CN-122001689-A - Subway network toughness assessment method and device

CN122001689ACN 122001689 ACN122001689 ACN 122001689ACN-122001689-A

Abstract

The invention discloses a subway network toughness assessment method and device, and relates to the technical field of traffic toughness assessment. A subway network toughness assessment method comprises the steps of constructing a directional weighted network model of a subway network according to subway stations and running routes, determining subway network variable indexes according to the directional weighted network model, carrying out node initial load distribution of the directional weighted network model according to the subway network variable indexes, carrying out iterative attack on the directional weighted network model distributed with initial loads, carrying out redistribution on node loads after each attack, calculating subway network efficiency after each attack according to redistribution results, and assessing subway network toughness according to the subway network efficiency after each attack. The method and the system can accurately identify the key nodes in the network, the network toughness assessment result is more comprehensive and reliable, and the operation efficiency and the management level of the subway network are improved.

Inventors

DU CHUNHUI
GUO DONGJUN
WU YANHUA
LI JINGZHUO
GUO YALING

Assignees

中国人民解放军陆军工程大学

Dates

Publication Date: 20260508
Application Date: 20260409

Claims (10)

1. The subway network toughness assessment method is characterized by comprising the following steps of: constructing a directional weighted network model of the subway network according to the subway station and the operation route; Determining subway network variable indexes according to the directed weighted network model, and performing node initial load distribution of the directed weighted network model according to the subway network variable indexes; Performing iterative attack on the directional weighted network model distributed with the initial load, performing reallocation on the node load after each attack, and calculating subway network efficiency after each attack according to a reallocation result; and evaluating the toughness of the subway network according to the subway network efficiency after each attack.
2. The subway network toughness evaluation method according to claim 1, wherein in the directed weighted network model, subway stations are taken as nodes, running routes are taken as edges, and edges are added between the nodes corresponding to the transfer stations; The weight of the edge is a composite function value of the passenger flow volume and the traffic capacity between the nodes, wherein the composite function value increases along with the increase of the passenger flow volume and decreases along with the increase of the traffic capacity.
3. The subway network toughness assessment method according to claim 1, wherein the subway network variable indexes comprise centrality, medium centrality, near centrality, feature vector centrality, transfer station score, geographic centrality, neighbor importance and line intersection; Said degree of centrality The calculation formula of (2) is as follows: ; in the formula, Degree for node i; Is the total number of nodes; Said mesogenic properties The calculation formula of (2) is as follows: ; in the formula, From node s to node Is the shortest path total number of (a); the shortest path number passing through the node i; The proximity centrality The calculation formula of (2) is as follows: ; in the formula, Is a node To the node Is the shortest path length of (a); The calculation formula of the characteristic vector centrality is as follows: ; in the formula, Is a directed weighted network adjacency matrix; Is that Is the maximum eigenvalue of (2); Is the feature vector corresponding to the maximum feature value, the components thereof I.e. the node Is characterized by the feature vector centrality of (1); Solving eigenvector approximation by adopting a power iteration method: ; in the formula, Is the first The feature vector approximation at the time of the iteration, Is the first The eigenvector approximation value in the next iteration, the eigenvector corresponding to the maximum eigenvalue is obtained after the iteration is converged, Is the euclidean norm; Said geographic centrality According to the exponential decay function, the calculation formula is: ; in the formula, As the center point Weights of (2); Is a node To the central point Is a geographic distance of (2); is the attenuation coefficient; the number of the central points is the geographic coordinates of a main passenger flow distribution center determined according to the urban overall planning; Wherein the geographic distance Based on the calculation of the earth spherical model, the calculation formula is as follows: ; ; ; in the formula, And Respectively nodes And a center point Is a function of the latitude of (1), Is a node And a center point The difference in altitude between the two; Is a node And a center point Longitude differences; Is the earth radius; Is an intermediate variable; Is a node And a center point A spherical center angle therebetween; The neighbor importance is obtained by calculating the centrality of all neighbor nodes of the node; The line intersection is the number of subway operation lines through which the node passes; The transfer station score Scoring according to degree Known transfer station scoring Scoring of line intersection Clustering scoring And neighbor importance scoring Obtaining: ; The degree score is calculated according to the degree of the transfer station: ; the known transfer station scores are obtained according to transfer station information predefined in a subway network; The line intersection score is the number of subway operation lines passing through the transfer station; the neighbor importance scores are obtained by calculating the degree centrality of all neighbor nodes of the transfer station; the calculation formula of the cluster score is as follows: ; in the formula, Is a node The number of edges present between neighboring nodes.
4. A method of assessing toughness of a metro network as claimed in claim 3 wherein the node initial load distribution of the directionally weighted network model is based on metro network variable indicators, comprising: calculating node importance according to subway network variable indexes; calculating node initial load according to node importance and initial load coefficient; calculating a load difference coefficient according to the maximum initial load of the node and the minimum initial load of the node; If the load difference coefficient is larger than the threshold value, amplifying initial loads corresponding to the first X nodes, and taking the amplified initial loads as final initial loads of the first X nodes, wherein the first X nodes are the first X nodes of node importance ordering.
5. The subway network toughness assessment method according to claim 4, wherein the calculation formula of the node importance is: ; in the formula, Is a node Is of importance of (2); Is the first Weights of the individual variable indicators; Is normalized to the first A variable index; Is the total number of variable indexes; the node initial load is obtained by multiplying the node importance by an initial load coefficient; the load difference coefficient The calculation formula of (2) is as follows: ; in the formula, The maximum initial load of the node is set; the minimum initial load for the node.
6. The subway network toughness evaluation method according to claim 1, wherein performing iterative attack on the directional weighted network model to which the initial load is allocated, performing redistribution on the node load after each attack, and calculating subway network efficiency after each attack according to the redistribution result, includes: The method comprises the steps of carrying out attack on a directional weighted network model distributed with initial loads, carrying out once iteration, attacking nodes in the directional weighted network to disable the nodes, carrying out redistribution on loads of disabled nodes, and calculating node loads and node capacities after redistribution; checking whether the node load after the redistribution is overloaded or not, and redistributing the node load with the overload load until all the node loads are normal, so as to obtain a redistributing result; And calculating subway network efficiency after each attack according to the reassignment result.
7. The subway network toughness assessment method according to claim 6, wherein the load redistribution process of the failed node is that the load of the failed node is proportionally distributed to the neighbor nodes, and the load redistribution calculation formula is as follows: ; in the formula, Is a neighbor node Increased load; the load is redistributed in proportion; Is a failure node Is a load of (2); Is a failure node Active neighbor number of (a); the process judgment formula for checking whether the node load after reassignment is overloaded is as follows: ; in the formula, Is a node Is a load of (2); Is a node Is a capacity of (2); ; in the formula, Is a node Is set to the initial load of (1); Is the node capacity coefficient; and when the node fails due to the fact that the load exceeds the capacity, continuing the load reassignment process for the node with overload load until all the nodes are loaded normally, and obtaining reassignment results.
8. The subway network toughness evaluation method according to claim 6, wherein the calculation formula of the subway network efficiency is; ; in the formula, Network efficiency for the attack step t; And Is a time-varying weight; The number of edges in the directional weighting network for the step t of attack; To attack step t number of network active nodes; the average path length of the directional weighted network in the step t is attacked; adjusting the coefficient for the path efficiency; the time-varying weight adjustment formula is: ; ; ; in the formula, Is a critical attack step threshold; The total number of steps for the attack.
9. The subway network toughness evaluation method according to claim 8, wherein the process of evaluating the subway network toughness is: measuring the dynamic efficiency toughness of the subway network according to a robustness index, wherein the robustness index is obtained through parameter sensitivity analysis, and the parameter sensitivity analysis process is as follows: ; in the formula, As a coefficient of capacity of the node, Is that Is used for the discrete value points of the (a), Is that Discrete number of points of value; the proportion is redistributed for the load, Is that Is used for the discrete value points of the (a), Is that Discrete number of points of value; the robust response matrix is expressed as: ; in the formula, As node capacity coefficient The first of (3) The number of the value points is one, Re-distribution of ratios for loads The first of (3) A plurality of value points; ; ; As a robustness evaluation function, a robustness response matrix element Is a combination of parameters The robustness index obtained by the calculation is calculated; By indexing robustness Structural vulnerability penalty factor And parameter optimized gain factor Multiplying together to obtain subway network toughness score : ; ; ; ; ; In the formula, And Variance of degree centrality and medium centrality, respectively; the coefficient of the key which is the importance of the node; The number of nodes is the maximum cascade failure of the network; Is the total number of nodes; Is the critical attack proportion; The attack step number when the network efficiency is reduced to 50%; And The robustness index at the optimal and worst parameter combination, respectively.
10. The utility model provides a subway network toughness evaluation device which characterized in that includes: The network construction module is used for constructing a directional weighted network model of the subway network according to the subway station and the running route; The toughness evaluation module is used for determining subway network variable indexes according to the directed weighted network model and carrying out node initial load distribution of the directed weighted network model according to the subway network variable indexes; Performing iterative attack on the directional weighted network model distributed with the initial load, performing reallocation on the node load after each attack, and calculating subway network efficiency after each attack according to a reallocation result; and evaluating the toughness of the subway network according to the subway network efficiency after each attack.

Description

Subway network toughness assessment method and device Technical Field The invention relates to a subway network toughness assessment method and device, and belongs to the technical field of traffic toughness assessment. Background The subway is a backbone part of an urban comprehensive traffic system and plays an irreplaceable role in improving urban toughness. Along with the rapid development of cities, subway construction is also paid more and more attention, subway networking operation safety is also paid more attention, and how to cope with risks and external intervention becomes a problem to be solved urgently. In extreme cases such as war or emergencies, the survivability of the subway system is directly related to the emergency response capability of the city and the life safety of residents. Therefore, the deep research on the subway network survivability not only has theoretical significance, but also has important practical application value. Currently, the technology for evaluating the toughness of a subway network is limited to analysis of a static topological structure, for example, indexes such as degree and medium number based on graph theory. Although the method can reflect the inherent structural attribute of the network, the method has the main defects that the dynamic distribution and transfer of the passenger flow in the real scene cannot be effectively simulated, the nonlinear failure mechanism after node overload is difficult to quantify, and the linkage effect of failure event propagation in the network cannot be captured. Therefore, the traditional evaluation result and the actual response behavior of the subway system under the extreme working condition have larger access, and it is difficult to provide accurate quantitative basis for the formulation of the toughness improvement strategy. Disclosure of Invention The invention aims to provide a subway network toughness assessment method and device, which are used for respectively simulating the running conditions of a subway network under two different attack modes, namely random attack and intentional attack, by establishing a reasonable subway network model and applying a complex network cascade failure theory, carrying out toughness assessment on the subway network, identifying and preferentially reinforcing inherent weak points in the network, and realizing the planning and design optimization of 'toughness guidance'. In order to achieve the above purpose, the invention is realized by adopting the following technical scheme. In one aspect, the invention provides a subway network toughness assessment method, which comprises the following steps: constructing a directional weighted network model of the subway network according to the subway station and the operation route; Determining subway network variable indexes according to the directed weighted network model, and performing node initial load distribution of the directed weighted network model according to the subway network variable indexes; Performing iterative attack on the directional weighted network model distributed with the initial load, performing reallocation on the node load after each attack, and calculating subway network efficiency after each attack according to a reallocation result; and evaluating the toughness of the subway network according to the subway network efficiency after each attack. Optionally, in the directional weighted network model, subway stations are taken as nodes, running routes are taken as edges, and edges are added between the nodes corresponding to the transfer stations; The weight of the edge is a composite function value of the passenger flow volume and the traffic capacity between the nodes, wherein the composite function value increases along with the increase of the passenger flow volume and decreases along with the increase of the traffic capacity. Optionally, the subway network variable indexes comprise centrality, medium centrality, near centrality, feature vector centrality, transfer station score, geographic centrality, neighbor importance and line intersection; Said degree of centrality The calculation formula of (2) is as follows: ; in the formula, Degree for node i; Is the total number of nodes; Said mesogenic properties The calculation formula of (2) is as follows: ; in the formula, From node s to nodeIs the shortest path total number of (a); the shortest path number passing through the node i; The proximity centrality The calculation formula of (2) is as follows: ; in the formula, Is a nodeTo the nodeIs the shortest path length of (a); The calculation formula of the characteristic vector centrality is as follows: ; in the formula, Is a directed weighted network adjacency matrix; Is that Is the maximum eigenvalue of (2); Is the feature vector corresponding to the maximum feature value, the components thereof I.e. the nodeIs characterized by the feature vector centrality of (1); Solving eigenvector approximation by adopting a