A method, system, terminal and storage medium for analyzing the robustness of an urban road network based on primitives

Abstract

The present invention relates to the technical field of network performance analysis, and discloses a method, system, terminal and storage medium for analyzing the robustness of an urban road network based on primitives. The method includes: obtaining data of the urban road network and modeling the urban road network; in the urban road network, selecting primitives as the research objects, and calculating the corresponding structural robustness scores of each type of primitive according to the structures of each type of primitive; according to the structural robustness scores, deleting and restoring each primitive in the urban road network one by one, and calculating global network metrics; according to the global network metrics, plotting the robustness measure curve of the urban road network, and calculating the robustness measure index of the urban road network. The present invention introduces the perspective of primitives in network theory, takes primitives as microscopic structural units, deeply analyzes the local complex structures of the road network, and significantly improves the accuracy of the analysis results of the robustness of the urban road network.

Description

Technical Field

[0001] The present invention relates to the technical field of urban road network performance analysis, and particularly relates to a method, system, terminal and computer-readable storage medium for analyzing the robustness of an urban road network based on primitives. Background Art

[0002] With the acceleration of the urbanization process, urban roads, as the core component of the transportation system, undertake important economic and social functions. It not only directly affects the quality of life of urban residents, but also is an important lifeline for the operation of the city. Urban road networks usually exhibit typical characteristics of complex networks such as small-worldness and scale-freeness, and have significant topological regularities at the global and local levels. These characteristics enable complex network metrics (such as degree centrality, betweenness centrality, largest connected subgraph ratio, etc.) to be widely used in the vulnerability analysis and performance optimization of transportation networks.

[0003] However, existing research mainly focuses on the global characteristics of transportation networks or the local importance of a single node, and lacks in-depth analysis of how local complex structures (such as roundabouts, bridge sections, etc.) affect the overall robustness of the transportation network. That is, in the existing urban road network robustness analysis technology, the influence of local complex structures on the overall network robustness is ignored, resulting in low accuracy of the urban road network robustness analysis results and being unable to provide reliable theoretical basis and technical support for the improvement of the robustness and risk prevention and control of urban complex road networks.

[0004] Therefore, the existing technology still needs to be improved and developed. Summary of the Invention

[0005] The main purpose of the present invention is to provide a method, system, terminal and computer-readable storage medium for analyzing the robustness of an urban road network based on primitives, aiming to solve the problem that in the existing urban road network robustness analysis, the influence of local complex structures on the overall network robustness is ignored, resulting in low accuracy of the overall network robustness analysis results.

[0006] To achieve the above invention purpose, the present invention provides a method for analyzing the robustness of an urban road network based on primitives, and the method for analyzing the robustness of an urban road network based on primitives includes:

[0007] Obtain data of the urban road network, and model the urban road network, taking the road sections in the urban road network as edges and the intersections in the urban road network as nodes;

[0008] In the urban road network, select primitives of a preset number of nodes as the research object, obtain various types corresponding to the primitives, and calculate the structure robustness scores corresponding to each type of primitive according to the structures of each type of primitive;

[0009] Delete and recover each primitive in the urban road network one by one according to the structural robustness score, and calculate the global network metrics after deleting and recovering the primitive;

[0010] Draw the robustness measure curve of the urban road network according to the global network metrics, and calculate the robustness measure index of the urban road network based on the robustness measure curve.

[0011] Optionally, obtaining the data of the urban road network and modeling the urban road network, using the road segments in the urban road network as edges and the intersections in the urban road network as nodes, specifically includes:

[0012] Obtain the data of the urban road network based on the OSM platform, where the data is road vector data;

[0013] Model the urban road network using the ArcGIS platform according to the road vector data, using the road segments in the urban road network as edges and the intersections in the urban road network as nodes, to obtain an unweighted undirected graph corresponding to the urban road network.

[0014] Optionally, in the urban road network, select the primitives of a preset number of nodes as the research objects, obtain various types corresponding to the primitives, and calculate the structural robustness scores corresponding to each type of primitive according to the structures of each type of primitive, specifically including:

[0015] In the unweighted undirected graph corresponding to the urban road network, select the primitives of a preset number of nodes as the research objects, and obtain various types corresponding to the primitives;

[0016] Calculate the node-edge ratio and average node degree corresponding to each type of primitive according to the structures of each type of primitive:

[0017] ;

[0018] ;

[0019] Among them, represents the node-edge ratio, represents the number of edges in the primitive, represents the number of nodes in the primitive, represents the average node degree, represents the number of connected edges of the i-th node in the primitive;

[0020] Calculate the structural robustness scores corresponding to each type of primitive according to the node-edge ratio and the average node degree corresponding to each type of primitive:

[0021] ;

[0022] Among them, represents the structural robustness score;

[0023] Among them, the primitive element is a local complex structure in the urban road network, and the local complex structure includes a roundabout and a bridge section.

[0024] Optionally, before deleting and restoring each primitive element in the urban road network one by one according to the structural robustness score and calculating the global network index after deleting and restoring the primitive element, it further includes:

[0025] Calculating the initial global network index of the urban road network;

[0026] Among them, the initial global network index includes the initial maximum connected subgraph ratio or the initial network efficiency.

[0027] Optionally, deleting and restoring each primitive element in the urban road network one by one according to the structural robustness score and calculating the global network index after deleting and restoring the primitive element specifically includes:

[0028] Deleting each primitive element in the urban road network one by one in the order of the structural robustness scores corresponding to each type of primitive element from large to small;

[0029] Calculating the global network index once after deleting each primitive element;

[0030] Restoring each primitive element in the urban road network one by one in the order of the structural robustness scores corresponding to each type of primitive element from large to small;

[0031] Calculating the global network index once after restoring each primitive element;

[0032] Among them, the global network index includes the maximum connected subgraph ratio or the network efficiency.

[0033] Optionally, the calculation formula of the maximum connected subgraph ratio is:

[0034] GC = ;

[0035] Among them, GC represents the maximum connected subgraph ratio, represents the number of nodes in the largest connected subgraph in the urban road network after being perturbed or restored, and N represents the total number of nodes in the urban road network after being perturbed or restored;

[0036] The calculation formula of the network efficiency is:

[0037] ;

[0038] Among them, NE represents the network efficiency, and G represents the urban road network after being perturbed or restored. represents the shortest path length between the i-th node and the j-th node.

[0039] Optionally, the robustness measure indicators include redundancy, resourcefulness, robustness loss, resistance, rapidity, and resilience.

[0040] Drawing the robustness measure curve of the urban road network according to the global network indicator, and calculating the robustness measure indicator of the urban road network based on the robustness measure curve, specifically including:

[0041] Drawing the robustness measure curve of the urban road network according to the largest connected subgraph ratio or the network efficiency. The vertical axis of the robustness measure curve is the value of the largest connected subgraph ratio or the network efficiency, and the horizontal axis of the robustness measure curve is the time for calculating the largest connected subgraph ratio or the network efficiency. And taking the value of the initial largest connected subgraph ratio or the initial network efficiency as the ordinate of the intersection point of the robustness measure curve and the vertical axis.

[0042] Calculating the redundancy A of the urban road network based on the robustness measure curve:

[0043] ;

[0044] Among them, represents the robustness measure curve, T represents the time for calculating the largest connected subgraph ratio or the network efficiency, and T1 represents the abscissa corresponding to the inflection point in the robustness measure curve.

[0045] Calculating the resourcefulness B of the urban road network based on the robustness measure curve:

[0046] ;

[0047] Among them, T2 represents the abscissa corresponding to the highest point in the increasing part of the robustness measure curve.

[0048] Calculating the robustness loss C of the urban road network based on the robustness measure curve:

[0049] ;

[0050] Among them, P represents the initial connected subgraph ratio or the initial network efficiency.

[0051] Based on the robustness measure curve, taking the abscissa T1 corresponding to the inflection point in the robustness measure curve as the resistance of the urban road network.

[0052] Based on the robustness measure curve, the abscissa T2 corresponding to the highest point of the increasing part in the robustness measure curve is taken as the rapidity of the urban road network;

[0053] Based on the robustness measure curve, the difference between the abscissa T2 corresponding to the highest point of the increasing part in the robustness measure curve and the abscissa T1 corresponding to the inflection point in the robustness measure curve is taken as the resilience of the urban road network.

[0054] To achieve the above-mentioned invention purpose, the present invention also provides a primitive-based urban road network robustness analysis system, and the primitive-based urban road network robustness analysis system includes:

[0055] Road network modeling module: used to obtain data of the urban road network, model the urban road network, take the road sections in the urban road network as edges, and take the intersections in the urban road network as nodes;

[0056] Primitive structure robustness evaluation module: used to select primitives of a preset number of nodes in the urban road network as research objects, obtain various types corresponding to the primitives, and calculate the structure robustness scores corresponding to each type of primitive according to the structures of each type of primitive;

[0057] Road network perturbation or recovery module: used to delete and recover the primitives in the urban road network one by one according to the structure robustness scores, and calculate the global network indicators after deleting and recovering the primitives;

[0058] Road network robustness analysis module: used to draw the robustness measure curve of the urban road network according to the global network indicators, and calculate the robustness measure indicators of the urban road network based on the robustness measure curve.

[0059] To achieve the above-mentioned invention purpose, the present invention also provides a terminal, and the terminal includes: a memory, a processor, and a primitive-based urban road network robustness analysis program stored on the memory and executable on the processor. When the primitive-based urban road network robustness analysis program is executed by the processor, the steps of the above-mentioned primitive-based urban road network robustness analysis method are implemented.

[0060] To achieve the above-mentioned invention purpose, the present invention also provides a computer-readable storage medium, and the computer-readable storage medium stores a primitive-based urban road network robustness analysis program. When the primitive-based urban road network robustness analysis program is executed by a processor, the steps of the above-mentioned primitive-based urban road network robustness analysis method are implemented.

[0061] In the present invention, data of an urban road network is acquired, and the urban road network is modeled. Road segments in the urban road network are used as edges, and intersections in the urban road network are used as nodes. In the urban road network, primitives of a preset number of nodes are selected as research objects, multiple types corresponding to the primitives are obtained, and according to the structures of the primitives of each type, structural robustness scores corresponding to the primitives of each type are calculated. According to the structural robustness scores, the primitives in the urban road network are deleted and restored one by one, and global network metrics are calculated after deleting and restoring the primitives. According to the global network metrics, a robustness measure curve of the urban road network is drawn, and based on the robustness measure curve, a robustness measure index of the urban road network is calculated. The present invention introduces the perspective of primitives in network theory, takes primitives as microscopic structural units, deeply analyzes the local topological characteristics of the road network, breaks through the limitations of only focusing on global topological characteristics in the past, more finely depicts the local complex structural characteristics of the road network, considers the influence of local complex structures on the overall robustness of the network, significantly improves the accuracy of the analysis results of the robustness of the urban road network, provides a new perspective for optimizing traffic planning and emergency management, provides a reliable theoretical basis and technical support for enhancing the robustness and risk prevention and control of urban complex road networks; combines primitives with global network metrics to construct a robustness measure curve, quantifies the robustness performance of the road network under different perturbation scenarios, and more intuitively and systematically reveals the key characteristics and laws in the process of attacking and repairing the road network. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a flowchart of a preferred embodiment of the method for analyzing the robustness of an urban road network based on primitives of the present invention;

[0063] Figure 2 is a structural diagram of primitives of various types of the present invention;

[0064] Figure 3 is a robustness measure curve diagram of the present invention;

[0065] Figure 4 is a structural diagram of a preferred embodiment of the system for analyzing the robustness of an urban road network based on primitives of the present invention;

[0066] Figure 5 is a structural diagram of a preferred embodiment of a terminal of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0067] To make the objectives, technical solutions and advantages of the present invention clearer and more definite, the following further describes the present invention in detail with reference to the accompanying drawings and by way of examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0068] With the acceleration of the urbanization process, urban roads, as the core component of the transportation system, undertake important economic and social functions. They not only directly affect the quality of life of urban residents but also are the vital arteries for the operation of the city. Urban road networks usually exhibit typical characteristics of complex networks such as small-worldness and scale-freeness, and have significant topological regularities at both the global and local levels. These characteristics enable complex network metrics (such as degree centrality, betweenness centrality, largest connected subgraph ratio, etc.) to be widely applied to the vulnerability analysis and performance optimization of transportation networks.

[0069] However, existing studies mainly focus on the global characteristics of transportation networks or the local importance of individual nodes, lacking in-depth analysis of how local complex structures (such as roundabouts, bridge sections, etc.) affect the overall robustness of the transportation network. That is, in the existing urban road network robustness analysis techniques, the influence of local complex structures on the overall network robustness is ignored, resulting in low accuracy of the analysis results of urban road network robustness and being unable to provide reliable theoretical basis and technical support for the improvement of the robustness and risk prevention and control of urban complex road networks.

[0070] In recent years, network motifs, as frequently occurring local structural modules in complex networks, have received increasing attention from researchers. Network motifs can reveal the highly organized local structural characteristics in networks and have been proven to be closely related to the robustness and dynamic behavior of systems in fields such as biological networks and social networks. The motif structures in transportation networks, such as roundabouts or bridge sections, often have important impacts on the stability and redundancy of traffic flow, but their application in traffic robustness research is still in the initial exploration stage. By analyzing the differences in the functional performance of motifs in the road network and their impact on the overall robustness, the contribution of local structures to network functions can be more accurately revealed, providing a new theoretical basis for the optimal design of the network.

[0071] To solve the above technical problems, the present invention provides a method for analyzing the robustness of an urban road network based on primitives, which includes obtaining data of the urban road network, modeling the urban road network, taking the road segments in the urban road network as edges, and taking the intersections in the urban road network as nodes; in the urban road network, selecting primitives of a preset number of nodes as the research object, obtaining various types corresponding to the primitives, and calculating the structural robustness scores corresponding to each type of primitive according to the structure of each type of primitive; according to the structural robustness scores, deleting and restoring each primitive in the urban road network one by one, and calculating global network indicators after deleting and restoring the primitive; according to the global network indicators, drawing a robustness measure curve of the urban road network, and calculating a robustness measure index of the urban road network based on the robustness measure curve. The present invention introduces the perspective of primitives in network theory, takes primitives as microscopic structural units, deeply analyzes the local topological characteristics of the road network, breaks through the limitations of only focusing on global topological characteristics in the past, more carefully depicts the local complex structural characteristics of the road network, considers the influence of local complex structures on the overall robustness of the network, significantly improves the accuracy of the analysis results of the robustness of the urban road network, provides a new perspective for optimizing traffic planning and emergency management, and provides a reliable theoretical basis and technical support for improving the robustness and risk prevention and control of urban complex road networks; combines primitives with global network indicators to construct a robustness measure curve, quantifies the robustness performance of the road network under different perturbation scenarios, and more intuitively and systematically reveals the key characteristics and laws in the process of attacking and repairing the road network.

[0072] The following further describes the application content by describing the embodiments in conjunction with the accompanying drawings.

[0073] A preferred embodiment of the method for analyzing the robustness of an urban road network based on primitives according to the present invention is as Figure 1 shown, and specifically includes:

[0074] S1. Obtain data of the urban road network, model the urban road network, take the road segments in the urban road network as edges, and take the intersections in the urban road network as nodes.

[0075] In an implementation manner of this embodiment, the obtaining data of the urban road network, modeling the urban road network, taking the road segments in the urban road network as edges, and taking the intersections in the urban road network as nodes specifically includes:

[0076] Obtain data of the urban road network based on the OSM (OpenStreetMap, Open Street Map) platform, where the data is road vector data;

[0077] Based on the road vector data, use the ArcGIS (Arc Geographic Information System) platform to model the urban road network. Take the road segments in the urban road network as edges and the intersections in the urban road network as nodes to obtain an unweighted and undirected graph corresponding to the urban road network.

[0078] Specifically, the acquisition of road vector data is based on the open geographic information platform OSM, and the ArcGIS platform is used to model the road network (i.e., the urban road network). The road segments are regarded as edges and the intersections are regarded as nodes to obtain an unweighted and undirected graph corresponding to the road network. It should be noted that the urban road network described below in this embodiment actually refers to the unweighted and undirected graph corresponding to the urban road network, that is, the result (unweighted and undirected graph) after modeling the urban road network in this embodiment is also called the urban road network.

[0079] S2. In the urban road network, select the primitives of a preset number of nodes as the research objects, obtain various types corresponding to the primitives, and calculate the structural robustness scores corresponding to each type of primitive according to the structures of each type of primitive.

[0080] In one implementation manner of this embodiment, the step of selecting the primitives of a preset number of nodes as the research objects in the urban road network, obtaining various types corresponding to the primitives, and calculating the structural robustness scores corresponding to each type of primitive according to the structures of each type of primitive specifically includes:

[0081] In the unweighted and undirected graph corresponding to the urban road network, select the primitives of a preset number of nodes as the research objects to obtain various types corresponding to the primitives;

[0082] According to the structures of each type of primitive, calculate the node-edge ratio and average node degree corresponding to each type of primitive:

[0083] ;

[0084] ;

[0085] Among them, represents the node-edge ratio, represents the number of edges in the primitive, represents the number of nodes in the primitive, represents the average node degree, represents the number of connecting edges of the i-th node in the primitive;

[0086] According to the node-edge ratio and the average node degree corresponding to each type of primitive, calculate the structural robustness scores corresponding to each type of primitive:

[0087] ;

[0088] wherein, represents the structural robustness score;

[0089] wherein, the primitive is a local complex structure in the urban road network, and the local complex structure includes a roundabout and a bridge section.

[0090] Specifically, a primitive is a non-isomorphic subgraph composed of several (usually 3 - 8) nodes, and all nodes are connected to at least one other node by at least one edge. Primitives appear frequently in the network. Studying their partitioning helps to understand the connection structure of the network in more detail and explore the self-organizing topological features of the network. It has been proven by research that primitives have an important impact on the structural and functional characteristics of the network. In the urban road network, a primitive is defined as an unweighted undirected graph. It should be noted that the primitive structure in the urban road network refers to the local complex structure in the urban road network, such as roundabouts and bridge sections. There are 2 types of primitives composed of 3 nodes and 6 types of primitives composed of 4 nodes. When the number of nodes increases further, the number of primitives will show an exponential growth state. Therefore, the present invention selects primitives composed of 4 nodes as the research object (i.e., the preset number is 4), namely: chain primitive a, tail primitive b, ring-tail primitive c, ring primitive d, semi-network primitive e, and full-network primitive f. The structure of each type of primitive is as Figure 2 shown. Since the structure of each primitive has its characteristics, it is necessary to evaluate their structural robustness for differentiation, which mainly depends on two aspects: the node-edge ratio and the average node degree. Among them, by analyzing the node-edge ratio between nodes, the redundancy degree of the primitive can be intuitively evaluated; while the connectivity can be accurately reflected by the index of the average node degree; and the product result of the node-edge ratio and the average node degree can effectively characterize the level of the structural robustness of the primitive. As shown in Table 1, the score situations of different primitives are listed in Table 1. For example, the connections between nodes of the chain primitive and the tail primitive are relatively few, so the scores are relatively low, while the connections between nodes of the full-network primitive and the semi-network primitive are relatively many, so the scores are relatively high.

[0091] Table 1: Structural Robustness Score Table of Each Type of Primitive

[0092]

[0093] S3. According to the structural robustness score, delete and restore each primitive in the urban road network one by one, and calculate the global network index after deleting and restoring the primitive.

[0094] In one implementation of this embodiment, before deleting and restoring the primitives in the urban road network one by one according to the structural robustness score and calculating the global network metrics after deleting and restoring the primitives, it further includes:

[0095] Calculating the initial global network metrics of the urban road network;

[0096] Wherein, the initial global network metrics include the initial maximum connected subgraph ratio or the initial network efficiency.

[0097] In one implementation of this embodiment, deleting and restoring the primitives in the urban road network one by one according to the structural robustness score and calculating the global network metrics after deleting and restoring the primitives specifically includes:

[0098] Deleting the primitives in the urban road network one by one in the order of the structural robustness scores corresponding to each type of primitive from large to small;

[0099] After deleting each primitive, calculating the global network metrics once;

[0100] Restoring the primitives in the urban road network one by one in the order of the structural robustness scores corresponding to each type of primitive from large to small;

[0101] After restoring each primitive, calculating the global network metrics once;

[0102] Wherein, the global network metrics include the maximum connected subgraph ratio or the network efficiency.

[0103] In one implementation of this embodiment, the calculation formula of the maximum connected subgraph ratio is:

[0104] GC = ;

[0105] Wherein, GC represents the maximum connected subgraph ratio, represents the number of nodes in the maximum connected subgraph in the urban road network after being perturbed or restored, and N represents the total number of nodes in the urban road network after being perturbed or restored;

[0106] The calculation formula of the network efficiency is:

[0107] ;

[0108] Wherein, NE represents the network efficiency, G represents the urban road network after being perturbed or restored (i.e., the entire road network or the corresponding unweighted undirected graph of the entire road network), represents the shortest path length between the i-th node and the j-th node.

[0109] Specifically, first calculate the initial global network metrics (i.e., initial performance) of the urban road network in the initial state (without being disturbed or restored). The calculation method of the initial global network metrics is the same as that of the global network metrics described below. The global network metrics of the present invention can be the giant component ratio or network efficiency, which is specifically selected according to the actual application situation. The giant component of a network refers to the largest subgraph in a graph (network) where there are paths connecting all nodes, and it is used to reflect the connectivity of the entire network. The giant component ratio (GC) is the ratio of the number of nodes in the giant component to the total number of nodes in the network. The network efficiency (NE) mainly describes the transmission efficiency of information or traffic in the network, and it is calculated by considering the average value of the shortest path lengths between all node pairs in the network. Both the giant component ratio and network efficiency are effective metrics for evaluating the robustness of the network. By identifying and calculating the global network metrics after perturbation and restoration, the connectivity and overall operating state of the traffic network (i.e., the urban road network) can be evaluated. A traffic network with high connectivity (i.e., a high giant component ratio) indicates fewer road breaks and higher redundancy. The network efficiency reflects the overall traffic flow capacity in the traffic network. The higher the efficiency, the faster vehicles or people can reach their destinations.

[0110] Based on the above calculation results of the global network metrics, the present invention uses the primitive strategy to measure the robustness of the urban road network. The specific measurement method is as follows: Delete the primitives in descending order according to the structural robustness scores of each primitive. For primitives with the same score, delete them in the order of their numbers (in step S1, the ArcGIS platform will be used to number each primitive to distinguish them), and then restore them in this order. During this process, calculate the global network metrics (giant component ratio or network efficiency) every time a primitive changes (i.e., every time a primitive is deleted or restored). Taking the score table in Table 1 as an example, first delete the full - network primitive f in descending order of scores, then delete the semi - network primitive e. Then, considering that the loop - end primitive c and the loop primitive d have the same score, delete the loop - end primitive c first and then the loop primitive d in the order of their numbers, and so on. Then delete the chain primitive a and the tail primitive b in turn, and then restore each type of primitive one by one in the same order. During this process, calculate the global network metrics every time a primitive is deleted or restored.

[0111] S4. According to the global network metrics, draw the robustness measurement curve of the urban road network, and based on the robustness measurement curve, calculate the robustness measurement index of the urban road network.

[0112] In an implementation of this embodiment, the robustness measurement indexes include redundancy, resourcefulness, robustness loss, resistance, rapidity, and resilience;

[0113] Drawing the robustness measurement curve of the urban road network according to the global network indexes, and calculating the robustness measurement indexes of the urban road network based on the robustness measurement curve, specifically including:

[0114] Drawing the robustness measurement curve of the urban road network according to the largest connected subgraph ratio or the network efficiency, where the vertical axis of the robustness measurement curve is the value of the largest connected subgraph ratio or the network efficiency, and the horizontal axis of the robustness measurement curve is the time for calculating the largest connected subgraph ratio or the network efficiency, and using the value of the initial largest connected subgraph ratio or the initial network efficiency as the ordinate of the intersection point of the robustness measurement curve and the vertical axis;

[0115] Calculating the redundancy A of the urban road network based on the robustness measurement curve:

[0116] ;

[0117] where, represents the robustness measurement curve, T represents the time for calculating the largest connected subgraph ratio or the network efficiency, and T1 represents the abscissa corresponding to the inflection point in the robustness measurement curve;

[0118] Calculating the resourcefulness B of the urban road network based on the robustness measurement curve:

[0119] ;

[0120] where, T2 represents the abscissa corresponding to the highest point in the increasing part of the robustness measurement curve;

[0121] Calculating the robustness loss C of the urban road network based on the robustness measurement curve:

[0122] ;

[0123] where, P represents the initial connected subgraph ratio or the initial network efficiency;

[0124] Based on the robustness measurement curve, taking the abscissa T1 corresponding to the inflection point in the robustness measurement curve as the resistance of the urban road network;

[0125] Based on the robustness measurement curve, taking the abscissa T2 corresponding to the highest point in the increasing part of the robustness measurement curve as the rapidity of the urban road network;

[0126] Based on the robustness measure curve, the difference between the abscissa T2 corresponding to the highest point of the increasing part in the robustness measure curve and the abscissa T1 corresponding to the inflection point in the robustness measure curve is used as the resilience of the urban road network.

[0127] Specifically, the final calculation results (global network metrics) are plotted on a coordinate axis to form a broken line graph roughly in the shape of a "V". Among them, the horizontal axis is the time T for calculating the global network metrics, and the vertical axis is the value of the global network metrics. , it should be noted that the initial global network metric (i.e., the initial performance P) is also used as . Through information such as the trend changes and inflection point mutations of the curve, key information about the road network robustness and vulnerable edges can be obtained. In addition, different perturbation and recovery methods (referring to different perturbation and recovery strategies, such as degree centrality strategy and betweenness centrality strategy) can be compared to explore the best resistance and repair strategies for the road network after congestion and interruption. Among them, the degree centrality strategy means deleting and recovering edges or nodes in the order of decreasing degree centrality values, then calculating the global network metrics, and plotting the robustness measure curve based on the global network metrics. The betweenness centrality strategy means deleting and recovering edges or nodes in the order of decreasing betweenness centrality values, then calculating the global network metrics, and plotting the robustness measure curve based on the global network metrics.

[0128] For the change results of the curve, each metric can be calculated through the coordinate axis and area of the curve. Among them, the curve function is defined as , the horizontal axis is defined as time, and the vertical axis is defined as the global network metric. As Figure 3 shown, the robustness measure is mainly divided into the following metrics: 1) Redundancy: The ability of the road network to resist attacks, calculated as the area S1 enclosed by the two coordinate axes, the descending part of the curve, and x = T1; 2) Resourcefulness: The ability of the road network to restore effectiveness, calculated as the area S2 enclosed by the ascending part of the curve, the horizontal axis, x = T1, and x = T2; 3) Robustness loss: The degree to which the road network is lower than the initial performance during the whole process of attack and recovery, calculated as the area S3 enclosed by the entire curve and y = P; 4) Resistance: The total duration T1 of the road network experiencing the attack; 5) Resilience: The total duration T2 - T1 of the road network experiencing the recovery; 6) Rapidity: The total duration T2 of the road network experiencing the whole process of attack and recovery.

[0129] The present invention introduces the primitive perspective in network theory. By taking primitives as microscopic structural units, it deeply analyzes the local topological features of road networks, reveals the differences in the functional performance of different primitives and their impact on the overall robustness, and innovatively applies the primitive structure to the study of road network robustness, breaking through the limitations of only focusing on global topological indicators in the past and more precisely depicting the local complex structural features of road networks. The present invention combines the structural analysis and functional evaluation of complex networks, and proposes a complete structural-functional coupling framework for measuring the robustness of road networks, which can quantitatively analyze the response mechanism and recovery process of road networks under perturbation and recovery conditions, and reveal the self-organization and evolution characteristics of the network in a dynamic environment. The present invention has multi-dimensional innovations in robustness evaluation. It comprehensively introduces quantitative indicators such as redundancy, resourcefulness, and robustness loss, constructs a scientific curve, and comprehensively reflects the functional attenuation and recovery of road networks after being attacked. This dynamic evolution evaluation method can more intuitively and systematically reveal the key features and laws of road networks during the process of attack and repair.

[0130] In another implementation of this embodiment, based on the python platform, the subgraph isomorphism algorithm can be used to identify and count the primitives in the road network. To evaluate the rationality of each primitive in the real road network, it is necessary to compare the number of times each primitive appears in the urban road network with the average number of times it appears in a random network with the same number of nodes and the same average node degree, and calculate the standard score to evaluate its rationality. The specific calculation formula is:

[0131] ;

[0132] Where, is the standard score Z-score of the th primitive, is the number of the th primitive in the road network, is the average number of the th primitive in the random network, is the standard deviation of the th primitive in the random network. Primitives with Z-score > 1.96 (or Z-score < -1.96) are regarded as significant primitives, that is, those with a number greater than (or less than) the number of primitives in the random network.

[0133] In the comparative analysis of the number of primitive elements between the urban road network and the random network, the overall number of chain primitives a and tail primitives b in the urban road network shows a significant lack, while the number of loop-tail primitives c and loop primitives d is significantly higher than that of the random network. At the same time, semi-network primitives e and full-network primitives f are almost non-existent in both types of networks. This phenomenon reveals that the urban road network has a more complex and stable structural feature compared to the random network, and the formation of this feature is closely related to the significant enrichment of loop-tail primitives c and loop primitives d. Through in-depth analysis, it can be seen that local loop structures widely exist in the urban road network, and these features are specifically mapped in the spatial layout of actual road facilities such as short-distance adjacent intersections, loop intersections, and interchange intersections. However, it is worth noting that there is almost no internal connection within the loop primitive d. The reason for this phenomenon stems from multiple practical constraints. From the perspective of urban construction practice, in the real road network, there are very few three-intersection loop structures sharing the same road. This structure will appear in a few interchange hubs. Moreover, if a loop of internally connected roads as presented by the full-network primitive f is constructed, it will inevitably occupy a large amount of urban land area. Under the objective condition of scarce urban land resources, this obviously lacks general construction operability.

[0134] In addition, based on the above-mentioned primitive-based urban road network robustness analysis method, the present invention also provides a primitive-based urban road network robustness analysis system. Among them, a preferred embodiment of the primitive-based urban road network robustness analysis system is as Figure 4 shown, and specifically includes:

[0135] Road network modeling module 01: used to obtain data of the urban road network, model the urban road network, take the road segments in the urban road network as edges, and take the intersections in the urban road network as nodes;

[0136] Primitive structure robustness evaluation module 02: used to select primitives of a preset number of nodes in the urban road network as the research object, obtain various types corresponding to the primitives, and calculate the structure robustness scores corresponding to each type of primitive according to the structures of each type of primitive;

[0137] Road network perturbation or recovery module 03: used to delete and recover the primitives in the urban road network one by one according to the structure robustness scores, and calculate the global network indicators after deleting and recovering the primitives;

[0138] Road network robustness analysis module 04: used to draw the robustness measure curve of the urban road network according to the global network indicators, and calculate the robustness measure index of the urban road network based on the robustness measure curve.

[0139] In addition, based on the above-described primitive-based urban road network robustness analysis method and system, the present invention also correspondingly provides a terminal. In a preferred embodiment of the terminal, as Figure 5 shown, it specifically includes a processor 10, a memory 20, and a display 30. Figure 5 Only some components of the terminal are shown. However, it should be understood that it is not required to implement all the shown components, and more or fewer components can be alternatively implemented.

[0140] In some embodiments, the memory 20 can be an internal storage unit of the terminal, such as the hard disk or memory of the terminal. In other embodiments, the memory 20 can also be an external storage device of the terminal, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, and a Flash Card equipped on the terminal, etc. Further, the memory 20 can also include both the internal storage unit and the external storage device of the terminal. The memory 20 is used to store application software installed on the terminal and various types of data, such as storing the program code of the terminal, etc. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, a primitive-based urban road network robustness analysis program 40 is stored on the memory 20, and the primitive-based urban road network robustness analysis program 40 can be executed by the processor 10, thereby implementing the steps of the primitive-based urban road network robustness analysis method in the present application.

[0141] In some embodiments, the processor 10 can be a Central Processing Unit (CPU), a microprocessor, or other data processing chips, and is used to run the program code stored in the memory 20 or process data, such as executing the primitive-based urban road network robustness analysis program 40, etc.

[0142] In some embodiments, the display 30 can be an LED display, a liquid crystal display, a touch liquid crystal display, and an OLED (Organic Light-Emitting Diode) toucher, etc. The display 30 is used to display information on the terminal and to display a visual user interface.

[0143] In one embodiment, when the processor 10 executes the primitive-based urban road network robustness analysis program 40 in the memory 20, the steps of the primitive-based urban road network robustness analysis method as described above are implemented.

[0144] The present invention also correspondingly provides a computer-readable storage medium. The computer-readable storage medium stores a program for analyzing the robustness of an urban road network based on primitives. When the program for analyzing the robustness of an urban road network based on primitives is executed by a processor, the steps of the method for analyzing the robustness of an urban road network based on primitives as described above are implemented.

[0145] It should be noted that in this document, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal including a series of elements not only includes those elements but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or terminal. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or terminal including such element.

[0146] Certainly, those of ordinary skill in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware (such as a processor, a controller, etc.) through a computer program. The program can be stored in a computer-readable storage medium readable by a computer. When the program is executed, it can include the processes of the above method embodiments. The computer-readable storage medium can be a memory, a magnetic disk, an optical disc, etc.

[0147] It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or transformations can be made according to the above description. All such improvements and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for analyzing the robustness of an urban road network based on primitives, characterized in that The method for analyzing the robustness of an urban road network based on primitives includes: Obtaining data of the urban road network, modeling the urban road network, taking road segments in the urban road network as edges, and taking intersections in the urban road network as nodes; In the urban road network, selecting primitives of a preset number of nodes as research objects, obtaining various types corresponding to the primitives, and calculating structure robustness scores corresponding to each type of primitive according to the structures of each type of primitive; According to the structure robustness scores, deleting and restoring each primitive in the urban road network one by one, and calculating global network metrics after deleting and restoring the primitive; According to the global network metrics, plotting a robustness measure curve of the urban road network, and calculating a robustness measure index of the urban road network based on the robustness measure curve; Before the step of deleting and restoring each primitive in the urban road network one by one according to the structure robustness scores and calculating global network metrics after deleting and restoring the primitive, it further includes: Calculating an initial global network metric of the urban road network; Wherein, the initial global network metric includes an initial maximum connected subgraph ratio or an initial network efficiency; The step of deleting and restoring each primitive in the urban road network one by one according to the structure robustness scores and calculating global network metrics after deleting and restoring the primitive specifically includes: Deleting each primitive in the urban road network one by one in the order of decreasing structure robustness scores corresponding to each type of primitive; Calculating a global network metric once after deleting each primitive; Restoring each primitive in the urban road network one by one in the order of decreasing structure robustness scores corresponding to each type of primitive; Calculating a global network metric once after restoring each primitive; Wherein, the global network metric includes a maximum connected subgraph ratio or a network efficiency; The calculation formula for the maximum connected subgraph ratio is: GC= ; Among them, GC represents the maximum connected subgraph rate, which represents the number of nodes in the maximum connected subgraph of the urban road network after being perturbed or restored, and N represents the total number of nodes in the urban road network after being perturbed or restored; The calculation formula for the network efficiency is: ； Among them, NE represents the network efficiency, and G represents the urban road network after being disturbed or restored. represents the shortest path length between the i-th node and the j-th node.

2. The method for analyzing the robustness of an urban road network based on primitives according to claim 1, wherein The step of obtaining data of the urban road network, modeling the urban road network, taking road segments in the urban road network as edges, and taking intersections in the urban road network as nodes specifically includes: Obtaining data of the urban road network based on the OSM platform, wherein the data is road vector data; According to the road vector data, using the ArcGIS platform to model the urban road network, taking road segments in the urban road network as edges, and taking intersections in the urban road network as nodes, to obtain an unweighted undirected graph corresponding to the urban road network.

3. The method for analyzing the robustness of an urban road network based on primitives according to claim 2, wherein The step of selecting primitives of a preset number of nodes as research objects in the urban road network, obtaining various types corresponding to the primitives, and calculating structure robustness scores corresponding to each type of primitive according to the structures of each type of primitive specifically includes: In the unweighted undirected graph corresponding to the urban road network, selecting primitives of a preset number of nodes as research objects, and obtaining various types corresponding to the primitives; According to the structures of various types of primitives, the node-edge ratio and average node degree corresponding to each type of primitive are calculated: ； ； Among them, represents the node-edge ratio, represents the number of edges in the primitive, represents the number of nodes in the primitive, represents the average node degree, represents the number of connected edges of the i-th node in the primitive; According to the node-edge ratio and the average node degree corresponding to each type of primitive, the structural robustness scores corresponding to each type of primitive are calculated: ； Among them, represents the structural robustness score; Wherein, the primitive is a local complex structure in the urban road network, and the local complex structure includes a roundabout and a bridge section.

4. The method for analyzing the robustness of an urban road network based on primitives according to claim 1, wherein The robustness measure indicators include redundancy, resourcefulness, robustness loss, resistance, rapidity, and resilience; Based on the global network indicators, a robustness measure curve of the urban road network is drawn, and based on the robustness measure curve, the robustness measure indicators of the urban road network are calculated, specifically including: According to the largest connected subgraph ratio or the network efficiency, a robustness measure curve of the urban road network is drawn. The vertical axis of the robustness measure curve is the value of the largest connected subgraph ratio or the network efficiency, and the horizontal axis of the robustness measure curve is the time for calculating the largest connected subgraph ratio or the network efficiency. The value of the initial largest connected subgraph ratio or the initial network efficiency is used as the ordinate of the intersection point of the robustness measure curve and the vertical axis; Based on the robustness measure curve, the redundancy A of the urban road network is calculated: ； Among them, represents the robustness measure curve, T represents the time for calculating the largest connected subgraph rate or network efficiency, and T1 represents the abscissa corresponding to the inflection point in the robustness measure curve; Based on the robustness measure curve, the resourcefulness B of the urban road network is calculated: ； Wherein, T2 represents the abscissa corresponding to the highest point of the increasing part in the robustness measure curve; Based on the robustness measure curve, the robustness loss C of the urban road network is calculated: ； Wherein, P represents the initial connected subgraph ratio or the initial network efficiency; Based on the robustness measure curve, the abscissa T1 corresponding to the inflection point in the robustness measure curve is used as the resistance of the urban road network; Based on the robustness measure curve, the abscissa T2 corresponding to the highest point of the increasing part in the robustness measure curve is used as the rapidity of the urban road network; Based on the robustness measure curve, the difference between the abscissa T2 corresponding to the highest point of the increasing part in the robustness measure curve and the abscissa T1 corresponding to the inflection point in the robustness measure curve is used as the resilience of the urban road network.

5. A primitive-based urban road network robustness analysis system, characterized in that, The primitive-based urban road network robustness analysis system is applied to the primitive-based urban road network robustness analysis method according to any one of claims 1-4. The primitive-based urban road network robustness analysis system includes: A road network modeling module: used to obtain the data of the urban road network, model the urban road network, take the road sections in the urban road network as edges, and take the intersections in the urban road network as nodes; A primitive structure robustness evaluation module: used to select primitives with a preset number of nodes in the urban road network as research objects, obtain various types corresponding to the primitives, and calculate the structural robustness scores corresponding to each type of primitive according to the structures of each type of primitive; Road network perturbation or recovery module: used to delete and recover each primitive in the urban road network one by one according to the structural robustness score, and calculate the global network metrics after deleting and recovering the primitive; Road network robustness analysis module: used to draw the robustness measure curve of the urban road network according to the global network metrics, and calculate the robustness measure index of the urban road network based on the robustness measure curve.

6. A terminal, characterized in that, The terminal includes: a memory, a processor, and a primitive-based urban road network robustness analysis program stored on the memory and executable on the processor. When the primitive-based urban road network robustness analysis program is executed by the processor, it implements the steps of the primitive-based urban road network robustness analysis method according to any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a primitive-based urban road network robustness analysis program. When the primitive-based urban road network robustness analysis program is executed by a processor, it implements the steps of the primitive-based urban road network robustness analysis method according to any one of claims 1-4.

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