Ctrip.com to obtain car commuting information and use Niu.com to obtain train commuting information, so as to calculate the network attribute travel cost. , travel time and travel impedance Unit time value indicator calculated based on the income method , represents the economic value corresponding to the time loss during the trip, and is defined as follows: ,in, For nodes The per capita annual income of the district or county where the applicant is located (data source: the Seventh National Population Census and Guangdong Provincial Statistical Yearbook), The effective working time is 1992 hours per year. The intercity passenger transport demand data comes from Baidu migration data, and a total of 15252 road and 15252 railway travel OD pairs are obtained. The passenger flow of all OD pairs will be distributed along their shortest path to obtain the edge Passenger flow weight .

[0165] S2: Using the Batts typhoon meteorological model and combining the spatial-temporal dynamic characteristics of Typhoon Nida, a typhoon disaster scenario is generated to simulate the spatial and temporal distribution and intensity changes of typhoon disasters, such as Figure 2 As shown,

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

[0167] 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.

[0168] Specifically, the site is obtained according to the vulnerability curve Failure probability value corresponding to wind speed ,The Monte Carlo method is used to simulate 100 times to obtain the stable failure probability of the site and determine whether it is in a failure state.

[0169] S4: Establish a transportation network cascading failure model to simulate the structural and functional loss process of transportation network stations and lines under disaster conditions.

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

[0171] S4.2: Calculate node capacity .

[0172] S4.3: Determine whether a node is failed based on passenger flow transfer and load redistribution rules.

[0173] S4.3.1: Initial node failure judgment. Figure 3 As shown, if the node When a node fails, it is removed from the network and its load Will be in proportion Reassigned to adjacent non-terminal neighbor nodes , considering the flexible travel ratio ,final The updated load is .

[0174] S4.3.2: Cascading failure node failure judgment. Figure 3 As shown, 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, it will be deleted 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.

[0175] 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.

[0176] Specifically, according to the evolution of the network structure at each perturbation time step, the network connectivity at the corresponding moment is calculated ( ) and global efficiency ( ). According to the actual passenger flow loss and transfer, the service capacity at the corresponding time is calculated ( ) and network service efficiency ( In addition, by changing the tolerance parameter and and flexible travel ratio The performance curves under different combinations are plotted (e.g. Figure 4 and Figure 5 ) and the overall robustness index value (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 elastic 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 effect that certain intermediate capacity values ​​may induce and the passenger flow loss 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 the intercity public transportation network from the perspectives of topological structure and service function.

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 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, with a speed of 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 to equal 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 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.

6. The method for calculating the robustness of a multimodal transportation network under typhoon disasters according to claim 1, characterized in that: 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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