A method for measuring urban road network resilience under multi-layer transportation network dependence

Abstract

The present invention discloses a method for measuring the resilience of an urban road network under the dependence of a multi-layer transportation network, including the following steps: collecting spatial vector data of urban roads, subways and bus networks; mapping data of different spatial layers into a multi-layer network model composed of nodes and edges; gradually removing road network edges and other transportation network lines connected thereto; drawing a relationship curve between the road network structure index and the removal ratio under the support of the remaining different transportation layer network connections, and comparing the phase change threshold and disaster bearing capacity change of the spatial structure of the road network under the support of different transportation layer networks. The present invention constructs an interconnection model and a resilience measurement model of road networks and other multi-layer transportation networks, which can reveal the complex mechanism of mutual support and destruction propagation between road networks and transportation networks, identify the key thresholds and important areas of road spatial structure changes under the support of multi-layer transportation, and provide technical tools for accurately measuring the resilience of urban road networks.

Description

Technical Field

[0001] The present invention relates to the research field of urban road network resilience, and in particular to a method for measuring urban road network resilience under multi-layer traffic network dependence. Background Art

[0002] Today's cities have been facing various external and internal shocks and risks, including natural disasters and man-made disasters, which will pose a great threat to urban operations and residents' lives. This also makes it particularly important to conduct resilience assessments on various urban systems. As the core dimension of the urban spatial system, the road network plays a key role in supporting the flow and daily operation of various elements. Conducting resilience measurement and assessment on it is conducive to understanding the disaster resistance level and resilience characteristics of the road network in advance, and is convenient for supporting urban planning to carry out practical work to improve the resilience level.

[0003] The study of urban road network resilience has gradually shifted from simple static qualitative descriptions to modeling of dynamic disturbance processes. Among them, there have been studies on disturbance simulations for road networks, subway networks, etc. to evaluate resilience, but the main research objects are concentrated on the physical structure of a single network, lacking flow modeling of network dependence. In fact, there are cascading effects both within and between networks (for example, local power grid failures cause other areas to be overloaded and thus cause the entire network to be paralyzed, and floods that submerge roads will also affect the power supply system), which makes it difficult for existing resilience assessment methods for road networks to accurately portray the true network evolution characteristics.

[0004] Therefore, a more comprehensive and effective technical method for measuring road network resilience is urgently needed. The multi-layer network propagation mechanism is consistent with the complex role of multi-system coupling in the city, and the network interdependence and interaction it embodies is a mapping of the real urban system. By modeling multiple key spatial network layers in the city, the impact of complex network dependencies on resilience in attack scenarios can be simulated to explore the measurement and mechanism analysis of urban road network resilience supported by multi-layer networks. However, there is currently no method to analyze road network resilience from the perspective of multi-layer transportation networks. Summary of the invention

[0005] In view of the above problems existing in the prior art, the present invention provides a method for measuring the resilience of an urban road network under the reliance on a multi-layer transportation network. The data of the urban road network, subway network and bus network are first transformed into a three-layer topological network diagram, and then the roads and the buses and subways connected to them are gradually removed from the diagram to analyze the changes in indicators such as the maximum connected subgraph scale of the road network, network efficiency and the Gini coefficient of the betweenness centrality. The present invention can reveal the complex mechanism of mutual support and destruction propagation between road networks and transportation networks, identify the key thresholds and important areas of changes in road space structure under multi-layer transportation support, and provide a quantitative measurement method for resilience on an urban road network under the reliance on a multi-layer transportation network, providing a technical tool for accurately measuring the resilience of a road space network.

[0006] The technical solution of the present invention is as follows:

[0007] A method for measuring the resilience of an urban road network under multi-layer traffic network dependence comprises the following steps:

[0008] S1. Collect different spatial layer data of roads, subways and buses above the branch level, which are called road layer raw data, subway layer raw data and bus layer raw data respectively;

[0009] S2, preprocessing the original data of the road layer, the original data of the subway layer and the original data of the bus layer, specifically as follows: preprocessing the original data of the road layer into the data of the road centerline, called the road layer data; preprocessing the original data of the subway layer into the data of the subway one-way line, called the subway layer data; preprocessing the original data of the bus layer into the data of the bus one-way line, called the bus layer data;

[0010] S3, mapping the road layer data, subway layer data and bus layer data into a multi-layer network topology model consisting of nodes and edges respectively. The specific steps are as follows:

[0011] S3-1. Map the road intersections in the road layer data into nodes to obtain a set V Road ; Map the road segments to edges and get the set E Road ; The travel time of the road segment is taken as E Road The weights of the edges are used to construct the road weighted adjacency matrix A Road , forming a weighted undirected graph G Road (V Road ,E Road ), called the road network graph;

[0012] S3-2. Map the subway stations in the subway layer data into nodes to obtain the set V Subway ; Map the subway line segments to edges and get the set E Subway ; The travel time of the subway line section is taken as E SubwayThe weights of the edges are used to construct the subway weighted adjacency matrix A Subway , forming a weighted undirected graph G Subway (V Subway ,E Subway ), called the subway network diagram;

[0013] S3-3. Connect the road network diagram and the subway network diagram according to the following rules to form G Road+Subway Two-layer topology network diagram:

[0014] (1-1) The road intersections and subway stations are used as connecting nodes of the road network graph and the subway network graph respectively;

[0015] (1-2) If there is a subway station within a 100m range centered on the road intersection, a connection relationship between the two is established as a connecting edge between the road network graph and the subway network graph;

[0016] S3-4, map the bus stops of the bus layer data into nodes to obtain the set V Bus ; Map bus line segments to edges and get set E Bus ; The travel time of the bus line segment is taken as E Bus The weights of the edges are used to construct the bus weighted adjacency matrix A Bus , forming a weighted undirected graph G Bus (V Bus ,E Bus ), called the bus network graph;

[0017] S3-5. Compare the bus network diagram with G according to the following rules. Road+Subway The two-layer topology network graph is connected to form G Road+Subway+Bus Three-layer topology network diagram:

[0018] (2-1) The bus stops, road intersections and subway stations are combined as the bus network diagram and G Road+Subway Connection nodes of a two-layer topology network graph;

[0019] (2-2) If there is a road intersection within 100m of the bus stop, the connection relationship between the two is established as the bus network diagram and G Road+Subway The connection edges of the two-layer topology network graph;

[0020] S4. Gradually remove G Road , G Road+Subway and G Road+Subway+Bus E Road The edge and the E connected to this edge Subway 、E Bus The edges are then removed and the road network resilience is analyzed under different removal ratios and with different traffic layer network connection support.

[0021] Furthermore, step S4 analyzes the road network resilience through the following road network structure indicators:

[0022] (3-1) Network efficiency:

[0023]

[0024] Where N is the total number of nodes in the network G, d ij is the shortest path travel time between any node i and node j in the network;

[0025] (3-2) Network efficiency change rate:

[0026]

[0027] Among them, E X (G) is the network efficiency of network G when the road removal ratio is X, E0(G) is the network efficiency of network G in the initial state of the road;

[0028] (3-3) Maximum subgraph size:

[0029]

[0030] Among them, N max is the number of nodes in the largest subgraph;

[0031] (3-4) The rate of change of the maximum connected subgraph size:

[0032]

[0033] Among them, S X (G) is the maximum subgraph size of network G when the road removal ratio is X, S0(G) is the maximum subgraph size of network G in the road initial state;

[0034] (3-5) Gini coefficient of betweenness centrality:

[0035]

[0036] Among them, M i The i-th smallest value of the edge betweenness centrality that needs to be calculated for the network G.

[0037] Furthermore, the specific steps of S4 are as follows:

[0038] S4-1. Calculate G Road , G Road+Subway and G Road+Subway+Bus The maximum connected subgraph size, network efficiency, and betweenness centrality Gini coefficient of the road network graph in the initial state;

[0039] S4-2. Calculate GRoad , G Road+Subway and G Road+Subway+Bus E Road The betweenness centrality of the edge is ranked from high to low according to the calculation results. Road Sort the edges and remove the top 1% of the edges;

[0040] The calculation method of betweenness centrality is as follows:

[0041] BC k (G) = Σ i≠k≠j σ ij (k)

[0042] Among them, BC k (G) is the betweenness centrality of edge k in network G, σ ij (k) is the number of paths passing through edge k in the shortest path between node i and node j;

[0043] S4-3. In step S4-2, remove E Road After the operation of the edges is completed, if there is a road intersection that is not connected to any other road intersection, the road intersection is defined as the removed road node V1; the subway station connected to V1 is defined as the removed subway station V2; the bus station connected to V1 is defined as the removed bus station V2;

[0044] Remove the following nodes and edges:

[0045] (4-1) The removed road node V1;

[0046] (4-2) the removed subway station V2 and the removed bus station V3 in the subway network diagram and the bus network diagram;

[0047] (4-3) All nodes and edges of the subway line where the subway station V2 is located are removed;

[0048] (4-4) All nodes and edges of the bus line where bus stop V3 is located are removed;

[0049] S4-4. Calculate G again Road and G Road+Subway , G Road+Subway+Bus The maximum connected subgraph size, network efficiency and betweenness centrality Gini coefficient of the road network in;

[0050] S4-5, repeat S4-2 to S4-4 until E Road All edges of are removed;

[0051] S4-6. Draw the relationship curve between the road network structure index and the removal ratio X under the support of different traffic layer network connections, compare the phase change threshold and disaster bearing capacity changes of the spatial structure of the road network under the support of different traffic layer networks, and realize the quantitative measurement of road network resilience.

[0052] The beneficial technical effects of the present invention are:

[0053] (1) It deepens the understanding of the interconnectedness and interdependence between urban roads and transportation networks, and helps to better understand the process and mechanism of the impact of multi-layer transportation networks on road network resilience;

[0054] (2) The method of measuring urban multi-layer network resilience was expanded, the measurement objects and disturbance objects were clarified, the cascade and support mechanisms were clarified, and a quantitative assessment of the impact of multi-layer transportation networks on road network resilience was conducted;

[0055] (3) It provides a reference for the development of spatial and transportation resilience, and also provides technical tools for targeted enhancement of road network resilience in planning practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of an embodiment;

[0057] Figure 2 is a graph showing a change rate of the maximum connected subgraph size as a function of edge removal ratio in an embodiment;

[0058] Figure 3 is a graph showing a change in network efficiency rate as a function of edge removal ratio in an embodiment;

[0059] Figure 4 3 is a graph showing how the Gini coefficient of betweenness centrality changes with the ratio of edge removal in an embodiment. DETAILED DESCRIPTION

[0060] The present invention is described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] The embodiment adopts the present invention to quantitatively measure the road network resilience level supported by bus and subway network connections in Shanghai (excluding Chongming Island) in 2023.

[0062] Figure 1 is a flow chart of an embodiment, comprising the following steps:

[0063] S1. Collect multi-layer spatial vector data sets of urban roads, subways and buses above the branch level within the research scope based on the urban open source map data, which are called road layer raw data, subway layer raw data and bus layer raw data respectively;

[0064] S2. Preprocess the original data of the road layer, subway layer and bus layer into concise, clear and usable data of the road centerline, subway one-way line and bus one-way line, which are called road layer data, subway layer data and bus layer data respectively. The specific steps of data preprocessing are as follows:

[0065] S2-1. Use the buffer tool in ArcGIS Pro to generate buffers of different bandwidths for roads of different levels, and then use the polygon to centreline tool to identify the road centreline from the buffer polygon. Use the simplification line tool to eliminate redundant nodes in the line segment and delete the broken route segments with a length of less than 50 meters.

[0066] S2-2. Use the buffer tool in ArcGIS Pro to generate a buffer zone for subway or bus lines, and then use the polygon to centreline tool to identify one-way subway lines and one-way bus lines from the buffer zone polygons. Use the select by attribute tool to filter out stations with the same name but different lines and confirm the connection between them;

[0067] S2-3. The data of road center lines, subway one-way lines and bus one-way lines are spatially projected using the "Gauss-Krucker projection" and the coordinate system is the "2000 National Geodetic Coordinate System (CGCS2000)".

[0068] S3. Map the road layer data, subway layer data and bus layer data into a multi-layer network topology model consisting of nodes and edges, indicating the intra-layer and inter-layer modeling methods. And adopt the method of superimposing the subway and bus networks on the road network layer by layer to form three sets of comparable weighted undirected multi-layer topology network graphs. The specific steps are as follows:

[0069] S3-1. Call the Geopandas and Networkx third-party model libraries in Python to convert the road layer data, subway layer data, and bus layer data into GeoDataFrame data structures with attributes and spatial locations.

[0070] S3-2. Add the road intersections as nodes and the connections between the road intersections as edges into the network object Graph, and set the travel time of the road segment as the weight of the edge to obtain the weighted undirected graph G. Road (V Road ,E Road ).

[0071] S3-3. Take subway stations as nodes and the connections between subway stations as edges, add them to the network object Graph, and set the travel time of subway lines as the weight of the edges to obtain the weighted undirected graph G. Subway (V Subway ,E Subway ).

[0072] S3-4. Connect the road network diagram and the subway network diagram according to the following rules to form G Road+Subway Two-layer topology network diagram:

[0073] (1-1) Add the road intersections and subway stations as connecting nodes of the road network graph and the subway network graph respectively into the network object Graph;

[0074] (1-2) If there is a subway station within a 100m range centered on the road intersection, a connection relationship between the two is established as a connecting edge between the road network graph and the subway network graph, and added to the network object Graph.

[0075] S3-5. Take the bus stops as nodes and the connections between the bus stops as edges, add them to the network object Graph, and set the travel time of the bus lines as the weight of the edges to obtain the weighted undirected graph G. Bus (V Bus ,E Bus ).

[0076] S3-6. Compare the bus network diagram with G according to the following rules. Road+Subway The two-layer topology network graph is connected to form G Road+Subway+Bus Three-layer topology network diagram:

[0077] (2-1) The bus stops, road intersections and subway stations are combined as the bus network diagram and G Road+Subway The connection nodes of the two-layer topology network graph are added to the network object Graph;

[0078] (2-2) If there is a road intersection within 100m of the bus stop, the connection relationship between the two is established as the bus network diagram and G Road+Subway The connection edges of the two-layer topology network graph are added to the network object Graph.

[0079] S4. Use the weighted undirected multi-layer topological network graph obtained in S3 as the initial simulation scenario, set the attack scenario to sort and remove the road network edges and other traffic network lines connected to them; calculate the network structure indicators of the road topological network supported by different traffic layer network connections under different edge removal ratios. The specific steps are as follows:

[0080] S4-1. Call betweenness_centrality to calculate the betweenness centrality of each road network segment, sort the segments from high to low, and call the remove function to delete E in order. Road The top 1% edge.

[0081] The betweenness centrality of a road segment is calculated as follows:

[0082] BC k (G) = ∑ i≠k≠j σ ij (k)

[0083] Among them, BC k (G) is the betweenness centrality of edge k in network G, σ ij (k) is the number of paths passing through edge k in the shortest path between node i and node j.

[0084] S4-2, Remove E Road After the operation of the edges is completed, if there is a road intersection that is not connected to any other road intersection, the road intersection is defined as the removed road node V1; the subway station connected to V1 is defined as the removed subway station V2; the bus station connected to V1 is defined as the removed bus station V2;

[0085] Remove the following nodes and edges:

[0086] (4-1) The removed road node V1;

[0087] (4-2) the removed subway station V2 and the removed bus station V3 in the subway network diagram and the bus network diagram;

[0088] (4-3) All nodes and edges of the subway line where the subway station V2 is located are removed;

[0089] (4-4) All nodes and edges of the bus line where bus stop V3 is located are removed.

[0090] S4-3. Calculate the betweenness centrality of each road segment in the remaining network to redetermine the removal order.

[0091] S4-4. Call the remove function to iteratively remove the remaining E Road Repeat this process for the first 1% of the remaining edges in E Road All edges are removed.

[0092] Under different removal ratios, G is solved by calling the connected_components function, global_efficiency function, and betweenness_centrality function in the NetworkX library and the Gini coefficient formula.Road , G Road+Subway and G Road+Subway+Bus Maximum connected subgraph size, network efficiency, and betweenness centrality Gini coefficient of road networks in China.

[0093] Network efficiency, the rate of change of the maximum connected subgraph size, and the Gini coefficient of betweenness centrality are calculated as follows:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] Among them, E X (G) is the network efficiency of network G when the road x is removed, E0(G) is the network efficiency of network G in the initial state of the road, is the rate of change of network efficiency of network G. N is the total number of nodes in network G, d ij S is the shortest path travel time between any node i and node j in the network. X (G) is the maximum subgraph size of network G when the road x is removed, S0(G) is the maximum subgraph size of network G in the initial state of the road, is the maximum subgraph size change rate of the network G, N max is the number of nodes in the largest subgraph. Gini(G) is the Gini coefficient of the betweenness centrality of network G, M i The i-th smallest value of the edge betweenness centrality that needs to be calculated for the network G.

[0100] S5. Draw the relationship curve between the road network structure indicators and the removal ratio under the support of different traffic layer network connections, compare the phase change threshold and disaster bearing capacity changes of the spatial structure of the road network under the support of different traffic layer networks, and finally achieve quantitative measurement of road network resilience.

[0101] Call the Matplotlib library and set G Road , G Road+Subway and G Road+Subway+Bus Visual expression of the maximum connected subgraph size of the road network, the rate of change of network efficiency, and the Gini coefficient of betweenness centrality in the three groups of networks as the proportion of removed edges changes.

[0102] According to the phase transition thresholds of the three types of index change curves, the critical state of the network structure phase transition is identified. Road+Subway , G Road+Subway+Bus and GRoad The phase change thresholds of different network indicators determine the impact of multi-layer dependencies on the phase change of road network structure.

[0103] The integral areas of the three types of index change curves are calculated as the resilience levels of different dimensions of the road network, and compared with G Road+Subway , G Road+Subway+Bus and G Road The integrated areas of different network indicators determine the impact of multi-layer dependencies on the resilience level of the road network.

[0104] Furthermore, the integral areas of the three types of index change curves are calculated as follows:

[0105]

[0106] Among them, R(G) is the resilience level of the f(x) function dimension of the network G, and f(x) is the network efficiency, the rate of change of the maximum connected subgraph size, and the Gini coefficient index of betweenness centrality.

[0107] Figure 2-4 G is the scenario where Shanghai roads are removed in sequence and cascade damage is caused to the multi-layer transportation network. Road , G Road+Subway and G Road+Subway+Bus The change curves of the maximum connected subgraph size of the road network, the change rate of network efficiency and the Gini coefficient of betweenness centrality in the three groups of networks as the proportion of removed edges increases.

[0108] like Figure 2 As shown, G Road The phase transition threshold and toughness level of the maximum connected subgraph size of the road network in G are 6% and 0.108 respectively. Road+Subway The phase transition threshold and toughness level of the maximum connected subgraph size of the medium road network are 16% and 0.172 respectively, the threshold is delayed by 10% and the toughness is improved by 59.2%. Road+Subway+Bus The phase transition threshold and toughness level of the maximum connected subgraph size of the medium road network are 25% and 0.311, respectively. The threshold is delayed by 19% and the toughness is improved by 188.0%.

[0109] like Figure 3 As shown, G Road The phase transition threshold and toughness level of the network efficiency of the medium road network are 6% and 0.078 respectively. Road+Subway The phase transition threshold and toughness level of the network efficiency of the medium road network are 9% and 0.097 respectively, the threshold is delayed by 3% and the toughness is improved by 24.4%. Road+Subway+Bus The phase transition threshold and toughness level of the network efficiency of the medium road network are 11% and 0.126 respectively, with the threshold delayed by 5% and improved by 61.5%.

[0110] like Figure 4 As shown, G Road The phase transition threshold and toughness level of the Gini coefficient of the betweenness centrality of the road network are 6% and 0.438 respectively. Road+Subway The phase transition threshold and toughness level of the Gini coefficient of the betweenness centrality of the road network are 16% and 0.469 respectively, and the threshold is delayed by 10% and improved by 7.1%. Road+Subway+Bus The phase transition threshold and toughness level of the Gini coefficient of betweenness centrality of the road network are 38% and 0.652, respectively, with the threshold delayed by 32% and improved by 48.9%.

[0111] This example realizes the identification and comparison of key thresholds of road network structure under different traffic layer dependencies, and realizes the quantitative evaluation of the impact of multi-layer traffic networks on road network resilience.

[0112] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and implementation modes, and can be fully applicable to various fields suitable for the present invention. For those familiar with the art, for those of ordinary skill in the art, various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present invention. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to specific details.

Claims

1. A method for measuring the resilience of an urban road network under multi-layer traffic network dependence, comprising the following steps: S1. Collect different spatial layer data of roads, subways and buses above the branch level, which are called road layer raw data, subway layer raw data and bus layer raw data respectively; S2, preprocessing the original data of the road layer, the original data of the subway layer and the original data of the bus layer, specifically as follows: preprocessing the original data of the road layer into the data of the road centerline, called the road layer data; preprocessing the original data of the subway layer into the data of the subway one-way line, called the subway layer data; preprocessing the original data of the bus layer into the data of the bus one-way line, called the bus layer data; S3, mapping the road layer data, subway layer data and bus layer data into a multi-layer network topology model consisting of nodes and edges respectively. The specific steps are as follows: S3-1. Map the road intersections in the road layer data into nodes to obtain a set V Road ; Map the road segments to edges and get the set E Road ; The travel time of the road segment is taken as E Road The weights of the edges are used to construct the road weighted adjacency matrix A Road , forming a weighted undirected graph G Road (V Road ,E Road ), called the road network graph; S3-2. Map the subway stations in the subway layer data into nodes to obtain the set V Subway ; Map the subway line segments to edges and get the set E Subway ; The travel time of the subway line section is taken as E Subway The weights of the edges are used to construct the subway weighted adjacency matrix A Subway , forming a weighted undirected graph G Subway (V Subway ,E Subway ), called the subway network diagram; S3-3. Connect the road network diagram and the subway network diagram according to the following rules to form G Road+Subway Two-layer topology network diagram: (1-1) The road intersections and subway stations are used as connecting nodes of the road network graph and the subway network graph respectively; (1-2) If there is a subway station within a 100m range centered on the road intersection, a connection relationship between the two is established as a connecting edge between the road network graph and the subway network graph; S3-4, map the bus stops of the bus layer data into nodes to obtain the set V Bus ; Map bus line segments to edges to get set E Bus ; The travel time of the bus line segment is taken as E Bus The weights of the edges are used to construct the bus weighted adjacency matrix A Bus , forming a weighted undirected graph G Bus (V Bus ,E Bus ), called the bus network graph; S3-5. Compare the bus network diagram with G according to the following rules. Road+Subway The two-layer topology network graph is connected to form G Road+Subway+Bus Three-layer topology network diagram: (2-1) The bus stops, road intersections and subway stations are combined as the bus network diagram and G Road+Subway Connection nodes of a two-layer topology network graph; (2-2) If there is a road intersection within 100m of the bus stop, the connection relationship between the two is established as the bus network diagram and G Road+Subway The connection edges of the two-layer topology network graph; S4. Gradually remove G Road , G Road+Subway and G Road+Subway+Bus E in Road The edge and the E connected to this edge Subway 、E Bus The edges are then analyzed under different removal ratios and with different traffic layer network connection supports. That is, the relationship curves between the road network structure indicators and the removal ratio X under different traffic layer network connection supports are plotted. The phase change thresholds and disaster bearing capacity changes of the spatial structure of the road network under different traffic layer network supports are compared to achieve a quantitative measurement of the road network resilience.

2. According to claim 1, a method for measuring urban road network resilience under multi-layer traffic network dependence is characterized by: Step S4 analyzes the road network resilience through the following road network structure indicators: (3-1) Network efficiency: Where N is the total number of nodes in the network G, d ij is the shortest path travel time between any node i and node j in the network; (3-2) Network efficiency change rate: Among them, E X (G) is the network efficiency of network G when the road removal ratio is X, and E0(G) is the network efficiency of network G in the initial state of the road; (3-3) Maximum subgraph size: Among them, N max is the number of nodes in the largest subgraph; (3-4) Change rate of the maximum connected subgraph size: Among them, S X (G) is the maximum subgraph size of network G when the road removal ratio is X, S0(G) is the maximum subgraph size of network G in the road initial state; (3-5) Gini coefficient of betweenness centrality: Among them, M i The i-th smallest value of the edge betweenness centrality that needs to be calculated for the network G.

3. According to the method for measuring urban road network resilience under multi-layer traffic network dependence in claim 2, it is characterized in that: The specific steps of S4 are as follows: S4-1. Calculate G Road , G Road+Subway and G Road+Subway+Bus The maximum connected subgraph size, network efficiency, and betweenness centrality Gini coefficient of the road network graph in the initial state; S4-2. Calculate G Road , G Road+Subway and G Road+Subway+Bus E in Road The betweenness centrality of the edge is ranked from high to low according to the calculation results. Road Sort the edges and then remove the top 1% of the edges; The calculation method of betweenness centrality is as follows: BC k (G)=∑ i≠k≠j s ij (k) Among them, BC k (G) is the betweenness centrality of edge k in network G, σ ij (k) is the number of paths passing through edge k in the shortest path between node i and node j; S4-3. In step S4-2, remove E Road After the operation of the edges is completed, if there is a road intersection that is not connected to any other road intersection, the road intersection is defined as the removed road node V1; the subway station connected to V1 is defined as the removed subway station V2; the bus station connected to V1 is defined as the removed bus station V2; Remove the following nodes and edges: (4-1) The removed road node V1; (4-2) the removed subway station V2 and the removed bus station V3 in the subway network diagram and the bus network diagram; (4-3) All nodes and edges of the subway line where the subway station V2 is located are removed; (4-4) All nodes and edges of the bus line where bus stop V3 is located are removed; S4-4. Calculate G again Road and G Road+Subway , G Road+Subway+Bus The maximum connected subgraph size, network efficiency and betweenness centrality Gini coefficient of the road network in; S4-5, repeat S4-2 to S4-4 until E Road All edges are removed.

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