Urban road network toughness management platform and evaluation method based on dynamic cascade failure

Abstract

The invention relates to the field of traffic engineering, and discloses an urban road network toughness management platform and evaluation method based on dynamic cascade failure, and the platform comprises a disturbance scene simulation and random capacity degradation module, a dynamic cascade failure process simulation module, and a multi-dimensional toughness index calculation and uncertainty evaluation module. A toughness three-dimensional vector is formed by integrating system robustness, restorability and performance accumulated loss, and a time-varying dynamic traffic distribution model considering road network structure change is used for depicting a cascade failure dynamic process; a random variable is introduced into a damaged road section capacity index, and a new evaluation method is provided for solving the defect that the existing toughness evaluation method is difficult to comprehensively quantify the robustness and the restorability of a road network. A failure diffusion mechanism in an abnormal scene is truly restored, and an effective method is provided for overcoming the double defects that a traditional model is insufficient in quantification of travel behavior dynamics and a system recovery process.

Description

Technical Field

[0001] This invention relates to the field of traffic engineering, specifically to a city road network resilience management platform and assessment method based on dynamic cascading failure. Background Technology

[0002] Urban road traffic systems are massive systems composed of multiple subsystems with strong randomness. Due to abnormal events such as traffic accidents, road construction, and large-scale events, individual road segments or intersections may fail, leading to further failures of related road segments or intersections—a cascading failure of the road traffic network. Understanding the dynamic cascading failure process and resilience evolution of urban road networks under the impact of abnormal events, and developing a dynamic cascading failure resilience analysis system for urban road networks that integrates failure simulation and resilience assessment, is of urgent practical need and significant theoretical value.

[0003] In the field of urban road network resilience assessment, existing technologies have significant shortcomings. These shortcomings are primarily reflected in the fact that most current studies employ static traffic assignment models to construct cascading failure models, simulating the chain reaction triggered by traffic flow redistribution under disturbances by coupling traffic assignment with failure mechanisms. This approach treats dynamic processes statically, simulating dynamic cascading within a static framework. It only approximates the failure steady state through iterative assignment, thus failing to accurately reproduce the failure propagation mechanism under abnormal scenarios.

[0004] Therefore, this paper proposes a city road network resilience management platform and evaluation method based on dynamic cascading failure to address the above problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an urban road network resilience management platform and evaluation method based on dynamic cascading failure, thus solving the problems mentioned in the background section.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for assessing the resilience of urban road networks based on dynamic cascading failures, comprising the following steps: Step 001: Establish a road network model and determine road segment attributes such as free flow time and capacity based on road level. Based on the urban road network model and traffic flow survey results, establish an adjacency matrix and a traffic flow matrix.

[0007] Step 002: Using a three-dimensional vector as the resilience metric for the road traffic system, construct a three-dimensional resilience assessment method that integrates the robustness, resilience, and cumulative performance loss of the road traffic system into the three-dimensional resilience vector. middle.

[0008] Step 003: Establish a cascading failure model based on dynamic traffic assignment, and use a time-varying dynamic traffic assignment model that considers changes in road network structure to fit the cascading failure process.

[0009] Step 004: When describing the cascading failure process of the road network under a traffic event, set the failure process constraint system, set the initial traffic flow of the road segment, and calculate the traffic impedance of all road segments.

[0010] Step 005: Define the road segment damage status and traffic constraints caused by abnormal events. According to the formula, let n=1, recalculate and update the traffic impedance Rn of all road segments, and redistribute traffic flow based on the traffic impedance Rn.

[0011] Step 006: Determine whether the iteration has converged. Search for the optimal step size under the condition of minimizing the total impedance of the road network. Determine whether the traffic volume of the corresponding road segment meets the convergence requirement after n iterations. If it has converged, jump to step 007. If the convergence fails, let n = n + 1 and return to step 005.

[0012] Step 007: Calculate and record the road network performance index f(tk).

[0013] Step 008: Determine whether the road network repair is complete. If the road network has been repaired at time tk, proceed to step 009. If the repair is not completed, set tk=tk+1 and k=k+1, and return to step 004.

[0014] Step 009: Calculate the toughness index based on step 002. .

[0015] Preferably, step 001 establishes an urban road network model, and the specific calculations further include the following steps: Step 101: Establish the urban road network, define the road network node set V and edge set E, and set road segment attributes, including free-flow travel time and capacity.

[0016] Step 102: Based on the urban road network model and traffic flow survey results, establish the adjacency matrix and the traffic flow matrix.

[0017] Preferably, step 002 involves constructing a road traffic system resilience assessment method based on three-dimensional vectors, and the specific calculation further includes the following steps: Step 201: Integrate the three-dimensional toughness vector .

[0018] ; ; ; In the formula, r represents the robustness of the road traffic system, v represents the recovery speed of the road traffic system after an abnormal event, and c represents the cumulative loss of system performance under resilient processes. This represents the performance of the road traffic system at time t.

[0019] Step 202: Establish a road traffic system performance measurement method. When assessing the resilience of the road traffic network, unlike most past studies that focused on the degree of change in network structure or only on the changes in traffic flow operation status that are damaged during traffic flow, this application establishes a road traffic system performance measurement method from two aspects: road network transportation performance indicators and structural indicators. The specific formulas for measuring the performance of road traffic systems are as follows: ; In the formula: Characterizing the loss of road network transport performance; Characterizing the structural loss of the road network; This represents the traffic impedance of road segment a at time t; This represents the traffic flow on road segment a at time t; This represents the traffic impedance of road segment a at time t, assuming the road network remains intact. This represents the traffic flow on road segment a at time t, assuming the road network remains intact. The betweenness of segment a at time t; Let represent the set of surviving road segments in the road network at time t; This indicates the percentage of road network transport performance in traffic resilience performance.

[0020] Preferably, step 003 establishes a cascading failure model based on dynamic traffic assignment, and the specific calculation further includes the following steps: Step 301: Propose the objective function of the time-varying dynamic traffic assignment model based on Wardrop's second principle user equilibrium. The objective function formula is as follows: ; In the formula: Z represents the sum of traffic impedances of all road segments a in the road segment set A during the study period from time 0 to T; This represents the traffic volume on road segment a at time t; This represents the traffic impedance value of road segment a at time t.

[0021] Preferably, step 004 specifically establishes constraints from the perspective of flow conservation constraints and solves for the corresponding initial traffic flow X1. The specific calculation further includes the following steps: Step 401: Establish a road travel time function based on the BPR road resistance function that conforms to the flow conservation constraint. The specific formula is as follows: ; ; ; ; In the formula, This represents the traffic volume on path p between OD and w at time t. This represents the traffic volume on road segment a between OD and w at time t. This represents the traffic demand between OD and w. This represents the set of paths between OD pairs w at time t. It is a representation Does a 0-1 variable exist on road segment a? This represents the set of road segments that have not been affected by abnormal events.

[0022] Step 402: Solve using the Frank-Wolfe algorithm with time iteration, setting the initial time tk=0 and letting k=1; Set the traffic flow of all road segments to 0, calculate the traffic impedance of all road segments, search for the shortest path set W of all OD pairs in the road network, allocate the travel demand of all OD pairs to the path set W, and generate the initial traffic flow X1.

[0023] Preferably, step 005 defines the road segment damage state constraints caused by abnormal events from the aspects of road function damage constraints and road traffic time constraints. The specific calculation further includes the following steps: Step 501: Define the road segment damage state constraints caused by abnormal events, as shown in the following formula: ; ; ; ; ; In the formula, Let t be the road capacity of the undamaged section. Let t be the road capacity of the damaged section; This represents the initial road capacity of road segment a. This represents the set of road segments affected by abnormal events. This indicates the percentage reduction in road capacity for the affected road sections. Speed ​​limits are set for the undamaged road sections at time t. Speed ​​limit for the damaged section of road at time t. Let t represent the degree of damage to the affected road sections. This indicates the duration of damage to road segment b, which is the time when road segment b is repaired within the resilience assessment framework.

[0024] Step 502: Define road segment travel time constraints to reflect changes in road traffic efficiency caused by abnormal events. The Federal Highway Administration (BPR) road resistance function is used, and the specific formula is as follows: ; ; ; In the formula: α and β are model parameters, α=0.15, β=4; This represents the traffic capacity of road segment a at time t; The zero-passage time for the undamaged road sections at each time t; Let t be the zero-recovery time of the damaged road section. At that time, the 0-speed passage time is equal to the road segment length lb and the speed limit of that road segment at time t. The ratio when At that time, the road section is not connected, and the 0-hour traffic flow time is equal to... .

[0025] Step 503: According to the formula, let n=1, recalculate and update the traffic impedance Rn of all road segments, and redistribute traffic flow based on the traffic impedance Rn.

[0026] Preferably, step 006 determines whether the iteration has converged, and the specific calculation further includes the following steps: Step 601: Let and search for the desired results. The optimal step size st*.

[0027] Step 602: Based on the calculation results, if If true, proceed to step 007; if If it is false, then let n = n + 1 and return to step 005.

[0028] A city road network resilience management platform based on dynamic cascading failures includes: The perturbation scenario simulation and random capacity degradation module is used to define and simulate the initial perturbation scenario library for different types of abnormal events; The core function is to embed preset random variables or probability distribution models into the capacity indicators of damaged road sections to simulate the uncertainty of the impact of abnormal events on the traffic capacity of road sections and generate an initial road network damage state with random characteristics. The dynamic cascading failure process simulation module is used to drive the dynamic traffic assignment model and simulate the traffic flow redistribution process based on the randomly generated initial road network damage state and time-varying traffic demand. Real-time tracking and updating of new road segment failures or performance degradation caused by congestion overflow and changes in path selection behavior; dynamic plotting of the propagation path, spatial range and intensity evolution of failures in the road network topology; outputting a complete dataset of dynamic cascading failure processes. The multidimensional resilience index calculation and uncertainty assessment module is used to analyze dynamic cascading failure process data, calculate multidimensional resilience quantitative indices, and provide quantitative basis for multidimensional resilience assessment methods.

[0029] Compared with existing technologies, this invention provides an urban road network resilience management platform and evaluation method based on dynamic cascading failures, which has the following beneficial effects: This invention integrates system robustness, resilience, and cumulative performance loss to form a three-dimensional resilience vector, utilizing a time-varying dynamic traffic assignment model that considers changes in road network structure to accurately characterize the dynamic process of cascading failures. By introducing random variables into the capacity index of damaged road segments, this invention proposes a new assessment method to address the shortcomings of existing resilience assessment methods in comprehensively quantifying the robustness and resilience of road networks.

[0030] This model first constructs a multi-dimensional resilience assessment method for urban roads based on the functional requirements of urban road networks in the face of abnormal events. Second, it establishes a cascading failure analysis method for road networks based on a dynamic traffic assignment model. Finally, by adjusting the road segment damage severity parameter, it analyzes the impact of the randomness of the impact of abnormal events on the robustness of the road network, and analyzes the reliability of the urban road network under abnormal events. This realistically recreates the failure propagation mechanism under abnormal scenarios, providing an effective method to overcome the dual shortcomings of traditional models in insufficient quantification of the dynamics of travel behavior and the system recovery process. Attached Figure Description

[0031] Figure 1 This is a flowchart of the urban road network resilience assessment method based on dynamic cascading failure of the present invention; Figure 2 The flowchart is solved using the Frank-Wolfe algorithm with time iteration. Figure 3This is the urban road topology network diagram in Example 1; Figure 4 It is the adjacency matrix diagram in Implementation Example 1; Figure 5 This is a partial traffic flow matrix diagram from Example 1; Figure 6 This is a design diagram of a fault scenario in the urban road network in Example 1; Figure 7 This is a statistical characteristic diagram of the cumulative loss c of urban road network resilience in Example 1; Figure 8 This is a statistical characteristic diagram of the robustness r of the urban road network in Example 1; Figure 9 This is a statistical characteristic graph of the urban road network recovery speed v in Example 1; Figure 10 This is a distribution map of urban road network resilience indicators in Example 1; Figure 11 This is a distribution map of urban road network resilience indicators in scenarios S1-S4 of Example 1; Figure 12 This is a comparison chart of the distribution of urban road network resilience indicators in scenarios S1 and S2 of Example 1; Figure 13 This is a distribution map of road network resilience indicators for scenario S2 under different parameters γ in Example 1; Figure 14 This is a diagram showing the road network resilience assessment results under fixed and random road segment damage levels in scenario S1 of Example 1. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] See Figure 1 As shown, the urban road network resilience assessment method based on dynamic cascading failure includes the following steps: Step 001: Establish a road network model and determine road segment attributes such as free flow time and capacity based on road level. Based on the urban road network model and traffic flow survey results, establish an adjacency matrix and a traffic flow matrix.

[0034] Step 002: Construct a three-dimensional resilience assessment method using a three-dimensional vector as the resilience metric for the road traffic system. Integrate the robustness, resilience, and cumulative performance loss of the road traffic system into the three-dimensional resilience vector. middle.

[0035] In the formula: It serves as a three-dimensional resilience assessment index for road networks; For the robustness of the road traffic system; This refers to the recovery speed of the road traffic system after an abnormal event occurs; This represents the cumulative performance loss of the system under the resilient process.

[0036] Step 003: Establish a cascading failure model based on dynamic traffic assignment, and use an hour-to-hour dynamic traffic assignment model that considers changes in road network structure to fit the cascading failure process.

[0037] Step 004: When describing the cascading failure process of the road network under a traffic event, set the failure process constraint system, set the initial traffic flow of the road segment, and calculate the traffic impedance of all road segments.

[0038] Step 005: Define the road segment damage status and traffic constraints caused by abnormal events. According to the formula, let n=1, recalculate and update the traffic impedance Rn of all road segments, and redistribute traffic flow based on the traffic impedance Rn.

[0039] Step 006: Determine if the iteration has converged. Search for the optimal step size under the condition of minimizing the total impedance of the road network, and determine whether the traffic volume of the corresponding road segment meets the convergence requirement after n iterations. If it has converged, proceed to step 007. If the convergence fails, let n = n + 1 and return to step 005.

[0040] Step 007: Calculate and record the road network performance index f(tk).

[0041] Step 008: Determine whether the road network repair is complete. If the road network has been repaired at time tk, proceed to step 009. If the repair is not completed, set tk=tk+1 and k=k+1, and return to step 004.

[0042] Step 009: Calculate the toughness index based on step 002. .

[0043] Step 001: Establish the urban road network model. Specific calculations further include the following steps: Step 101: Establish the urban road network. Define the road network node set V and edge set E, and set road segment attributes, including free-flow travel time and capacity.

[0044] Step 102: Based on the urban road network model and traffic flow survey results, establish the adjacency matrix and the traffic flow matrix.

[0045] Step 002 involves constructing a road traffic system resilience assessment method based on three-dimensional vectors. The specific calculations further include the following steps: Step 201: Integrate the three-dimensional toughness vector .

[0046] ; ; ; In the formula, r represents the robustness of the road traffic system; v represents the recovery speed of the road traffic system after an abnormal event occurs; and c represents the cumulative loss of system performance under resilient processes. This represents the performance of the road traffic system at time t.

[0047] Step 202: Establish a performance measurement method for the road traffic system. Unlike most past studies that focused on changes in network structure or only on the degree of disruption to traffic flow during operation, this application establishes a performance measurement method for the road traffic system from two aspects: road network transport performance indicators and structural indicators. The specific formulas for the road traffic system performance measurement method are as follows: ; In the formula, Characterizing the loss of road network transport performance; Characterizing the structural loss of the road network; This represents the traffic impedance of road segment a at time t; This represents the traffic flow on road segment a at time t; This represents the traffic impedance of road segment a at time t, assuming the road network remains intact. This represents the traffic flow on road segment a at time t, assuming the road network remains intact. The betweenness of segment a at time t; Let represent the set of surviving road segments in the road network at time t; This indicates the percentage of road network transport performance in traffic resilience performance.

[0048] Step 003 establishes a cascading failure model based on dynamic traffic assignment. The specific calculations further include the following steps: Step 301: Propose the objective function of the hour-to-hour dynamic traffic assignment model based on Wardrop's second principle user equilibrium. The objective function formula is as follows: ; In the formula, Z represents the sum of traffic impedances of all road segments a in the road segment set A during the study time period from time 0 to T; This represents the traffic volume on road segment a at time t; This represents the traffic impedance value of road segment a at time t.

[0049] Step 004 specifically establishes constraints from the perspective of flow conservation and solves for the corresponding initial traffic flow X1. The specific calculation further includes the following steps: Step 401: Establish a road travel time function based on the BPR road resistance function that conforms to the flow conservation constraint. The specific formula is as follows: ; ; ; ; In the formula, This represents the traffic volume on path p between OD and w at time t; This represents the traffic volume on road segment a between OD and w at time t; This indicates the traffic demand between OD and w; This represents the set of paths between OD pairs w at time t; It is a representation Does a 0-1 variable exist on road segment a? This represents the set of road segments that have not been affected by abnormal events.

[0050] Step 402: Solve using the Frank-Wolfe algorithm with time iteration, setting the initial time tk=0 and k=1. Set the traffic flow of all road segments to 0 and calculate the traffic impedance of all road segments. Search for the shortest path set W for all OD pairs in the road network. Assign the travel demand of all OD pairs to the path set W to generate the initial traffic flow X1.

[0051] Step 005 defines the road segment damage state constraints caused by abnormal events from the aspects of road function disruption constraints and road traffic time constraints. The specific calculation further includes the following steps: Step 501: Define the road segment damage state constraints caused by abnormal events, as shown in the following formula: ; ; ; ; ; In the formula, Let t be the road capacity of the undamaged section. Let t be the road capacity of the damaged section; This represents the initial road capacity of road segment a; This represents the set of road segments affected by abnormal events. Indicates the percentage reduction in road capacity for the affected road sections; Speed ​​limits are set for the undamaged road sections at time t; Speed ​​limit for the damaged section of road at time t; The extent of damage to the affected road sections at each time point t; This indicates the duration of damage to road segment b, which is the time when road segment b is repaired within the resilience assessment framework.

[0052] Step 502: Define road segment travel time constraints to reflect changes in road traffic efficiency caused by abnormal events. The Federal Highway Administration (BPR) road resistance function is used, with the specific formula as follows: ; ; ; In the formula, α and β are model parameters, α=0.15, β=4; This represents the traffic capacity of road segment a at time t; The zero-passage time for the undamaged road sections at each time t; Let t be the zero-recovery time of the damaged road section. At that time, the 0-speed passage time is equal to the road segment length lb and the speed limit of that road segment at time t. The ratio; when At that time, the road section is not connected, and the 0-hour traffic flow time is equal to... .

[0053] Step 503: According to the formula, let n=1, recalculate and update the traffic impedance Rn of all road segments, and redistribute traffic flow based on the traffic impedance Rn.

[0054] Step 006 determines whether the iteration has converged. The specific calculation further includes the following steps: Step 601: Let and search for the desired results. The optimal step size st*.

[0055] Step 602: Based on the calculation results, if If true, proceed to step 007; if If it is false, then let n = n + 1 and return to step 005.

[0056] A city road network resilience management platform based on dynamic cascading failures includes: The perturbation scenario simulation and random capacity degradation module is used to define and simulate the initial perturbation scenario library for different types of abnormal events; The core function is to embed preset random variables or probability distribution models into the capacity indicators of damaged road sections to simulate the uncertainty of the impact of abnormal events on the traffic capacity of road sections and generate an initial road network damage state with random characteristics. The dynamic cascading failure process simulation module is used to drive the dynamic traffic assignment model and simulate the traffic flow redistribution process based on the randomly generated initial road network damage state and time-varying traffic demand. Real-time tracking and updating of new road segment failures or performance degradation caused by congestion overflow and changes in path selection behavior; dynamic plotting of the propagation path, spatial range and intensity evolution of failures in the road network topology; outputting a complete dataset of dynamic cascading failure processes. The multidimensional resilience index calculation and uncertainty assessment module is used to analyze dynamic cascading failure process data, calculate multidimensional resilience quantitative indices, and provide quantitative basis for multidimensional resilience assessment methods. Example

[0057] This application selects a portion of the road network in Xi'an City for topology network construction to analyze the resilience of the urban road network. This area includes 21 intersections and 31 roads. See [link to relevant documentation]. Figure 3 Based on the urban road network model and traffic flow survey results, an adjacency matrix M is established: see [link to relevant documentation]. Figure 4 Traffic flow matrix F: see Figure 5 The framework primarily simulated seven failure scenarios to test its resilience assessment capabilities: see [link to relevant documentation]. Figure 6 Calculate the three-dimensional resilience assessment index of the road network and road traffic system performance indicators .

[0058] According to the formula: ; ; ; ; In the formula, r represents the robustness of the road traffic system, v represents the recovery speed of the road traffic system after an abnormal event, and c represents the cumulative loss of system performance under resilient processes. This represents the performance of the road traffic system at time t; Characterizing the loss of road network transport performance; Characterizing the structural loss of the road network; This represents the traffic impedance of road segment a at time t; This represents the traffic flow on road segment a at time t; This represents the traffic impedance of road segment a at time t, assuming the road network remains intact. This represents the traffic flow on road segment a at time t, assuming the road network remains intact. Let represent the betweenness number of road segment a at time t; Let represent the set of surviving road segments in the road network at time t; This indicates the percentage of road network transport performance in traffic resilience performance.

[0059] A cascading failure model based on dynamic traffic assignment is established, and a traffic assignment model based on the user equilibrium principle is established based on Wardrop's second principle. An objective function is also established.

[0060] According to the formula: ; In the formula, Z represents the sum of traffic impedance of all road segments a in the road segment set A during the study time period from time 0 to T. This represents the traffic volume on road segment a at time t; This represents the traffic impedance value of road segment a at time t.

[0061] This paper describes the cascading failure process of the road network under traffic events and establishes flow conservation constraints based on the traffic assignment model.

[0062] According to the formula: ; ; ; ; In the formula, This represents the traffic volume on path p between OD and w at time t; This represents the traffic volume on road segment a between OD and w at time t; This represents the traffic demand between OD and w. This represents the set of paths between OD pairs w at time t; It is a representation Does a 0-1 variable exist on road segment a? This represents the set of road segments that have not been affected by abnormal events.

[0063] Based on the cascading failure model of completely damaged road segments and the cascading failure model of partially damaged road segments, road segment damage state constraints caused by abnormal events are defined, and the road attributes of undamaged and damaged road segments at each time t are calculated.

[0064] According to the formula: ; ; ; ; ; In the formula, Let t be the road capacity of the undamaged section. Let t be the road capacity of the damaged section; This represents the initial road capacity of road segment a; This represents the set of road segments affected by abnormal events. Indicates the percentage reduction in road capacity for the affected road sections; Speed ​​limits are set for the undamaged road sections at time t; Speed ​​limit for the damaged section of road at time t; The extent of damage to the affected road sections at each time point t; This indicates the duration of damage to road segment b, which is the time when road segment b is repaired within the resilience assessment framework.

[0065] The extent of damage to some sections of the road Set it to 0.5.

[0066] Define road segment travel time constraints in the constraints to reflect changes in road traffic efficiency caused by abnormal events damaging the road.

[0067] According to the formula: ; ; ; In the formula, α and β are model parameters, α=0.15, β=4; This represents the traffic capacity of road segment a at time t; The zero-passage time for the undamaged road sections at each time t; Let t be the zero-recovery time of the damaged road section. At that time, the 0-speed passage time is equal to the road segment length lb and the speed limit of that road segment at time t. The ratio; when At that time, the road section is not connected, and the 0-hour traffic flow time is equal to... .

[0068] See Figure 2 The Frank-Wolfe algorithm with time iteration is used to solve the model in this application.

[0069] The model proposed in the application is used to Figure 6The resilience assessment was conducted using nine scenarios, and the statistical distribution characteristics of the road traffic network resilience assessment indices c, r, and v were obtained as follows: Figure 7-9 As shown.

[0070] Select scenarios S1-S5 and plot a scatter plot of resilience indicators as follows: Figure 10 As shown in the figure, the c-axis represents the cumulative performance loss of the road network, the r-axis represents the robustness index of the road network, and the v-axis represents the recovery speed of the road network.

[0071] in addition, Figure 11 There is interleaving between S1 and S2, and between S3 and S4. From... Figure 11 (a) It was found that the boundary between S1 and S2 was not clear enough, which indicates that the difference in road network performance between complete and partial damage of a road segment is not significant. Figure 11 (b) indicates a situation where there is a clear overlap in resilience index values ​​between scenarios S3 and S4. This means that in scenarios S3 and S4, when one road segment is completely destroyed, although the degree of road network performance degradation will be greater, the degree of road network performance degradation will still be affected by the location of the completely destroyed road segment.

[0072] To explore the impact mechanism of damaged road segment characteristics on road network resilience, this application analyzes the relationship between the nodal degree of relevant intersections of damaged road segments and resilience assessment indices c, r, and v based on scenarios S1 and S2. (See...) Figure 12 .in Figure 12 (a) Figure 12 (c) and Figure 12 (e) represents the relationship between the cumulative loss value c of road network performance, the robustness r of road network, and the recovery speed v of road network and the network structure characteristics of the partially damaged road segment under scenario S1.

[0073] This application combines road network transport efficiency indicators and road network structure indicators when constructing a road network performance evaluation method, and adjusts the proportion of transport efficiency indicators and road network structure indicators through the parameter γ. To explore the impact of parameter γ on the resilience evaluation effect, the resilience evaluation results for scenario S2 were analyzed. By setting the parameter γ value to 0.3, 0.5, and 0.7, the distribution of resilience indicators under different γ values ​​was compared, see [see...]. Figure 13 . Figure 13 (a)- Figure 13 (c) Characterizes the relationship between the cumulative loss value c of road network performance, road network robustness r, and road network recovery speed v and the network structure characteristics of the partially damaged road segment under scenario S2 when the parameter γ is 0.3.

[0074] This application introduces random variables into the capacity index of damaged road segments to analyze the reliability of urban road networks when non-normal events with random impacts on road segments occur. Random numbers representing the degree of road segment damage within the range [0.2, 0.8] are generated and applied to the resilience assessment of scenario S1. The differences between these results and the resilience results for scenario S1 under a fixed road segment damage level are compared (see [link]). Figure 14 .

[0075] The examples demonstrate that anomalous events leading to complete road blockage have a greater impact on the resilience of urban road networks, and the robustness of the road network decreases more rapidly with the increase in the number of damaged road segments. Secondly, the network structure characteristics of damaged road segments significantly affect resilience indices; the cumulative loss of road network function and the road network recovery capacity increase with the increase in the degree of the nodes related to the damaged edges, while the robustness of the road network decreases with the increase in the degree of the nodes related to the damaged edges. Thirdly, the weight given to transport efficiency and road network structure characteristics in resilience assessment also greatly influences the resilience estimation results; searching for a suitable parameter γ can significantly improve the accuracy and effectiveness of the three-dimensional resilience assessment results. Finally, the impact of the randomness of the impact of anomalous events on road network robustness was analyzed by adjusting the road segment damage degree parameter. The results show that random damage results in a wider distribution range of resilience indices, making it easier to cause more verifiable damage to road network performance and structure. The resilience analysis framework proposed in this application is effective.

[0076] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0077] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for assessing the resilience of urban road networks based on dynamic cascading failures, characterized by: Includes the following steps: Step 001: Establish a road network model. Based on the road level, determine the free flow time, capacity, and other road segment attributes. Based on the urban road network model and traffic flow survey results, establish an adjacency matrix and a traffic flow matrix. Step 002: Using a three-dimensional vector as the resilience metric for the road traffic system, construct a three-dimensional resilience assessment method that integrates the robustness, resilience, and cumulative performance loss of the road traffic system into the three-dimensional resilience vector. middle; In the formula, It serves as a three-dimensional resilience assessment index for road networks; For the robustness of the road traffic system; This refers to the recovery speed of the road traffic system after an abnormal event occurs; This represents the cumulative performance loss of the system under the resilient process. Step 003: Establish a cascading failure model based on dynamic traffic assignment, and use a time-varying dynamic traffic assignment model that considers changes in road network structure to fit the cascading failure process. Step 004: When describing the cascading failure process of the road network under a traffic event, set the failure process constraint system, set the initial traffic flow of the road segment, and calculate the traffic impedance of all road segments; Step 005: Define the road segment damage status and traffic constraints caused by abnormal events. According to the formula, let n=1, recalculate and update the traffic impedance Rn of all road segments, and redistribute traffic flow based on the traffic impedance Rn. Step 006: Determine whether the iteration has converged. Search for the optimal step size under the condition of minimizing the total impedance of the road network. Determine whether the traffic volume of the corresponding road segment meets the convergence requirement after n iterations. If it has converged, jump to step 007. If the convergence fails, let n = n + 1 and return to step 005; Step 007: Calculate and record the road network performance index f(tk); Step 008: Determine whether the road network repair is complete. If the road network has been repaired at time tk, proceed to step 009. If the repair is not completed, let tk = tk + 1 and k = k + 1, and return to step 004; Step 009: Calculate the toughness index based on step 002. .

2. The urban road network resilience assessment method based on dynamic cascading failure as described in claim 1, characterized in that: Step 001: Establish the urban road network model. Specific calculations further include the following steps: Step 101: Establish the urban road network, define the road network node set V and edge set E, and set road segment attributes, including free-flow travel time and capacity; Step 102: Based on the urban road network model and traffic flow survey results, establish the adjacency matrix and the traffic flow matrix.

3. The urban road network resilience assessment method based on dynamic cascading failure as described in claim 1, characterized in that: Step 002 involves constructing a road traffic system resilience assessment method based on three-dimensional vectors. The specific calculations further include the following steps: Step 201: Integrate the three-dimensional toughness vector ; ； ； ； In the formula, r represents the robustness of the road traffic system, v represents the recovery speed of the road traffic system after an abnormal event, and c represents the cumulative loss of system performance under resilient processes. This represents the performance of the road traffic system at time t; Step 202: Establish a road traffic system performance measurement method. When assessing the resilience of the road traffic network, unlike most past studies that focused on the degree of change in network structure or only on the changes in traffic flow operation status that are damaged during traffic flow, this application establishes a road traffic system performance measurement method from two aspects: road network transportation performance indicators and structural indicators. The specific formulas for measuring the performance of road traffic systems are as follows: ； In the formula: Characterizing the loss of road network transport performance; Characterizing the structural loss of the road network; This represents the traffic impedance of road segment a at time t; This represents the traffic flow on road segment a at time t; This represents the traffic impedance of road segment a at time t, assuming the road network remains intact. This represents the traffic flow on road segment a at time t, assuming the road network remains intact. The betweenness of segment a at time t; Let represent the set of surviving road segments in the road network at time t; This indicates the percentage of road network transport performance in traffic resilience performance.

4. The urban road network resilience assessment method based on dynamic cascading failure as described in claim 1, characterized in that: Step 003 establishes a cascading failure model based on dynamic traffic assignment. The specific calculations further include the following steps: Step 301: Propose the objective function of the time-varying dynamic traffic assignment model based on Wardrop's second principle user equilibrium. The objective function formula is as follows: ； In the formula: Z represents the sum of traffic impedances of all road segments a in the road segment set A during the study period from time 0 to T; This represents the traffic volume on road segment a at time t; This represents the traffic impedance value of road segment a at time t.

5. The urban road network resilience assessment method based on dynamic cascading failure as described in claim 1, characterized in that: Step 004 specifically establishes constraints from the perspective of flow conservation constraints and solves for the corresponding initial traffic flow X1. The specific calculation further includes the following steps: Step 401: Establish a road travel time function based on the BPR road resistance function that conforms to the flow conservation constraint. The specific formula is as follows: ； ； ； ； In the formula, This represents the traffic volume on path p between OD and w at time t. This represents the traffic volume on road segment a between OD and w at time t. This represents the traffic demand between OD and w. This represents the set of paths between OD pairs w at time t. It is a representation Does a 0-1 variable exist on road segment a? This represents the set of road segments that were not affected by abnormal events. Step 402: Solve using the Frank-Wolfe algorithm with time iteration, setting the initial time tk=0 and letting k=1; Set the traffic flow of all road segments to 0, calculate the traffic impedance of all road segments, search for the shortest path set W of all OD pairs in the road network, allocate the travel demand of all OD pairs to the path set W, and generate the initial traffic flow X1.

6. The urban road network resilience assessment method based on dynamic cascading failure as described in claim 1, characterized in that: Step 005 defines the road segment damage state constraints caused by abnormal events from the aspects of road function destruction constraints and road traffic time constraints. The specific calculation further includes the following steps: Step 501: Define the road segment damage state constraints caused by abnormal events, as shown in the following formula: ； ； ； ； ； In the formula, Let t be the road capacity of the undamaged section. Let t be the road capacity of the damaged section; This represents the initial road capacity of road segment a. This represents the set of road segments affected by abnormal events. This indicates the percentage reduction in road capacity for the affected road sections. Speed ​​limits are set for the undamaged road sections at time t. Speed ​​limit for the damaged section of road at time t. Let represent the degree of damage to the damaged road segment at each time t. This indicates the duration of damage to road segment b, i.e., the time when road segment b is repaired within the resilience assessment framework. Step 502: Define road segment travel time constraints to reflect changes in road traffic efficiency caused by abnormal events. The Federal Highway Administration (BPR) road resistance function is used, and the specific formula is as follows: ； ； ； In the formula: α and β are model parameters, α=0.15, β=4; This represents the traffic capacity of road segment a at time t; The zero-passage time for the undamaged road sections at each time t; Let t be the zero-recovery time of the damaged road section. At that time, the 0-speed passage time is equal to the road segment length lb and the speed limit of that road segment at time t. The ratio when At that time, the road section is not connected, and the 0-hour traffic flow time is equal to... ; Step 503: According to the formula, let n=1, recalculate and update the traffic impedance Rn of all road segments, and redistribute traffic flow based on the traffic impedance Rn.

7. The urban road network resilience assessment method based on dynamic cascading failure as described in claim 1, characterized in that: Step 006 determines whether the iteration has converged. The specific calculation further includes the following steps: Step 601: Let and search for the desired results. The optimal step size st*; Step 602: Based on the calculation results, if If true, proceed to step 007; if If it is false, then let n = n + 1 and return to step 005.

8. A city road network resilience management platform based on dynamic cascading failure, used to implement the city road network resilience assessment method based on dynamic cascading failure as described in any one of claims 1-8, characterized in that: include: The perturbation scenario simulation and random capacity degradation module is used to define and simulate the initial perturbation scenario library for different types of abnormal events; The core function is to embed preset random variables or probability distribution models into the capacity indicators of damaged road sections to simulate the uncertainty of the impact of abnormal events on the traffic capacity of road sections and generate an initial road network damage state with random characteristics. The dynamic cascading failure process simulation module is used to drive the dynamic traffic assignment model and simulate the traffic flow redistribution process based on the randomly generated initial road network damage state and time-varying traffic demand. Real-time tracking and updating of new road segment failures or performance degradation caused by congestion overflow and changes in path selection behavior; dynamic plotting of the propagation path, spatial range and intensity evolution of failures in the road network topology; outputting a complete dataset of dynamic cascading failure processes. The multidimensional resilience index calculation and uncertainty assessment module is used to analyze dynamic cascading failure process data, calculate multidimensional resilience quantitative indices, and provide quantitative basis for multidimensional resilience assessment methods.

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