A vulnerability assessment and vulnerable node identification method for regional bridge tunnel network security operation and maintenance

Abstract

The present application provides a kind of vulnerability assessment and vulnerable node identification method for regional bridge and tunnel network security operation and maintenance.The method comprises the following steps:1, the basic information of regional bridge and tunnel is preprocessed and integrated, and regional bridge and tunnel network is established;2, based on graph theory and complex network theory analysis bridge and tunnel network characteristics, get the key node of bridge and tunnel network topology structure;3, comprehensive accessibility and network efficiency, select appropriate vulnerability index, take different node failure strategy, calculate the corresponding relationship of node removal ratio and vulnerability index;4, calculate the overall vulnerability of bridge and tunnel network, analyze the vulnerability of network and record the vulnerability of each bridge and tunnel node;5, using Monte Carlo sampling method, through multiple random calculation of the vulnerability of bridge and tunnel node, identify the vulnerable node of bridge and tunnel network.The present application is suitable for the topological analysis, vulnerability analysis and key vulnerable node identification process of general regional bridge and tunnel network.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of complex networks, vulnerability analysis, and civil engineering infrastructure health monitoring, and particularly relates to a vulnerability assessment and vulnerable node identification method for regional bridge-tunnel network security operation and maintenance. BACKGROUND

[0002] Bridges and tunnels are critical infrastructure in urban transportation networks, serving important transportation functions. Once a bridge-tunnel node fails, it will seriously affect the connectivity of traffic flow and the stability of regional transportation networks, and even cause large-scale social and economic losses. Traditional transportation infrastructure maintenance mainly relies on periodic inspection and maintenance, but fails to fully utilize modern technology for systematic analysis of network vulnerability. Therefore, using complex network theory to assess the vulnerability of bridge-tunnel networks can provide a scientific basis for the safe operation and maintenance of bridges and tunnels, and improve the robustness and risk resistance of transportation networks.

[0003] Vulnerability analysis can be applied to various complex systems, especially network structures, infrastructure, and information systems. Vulnerability analysis assesses the importance and failure probability of each element in the system to determine which elements play a key role in the system's function. Once these critical elements fail, it may lead to system collapse or severe function impairment. In bridge-tunnel networks, managers can identify weak links in the network through vulnerability analysis, optimize emergency response and resource allocation, and improve the risk resistance of bridge-tunnel networks. By identifying and strengthening critical vulnerable nodes through vulnerability analysis, traffic congestion and delays caused by network node failure can be avoided, improving the efficiency of bridge-tunnel networks, improving the travel experience of society, and ensuring public safety. In the construction of smart bridge-tunnel systems, dynamic and real-time vulnerability assessment can provide optimization suggestions for traffic flow regulation, road load distribution, and other aspects, thereby better serving the safe and efficient operation of regional bridge-tunnel networks.

[0004] Current vulnerability research of transportation networks mostly focuses on highway networks and intersections, focusing on the impact of road node failure on traffic flow. Complex network theory is increasingly applied in the field of transportation, abstracting transportation networks as a collection of nodes and edges through graph theory, analyzing the role of different nodes in the network, and assessing the robustness of the overall network. Typical research directions include identifying key nodes in transportation networks based on centrality indicators, analyzing network structure connectivity, and evaluating traffic network failure propagation effects. These studies lay the theoretical foundation for vulnerability assessment of transportation networks.

[0005] In the field of bridge and tunnel vulnerability analysis, there are several deficiencies in existing research. First, the unique nature of bridge and tunnel facilities is not adequately considered. Unlike ordinary highway nodes, bridges and tunnels have complex structural characteristics and higher construction costs, and their failure has a more significant impact on traffic flow and regional connectivity. Existing research has failed to fully explore the role of bridge and tunnel facilities in the entire network, using the same analysis method as ordinary nodes, resulting in inaccurate assessment of their vulnerability. Second, current vulnerability analysis lacks dynamicity. Most vulnerability analyses are based on static network models, making it difficult to assess the dynamic adjustment and connectivity changes of the traffic network after node failure. However, real-world traffic networks often encounter unexpected events such as natural disasters, bridge damage, and traffic accidents, which can lead to redistribution of network structure and traffic flow. Additionally, the study of cross-system coupling effects is limited. Existing research is mostly limited to single objects, lacking consideration of the coupling effects of multiple types of nodes. In summary, while current research on traffic network vulnerability analysis provides a theoretical basis for bridge and tunnel safety evaluation, there are significant deficiencies in the particularity of bridge and tunnel networks, dynamicity, and multi-type coupling.

[0006] In the practical needs of traffic management, traditional management and maintenance methods usually rely on regular inspections, with the target bridges and tunnels being determined by experience. While this approach provides some assurance, it lacks scientific and systematic evaluation methods. Especially for critical transportation facilities such as bridges and tunnels, a more precise analysis tool is needed to quantify the vulnerability of bridge and tunnel facilities and identify the most influential bridge and tunnel nodes on network robustness. Through this quantitative analysis method, traffic managers can not only optimize resource allocation and prioritize reinforcement of high-risk nodes, but also provide reliable decision-making basis for emergency management and maintenance strategies, ensuring the risk resistance and safety of bridge and tunnel networks in the event of emergencies.

[0007] Therefore, the present invention starts from the theory of complex networks and combines the characteristics of bridges and tunnels to propose a practical method for bridge and tunnel network vulnerability assessment and key node identification. The Monte Carlo sampling method is used to improve the consistency and reliability of key vulnerable node identification. The present invention can effectively address the deficiencies in existing research on bridge and tunnel infrastructure vulnerability analysis, providing reliable technical support for the safe operation and maintenance of regional bridge and tunnel networks, and has wide engineering application value. SUMMARY

[0008] The present application aims to provide a vulnerability evaluation and vulnerable node identification method for regional bridge and tunnel network security operation and maintenance, to solve the problem of lack of systematic evaluation of bridge and tunnel facility vulnerability in traditional traffic management. The method analyzes the topology of the bridge and tunnel network through complex network theory, establishes a vulnerability index, and combines the Monte Carlo sampling method to improve the consistency and reliability of the identification of vulnerable nodes. The advantage is that it can accurately identify the bridge and tunnel nodes that have the greatest impact on network stable operation, thereby providing a scientific basis for the maintenance, reinforcement and emergency management of regional bridge and tunnel facilities, and improving the overall robustness and security of the network.

[0009] The present application is realized by the following technical solutions, the present application proposes a vulnerability evaluation and vulnerable node identification method for regional bridge and tunnel network security operation and maintenance, the method comprises the following steps:

[0010] Step one, preprocessing and integration of regional bridge and tunnel information, establishing a regional bridge and tunnel network;

[0011] Step two, analyze the characteristics of the bridge and tunnel network based on graph theory and complex network theory, and get the key nodes of the bridge and tunnel network topology;

[0012] Step three, select vulnerability index by combining reachability and network efficiency, adopt different node failure strategies, and calculate the corresponding relationship between node removal ratio and vulnerability index;

[0013] Step four, calculate the overall vulnerability of the bridge and tunnel network, analyze the vulnerability of the network and record the vulnerability degree of each bridge and tunnel node;

[0014] Step five, use Monte Carlo sampling method to calculate the vulnerability degree expectation of the bridge and tunnel nodes through multiple random calculations, and identify the vulnerable nodes of the bridge and tunnel network.

[0015] Further, the step one is specifically:

[0016] Preprocess the information of regional bridges and tunnels, use the Mercator projection, and convert the bridge and tunnel geographic coordinates WGS84 to projected coordinates UTM; for latitude and longitude λ, the conversion formula is:

[0017] x=k0N(λ-λ0)+EastOffset

[0018]

[0019] In the formula, k0 is the scaling factor; N is the latitude and longitude ellipsoid radius; λ0 is the central meridian longitude; EastOffset is the east offset; is the arc length from the equator to the latitude ;

[0020] The regional bridge and tunnel network is divided into three types of bridge, viaduct and tunnel, and the number, coordinates, connectivity and distance are extracted as the main features to establish the regional bridge and tunnel network.

[0021] Further, the step two is specifically:

[0022] Step two one, performing a depth-first search (DFS) on the established bridge and tunnel network to obtain the connectivity and cut point of the network;

[0023] Step two two, counting the number of edges connected to each bridge and tunnel node to obtain the node degree and degree distribution of the network; analyzing the connection characteristics between nodes to calculate the homophily and average clustering coefficient of the network, and the calculation formula is:

[0024]

[0025] In the formula, R and C are the homophily coefficient and average clustering coefficient of the network, respectively; j i , k i represent the degrees of the two end points of an edge; M is the number of edges in the network; N is the number of nodes in the network, l i is the degree of node i; E i is the number of edges between the neighbor nodes of node i;

[0026] Step two three, analyzing the path characteristics of the network, including the average path length a, network diameter l, eccentricity p and radius r, and searching for the central node, and the calculation formula is:

[0027]

[0028] r = min p

[0029] In the formula, d(i, j) is the shortest path between node i and node j; the node with the eccentricity equal to the radius is the central node of the network;

[0030] Step two four, analyzing the network topology importance of each bridge and tunnel node, and calculating the degree centrality, eigenvector centrality, betweenness centrality and closeness centrality of the node, and the calculation formula is:

[0031]

[0032] In the formula, λ is the eigenvalue; a ij is the element of the adjacency matrix, indicating whether there is an edge between node i and node j; σ st is the total number of shortest paths between node s and node t; σ st (i) is the number of shortest paths passing through node i.

[0033] Further, the step two one is specifically:

[0034] Step two-1, initialize a timestamp variable time to track the order of visiting nodes; initialize the visiting time of nodes discovery and the earliest traceable time low;

[0035] Step two-2, select an initial node i, and set the visiting time of the node dis[i] and the initial earliest traceable time low[i] to the current time;

[0036] Step two-3, traverse all neighbors j of the node: if j is not visited, continue to execute step two-3 and update low[i]; if j has been visited and is not the parent node of i, update low[i] to min(low[i], dis[j]) to represent that j can be reached through the traceable path;

[0037] After completing step two-3, if there are still unvisited nodes, initialize the nodes again and repeat steps two-1 to two-3, and each time the number of connected components increases by one. For each node i, if i is a root node and there are two or more subtrees, i is a cut point; if i is a non-root node, check whether low[j] is greater than or equal to dis[i], that is, if the child node j and its descendants cannot return to the ancestor of i through the traceable path, then i is a cut point.

[0038] Further, the step three is specifically:

[0039] Step three-1, select the relative size of the largest connected subgraph and the network efficiency in the characteristics of the bridge tunnel network as the vulnerability index of the network, and the calculation formula is:

[0040]

[0041] In the formula, LCC(G) is the relative size of the largest connected subgraph; E(G) is the network efficiency; N is the total number of bridges and tunnels; n lc is the number of nodes in the largest connected component; is the connected node penalty item of the network efficiency, where n c is the total number of network connected nodes, and n is the number of nodes in the current network;

[0042] Step three-2, sort the bridge and tunnel nodes according to the degree centrality, weighted degree centrality, intermediate centrality and weighted intermediate centrality to simulate the static failure order; remove the node with the largest weighted intermediate centrality in the graph, and then recalculate the weighted intermediate centrality of each point, and perform this step in turn until all nodes are removed, to obtain the dynamic sorting of the weighted intermediate centrality, simulating the dynamic failure order; randomly sort the nodes to simulate the random failure order;

[0043] Step three three, according to the different failure order obtained in step three two, the node removal strategy is carried out on the bridge tunnel network respectively. Each time a node is removed, the network damage ratio is calculated and the corresponding network vulnerability index is recorded.

[0044] Further, the step three three is specifically:

[0045] Step three one, input the initial bridge tunnel network, calculate the network efficiency and the number of nodes in the initial state, and select the removal strategy of the bridge tunnel node;

[0046] Step three two, select a bridge tunnel node according to the corresponding node sorting, remove it in the network to simulate the damage of the bridge tunnel, calculate the network efficiency and the relative size of the maximum connected subgraph after damage;

[0047] Step three three, count the node damage ratio, judge whether all nodes have been traversed, if not, continue to execute step three two until all nodes are removed, and output the vulnerability index statistical result.

[0048] Further, the step four is specifically:

[0049] Step four one, comprehensively consider the relative size of the network maximum connected subgraph and the network efficiency, and propose a unified index to quantify the vulnerability of the bridge tunnel network, and the calculation formula is:

[0050]

[0051] In the formula, SV(G') is the static vulnerability of the network, ΔE(G') is the change of the network efficiency, and a is the connected importance coefficient.

[0052] The vulnerability threshold of network failure is set to 1. When the vulnerability of the network reaches the threshold, E(G') is 0 or LCC(G') is 1%, which can be used as the trigger condition of network collapse;

[0053] Step four two, calculate the network vulnerability change caused by removing each node, and according to the node removal order recorded in step three three, correspond the vulnerability to the node, and calculate the vulnerability degree of each bridge tunnel node.

[0054] Further, the step five is specifically:

[0055] Step five one, take a random failure order, and according to step three three, obtain the vulnerability analysis result of the bridge tunnel network under the random node failure, and record the vulnerability degree of each bridge tunnel node;

[0056] Step five two, based on the Monte Carlo principle, repeat step five one, and estimate the vulnerability degree expectation of each bridge tunnel node as its overall vulnerability degree by a large number of sampling in the random failure strategy; According to the overall vulnerability degree, identify the vulnerable nodes of the bridge tunnel network, and mark and visualize the bridge tunnel network topology diagram.

[0057] The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method for vulnerability assessment and vulnerable node identification of a regional bridge-tunnel network security operation and maintenance when executing the computer program.

[0058] The application further provides a computer readable storage medium for storing computer instructions, wherein the computer instructions implement the steps of the method for vulnerability assessment and vulnerable node identification of a regional bridge-tunnel network security operation and maintenance when executed by a processor.

[0059] Compared with the prior art, the application has the following beneficial effects:

[0060] 1. Quantitative vulnerability assessment. The proposed method establishes a quantitative calculation model for bridge-tunnel network vulnerability, providing accurate evaluation criteria. Compared with traditional evaluation methods that rely on experience or static models, the method provides a scientific basis for vulnerability analysis and quantifies the potential risks of bridge-tunnel facilities through data.

[0061] 2. Accurate identification of key vulnerable nodes. By combining complex network theory and Monte Carlo sampling method, the application can accurately identify the key vulnerable nodes that have the greatest impact on the connectivity and overall stability of the bridge-tunnel network. Traditional methods are easily disturbed by random factors when identifying key nodes, while the method improves the consistency and credibility of the identification results through repeated analysis and simulation.

[0062] 3. Improve monitoring and maintenance efficiency. By accurately identifying vulnerable nodes, traffic managers can prioritize monitoring or maintenance of key bridge-tunnel facilities based on vulnerability analysis results. This targeted monitoring and maintenance strategy can significantly improve resource utilization efficiency, saving operation and maintenance costs while ensuring the overall safety and stability of the network.

[0063] 4. Wide engineering application value. The application is not only suitable for single bridge-tunnel networks, but also applicable to various sizes and complexity of regional traffic networks, with strong adaptability and universality. Whether in daily maintenance or emergency response, the method can provide strong support for the management of traffic facilities and ensure the sustained and stable operation of the network. BRIEF DESCRIPTION OF DRAWINGS

[0064] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute the embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of the provided drawings.

[0065] Figure 1 Figure 1 is a flow chart of the vulnerability analysis and vulnerable node identification process;

[0066] Figure 2 Figure 2 is a structure diagram of the bridge and tunnel network in a certain region;

[0067] Figure 3 Figure 3 is a degree distribution diagram of the bridge and tunnel network in a certain region;

[0068] Figure 4 Figure 4 is a centrality visualization diagram of the bridge and tunnel network in a certain region; (a) is the degree centrality; (b) is the betweenness centrality; (c) is the closeness centrality; (d) is the eigenvector centrality;

[0069] Figure 5 Figure 5 is a diagram of the change of the relative size of the largest connected component of the network under different failure modes;

[0070] Figure 6 Figure 6 is a diagram of the change of the network efficiency and weighted network efficiency under different failure modes; Figure 6 The left is the relative network efficiency; Figure 6 The right is the path-weighted relative network efficiency;

[0071] Figure 7 Figure 7 is a diagram of the vulnerability of the bridge and tunnel network under different failure modes;

[0072] Figure 8 Figure 8 is a diagram of the change of the vulnerability caused by the removal of each node;

[0073] Figure 9 Figure 9 is a diagram of the identification result of the key vulnerable nodes of the bridge and tunnel network in a certain region. DETAILED DESCRIPTION

[0074] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0075] In combination with Figures 1-9 , the present application proposes a vulnerability evaluation and vulnerable node identification method for the security operation and maintenance of a regional bridge and tunnel network, which comprises the following steps:

[0076] Step 1, preprocessing and integration of the information of the bridges and tunnels in a region, and establishment of a regional bridge and tunnel network;

[0077] The step 1 specifically comprises:

[0078] The information of regional bridges and tunnels is preprocessed, and Mercator projection is adopted to convert the bridge and tunnel geographic coordinates WGS84 into projected coordinates UTM; for latitude and longitude λ, the conversion formula is:

[0079] x=k0N(λ-λ0)+EastOffset

[0080]

[0081] In the formula, k0 is a scaling factor, which is 0.9996; N is the latitude and longitude ellipsoid radius; λ0 is the central meridian longitude; EastOffset is the east offset, which is 500000 meters; is the arc length from the equator to the latitude ;

[0082] The regional bridges and tunnels are divided into three types of bridges, viaducts and tunnels, and the number, coordinates, connectivity and distance are extracted as main features to establish a regional bridge and tunnel network.

[0083] Step two, based on graph theory and complex network theory, the characteristics of the bridge and tunnel network are analyzed to obtain the key nodes of the bridge and tunnel network topology;

[0084] The step two is specifically:

[0085] Step two one, the established bridge and tunnel network is subjected to depth-first search (DFS) to obtain the connectivity and cut point of the network;

[0086] The step two one is specifically:

[0087] Step two one one, a timestamp variable time is initialized to track the order of visiting nodes; the visiting time discovery and the earliest backtracking time low of the node are initialized;

[0088] Step two one two, an initial node i is selected, and the visiting time dis[i] and the initial earliest backtracking time low[i] of the node are set to the current time;

[0089] Step two one three, all neighbors j of the node are traversed: if j is not visited, step two one three is continued and low[i] is updated; if j is visited and is not the parent node of i, low[i] is updated to min(low[i],dis[j]) to indicate that j can be reached through the backtracking path;

[0090] After step 213 is completed, if there are still unvisited nodes, the nodes are initialized again and steps 211-213 are repeated, and each time this is done, the number of connected components increases by one. For each node i, if i is a root node and there are two or more sub-trees, i is a cut point; if i is a non-root node, check whether low[j] is greater than or equal to dis[i], i.e. if a child node j and its descendants cannot return to the ancestor of i through the backtracking path, i is a cut point.

[0091] Step 222, count the number of edges connected to each bridge node to obtain the node degree and the degree distribution of the network; analyze the connection characteristics between nodes to calculate the homophily and average clustering coefficient of the network, and the calculation formula is:

[0092]

[0093] In the formula, R and C are the homophily coefficient and average clustering coefficient of the network, respectively; j i and k i represent the degrees of the two end points of an edge; M is the number of edges in the network; N is the number of nodes in the network, l i is the degree of node i; E i is the number of edges between the neighbor nodes of node i.

[0094] Step 223, analyze the path characteristics of the network, including the average path length a, the network diameter l, the eccentricity p and the radius r, and search for the central node, and the calculation formula is:

[0095]

[0096] r = min p

[0097] In the formula, d(i, j) is the shortest path between node i and node j; the node with the eccentricity equal to the radius is the central node of the network.

[0098] Step 224, analyze the network topology importance of each bridge node, and calculate the degree centrality, eigenvector centrality, betweenness centrality and closeness centrality of the node, and the calculation formula is:

[0099]

[0100] In the formula, λ is the eigenvalue; a ij is the element of the adjacency matrix, indicating whether there is an edge between node i and node j; σ st is the total number of shortest paths between nodes s and t; σ st (i) is the number of shortest paths passing through node i.

[0101] Step three, integrate the accessibility and network efficiency, select the vulnerability index, take different node failure strategies, calculate the corresponding relationship between the node removal ratio and the vulnerability index;

[0102] The step three is specifically:

[0103] Step three one, select the relative size of the largest connected subgraph and the network efficiency in the bridge tunnel network characteristics as the network vulnerability index, and the calculation formula is:

[0104]

[0105] In the formula, LCC(G) is the relative size of the largest connected subgraph; E(G) is the network efficiency; N is the total number of bridges and tunnels; n lc is the number of nodes in the largest connected component; is the connected node penalty item of the network efficiency, wherein n c is the total number of network connected nodes, and n is the number of nodes in the current network;

[0106] Step three two, sort the bridge and tunnel nodes according to the degree centrality, weighted degree centrality, intermediate centrality and weighted intermediate centrality, simulate the static failure order; remove the node with the largest weighted intermediate centrality in the graph, then recalculate the weighted intermediate centrality of each point, and perform this step in turn until all nodes are removed, obtain the dynamic sorting of the weighted intermediate centrality, simulate the dynamic failure order; randomly sort the nodes, simulate the random failure order;

[0107] Step three three, according to the different failure orders obtained in step three two, respectively remove the nodes of the bridge and tunnel network, each time a node is removed, the network damage ratio is calculated and the corresponding network vulnerability index is recorded.

[0108] The step three three is specifically:

[0109] Step three one, input the initial bridge and tunnel network, calculate the network efficiency and the number of nodes in the initial state, and select the removal strategy of the bridge and tunnel node;

[0110] Step three two, select a bridge and tunnel node according to the corresponding node sorting, remove it in the network to simulate the damage of the bridge and tunnel, calculate the network efficiency and the relative size of the largest connected subgraph after the damage;

[0111] Step three three, count the node damage ratio, judge whether all nodes are traversed, if not, continue to execute step three two until all nodes are removed, and output the vulnerability index statistical result.

[0112] Step four, calculate the overall vulnerability of the bridge and tunnel network, analyze the vulnerability of the network and record the vulnerability degree of each bridge and tunnel node;

[0113] The step four is specifically:

[0114] Step four one, according to the relative size of the largest connected subgraph of the network and the network efficiency, a unified index for quantifying the vulnerability of the bridge-tunnel network is proposed, and the calculation formula is:

[0115]

[0116] In the formula, SV(G') is the static vulnerability of the network; ΔE(G') is the change of the network efficiency; and a is the connectivity importance coefficient.

[0117] The vulnerability threshold of network failure is set to 1, and when the vulnerability of the network reaches the threshold, E(G') is 0 or LCC(G') is 1%, which can be used as the trigger condition for network collapse.

[0118] Step four two, the change of the network vulnerability caused by the removal of each node is calculated, and the vulnerability is corresponded to the node according to the node removal order recorded in step three, and the vulnerability degree of each bridge-tunnel node is calculated.

[0119] Step five, the Monte Carlo sampling method is adopted to calculate the expectation of the vulnerability degree of the bridge-tunnel node through multiple random calculations, and the vulnerable nodes of the bridge-tunnel network are identified.

[0120] The step five is specifically:

[0121] Step five one, a random failure order is adopted, and the vulnerability analysis result of the bridge-tunnel network under the random failure of the node is obtained according to step three, and the vulnerability degree of each bridge-tunnel node is recorded.

[0122] Step five two, based on the Monte Carlo principle, step five one is repeated, a large number of samples are taken in the random failure strategy, and the expectation of the vulnerability degree of each bridge-tunnel node is estimated as the overall vulnerability degree; the vulnerable nodes of the bridge-tunnel network are identified according to the overall vulnerability degree, and are marked and visualized in combination with the topology diagram of the bridge-tunnel network.

[0123] The purpose of the embodiment is to propose a bridge-tunnel network vulnerability evaluation and vulnerable node identification method, which is applied to the vulnerability analysis and safe operation and maintenance of the regional bridge-tunnel network.

[0124] The core of the present application is based on complex network theory, through topological analysis and vulnerability index modeling analysis of the vulnerability of regional bridge tunnel network, and based on Monte Carlo sampling to accurately identify the key vulnerable nodes of the network. The method mainly consists of three steps, the first step is the pretreatment of bridge tunnel information, the construction of parameterized graph model and the centrality feature analysis of the topological structure of the network, to identify the potential key nodes; the second step is to select the relative size of the maximum connected component and the network efficiency as the vulnerability index, to establish the quantitative calculation formula of network vulnerability, to evaluate the influence of node failure on the whole network; the third step is to apply Monte Carlo sampling method for multiple random simulation, to evaluate the change of the network under different conditions, to ensure that the identification result of the vulnerable node has high consistency and reliability. Traffic managers can make scientific decisions according to the analysis results, optimize resource allocation and emergency management strategies.

[0125] Embodiment

[0126] This embodiment is completed by a computer program based on Python language on the basis of the above specific embodiment, the implemented hardware environment is shown in Table 1, and the implementation target is a certain regional bridge tunnel group. The effect of the present application is illustrated by the following specific examples.

[0127] Table 1 Hardware environment parameters

[0128]

[0129] The basic information of the regional bridge tunnel group is collected and pretreated, including latitude and longitude coordinates, bridge and tunnel types and connectivity, etc. The regional bridge tunnel group has a total of 681 bridges and tunnels, including 186 elevated bridges, 57 tunnels and 438 bridges.

[0130] The Mercator projection is adopted, and the default values of various parameters are taken, wherein k0 is taken as 0.9996, EastOffset is taken as 500000m, the latitude and longitude geographic coordinate information is converted into projection coordinates. The regional bridge tunnels are divided into three types of bridges, elevated bridges and tunnels, the bridge and tunnel numbers, horizontal and vertical coordinates, relative distances and connectivity are extracted as main features, and the regional bridge tunnel network is established. The regional bridge tunnel network structure is shown in Figure 2 .

[0131] After the establishment of the bridge network structure, the network is searched in depth, and the connectivity and cut point of the network are obtained. After searching, the bridge network is connected, and there are 26 cut points, numbered 84, 227, 148, 150, 491, 489, 492, 72, 377, 429, 310, 321, 330, 335, 349, 347, 356, 640, 650, 651, 652, 648, 649, 167, 232, 313. These cut points are distributed throughout the network, and if the bridge at the network cut point fails, it will cause network interruption, and some nodes will no longer be connected.

[0132] The number of edges connected by each bridge node is counted to obtain the node degree and the overall degree distribution of the network, as shown in Figure 3 The connection characteristics between nodes are analyzed, and the homophily and average clustering coefficient of the network are calculated; the path characteristics of the network are calculated, including the average path length, network diameter, eccentricity and radius, and the central node is searched; the calculation method of each parameter is shown in Table 2.

[0133] Table 2 Network characteristic calculation method

[0134]

[0135] After calculation, the degree of the bridge network in this area is between 1 and 10, mostly around 4, showing certain Poisson distribution characteristics, and most bridge nodes are connected to about 4 other nodes; the homophily coefficient of the network is 0.1398, between -1 and 1, representing the network has homophily, but the correlation is weak; the average clustering coefficient of the network is 0.132, between 0 and 1, the clustering of the network is weak, that is, most high-degree nodes are connected to low-degree nodes; the average path length of the network is 12.24, the diameter is 39, and the radius is 21. Considering that the bridge network has a total of 681 nodes, the average path length is relatively short, reflecting certain small-world characteristics; the distance weighted values of the network average path length, diameter and radius are 73.28km, 231.87km and 116.16km respectively; the central nodes of the network are nodes 100, 112, 114, 115, 121, 136, 324, 326, 465, 468 and 471; the path weighted central node is node 468, and these nodes are distributed in the center of the network, with the shortest distance to the farthest node.

[0136] The importance of the topology of the bridge node is sorted, and the degree centrality, eigenvector centrality, betweenness centrality and closeness centrality of the node are calculated, the calculation method is shown in Table 3, and the calculation result is visualized as Figure 4The nodes with darker color have higher centrality, the majority of nodes have similar degree in the network when analyzing degree centrality, only a few nodes play a more important role in the shortest path of the network when analyzing betweenness centrality, the majority of nodes are around the central node of the network when analyzing closeness centrality, and the nodes around the node 342 have higher degree in the network when analyzing eigenvector centrality. The node centrality ranking reflects the importance of the nodes in the static network, and the cut point, central node and the like play a more important role in the network.

[0137] Table 3 Node centrality calculation method

[0138]

[0139] After the static topology analysis of the bridge-tunnel network, the vulnerability analysis process is performed. First, the relative size of the maximum connected subgraph and the network efficiency are selected as the evaluation indexes of the network vulnerability in the network characteristics, and the calculation method is shown in Table 4.

[0140] Table 4 Network vulnerability index calculation method

[0141]

[0142] Considering the connectivity and efficiency of the network, the bridge-tunnel nodes are sorted according to the degree centrality, weighted degree centrality, betweenness centrality and weighted betweenness centrality to simulate the static failure order. The node with the maximum weighted betweenness centrality in the figure is removed, and then the weighted betweenness centrality of each node is recalculated, and the step is performed in turn until all nodes are removed, and the dynamic sorting of the weighted betweenness centrality is obtained to simulate the dynamic failure order. In addition, the nodes are randomly sorted to simulate the random failure order. When performing the node removal test on the bridge-tunnel network, first, initialize the bridge-tunnel network, select the node removal strategy, calculate the network efficiency and the number of nodes in the initial state; then remove the nodes in the network in turn according to the corresponding node sorting to simulate the damage of the bridge-tunnel, and each time a node is removed, the damaged proportion of the node is counted and the current vulnerability index of the network is calculated; repeat the process until all nodes in the network are removed. The vulnerability index change curve of the bridge-tunnel network under different strategies is obtained, as shown in Figure 5 and Figure 6 .

[0143] Analysis Figure 5 It can be obtained that the relative size of the maximum connected component of the bridge-tunnel network under dynamic failure decreases sharply with the removal proportion of the nodes, and decreases to about 0.0 after removing about 20% of the nodes, and the network is no longer connected and the transportation function is disabled; under other failure strategies, the network fails after removing about 70% of the nodes, which shows that the nodes ranked at the front in the dynamic sorting are more important. From Figure 6The network efficiency under dynamic failure also decreases most, and reaches the lowest point when about 40% of the nodes are removed. In the network efficiency curve, the value of the network efficiency at the later stage increases with the removal of nodes. This is because, with the removal of nodes and edges, multiple independent nodes are formed in the network, which do not help the network efficiency, so the removal of these nodes will increase the efficiency. This phenomenon is more obvious in the weighted network efficiency.

[0144] According to the recorded vulnerability indicators, a unified indicator for quantifying network vulnerability is calculated, with a = 100, and the calculation formula is:

[0145]

[0146] The vulnerability curves of the bridge-tunnel network under different failure strategies are drawn as shown in Figure 7 When the value of vulnerability is greater than 1, the network efficiency of the current network is approximately 0, or the relative size of the maximum connected subgraph is about 1%, which can be considered as the bridge-tunnel network losing the ability to travel and the network being on the verge of collapse. Therefore, the vulnerability threshold of network failure is set to 1. In the process of removing nodes, the removal of each node will cause a change in network vulnerability, and the change value is the vulnerability degree of the node. The vulnerability degree of each removal of nodes before network collapse is calculated as shown in Figure 8

[0147] Analysis Figure 7 and Figure 8 It can be obtained that the failure speed of the bridge-tunnel network under dynamic failure is the fastest, and it is on the verge of collapse when about 18% of the nodes are removed. The failure speed of the bridge-tunnel network under the failure strategy based on intermediate centrality is slightly greater than that based on degree centrality, because the sorting of intermediate centrality is related to the shortest path between nodes. The vulnerability curve of the bridge-tunnel network under random failure is generally consistent with other static removal strategies, and it collapses when about 60% of the nodes are removed. From Figure 8 It can be obtained that the change in network vulnerability caused by each removal of nodes is different, and there are critical vulnerable nodes in the bridge-tunnel network, and the increase in network vulnerability caused by the failure of these nodes is much greater than that of other general nodes.

[0148] Based on the Monte Carlo sampling method, a single random sampling of a complex random process or system has a large uncertainty. Therefore, multiple random node failure strategies are repeated and the vulnerability degree of each test node is recorded. Through 2000 samplings, a unified vulnerable node identification result is obtained as shown in Figure 9 ​The numbers of the 10 nodes with the highest vulnerability are 72, 210, 213, 246, 468, 474, 481, 483, 572, and 576, respectively, and their failure will bring stronger impact on the overall bridge network in more cases. In order to effectively reduce the potential risk, it is suggested that the traffic network manager should pay more attention to the state of these high-vulnerability nodes, implement targeted monitoring and maintenance measures, and ensure regular inspection and necessary reinforcement of these key nodes by optimizing resource arrangement and allocation, which can significantly improve the overall stability and security of the network. In addition, the manager should develop emergency plans to deal with the impact of the failure of these nodes, ensure the rapid recovery of traffic flow in emergency situations, and reduce the negative impact on regional economy and social life.

[0149] The present application combines complex network theory and Monte Carlo method, not only provides a quantitative and scientific evaluation standard for the vulnerability analysis of regional bridge network, but also improves the consistency and reliability of the identification results of key vulnerable nodes, which can help traffic managers optimize bridge and tunnel facility monitoring, detection, maintenance and emergency strategy, reasonably allocate resources, and improve the anti-risk ability of regional bridge and tunnel network.

[0150] The present application also provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the vulnerability evaluation and vulnerable node identification method for the safe operation and maintenance of regional bridge and tunnel network when executing the computer program.

[0151] The present application also provides a computer readable storage medium for storing computer instructions, wherein the computer instructions implement the steps of the vulnerability evaluation and vulnerable node identification method for the safe operation and maintenance of regional bridge and tunnel network when executed by a processor.

[0152] The memory in the embodiments of the present application can be a volatile memory or a nonvolatile memory, or can include both volatile and nonvolatile memory. Among them, the nonvolatile memory can be a read only memory (ROM), a programmable ROM (PROM), an erasable programmable ROM (EPROM), an electrically EPROM (EEPROM), or a flash memory. The volatile memory can be a random access memory (RAM) used as an external cache. By way of example, and not limitation, many forms of RAM can be used, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous dynamic RAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DRRAM). It is noted that the memory of the methods described herein is intended to include, but not be limited to, these and any other suitable types of memory.

[0153] In the above embodiments, all or part of the method can be implemented by software, hardware, firmware or any combination thereof. When implemented by software, all or part of the method can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transferred from one website, computer, server or data center to another website, computer, server or data center through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available media can be magnetic media (such as floppy disk, hard disk, magnetic tape), optical media (such as high-density digital video disc (digital video disc, DVD)), or semiconductor media (such as solid state disc (solid state disc, SSD)) and the like.

[0154] In the implementation process, each step of the above method can be completed by integrated logic circuit of hardware in the processor or instruction in the form of software. The steps of the method disclosed in the embodiments of the present application can be directly embodied as hardware processor execution or executed by combination of hardware and software modules in the processor. The software module can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, register or other mature storage medium in the art. The storage medium is located in the memory, and the processor reads the information in the memory and combines the hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0155] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with processing capability of signals. In the implementation process, each step of the method embodiments can be completed by integrated logic circuits or instructions in the form of software in the processor. The processor mentioned above can be a general processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present application can be implemented or executed. The general processor can be a microprocessor or the processor can also be any conventional processor. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as hardware code processing executed by the processor, or executed by a combination of hardware and software modules in the code processing processor. The software module can be located in a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, and other mature storage media in the art. The storage medium is located in the storage, and the processor reads the information in the storage, and combines the hardware to complete the steps of the above method.

[0156] The above describes in detail the vulnerability assessment and vulnerable node identification method for regional bridge tunnel network security operation and maintenance proposed by the present application. In this paper, specific examples are applied to explain the principles and implementation modes of the present application. The above embodiment is only used to help understand the method of the present application and its core idea; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed; according to the above, the content of the specification should not be understood as the limitation of the present application.

Claims

1. A method for vulnerability assessment and vulnerable node identification for regional bridge tunnel network security operation and maintenance, characterized in that, The method comprises the following steps: Step one, preprocessing and integration of regional bridge and tunnel information, and establishment of regional bridge and tunnel network; Step two, analysis of bridge and tunnel network characteristics based on graph theory and complex network theory, and obtaining of key nodes of bridge and tunnel network topology structure; Step three, selection of vulnerability index by comprehensively considering reachability and network efficiency, adoption of different node failure strategies, and calculation of the correspondence between node removal ratio and vulnerability index; Step four, calculation of overall vulnerability of bridge and tunnel network, vulnerability analysis of the network, and recording of the vulnerability degree of each bridge and tunnel node; Step five, identification of vulnerable nodes of the bridge and tunnel network by calculating the vulnerability degree expectation of the bridge and tunnel nodes through multiple random calculations by using the Monte Carlo sampling method; The step three is specifically: Step three one, selection of the relative size of the largest connected component and network efficiency as the vulnerability index of the network in the bridge and tunnel network characteristics, and the calculation formula is: wherein LCC G is the relative size of the largest connected subgraph; E G is the network efficiency; N is the total number of bridges and tunnels; n lc is the number of nodes in the largest connected component; is the connected node penalty term for network efficiency, wherein n c is the total number of connected nodes in the network, n is the number of nodes in the current network;​​ Step three two, sorting of the bridge and tunnel nodes according to the degree centrality, weighted degree centrality, intermediate centrality and weighted intermediate centrality, simulation of static failure sequence, removal of the node with the largest weighted intermediate centrality in the graph, recalculation of the weighted intermediate centrality of each node, and sequential performance of this step until all nodes are removed to obtain the dynamic sorting of the weighted intermediate centrality and simulate the dynamic failure sequence; random sorting of the nodes to simulate the random failure sequence; Step three three, removal of the nodes of the bridge and tunnel network according to the different failure sequences obtained in step three two, statistics of the damaged network proportion and recording of the corresponding network vulnerability index after the removal of each node; The step three three is specifically: Step three three one, input of the initial bridge and tunnel network, calculation of the network efficiency and the number of nodes in the initial state, and selection of the removal strategy of the bridge and tunnel nodes; Step three three two, selection of a bridge and tunnel node according to the corresponding node sorting, removal of the node in the network to simulate the damage of the bridge and tunnel, and calculation of the network efficiency and the relative size of the largest connected component after the damage; Step three three three, statistics of the node damage ratio, judgment of whether all nodes are traversed, and, if not, continuous performance of step three three two until all nodes are removed, and output of the statistical results of the vulnerability index; The step four is specifically: Step four one, comprehensive consideration of the relative size of the largest connected component and the network efficiency, and proposal of a unified index for quantifying the vulnerability of the bridge and tunnel network, and the calculation formula is: wherein SV G’ is the static vulnerability of the network; Δ E G’ is the change in network efficiency; α is the connectivity importance coefficient;​​ The threshold of network failure vulnerability is set to 1, and when the vulnerability of the network reaches the threshold E ( G’ ) is 0 or LCC ( G’ ) is 1%, which can be the trigger condition for network collapse; Step four two, calculation of the network vulnerability change caused by the removal of each node, one-to-one correspondence between the vulnerability and the nodes according to the node removal sequence recorded in step three three, and calculation of the vulnerability degree of each bridge and tunnel node.

2. The method of claim 1, wherein, The step one is specifically: The information of regional bridges and tunnels is preprocessed, the horizontal Mercator projection is adopted, and the bridge and tunnel geographic coordinates WGS84 are converted into projection coordinates UTM; for latitude and longitude , the conversion formula is: wherein is a scaling factor; N is the latitude-longitude ellipsoid radius; is the central meridian longitude; and EastOffset is the east offset; M ( ) is the arc length from the equator to the latitude . The regional bridge and tunnel is divided into three types of bridge, viaduct and tunnel, the number, coordinates, connectivity and distance are extracted as the main features, and the regional bridge and tunnel network is established.

3. The method of claim 2, wherein, The step two is specifically: Step two one, deep-first search (DFS) of the established bridge and tunnel network to obtain the connectivity and cut points of the network; Step two two, statistics of the number of edges connected by each bridge and tunnel node to obtain the node degree and the degree distribution of the network; analysis of the connection characteristics between nodes, and calculation of the homomorphism and average clustering coefficient of the network, and the calculation formula is: wherein, R , C are the assortativity coefficient and the average clustering coefficient of the network, respectively; j i , k i denote the degrees of the two end points of an edge, respectively; M is the number of edges in the network; N is the number of nodes in the network, l i is the degree of a node i ; E i is the number of edges between the neighboring nodes of a node i ; Step two three, analyze the path characteristics of the network, including the average path length a , network diameter l , eccentricity ρ and radius r , and search for the center node, the formula is: wherein d ( i , j ) is the shortest path between the nodes i and the nodes j ; the node with an eccentricity equal to the radius is the central node of the network; Step two four, analyze the network topology importance of each bridge node, respectively calculate the degree centrality, eigenvector centrality, betweenness centrality and closeness centrality of the node, the calculation formula is: wherein is an eigenvalue; is an element of the adjacency matrix, indicating whether there is an edge between node i and node j ; is the total number of shortest paths between node s and node t ; is the number of shortest paths that pass through node i .

4. The method of claim 3, wherein, The step two one is specifically: Step two one, initialize a timestamp variable time for tracking the order of visiting nodes; initialize the node's access time discovery and the earliest traceable time low; Step two 112, select an initial node i Set the node's access time dis[ i ] and initial lowest back edge time low[ i ] to the current time; Step 213, traverse all neighbors of the node j If j is not visited, continue with step 213 and update low[ i ] If j has been visited and is not i 's parent, then update low[ i ] to min(low[ i ], dis[ j ]) to indicate that j can be reached by backtracking the path. After step 213 is completed, if there are still unvisited nodes, the node is initialized again and steps 211-213 are repeated, and each time this is done, the number of connected components increases by one, and for each node i If i is a root node and there are two or more subtrees, then i is a cut vertex; if i is a non-root node, then check if low[ j ] is greater than or equal to dis[ i ], i.e., the child node j cannot return to i 's ancestor through the backtracking path, then i is a cut vertex.

5. The method according to claim 4, characterized in that The step five is specifically: Step five one, take a random failure order, according to step three three, obtain the vulnerability analysis result of the bridge network under the node random failure, record the vulnerability degree of each bridge node; Step five two, based on the principle of Monte Carlo, repeat step five one, a large number of sampling in the random failure strategy, estimate the vulnerability degree expectation of each bridge node as its overall vulnerability; According to the overall vulnerability, identify the vulnerable node of the bridge network, and mark and visualize the bridge network topology diagram. 6.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The processor executes the computer program to realize the steps of the method of any one of claims 1-5.

7. A computer readable storage medium for storing computer instructions, characterized in that, The computer instructions are executed by the processor to realize the steps of the method of any one of claims 1-5.

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