Cascade reliability index determination method for multi-level intercity road network

Abstract

The invention provides a cascade reliability index determination method for a multi-level inter-city road network, and the method comprises the steps: constructing the multi-level inter-city road network of a target region, and the multi-level inter-city road network comprises a first node set and a road segment set; calculating the initial load and capacity of any first node of the first node set; utilizing an attack strategy based on betweenness centrality to trigger cascade failure of the multi-level intercity road network so as to determine an initial failure node from the first node set; taking the initial failure node as a starting point, and simulating a cascade failure propagation process by using a multipath load redistribution model identified and driven by an equiimpedance line until the propagation process is finished; and determining the number of newly added failure nodes, the network efficiency ratio, the global node cascading failure rate and the local node cascading failure rate in each round in the cascading failure propagation process as cascading reliability indexes of the multi-level intercity road network. According to the invention, the authenticity and accuracy of the cascade reliability index of the multi-level inter-city road network of the target area are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of road network reliability monitoring, in particular to a cascading reliability index determination method for a multi-level intercity road network. BACKGROUND

[0002] At present, the reliability index of a multi-level intercity road network in a region is usually determined by using a traffic network failure propagation mechanism. The existing propagation mechanism has two limitations, which reduces the accuracy and actual applicability of the reliability index determination: Firstly, most load redistribution methods assume that the failure load propagates along the adjacent edges step by step, ignoring the influence of impedance heterogeneity beyond the adjacent nodes. Therefore, these methods are difficult to effectively depict multi-path and cross-layer propagation behaviors. In a multi-level intercity road network, failure loads often bypass high impedance paths and transfer between different road levels. This limitation not only leads to distorted representation of the propagation mode, but also underestimates the spatial diffusion range of the cascading effect in the multi-level intercity road network.

[0003] Secondly, the existing load capacity model generally uses a static redundancy coefficient based on empirical data or simulation calibration, and fails to fully consider the influence of node attribute differences and regional economic dynamics. Such static setting is difficult to capture the capacity changes caused by heterogeneous economic conditions, and limits the adaptability and prediction accuracy of the model in the context of continuous evolution of regional environment. SUMMARY

[0004] Therefore, the present application provides a cascading reliability index determination method for a multi-level intercity road network, which can realistically simulate the cascading failure propagation and diffusion process of a multi-level intercity road network, and solve the technical problems of distorted representation of the propagation mode and underestimation of the spatial diffusion range of the cascading effect in the multi-level intercity road network existing in the prior art.

[0005] Firstly, the present application provides a cascading reliability index determination method for a multi-level intercity road network, comprising: constructing a multi-level intercity road network of a target region, comprising a first node set and a link set; calculating the initial load and capacity of any first node in the first node set; triggering cascading failure of the multi-level intercity road network by using an attack strategy based on the betweenness centrality to determine an initial failure node from the first node set; starting from the initial failure node, simulating the cascading failure propagation process by using an equal impedance line driven multi-path load redistribution model until the propagation process ends; The number of newly added failure nodes in each round of the cascade failure propagation process, the network efficiency ratio, the global node cascade failure efficiency, and the local node cascade failure efficiency are determined as the cascade reliability indexes of the multi-level intercity road network.

[0006] In a second aspect, an embodiment of the present application provides a device for determining cascade reliability indexes of a multi-level intercity road network, comprising: A construction unit is configured to construct a multi-level intercity road network of a target region, comprising a first node set and a link set. A calculation unit is configured to calculate an initial load and capacity of any first node in the first node set. A first determination unit is configured to trigger a multi-level intercity road network cascade failure by using an attack strategy based on the betweenness centrality, so as to determine an initial failure node from the first node set. A simulation unit is configured to simulate a cascade failure propagation process by using an equal impedance line identification driven multi-path load redistribution model, starting from the initial failure node, until the propagation process ends. A second determination unit is configured to determine the number of newly added failure nodes in each round of the cascade failure propagation process, the network efficiency ratio, the global node cascade failure efficiency, and the local node cascade failure efficiency as the cascade reliability indexes of the multi-level intercity road network.

[0007] In a third aspect, an embodiment of the present application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method of the embodiment of the present application when executing the computer program.

[0008] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, which stores computer instructions, and the computer instructions are executed by a processor to implement the method of the embodiment of the present application.

[0009] In a fifth aspect, an embodiment of the present application provides a computer program product, comprising computer programs / instructions, and the computer programs / instructions are executed by a processor to implement the method of the embodiment of the present application.

[0010] The embodiment of the present application improves the authenticity and accuracy of the cascade reliability indexes of the multi-level intercity road network of the target region. BRIEF DESCRIPTION OF DRAWINGS

[0011] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the description of the embodiments or the prior art. Obviously, the drawings described below are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without any creative effort.

[0012] Figure 1 A flow chart of a method for determining a cascading reliability index of a multi-level intercity road network according to an embodiment of the present application is provided. Figure 2 A schematic diagram of the role of a receiving node identification threshold and the number of feasible paths in failure load propagation according to an embodiment of the present application is provided. Figure 3 A schematic diagram of the number of newly added failure nodes in each round of a failure propagation process in a specific area according to an embodiment of the present application is provided. Figure 4 A schematic diagram of the network efficiency ratio in each round of a failure propagation process in a specific area according to an embodiment of the present application is provided. Figure 5 A schematic diagram of the global node cascading failure rate in each round of a failure propagation process in a specific area according to an embodiment of the present application is provided. Figure 6 A schematic diagram of the local node cascading failure rate in each round of a failure propagation process in a specific area according to an embodiment of the present application is provided. Figure 7 A schematic diagram of the number of newly added failure nodes in each round of a failure propagation process under multiple receiving node identification thresholds according to an embodiment of the present application is provided. Figure 8 A schematic diagram of the network efficiency ratio in each round of a failure propagation process under multiple receiving node identification thresholds according to an embodiment of the present application is provided. Figure 9 A schematic diagram of the global node cascading failure rate in each round of a failure propagation process under multiple receiving node identification thresholds according to an embodiment of the present application is provided. Figure 10 A schematic diagram of the local node cascading failure rate in each round of a failure propagation process under multiple receiving node identification thresholds according to an embodiment of the present application is provided. Figure 11 A schematic diagram of the number of newly added failure nodes in each round of a failure propagation process under multiple numbers of feasible paths according to an embodiment of the present application is provided. Figure 12 A schematic diagram of the network efficiency ratio in each round of a failure propagation process under multiple numbers of feasible paths according to an embodiment of the present application is provided. Figure 13 A schematic diagram of the global node cascading failure rate in each round of a failure propagation process under multiple numbers of feasible paths according to an embodiment of the present application is provided. Figure 14 A schematic diagram of the local node cascading failure rate in each round of a failure propagation process under multiple numbers of feasible paths according to an embodiment of the present application is provided. Figure 15 A functional structure diagram of a device for determining a cascading reliability index of a multi-level intercity road network according to an embodiment of the present application is provided. Figure 16 A structural diagram of an electronic device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0013] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application but not all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0014] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor are within the scope of protection of the present application.

[0015] First, the design idea of the embodiments of the present application is briefly introduced.

[0016] As a key component of the transportation system, the intercity road network not only bears the important function of large-scale passenger and freight transportation, but also plays a crucial role in promoting regional economic integration and maintaining social stability. In recent years, climate change has led to frequent extreme weather events, bringing increasingly serious systemic risks to the transportation network, among which cascading failure is one of the most challenging threats. Cascading failure refers to the failure of a component (node or link) in the network, which rapidly spreads to the entire system through a chain reaction, and eventually may lead to the overall paralysis of the system. Therefore, in-depth understanding of the propagation mechanism of cascading failure in the intercity road network has become a key issue to improve its reliability.

[0017] Most existing cascade failure models usually assume that failure load propagates along the adjacent edges step by step, failing to fully consider the traffic impedance heterogeneity caused by road attributes, toll policies or congestion effects. In fact, impedance heterogeneity can significantly affect the speed and path selection of failure propagation: high impedance road segments may delay or even block the propagation process, causing failure load to bypass the physically adjacent nodes and spread along alternative paths with lower impedance, forming a multi-path propagation pattern. This phenomenon is particularly pronounced in multi-level intercity road networks. There are significant impedance differences between different road levels (such as highways, national roads and provincial roads), and the interdependence between levels further exacerbates the complexity of failure propagation. For example, highways may become high-impedance paths due to tolls or congestion, causing failure load to be redistributed to adjacent national or provincial roads. Such impedance-driven cross-layer path selection behavior breaks the basic assumption in traditional models that failure only propagates within the same layer. Therefore, failure propagation in multi-level intercity road networks is not only influenced by physical adjacency, but also driven by intra- and inter-layer impedance heterogeneity.

[0018] Under normal traffic conditions, individual travel or evacuation behavior usually has a clear destination, and even if there are obstructions such as damaged roads or nodes, they will reach the intended target through alternative paths. However, in extreme events, traditional cascade failure models often only consider the step-by-step propagation of failure load along topological adjacency, i.e., in each iteration, only the redistribution of failure load from the failed node to its adjacent nodes and the corresponding failure judgment are simulated. This assumption ignores the risk-averse behavior of individuals based on impedance perception in emergency situations. In fact, in disaster or emergency situations, people's first reaction is to move as far away from the danger zone as possible and choose relatively better evacuation paths based on the principle of minimum travel time or minimum generalized impedance. Therefore, the failure propagation process should reflect this impedance-driven load redistribution feature.

[0019] To this end, the present application constructs an analysis framework for quantifying the cascade reliability of multi-level intercity road networks. First, a modeling method for multi-level intercity road networks is proposed, which integrates road level structure, spatial travel demand and user decision-making behavior to depict cross-layer path selection process and thus establish the basis for failure propagation. Further, a multi-path failure propagation mechanism driven by iso-impedance line identification is proposed, which identifies downstream nodes with the ability to receive and transmit failure load through a receiving node identification threshold, and integrates with the stochastic user equilibrium model to realize the realistic simulation of multi-path and cross-layer cascade failure. Subsequently, based on betweenness centrality, a deliberate attack scenario is designed, and four cascade reliability indicators: the number of new failed nodes, the network efficiency ratio, the global cascade failure rate and the local cascade failure rate are used to systematically evaluate the speed, range and intensity of propagation.

[0020] After introducing the application scenarios and design ideas of the embodiments of the present application, the technical solutions provided by the embodiments of the present application are described below.

[0021] As shown in Figure 1 The embodiments of the present application provide a method for determining a cascading reliability index of a multi-level intercity road network, comprising: Step 101: constructing a multi-level intercity road network of a target region, comprising a first node set and a road segment set; Step 102: calculating the initial load and capacity of any first node in the first node set; Step 103: triggering cascading failure of the multi-level intercity road network by using an attack strategy based on the betweenness centrality to determine an initial failure node from the first node set; Step 104: using an equal impedance line identification driven multi-path load redistribution model to simulate the cascading failure propagation process from the initial failure node as the starting point until the propagation process ends; Step 105: determining the number of newly added failure nodes, the network efficiency ratio, the global node cascading failure rate and the local node cascading failure rate in each round of the cascading failure propagation process as the cascading reliability index of the multi-level intercity road network.

[0022] The embodiments simulate the cascading failure propagation by using the equal impedance line identification driven multi-path load redistribution model, thereby realizing more real and accurate evaluation of the cascading reliability index.

[0023] In some embodiments, the multi-level intercity road network of the target region is constructed, comprising: For the expressway, ordinary national highway and ordinary provincial highway of the target region, a road segment parameter is set for each road segment, and the road segment parameter comprises: length, traffic capacity, design speed and two road nodes; A first node set comprising a plurality of first nodes is constructed , the first node being a road node or an intersection; and a road segment set comprising a plurality of road segments is constructed .

[0024] In some embodiments, the method further comprises: The center position of each traffic cell in the target region is determined by using the travel time centroid method, the center position is determined as a second node, and all the second nodes form a second node set ; The second node and its nearest road node are connected to determine a virtual edge, and an access time constant is assigned to each virtual edge to enable the virtual edge to access the multi-level intercity road network; The traffic of the second node enters the multi-level intercity road network through the virtual edge.

[0025] Specifically, the traffic zones within the target area are pre-defined.

[0026] In this embodiment, the complexity of the multi-level intercity road network stems from the functional differences between different road levels and the spatially uneven distribution of travel demand. Its modeling is achieved by coupling the structural layer and the demand layer. The first step is to construct the network's structural layer. Based on design speed, service range, and operational function, highways, national highways, and provincial highways are distinguished. The coupling relationships between road levels are not artificially defined but naturally formed through shared nodes. For example, a road intersection can simultaneously serve as a highway node and connect to a national highway, thus forming a multi-level network topology. The second step is to embed the demand layer. For each traffic analysis area, the travel time centroid method is used to determine demand nodes. This method selects locations that minimize the total travel time from all structural layer nodes. Candidate locations typically include administrative centers and industrial clusters, as they dominate in terms of travel generation and attraction. Since these centroids usually do not coincide with structural layer nodes, they need to be connected to the nearest road node through virtual edges. The connection relationship is determined by nearest neighbor analysis. Each virtual edge is assigned a very small access time constant (e.g., 0.001 seconds) to ensure that traffic flow can directly access the network. Demand intensity is determined by a smoothed annual origin-destination matrix to eliminate short-term fluctuations and capture long-term intercity travel patterns.

[0027] Through the above two steps, the structural layer and the demand layer are coupled, and the multi-level intercity road network is constructed as a unified framework that simultaneously represents the physical network and the spatial distribution of traffic demand, as described below:

[0028]

[0029]

[0030]

[0031] in, Represents a complete network; Indicates structural layers; Represents the requirements layer; It is a basic set of nodes (the first set of nodes), including road segment endpoints and intersections; For road sections, It is a collection of highways. This is a collection of ordinary national highways. This is a collection of ordinary provincial highways; each road segment consists of a pair of nodes. constitute, ; The demand node set (second node set) is composed of the centroid of the traffic zone. a set of virtual edges connecting the structure layer and the demand layer, each virtual edge being a pair of nodes , , is uniquely determined.

[0032] The embodiment couples the structure layer and the demand layer, reflecting the functional division of different road levels and the spatial heterogeneity of traffic demand.

[0033] In some embodiments, the initial load of any first node in the first node set is calculated, including: For a first node in the first node set , when the first node is a load node, its initial load is:

[0034] wherein, is the traffic flow of a road segment , and is the set of all road segments delivering traffic flow to the first node ; the formula indicates that nodes receiving larger traffic flows will be assigned higher loads, thereby reflecting the spatial distribution characteristics of traffic flows and the functional importance of nodes in the network. This representation is crucial for accurately simulating the propagation of failures within the network.

[0035] Although most nodes have traffic inflows, the inflow of some nodes may still be zero. To maintain the stability of the load distribution, the initial load of such nodes needs to be calculated based on the weighted contributions of all known load nodes, with the weight taken as the inverse of the shortest travel time. Therefore, the initial load of zero-flow nodes is obtained by weighted averaging rather than simple summation, ensuring that its numerical scale is consistent with that of known load nodes and maintaining stability and comparability within the entire network.

[0036] When the first node is a zero-flow node, its initial load is:

[0037] wherein, is the initial load of a first node in the first node set , and the first node is a load node; is the set of load nodes; is the shortest travel time between the first node and the first node .

[0038] ​In some embodiments, calculating the capacity of any first node in the first node set includes: First node capacity for:

[0039]

[0040]

[0041]

[0042] in, This is the redundancy coefficient; and These are the minimum and maximum values ​​of the redundancy coefficient, respectively. First node Normalized economic centrality; First node Economic centrality; For the second node ; economic output; For the second node With the first node The shortest travel time between them.

[0043] This embodiment constructs a node capacity model driven by regional economic activity to overcome the shortcomings of static redundancy coefficients in traditional load-capacity models. This model dynamically scales node capacity based on local economic centrality and observed traffic demand, enabling nodes in economically active regions to obtain larger capacities commensurate with their functional importance. By incorporating economic heterogeneity into capacity settings, a more realistic capacity allocation scheme can be formed, thereby improving the accuracy of cascading failure assessment.

[0044] The calculation method in this embodiment ensures that node capacity reflects both the node's own traffic demand and its role in supporting regional economic flows. By linking capacity to economic centrality, nodes in economically active regions are assigned higher capacities, conforming to the basic principle of "higher demand, greater capacity." Simultaneously, upper and lower bound constraints on redundancy coefficients prevent extreme capacity values, ensuring the model remains realistic while remaining sensitive to differences in economic activity. This representation reveals the impact of regional development levels on network performance and provides a stable and consistent basis for simulating cascading failure processes.

[0045] In some embodiments, the method further includes: Calculate the first node With the first node Shortest travel time between :

[0046] wherein, is a first node is a second node is a set of all feasible paths between the first node is a first node is a second node is any feasible path between the first node is the total impedance of the path

[0047] is the impedance of a road link included in the path

[0048] wherein, is the free-flow travel time; is the length of the road link is the unit distance toll rate of the road link is the traffic flow of the road link is the capacity of the road link is the monetary-time conversion factor; are congestion response parameters.

[0049] For example, the toll rate is 0.45 yuan / km for four-lane roads, 0.60 yuan / km for six-lane or more roads, and free for national and provincial highways. The monetary-time conversion factor is set to 0.01 hour / yuan. The congestion parameters are taken as 0.15, . The embodiment constructs a comprehensive impedance function to represent the cross-layer path selection behavior, which integrates road attributes, toll fees, and congestion effects to form a unified travel time metric. The path travel time is determined by aggregating the impedances of each road link, so that the path can include road links from multiple road levels. Therefore, the selection behavior of users between different road levels is guided by the travel cost of each road link that constitutes the path, thereby realizing cross-layer path selection.

[0050] In some embodiments, the initial failed node is determined from the first node set, including: any first node in the first node set any first node in the first node set​​​​​​​​​ betweenness centrality for:

[0051] in, Indicates the first node With the first node The number of shortest paths between them; First node With the first node Passing through the first node The number of paths; Set the first node All first nodes are sorted in descending order according to betweenness centrality to obtain the first node sequence; The first few first nodes in the first node sequence are determined as the initial failed nodes.

[0052] To explore the failure propagation mechanism in multi-level intercity road networks, this embodiment designs a deliberate attack strategy to trigger cascading failures and reveal network vulnerabilities. Compared with random attack methods, deliberate attacks, due to their direct targeting of critical nodes or weak edges, can more effectively expose network weaknesses under extreme conditions. This embodiment adopts a node-oriented strategy rather than an edge-oriented strategy because node failures have a more direct impact on network stability and traffic flow. Betweenness centrality measures the frequency of a node's occurrence on the shortest path between other node pairs, reflecting its role in traffic transmission. High betweenness centrality nodes often control a large amount of traffic flow; their removal may disrupt critical transit corridors and accelerate cascading failures.

[0053] In some embodiments, starting from the initial failure node, a multi-path load redistribution model driven by equiimpedance line identification is used to simulate the cascading failure propagation process until the propagation process ends; including: Step S1: Set the number of iteration rounds The initial value is 2, and the failure node after the first iteration is the initial failure node; Step S2: Statistical analysis of the first... The number of failed nodes after rounds of iteration, starting from the first node set. Selected from After each iteration, for each failed node, draw an equal impedance line with the failed node as the center and the preset receiving node identification threshold as the impedance radius, and take all the non-failed nodes in the area defined by the equal impedance line as the receiving nodes of the failed load. Step S3: If each failed node has no receiving node with failed load, proceed to step S8; otherwise, proceed to step S4. Step S4: For the failed node with existing failed load, select no more than a preset number of candidate paths for each pair of failed node and receiving node; Step S5: Distribute the failed node's load along all feasible paths, update the load and link impedance of the nodes along the path; Step S6: Determine whether the node with updated load is an overloaded node, and if yes, go to step S7, otherwise, go to step S8; Step S7: Determine the overloaded node as a new failed node, mark all connected links of the new failed node as disconnected and update the link set, and update to and then go back to step S2; Step S8: End the cascading failure propagation process.

[0054] The multi-path load redistribution model driven by equal impedance line recognition proposed in this embodiment takes the failed node as the starting point, screens potential receiving nodes through travel time (or generalized impedance) radius, and iteratively distributes the failed load on multiple feasible paths to more realistically depict the cascading failure propagation process under extreme conditions. Specifically, for each failed node, first determine the impedance radius according to the receiving node recognition threshold, and draw the equal impedance line (i.e. travel time contour) with the node as the center, identify all non-failed nodes with a shortest travel time not exceeding the threshold as receiving nodes, thereby limiting the effective propagation range of the failed load. Subsequently, enumerate no more than a preset number of candidate paths for each pair of failed-receiving node to control the diversity and complexity of the propagation path. In each failed round, based on the stochastic user equilibrium model, distribute the failed node's load to the selected paths according to the path selection probability distribution calculated by the path impedance, and accumulate the corresponding flow to the nodes along the path. The path can be an adjacent path containing only a single link, or a feasible path containing multiple links leading to non-adjacent nodes. Then update the node load and network connectivity state synchronously, if a new failed node is generated, go to the next iteration, until no new failed node appears.

[0055] From the perspective of propagation mechanism, the method allows the failure load to be redistributed in a candidate set consisting of multiple feasible paths according to a probabilistic mechanism of path impedance, rather than deterministic propagation along the path with the minimum impedance. This mechanism enables the failure propagation to exhibit both local adjacent diffusion and transmission to more distant nodes through paths consisting of multiple segments, thereby breaking through the limitation of traditional "single round of topological adjacent propagation". Through the unified framework of "equi-impedance line identification - multiple path enumeration - probabilistic distribution - state iteration", the method is controlled in propagation range and random in path selection, and can more accurately depict the process of multi-path, non-adjacent load redistribution and cascade evolution in complex networks.

[0056] The embodiment controls the range of paths participating in the redistribution of failure load by setting the two key parameters of the receiving node identification threshold and the number of feasible paths, thereby incorporating the multi-node, multi-path and cross-level propagation mechanism into the model representation. Coupling this mechanism with the stochastic user equilibrium model forms an iterative shortest path redistribution process. This combination not only improves the accuracy of the description of the propagation path and speed, but also enhances the practicality of the simulation of cascading failure evolution.

[0057] The multi-path load redistribution model proposed in the embodiment introduces a receiving node identification threshold for identifying downstream nodes that have the ability to receive and further transmit failure load, in order to overcome the limitation of previous models that only assume that failure propagates step by step along adjacent edges while ignoring the influence of traffic impedance. In practice, failure load may bypass high impedance paths and spread through multiple nodes and road levels, exhibiting multi-path and cross-level propagation characteristics. Specifically, if the shortest travel time between a non-failure node and a failure node does not exceed the receiving node identification threshold, the node is defined as a direct receiving node. This mechanism not only ensures the rationality of propagation, but also avoids the over-diffusion of failure.

[0058] Since there may be multiple feasible paths between the failure node and the direct receiving node, the number of paths participating in redistribution needs to be controlled. To this end, the application defines the number of feasible paths to limit the number of alternative paths that can participate in propagation in addition to the shortest path. In addition, for nodes with a shortest travel time exceeding the receiving node identification threshold, if they are located on a feasible path connecting the failure node and the direct receiving node, the nodes can participate in propagation as indirect receiving nodes; otherwise, they will be unaffected. As can be seen, the receiving node identification threshold and the number of feasible paths together constitute a unified mechanism that can capture both direct and indirect, single-path and multi-path failure propagation behaviors, and support modeling of cross-road level failure propagation.

[0059] For example, Figure 2As shown, in a four-node network containing nodes A, B, C, and D, their travel times are: AB = 3 min, AC = 1 min, BD = 2 min, CD = 1 min (as shown in the figure). Figure 2 (a)). Assume node A is inactive, the receiving node identification threshold is 2 minutes, and the number of feasible paths is 2. Then the shortest travel times from node A to each node are: C is 1 minute, D is 2 minutes, B is 3 minutes (e.g., ...). Figure 2 (b) and (c) in the table). If the shortest travel time from a non-failed node to a failed node does not exceed the receiving node identification threshold, then that node becomes a direct receiving node, i.e., nodes C and D are direct receiving nodes, while node B is not a direct receiving node. Since there are multiple feasible paths between node A and the direct receiving node (including ABD and ABDC, such as...), Figure 2 In (d) of the above, when the number of feasible paths allows for two paths, these paths containing node B will be considered. Therefore, even though node B's shortest travel time exceeds the receiving node identification threshold, it can still participate in propagation as an indirect receiving node because it is located on an included alternative path. At this time, load redistribution will occur along paths AC, ACD, and the included alternative paths ABD and ABDC, which may cause downstream nodes to overload and fail, while nodes unaffected by the paths remain normal (e.g., ...). Figure 2 (e)). In summary, the receiving node identification threshold is used to filter directly receiving nodes, and the number of feasible paths is used to control the number of alternative paths participating in propagation. The combination of the two effectively enhances the model's ability to represent multi-path and cross-level propagation behavior.

[0060] In some embodiments, step S5 specifically includes: Step T1: Calculate the initial impedance of each feasible path for each failed node; calculate the initial path selection probability of each feasible path using the Logit model based on the initial impedance; Step T2: Set the number of iterations The initial value is 2, and the path selection probability of each feasible path in the first iteration is the initial path selection probability; Step T3: In the first step In the next iteration, the load of the failed node is compared with the load of each feasible path. The product of the path selection probabilities in the next iteration determines the load of each feasible path. The load of each feasible path is then allocated to the road segments it comprises, and the road segment impedance is updated. The total impedance of each feasible path is calculated based on the updated road segment impedance. Finally, the Logit model is used to calculate the load of each feasible path based on its total impedance. The path selection probability in the next iteration; Step T4: Determine the first feasible path among all possible paths. The path selection probability of the nth iteration and the nth iteration If the maximum value of the difference in path selection probabilities in each iteration is less than a preset threshold, then the iteration is terminated and proceeded to step T5; otherwise, the iteration count is reduced. Updated to Proceed to step T3; Step T5: Match the load of the failed node with the load of each feasible path. The product of the path selection probabilities in each iteration is used to determine the load of each feasible path. The load of the failed node is then distributed to the corresponding feasible path according to the load of each feasible path, thereby updating the load of the nodes along each feasible path and the segment impedance.

[0061] The multipath load redistribution model proposed in this embodiment combines a receiver node identification threshold with a random user equilibrium model allocation mechanism to overcome the limitations of traditional models based on the adjacency assumption. The receiver node identification threshold filters downstream nodes with propagation capabilities based on travel time impedance, while the random user equilibrium model allocates failed loads from a controlled set of candidate paths. By introducing impedance heterogeneity and path diversity, this method can effectively characterize non-adjacent, multipath, and cross-layer propagation behaviors, thereby improving the accuracy of cascade dynamics representation and enhancing the accuracy of cascade reliability index determination.

[0062] This embodiment can reflect the random path selection behavior under complex traffic conditions and capture the dynamic interaction between nodes during the failure propagation process. It is particularly suitable for multi-path and cross-level cascading failure analysis in multi-level intercity road networks.

[0063] In terms of propagation characteristic quantification, this embodiment proposes four cascade reliability indicators from three dimensions: propagation speed, range, and intensity: the number of newly failed nodes, network efficiency ratio, global node cascade failure rate, and local node cascade failure rate. These indicators provide a comparable and operable basis for sensitivity analysis and network protection strategies.

[0064] The number of newly failed nodes in the current round (NFNCR) reflects the dynamic evolution of cascading failures and is a direct indicator of whether the failure continues to propagate. A value of zero indicates that the cascading process has terminated. The calculation formula is as follows:

[0065] in, Indicates the first The number of newly added failed nodes in each round; For the first The cumulative number of failed nodes after the i-th iteration The cumulative number of failed nodes after the i-th iteration The cumulative number of failed nodes after the i-th iteration

[0066] Network efficiency ratio (NER): measures the effectiveness of connections between nodes, with a higher value indicating stronger connectivity and greater traffic transmission capacity. To evaluate the degree of network function degradation during the cascading failure process, the NER of the initial network is denoted as NER0. The network efficiency ratio after the i-th iteration is:

[0067] wherein, is the initial network efficiency; is the network efficiency after the i-th iteration is:

[0068] wherein, is the number of nodes in the node set .

[0069] Global node cascading failure ratio (GNCFR): GNCFR describes network robustness from a macroscopic perspective and reflects the proportion of failed nodes in the entire network in the current iteration. The calculation formula is:

[0070] wherein, is the global node cascading failure ratio in the i-th iteration .

[0071] Local node cascading failure ratio (LNCFR): used to quantify the rate of failure propagation between consecutive iterations. This indicator normalizes the increase in failed nodes while considering the cumulative number of failed nodes in the previous iteration and the number of nodes still operating normally, thereby eliminating the influence of network size. A higher value indicates accelerated propagation, while a lower value indicates slowed propagation. The LNCFR of the initial network is denoted as LNCFR0. The local node cascading failure ratio after the i-th iteration is:

[0072] The technical solutions of the embodiments will be described in detail below with reference to a specific example.

[0073] The multi-level intercity road network in the Guangdong-Hong Kong-Macao region is selected as the research object due to its unique regional and structural characteristics. The economically developed Guangdong-Hong Kong-Macao Greater Bay Area and the relatively underdeveloped eastern, western, and northern regions of Guangdong have significant differences, providing a diverse scenario for studying network heterogeneity and node robustness. The multi-level and highly interconnected road network reflects the complexity of the intercity system, helping to identify key nodes, traffic bottlenecks, and cross-regional coordination issues while ensuring the research results have some promotional value.

[0074] The collection and processing of multi-level intercity road network data are divided into two stages to build a high-precision network model. In the first stage, the network basic elements are obtained through collaboration with the traffic department, and the road attribute information is collected, including location, direction, length, number of lanes, traffic capacity, design speed, and toll rules, as well as the annual origin-destination matrix. The collected vector data is standardized and topologically checked, overlapping or redundant road segments are merged, and fragmented road segments with a length less than 1 meter are removed to ensure network connectivity and computational stability. The processed multi-level intercity road network contains 4506 road segments, 2892 basic nodes, and 1246 demand nodes. In the second stage, the initial 1246 traffic analysis zones are aggregated into 238 regions using the "regional unit + double core positioning" principle. In each region, the administrative center and the main industrial hub are designated as activity cores, taking into account the administrative representation and the spatial distribution of key trip generation points. This aggregation method compresses the number of OD paths from millions to tens of thousands, significantly improving computational efficiency while preserving necessary path information. This method has been validated in previous studies and proven to be suitable for multi-regional traffic modeling.

[0075] The general rules of cascading failure evolution are studied using the attack strategy based on betweenness centrality. The model parameters are set as follows: the receiving node recognition threshold is 900s, the number of feasible paths is 3, the convergence threshold is , and the maximum number of iterations is 100. To maintain consistency in the judgment criteria, the network is considered to be in a saturated state when GNCFR≥0.8, indicating that the redundant resources are almost exhausted, and it is considered to reach a low-efficiency steady state when NER≤0.01. Preliminary test results show that node 1783 (highest betweenness centrality) is the most destructive single-node attack target, so it is chosen as the attack starting point in subsequent experiments.

[0076] As shown in Figure 3 , NFNCR increases from 1 in the first round to 184 in the seventh round, reaches a global peak of 206 in the 14th round, and decreases to 0 in the 36th round. This indicates that attacks on high-betweenness centrality hubs can induce concentrated and intermittent failure propagation peaks in the early stages. Figure 4As shown, the NER dropped sharply from 0.9942 in round 1 to 0.1567 in round 14, fell below 0.1 in round 16, and finally stabilized at 0.0027 in round 36, indicating that hub failures severely weakened network reachability in the early and mid-stages. Figure 5 As shown, GNCFR steadily increased from 0.0003 to 0.5363 in round 14, and approached a saturation value of 0.8842 in rounds 35-36, indicating that early local or staged failures gradually evolved into large-scale failures in later stages, and the system's redundant resources were gradually exhausted. Figure 6 As shown, LNCFR jumped to 0.0035 in the second round, then dropped rapidly to 0.0005-0.0008 in the third to eighth rounds, and slowly rebounded to 0.0030 in the third to third rounds. This reflects that the early failure propagation rate was low and there were short-term fluctuations, but the long-term risk accumulation effect led to the continuous expansion of the failure range.

[0077] Sensitivity analysis was performed on two control parameters: the receiver node identification threshold and the number of feasible paths. To evaluate their impact on cascade reliability, five values ​​were tested for each parameter: the receiver node identification threshold was set to 600 s, 900 s, 1200 s, 1500 s, and 1800 s; the number of feasible paths was set to 1, 2, 3, 4, and 5.

[0078] 1. The impact of the receiving node identification threshold on cascade reliability A higher receiver node identification threshold leads to more severe cascading failures and earlier termination cycles in multi-level intercity road networks, indicating that a high receiver node identification threshold accelerates failure propagation and shortens the propagation cycle. Figure 7 As shown, in round 6, the NFNCR corresponding to a receiver node identification threshold of 600 s is 60; while when the receiver node identification threshold is 1800 s, it increases to 222. When the receiver node identification threshold is 1800 s, the NFNCR shows a maximum single-round increment of 263 in round 12; while when the receiver node identification threshold is 600 s and 1800 s, the failure propagation terminates in round 48 and round 23, respectively.

[0079] A higher receiver node identification threshold leads to more severe cascading failures and earlier termination rounds in multi-layered intercity road networks, indicating that a high receiver node identification threshold accelerates failure propagation and shortens the propagation cycle. For example, in round 6, a receiver node identification threshold of 600 s corresponds to 60 newly added failed nodes in this round; while when the receiver node identification threshold is 1800 s, this increases to 222. When the receiver node identification threshold is 1800 s, the number of newly added failed nodes in this round shows the largest single-round increase of 263 in round 12; while when the receiver node identification threshold is 600 s and 1800 s, failure propagation terminates in round 48 and round 23, respectively.

[0080] As Figure 8 shown, NER exhibits a more dramatic downward trend as the receiving node identification threshold increases. For example, at the 6th round, the NER corresponding to a receiving node identification threshold of 600 s is 0.8430; while the NER corresponding to a receiving node identification threshold of 1800 s is 0.4879. At the final steady state, the NER corresponding to a receiving node identification threshold of 600 s is 0.1840; while the NER corresponding to a receiving node identification threshold of 1800 s is only 0.0005, indicating that a higher receiving node identification threshold not only amplifies the initial loss, but also makes the network quickly enter an inefficient state.

[0081] As Figure 9 shown, the growth rate and saturation value of GNCFR are also significantly affected by the receiving node identification threshold. For example, under the condition of a receiving node identification threshold of 600 s, the final GNCFR is about 0.5142; while under the condition of a receiving node identification threshold of 1800 s, GNCFR approaches saturation (0.9633) at the 22nd round, indicating that a larger receiving node identification threshold will consume redundant resources faster and trigger large-scale failure in fewer rounds.

[0082] As Figure 10 shown, LNCFR also presents stronger early fluctuations and late risk accumulation effects. For example, when the receiving node identification threshold is 600 s, LNCFR stabilizes at 0.0006-0.0007 after fluctuation at the 2nd round; while when the receiving node identification threshold is 1800 s, LNCFR rises rapidly in the early stage and reaches 0.0094 at the final round.

[0083] These results show that a larger receiving node identification threshold will amplify early impact, accelerate failure propagation, terminate the propagation process earlier, and increase global and local failure rates. Therefore, networks under high receiving node identification thresholds are more vulnerable and need to reinforce key hubs in the short term to suppress transient peaks, while enhancing redundant resources and load dispersion capabilities in the long term to alleviate cumulative risks.

[0084] Overall, increasing the receiving node identification threshold will amplify the initial impact and shorten the failure propagation period. Under the condition of a high receiving node identification threshold, the failure process presents a "short duration, high intensity" disturbance mode, characterized by higher single-round peaks, faster NER decline, and earlier GNCFR saturation. These findings indicate that effective protection measures need to focus on shortening response and recovery delays, implementing rapid isolation and flow control, and deploying redundant resources at key hubs to suppress transient peaks.

[0085] 2、The number of feasible paths affects the cascading reliability As Figure 11As shown, the NFNCR exhibits a pattern of "rapid growth in the early stage, fluctuation in the middle stage, and decline in the later stage." For example, when the number of feasible paths is 1, the NFNCR peaks at 89 in round 8, then gradually declines and drops to 0 in round 23, indicating that its impact is strong but short-lived. As the number of feasible paths increases, the failure scale expands significantly. For example, when the number of feasible paths is 3, the NFNCR peaks at 206 in round 14 and continues to fail until round 36; while when the number of feasible paths is 5, the NFNCR peaks at 192 in round 14 and only fails until round 32.

[0086] like Figure 12 As shown, the NER decreases more rapidly with a higher number of feasible paths. For example, when the number of feasible paths is 1, the NER drops to 0.6789 in round 8 and eventually stabilizes at 0.3652; when the number of feasible paths is 3, the NER drops to 0.1567 in round 14 and eventually stabilizes at 0.0027; when the number of feasible paths is 5, the NER drops sharply from an initial 0.9942 to 0.1629 in round 14 and eventually stabilizes at 0.0027, indicating that a larger number of feasible paths exacerbates the loss of connectivity.

[0087] like Figure 13 As shown, GNCFR increases faster and reaches a higher saturation value with a higher number of feasible paths. For example, when the number of feasible paths is 1, GNCFR only reaches 0.2960; while when the number of feasible paths is 3 and 5, GNCFR reaches 0.5363 and 0.5246 respectively in round 14, eventually stabilizing at 0.8842 and 0.8921, indicating that a larger number of feasible paths accelerates the consumption of redundant resources and drives global crash.

[0088] like Figure 14 As shown, LNCFR remained low in all cases, but the trends differed. For example, when the number of feasible paths was 1, LNCFR briefly rose to 0.0021 in the second round, then fell back and stabilized at 0.0005, indicating limited propagation strength. However, when the number of feasible paths was 5, LNCFR rose to 0.0038 in the second round and then briefly fell, but rose again later and stabilized at 0.0032, indicating that a larger number of feasible paths caused local failures to gradually accumulate into significant global failures.

[0089] In summary, the larger number of feasible paths amplifies the scale of failure and prolongs the duration of the cascading process. Although a higher number of feasible paths provides more alternative paths, it also concentrates the load on a few critical nodes, leading to larger peaks, slower recovery speed and more thorough consumption of redundant resources in the later stage. Therefore, network design should optimize path capacity allocation, supplemented by dynamic load balancing and capacity enhancement measures, to alleviate the long-term risk accumulation effect.

[0090] Based on the same inventive concept, the embodiment of the present application also provides a cascading reliability index determination device for a multi-level intercity road network. As shown in Figure 15 The cascading reliability index determination device 200 for the multi-level intercity road network provided by the embodiment of the present application at least includes: The construction unit 201 is configured to construct a multi-level intercity road network of a target region, including a first node set and a road segment set. The calculation unit 202 is configured to calculate the initial load and capacity of any first node in the first node set. The first determination unit 203 is configured to trigger cascading failure of the multi-level intercity road network by using an attack strategy based on the centrality of the intermediate number, so as to determine an initial failure node from the first node set. The simulation unit 204 is configured to simulate the cascading failure propagation process by using an equal impedance line driven multi-path load redistribution model, starting from the initial failure node, until the propagation process ends. The second determination unit 205 is configured to determine the number of newly added failure nodes, the network efficiency ratio, the global node cascading failure rate and the local node cascading failure rate in each round of the cascading failure propagation process as the cascading reliability index of the multi-level intercity road network.

[0091] It should be noted that the principle of the cascading reliability index determination device 200 for the multi-level intercity road network provided by the embodiment of the present application solves the technical problem, which is similar to the method provided by the embodiment of the present application. Therefore, the implementation of the cascading reliability index determination device 200 for the multi-level intercity road network provided by the embodiment of the present application can refer to the implementation of the method provided by the embodiment of the present application, and the repeated parts will not be described here.

[0092] Based on the same inventive concept, the embodiment of the present application also provides an electronic device, as shown in Figure 16 The electronic device includes a memory and a processor. The memory stores an executable program. The processor executes the executable program to implement the steps of the cascading reliability index determination method for the multi-level intercity road network provided by the above embodiment.

[0093] The processor can be a general processor, a digital signal processor, an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The PLD can be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof. The general processor can be a microprocessor or any conventional processor.

[0094] Since the electronic device introduced in the embodiments of the present application is provided with the memory for implementing the method for determining the cascading reliability index of the multi-level intercity road network disclosed in the embodiments of the present application, based on the method for determining the cascading reliability index of the multi-level intercity road network introduced in the embodiments of the present application, those skilled in the art can understand the structure and deformation of the electronic device introduced in the embodiments of the present application, and thus the details are not described herein.

[0095] The embodiments of the present application further provide a computer readable storage medium, which stores a computer program. When the computer program is run by a processor, the steps of the method for determining the cascading reliability index of the multi-level intercity road network provided by the above embodiments are implemented.

[0096] The storage medium in the embodiments can be included in the electronic device, or can exist separately and not be assembled into the electronic device. The storage medium carries one or more computer programs. When the one or more computer programs are executed, the steps of the method for determining the cascading reliability index of the multi-level intercity road network provided by the above embodiments are implemented.

[0097] It should be understood that each scheme in the embodiments has the corresponding technical effects in the method embodiments, which are not described herein.

[0098] According to the embodiments of the present application, the computer readable storage medium can be a nonvolatile computer readable storage medium, for example, can include but not limited to: portable computer disk, hard disk, random access memory (RAM), read only memory (ROM), erasable programmable read only memory (EPROM or flash memory), portable compact disk read only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination of the above. Alternatively, the specific examples in the embodiments can refer to the examples described in any embodiment of the present application, and the embodiments will not be repeated here. Obviously, those skilled in the art should understand that the above-mentioned modules or steps of the present application can be realized by a general computing device, which can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and alternatively, they can be realized by program codes executable by a computing device, so that they can be stored in a storage device and executed by a computing device, and in some cases, the steps shown or described can be executed in different order, or they can be manufactured into individual integrated circuit modules, or multiple modules or steps can be manufactured into a single integrated circuit module. Thus, the present application is not limited to any specific hardware and software combination.

[0099] The embodiments of the present application also provide a computer program product, which includes computer programs / instructions, and the computer programs / instructions are executed by a processor to realize the steps of the method for determining the cascade reliability index of the multi-level intercity road network provided by the above-mentioned embodiments.

[0100] The flowcharts and block diagrams in the drawings illustrate the possible implementation architecture, function and operation of the systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowcharts or block diagrams can represent a module, a program segment, or a part of code, which includes one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions targeted by the blocks can occur in different order from that targeted in the drawings. For example, two blocks represented in succession can actually be executed substantially in parallel, and sometimes they can be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and the combination of blocks in the block diagrams and / or flowcharts, can be realized by a special hardware-based system for implementing the specified functions or operations, or can be realized by a combination of special hardware and computer instructions.

[0101] Moreover, while operations are depicted in a particular order, this should not be understood as requiring the operations to be performed in the particular order shown or in sequential order, and that some operations can be performed in parallel or in any suitably enabled order. Similarly, while several specific implementation details are included herein, they should not be taken as limitations on the scope of the present application. Certain features that are described in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination.

Claims

1. A method for determining the cascade reliability index of a multi-level intercity road network, characterized in that, include: Construct a multi-level intercity road network for the target area, including: a first node set and a road segment set; Calculate the initial load and capacity of any first node in the first node set; A multi-level intercity road network cascading failure is triggered using an attack strategy based on betweenness centrality, so as to determine the initial failure node from the first node set; Starting from the initial failure node, the cascade failure propagation process is simulated using a multi-path load redistribution model driven by equiimpedance line identification until the propagation process ends. The number of newly failed nodes, network efficiency ratio, global node cascading failure rate, and local node cascading failure rate in each round of cascading failure propagation are determined as cascading reliability indicators for multi-level intercity road networks.

2. The method according to claim 1, characterized in that, Construct a multi-level intercity road network for the target area, including: For the highways, national highways and provincial highways in the target area, road segment parameters are set for each road segment, including: length, traffic capacity, design speed and two road nodes; Construct a first node set containing multiple first nodes The first node is a road node or intersection; construct a road segment set containing multiple road segments. .

3. The method according to claim 2, characterized in that, The method further includes: The centroid method based on travel time is used to determine the center location of each traffic zone in the target area. These center locations are then designated as second nodes, and all second nodes are grouped into a second node set. ; The second node is connected to its nearest road node to form a virtual edge, and each virtual edge is assigned an access time constant to enable the virtual edge to access the multi-level intercity road network; The traffic from the second node is routed through a virtual edge into the multi-level intercity road network.

4. The method according to claim 3, characterized in that, Calculate the initial load of any first node in the first node set, including: For the first node set The first node in When the first node As a load node, its initial load for: in, Road section Traffic flow, For all to the first node A collection of road segments that transport traffic; When the first node For a zero-flow node, its initial load for: in, For the first node set The first node in Initial load, first node As a load node; A set of load nodes; First node With the first node The shortest travel time between them.

5. The method according to claim 4, characterized in that, Calculate the capacity of any first node in the first node set, including: First node capacity for: in, This is the redundancy coefficient; and These are the minimum and maximum values ​​of the redundancy coefficient, respectively. First node The normalized economic centrality; First node Economic centrality; For the second node ; economic output; For the second node With the first node The shortest travel time between them.

6. The method according to claim 5, characterized in that, The method further includes: Calculate the first node With the first node Shortest travel time between : in, First node With the first node The set of all feasible paths, First node With the first node Any feasible path between them For path Total impedance: For path Road sections included impedance: in, For free-flow travel time; Road section Length; Road section The unit distance toll rate; Road section Traffic flow, Road section Traffic capacity; The time conversion factor for currency; and All of these are congestion response parameters.

7. The method according to claim 5, characterized in that, The initial failed nodes are determined from the first node set, including: The first node set any first node in betweenness centrality for: in, Indicates the first node With the first node The number of shortest paths between them; First node With the first node Passing through the first node The number of paths; The first node set All first nodes are sorted in descending order according to betweenness centrality to obtain the first node sequence; The first few first nodes in the first node sequence are determined as the initial failed nodes.

8. The method according to claim 7, characterized in that, Starting from the initial failure node, the cascade failure propagation process is simulated using a multi-path load redistribution model driven by equiimpedance line identification until the propagation process ends. include: Step S1: Set the number of iteration rounds The initial value is 2, and the failure node after the first iteration is the initial failure node; Step S2: Statistical analysis of the first... The number of failed nodes after rounds of iteration, from the first node set Selected from After each iteration, for each failed node, draw an equal impedance line with the failed node as the center and the preset receiving node identification threshold as the impedance radius, and take all the non-failed nodes in the area defined by the equal impedance line as the receiving nodes of the failed load. Step S3: If each failed node has no receiving node with failed load, proceed to step S8; otherwise, proceed to step S4. Step S4: For the failed nodes of the receiving nodes with failed load, select a feasible path for each pair of failed nodes and receiving nodes, not exceeding the number of preset candidate paths. Step S5: Distribute the load of the failed node along all feasible paths, and update the load and segment impedance of nodes along the feasible paths. Step S6: Determine whether the node updating the load is an overloaded node. An overloaded node is a node whose load exceeds its capacity. If yes, proceed to step S7; otherwise, proceed to step S8. Step S7: Identify the overloaded node as the new failed node, mark all connected road segments of the new failed node as disconnected and update the road segment set. Updated to Then proceed to step S2; Step S8: The cascading failure propagation process ends.

9. The method according to claim 8, characterized in that, Step S5 specifically includes: Step T1: Calculate the initial impedance of each feasible path for each failed node; calculate the initial path selection probability of each feasible path using the Logit model based on the initial impedance; Step T2: Set the number of iterations The initial value is 2, and the path selection probability of each feasible path in the first iteration is the initial path selection probability; Step T3: In the first step In the next iteration, the load of the failed node is compared with the load of each feasible path. The product of the path selection probabilities in the next iteration determines the load of each feasible path. The load of each feasible path is then allocated to the road segments it comprises, and the road segment impedance is updated. The total impedance of each feasible path is calculated based on the updated road segment impedance. Finally, the Logit model is used to calculate the load of each feasible path based on its total impedance. The path selection probability in the next iteration; Step T4: Determine the first feasible path among all possible paths. The path selection probability of the nth iteration and the nth iteration If the maximum value of the difference in path selection probabilities in each iteration is less than a preset threshold, then the iteration is terminated and proceeded to step T5; otherwise, the iteration count is reduced. Updated to Proceed to step T3; Step T5: Match the load of the failed node with the load of each feasible path. The product of the path selection probabilities in each iteration is used to determine the load of each feasible path. The load of the failed node is then distributed to the corresponding feasible path according to the load of each feasible path, thereby updating the load of the nodes along each feasible path and the segment impedance.

10. The method according to claim 8, characterized in that, The number of newly failed nodes, network efficiency ratio, global node cascading failure rate, and local node cascading failure rate in each round of cascading failure propagation are defined as cascading reliability indicators for multi-level intercity road networks, including: No. Number of newly failed nodes after round of iteration for: in, For the first The cumulative number of failed nodes after one round of iterations; For the first The cumulative number of failed nodes after one round of iterations; No. Network efficiency ratio after rounds of iteration for: in, For the initial network efficiency; For the first Network efficiency after rounds of iteration: in, For node set The number of nodes; No. Global node cascading failure rate after round iteration for: No. Local node cascading failure rate after round iteration for: 。

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