Road network toughness evaluation and recovery optimization method and system considering cascade failure under flood influence

Abstract

The invention discloses a road network toughness evaluation and recovery optimization method and system considering cascade failure under flood influence. The method comprises the following steps: step 100, constructing a road network cascade failure model; step 200, the road network cascade failure model outputs time sequence parameters, and cascade failure influence indexes, network efficiency and average shortest path length are determined based on the time sequence parameters; step 300, determining a road network toughness index according to the cascade failure influence index, the network efficiency and the average shortest path length; and constructing a road network toughness recovery optimization model considering cascade failure. According to the method, the urban road network cascade failure model considering the flood dynamic process and local traffic flow redistribution is constructed, and the accuracy of road network toughness evaluation under the flood condition is improved; a road network toughness recovery optimization method considering cascade failure is provided, and the emergency efficiency is improved.

Description

Technical Field

[0001] This invention relates to the fields of urban water management, disaster prevention and mitigation, and emergency research technology, and in particular to a method and system for assessing and optimizing road network resilience under the influence of floods, considering cascading failures. Background Technology

[0002] Urban flooding can easily lead to road inundation and failure, affecting residents' travel and emergency response capabilities. Therefore, research on road network resilience assessment and recovery strategies under urban flooding is crucial for mitigating the impact of floods. Traditional road network resilience assessment methods primarily use static indicators, such as network efficiency and betweenness centrality, to evaluate the resilience of urban road networks under flooding. These methods do not consider the dynamic propagation process of flood impacts on road traffic. When urban flooding occurs, some roads are flooded and become impassable. Traffic flow that would normally use these roads is dynamically diverted to other roads, potentially causing traffic congestion on the affected roads due to overload, triggering a wider chain reaction, and ultimately leading to a complete collapse of road traffic from localized paralysis. This dynamic process is called cascading failure of the road network. As cascading failure propagates, the performance of the road network significantly decreases, and network resilience dynamically changes. However, previous road network resilience assessment studies have neglected the cascading failure process, resulting in inaccurate resilience assessment results.

[0003] In addition, urban flooding causes road inundation failure, which seriously affects road network services, emergency rescue and residents' travel and causes significant losses. Post-disaster resources and time are limited, so it is necessary to determine the optimal road recovery sequence. Therefore, efficient road network resilience recovery strategies are crucial to improving urban emergency management capabilities. However, existing research still has shortcomings when applied to urban flood scenarios: (1) it lacks sufficient consideration of the dynamic process of cascading failure, resulting in inaccurate evaluation of the effectiveness of recovery strategies; (2) it lacks sufficient understanding of recovery laws such as critical thresholds, making it difficult to provide effective guidance for emergency management.

[0004] Therefore, there is an urgent need for a system and method that can precisely characterize cascade failures, dynamically assess resilience, and optimize recovery strategies. Summary of the Invention

[0005] The purpose of this invention is to provide a road network resilience assessment, recovery optimization method and system that considers cascading failures under the influence of floods, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the first aspect of this application proposes a method for assessing road network resilience under the influence of flooding, considering cascading failures, comprising: Step 100: Construct a road network cascading failure model; Step 200: The road network cascade failure model outputs time series data, and the cascade failure impact index, network efficiency, and average shortest path length are determined based on the road network resilience assessment index parameters. Step 300: Determine the road network resilience index based on the cascading failure impact index, network efficiency, and average shortest path length.

[0007] According to one embodiment of this application, step 100 includes: Step 101: Construct a road network topology model based on GIS road network data, abstracting the urban road network into an undirected network graph G={V, E}, where the node set... Represents an intersection, edge set E ={ e ij} represents a road, and road attribute information is obtained; Step 102: Calculate the capacity Ci and initial load Li of each road based on the ML model, initialize all roads to the normal state, and set the time step Δt.

[0008] According to one embodiment of this application, step S100 further includes an iterative process of cascading failure simulation: The identification of flooded and failed roads includes extracting the flooding depth hi(t) of each road; when hi(t) > a first preset depth threshold, road i is determined to be a flooded and failed road; Step 104: Traffic flow assignment: For failed roads, a local redistribution strategy based on betweenness centrality is used to calculate the assigned flow; Step 105: Propagation of road failure, including determining the road status after traffic redistribution. If there are no congested roads in the network, proceed directly to the next step. If there are congested roads, mark them as "congestion failure". The load exceeding the capacity of the road needs to be redistributed in the next iteration. Step 106: Dynamic iteration of the impact of flooding, including advancing the time step to t+Δt, reading the flooding data at the next moment, repeating steps 103 to 105, and simulating for a set duration until the end of the flooding process.

[0009] According to one embodiment of this application, the local redistribution strategy based on betweenness centrality in step S104 includes: Calculate the betweenness centrality of the failed edges: Calculate the weighting coefficients for adjacent normal edges:

[0010] Calculate flow allocation: ; In the formula: This refers to the node sTo the node t The total number of shortest paths, It refers to passing through the edge i From node s To the node t The number of shortest paths, EBC ( e k () represents adjacent normal edges e k betweenness centrality, ω k Adjacent normal edges e k The weighting coefficients, Adjacent normal edges e k The allocated traffic.

[0011] According to one embodiment of this application, step 200 further includes: The formula for calculating the cascading failure impact index is: In the formula: E This represents the total number of roads in the network. E c The number of congested and ineffective roads; E f This refers to the number of submerged and unusable roads. The formula for calculating network efficiency is: ; In the formula: N This represents the total number of network nodes. d ij For nodes i and nodes j The shortest path length between them; The formula for calculating the average shortest path length is: .

[0012] According to one embodiment of this application, step 300 further includes: The formula for calculating the road network resilience index is: ; In the formula: CFII The cascading failure impact index, NE'、APL' These represent the normalized network efficiency and the average shortest path length, respectively. α 1 、α 2 、α 3 represents the weights of different indicators.

[0013] According to one embodiment of this application, the first preset depth threshold is 0.3m.

[0014] According to one embodiment of this application, the road betweenness centrality is first calculated, then the weights of adjacent normal edges are calculated, and finally the flow distribution is calculated.

[0015] The second aspect of this application proposes a road network resilience assessment system considering cascading failures under the influence of flooding, including: a cascading failure modeling module for constructing a road network cascading failure model; The calculation module is used to obtain time-series data based on the road network cascade failure model, and determine the cascade failure impact index, network efficiency, and average shortest path length based on the time-series data; The resilience assessment module is used to determine the road network resilience index based on the cascading failure impact index, network efficiency, and average shortest path length.

[0016] The third aspect of this application proposes a road network resilience recovery optimization method considering cascading failures under the influence of floods, comprising: constructing a road network resilience recovery optimization model considering cascading failures, wherein the model takes maximizing the cumulative road network resilience index as the optimization objective, and solves the optimal road recovery sequence through a genetic algorithm, wherein the road network resilience index is obtained according to the aforementioned network resilience index formula.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) A cascade failure model of urban road network considering the dynamic process of flooding and local traffic flow redistribution was constructed to improve the accuracy of road network resilience assessment under flood conditions; (2) A local redistribution strategy was proposed, which allocates the traffic flow of the failed road only to the adjacent road, which is more in line with the short-distance transfer characteristics of actual traffic flow; (3) A road network resilience assessment method considering cascade failure scale, network efficiency and average shortest path length was proposed, which quantitatively characterized the dynamic evolution characteristics of urban road network resilience under the influence of floods. (4) With the goal of maximizing resilience, an optimization model for urban flood road network resilience recovery based on different strategies was established. The number and sequence of urban flooded roads to be recovered were optimized, improving the optimization effect of the recovery strategy and enhancing emergency response efficiency. Attached Figure Description

[0018] Figure 1 A flowchart of a road network resilience assessment method considering cascading failures under the influence of flooding, according to the present invention; Figure 2 A schematic diagram of a complex network topology; Figure 3 This is a flowchart for determining road conditions. Figure 4 This is a schematic diagram of local redistribution; Figure 5For the example, the time-series variation curves of road network resilience (R) considering cascading failure and road network resilience (R') not considering cascading failure under different return period rainfall: (a) 20-year return period rainfall; (b) 50-year return period rainfall; (c) 100-year return period rainfall; (d) 200-year return period rainfall; Figure 6 The recovery results of different strategies under different return periods of rainfall in the example are as follows: (a) 20-year return period rainfall; (b) 50-year return period rainfall; (c) 100-year return period rainfall; (d) 200-year return period rainfall. Detailed Implementation

[0019] 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.

[0020] Figure 1 This invention provides a road network resilience assessment method considering cascading failures under flood conditions, comprising: Step 100: Construct a road network cascading failure model; Step 200: The road network cascade failure model outputs time-series data, and the cascade failure impact index, network efficiency, and average shortest path length are determined based on the time-series data. Step 300: Determine the road network resilience index based on the cascading failure impact index, network efficiency, and average shortest path length.

[0021] Urban road networks, as typical complex systems, exhibit significant cascading failure characteristics when subjected to flooding. The failure of a single road can trigger a chain reaction through traffic flow redistribution mechanisms, leading to a sharp decline in the performance of the entire network. To accurately characterize the cascading failure mechanism of urban road networks under the influence of flooding, this invention constructs a cascading failure model based on complex network theory, considering the dynamic flooding process and local traffic redistribution. A road network resilience assessment index system is built from three dimensions: cascading failure impact index, network efficiency, and average shortest path length. This fully considers the dynamic propagation process of flood impact on road traffic (i.e., cascading failure of the road network) and improves the accuracy of resilience assessment results.

[0022] The time-series data includes the total number of roads in the network. E、 Number of congestion-affected roads E c , E f Number of submerged and unusable roads Ec Total number of network nodes N ,node i and nodes j Shortest path length between d ij .

[0023] According to one embodiment of this application, step 100 further includes: Step 101: Construct a coupled numerical model of urban flooding to simulate the depth, velocity, and volume of flood inundation.

[0024] This invention constructs a coupled urban numerical model based on the PCSWMM platform. The coupled numerical model is a one-dimensional and two-dimensional coupled numerical model of flooding, simulating flood inundation depth, velocity, and volume. This model dynamically couples a one-dimensional pipe network with two-dimensional surface runoff, enabling accurate simulation of urban flooding processes under different rainfall return periods. PCSWMM is a comprehensive and professional modeling tool for urban and watershed drainage and water supply systems, capable of efficiently simulating flooding. The main steps of PCSWMM flood modeling involve selecting rainfall-runoff and runoff generation / confluence models for hydrological and hydraulic modeling. In hydrological modeling, the study area is divided into several sub-modules with consistent hydrological characteristics based on its topography and related features. The Horton infiltration method is selected to simulate rainfall runoff and infiltration. In hydraulic modeling, connection points and pipes are added using ArcGIS, and dynamic waves are used for hydraulic simulation. The two-dimensional floodplain model consists of a uniformly sized grid. The one-dimensional pipe model and the two-dimensional floodplain model are connected through orifices to achieve coupling between the two-dimensional models, enabling calculations of surface runoff generation / confluence and pipe network hydrodynamics. The main modules and calculation principles of PCSWMM in simulating heavy rainfall scenarios are as follows: Surface runoff: Based on surface drainage patterns and land use, PCSWMM divides the study area into several catchment areas and assigns parameters to each. Each catchment area is considered a nonlinear reservoir, with inflows including precipitation and water from upstream catchments, and outflows including infiltration, evaporation, and downstream surface runoff. The nonlinear reservoir capacity equals the maximum depression storage, which is the maximum surface water storage composed of depression storage, surface wetting water, and vegetation interception.

[0025] In PCSWMM, only the reservoir water depth is considered. d Exceeding the maximum water storage depth of the depression d Runoff only occurs on the surface at that time. Q Equation (a) is obtained by calculating runoff per unit area using the Manning equation. q Traffic Q Divide by the catchment area AEquation (b) is calculated. By numerically solving the water balance equation of the catchment area, the change process of the water depth of the catchment area over time can be obtained.

[0026] (a) (b) In the formula: Q For runoff flow rate, m 3 / s; n The Manning coefficient for the catchment area; W Width of the catchment area, in meters; d The water depth is measured in meters (m). d s The maximum water depth in the depression is measured in meters. S Slope of the catchment area; A The area of ​​the catchment area is m. 2 .

[0027] Infiltration models: The main infiltration models include the Horton model, the Green-Ampt method, and the curve number method, with the Horton model being the most commonly used. The Horton model is an empirical formula derived from a large amount of experimental data. The parameters in this model themselves do not have specific physical meanings. Key parameters include maximum infiltration rate, minimum infiltration rate, attenuation constant, drying time, and maximum volume. It primarily describes the relationship between infiltration rate and rainfall time, but does not reflect the water content in saturated and unsaturated soil zones. The Horton infiltration curve equation is as follows: Horton infiltration curve: (c) In the formula, f p for t Infiltration rate at time t, mm / s; f 0 The infiltration rate at the initial moment is expressed in mm / s. f ∞ To stabilize the infiltration rate, mm / s; k d Attenuation coefficient related to soil physical characteristics, s -1 ; t For time, s.

[0028] The Horton model only considers the change in infiltration rate over time, but does not take into account the impact of soil water retention on infiltration rate.

[0029] (d) Equation (d) is an improved Horton model. When the rainfall intensity is low, this method can improve the accuracy of infiltration rate calculation. It uses the cumulative infiltration as the process variable, replacing equation (c), while keeping the input parameters unchanged.

[0030] Flow calculation: Pipe flow calculation is performed using the continuity equation and the momentum equation (determined by the Saint-Venant equation), and three calculation methods are provided: steady flow, moving wave, and dynamic wave. This paper selects dynamic wave to calculate pipe flow.

[0031] Continuity equation: (e) Momentum equation: (f) In the formula: x It is the distance along the direction of water flow, in meters (m). t It is time, s; A The cross-sectional area of ​​the water passage is m. 2 ; Q For outgoing flow, m 3 / s; H The water depth in the pipeline is in meters (m). S f This refers to the resistance gradient (head loss per unit length). g The acceleration due to gravity is m / s². 2 .

[0032] PCSWMM provides a fully integrated approach to one-dimensional and two-dimensional modeling, enabling seamless switching between the two modes. It facilitates modeling of dynamically sized dual drainage systems, two-dimensional floodplains, dam breaches, and watersheds in both one and two dimensions. PCSWMM can provide accurate two-dimensional models for urban and rural areas, including flood depth, velocity, and discharge parameters.

[0033] According to one embodiment of this application, step 101 further includes: constructing a road network topology model based on GIS road network data, abstracting the urban road network as an undirected network graph G={V, E}, wherein the node set Represents an intersection, edge set E ={ e ij} represents a road, and road attribute information is obtained.

[0034] Urban road networks are complex transportation systems composed of roads of different levels, such as expressways, arterial roads, and secondary arterial roads. To further investigate the impact of urban flooding on the cascading failure of road networks, this invention, based on complex network theory, abstracts the urban road network (URN) as an undirected network graph G = { V , E}, as shown in the diagram Figure 2 As shown. The node set... Represents intersection nodes in an urban road network; edge set E ={e ij} represents the road connecting adjacent intersections, where n is the total number of roads in the network; edges e ij Representative node With nodes There are direct road connections between them. Given the bidirectional nature of urban road networks, this invention uses an undirected network for modeling, which satisfies... e ij = e ji Based on the symmetry condition, road attribute information, including road length, number of lanes, and design speed, is read and obtained.

[0035] According to one embodiment of this application, step 100 includes: Step 102: Calculate the capacity Ci and initial load Li of each road based on the ML model, initialize all roads to the normal state, and set the time step Δt.

[0036] Road load and capacity are fundamental to determining the operational status of roads. To calculate the initial load and capacity of a road network, this invention employs the classic linear Motter-Lai model (ML model) proposed by Motter and Lai, which greatly simplifies the complexity of complex network problems. The ML model demonstrates a linear relationship between maximum capacity and initial load, and a similar linear relationship exists between initial load and capacity in real-world urban road networks. (1) In the formula: C i The capacity of the road is pcu / (h·ln); L i The initial load on the road is pcu / (h·ln). α ≥ 0 represents the capacity coefficient, indicating the level of ability to handle traffic flow. Preferably, α =0.2.

[0037] The road capacity is obtained according to the standard "Code for Design of Urban Road Engineering" (CJJ37-2012), specifically, the road capacity... C i This reflects the maximum traffic capacity of the road under ideal conditions. The road capacity calculation formula is derived based on the road's design speed, number of lanes, and the capacity of a single lane: (2) In the formula: C i The capacity of the road is pcu / (h·ln); N L The number of lanes on the road.C b1 The basic traffic capacity of a single lane is pcu / (h·ln).

[0038] According to one embodiment of this application, step S100 further includes an iterative process of cascading failure simulation: Step 103, Identification of flooded and failed roads: Extract the flooding depth hi(t) of each road; when hi(t) > the first preset depth threshold, road i is determined to be a flooded and failed road.

[0039] Specifically, GIS spatial overlay analysis is performed on the inundation depth raster data output by PCSWMM and the road network vector data to extract the inundation depth hi(t) for each road. When hi(t) > a first preset depth threshold, road i is determined to be an inundation failure road. The traffic flow Li of this road needs to be reallocated.

[0040] Preferably, the first preset depth threshold is 0.3m.

[0041] This invention categorizes road conditions into three types: normal, flood-failed, and congestion-failed. When the flood depth exceeds a first preset threshold, the road is defined as a flood-failed road; such roads completely lose their traffic function and no longer participate in traffic flow allocation. Congestion-failed roads, on the other hand, are classified when the road load exceeds its capacity. These congestion-failed roads do not alter the physical structure of the urban road network; they only experience a temporary loss of traffic capacity. The road condition determination process is as follows: Figure 3 As shown.

[0042] According to one embodiment of this application, step 100 further includes: Step 104, Traffic flow assignment: For failed roads, a local redistribution strategy based on betweenness centrality is used to calculate the assigned flow.

[0043] The local redistribution strategy based on betweenness centrality in step S104 includes: Calculate the betweenness centrality of the failed edges: Calculate the weighting coefficients for adjacent normal edges:

[0044] Calculate flow allocation: ; In the formula: This refers to the node s To the node t The total number of shortest paths, It refers to passing through the edge i From node s To the node t The number of shortest paths, EBC (e k () represents adjacent normal edges e k betweenness centrality, ω k Adjacent normal edges e k The weighting coefficients, q k Adjacent normal edges e k The allocated traffic.

[0045] Specifically, for each failed road (including roads that fail due to flooding and roads that fail due to congestion) e f First, the betweenness centrality of roads is calculated. Then, a local redistribution strategy based on betweenness centrality is used to calculate the traffic allocation weights of adjacent roads, and finally, the allocated traffic is calculated. This strategy not only ensures the spatial locality of traffic transfer (consistent with the short-distance transfer characteristics of traffic flow), but also considers the heterogeneity of roads through the betweenness centrality weights (more traffic is allocated to key network corridors).

[0046] To address the cascading failures of road networks during urban flooding, this invention proposes a local redistribution strategy based on betweenness centrality. The strategy uses the betweenness centrality of edges as weights to allocate traffic flow from failed roads to adjacent normal roads according to a weighted ratio. This prioritizes traffic redistribution to adjacent normal roads of failed roads, aligning with the short-distance transfer characteristics of actual traffic flow. Employing edge betweenness centrality as the traffic allocation weight ensures that more traffic is allocated to critical channels in the network. When allocating traffic, it distinguishes between flooded failed roads (completely impassable) and congested failed roads (traffic exceeding capacity), employing differentiated traffic processing methods. Compared to global redistribution, the local strategy only requires searching adjacent road information, significantly reducing computational complexity.

[0047] Failed edge e f The traffic to be allocated is Q f The flow rate to be allocated to a flooded or failed road is its load, and the flow rate to be allocated to a congested or failed road is its load minus its capacity.

[0048] Edge Betweenness Centrality EBC Betweenness centrality (BCC) is a metric for measuring the importance of edges in a network. It represents the proportion of all shortest paths that pass through that edge. The formula for calculating the betweenness centrality of a failed edge is: (3) In the formula: This refers to the nodes To the node t The total number of shortest paths, It refers to passing through the edge i From node s To the node t The number of shortest paths.

[0049] For the failed edge e f The traffic to be allocated is Q f Its set of adjacent normal edges is E ={ e 1, e 2, ... e n The flow distribution is illustrated as follows: Figure 4 As shown, the allocation process function is as follows: ①Assign weight coefficients to adjacent normal edges: (4) ② Traffic allocation: (5) In the formula: EBC ( e k () represents adjacent normal edges e k betweenness centrality, ω k Adjacent normal edges e k The weighting coefficients, Adjacent normal edges e k The allocated traffic.

[0050] According to one embodiment of this application, step 100 further includes: Step 105: After traffic redistribution, determine the road status. If there are no congested roads in the network, proceed directly to the next step. If there are congested roads, mark them as "congestion failure" and the load exceeding their capacity on these roads needs to be redistributed in the next iteration.

[0051] According to one embodiment of this application, step 100 further includes: Step 106: Proceed the time step to t+Δt, read the flood inundation data for the next moment, and repeat steps 103 to 105 to simulate for the set duration until the flood process ends.

[0052] Preferably, the simulation duration until the end of the flooding process is set to 3 hours after the end of the rainfall, in order to fully capture the occurrence, development and natural recovery process of cascading failure.

[0053] According to one embodiment of this application, step 100 further includes: Step 107: Output and analysis, including outputting time series data.

[0054] Specifically, after the simulation is completed, complete time-series data is output, including: road status distribution at each time point (normal / flood failure / congestion failure) and other data, which provide basic data for subsequent road network resilience assessment and recovery strategy optimization.

[0055] According to one embodiment of this application, step 200 further includes: The formula for calculating the cascading failure impact index is: (6) In the formula: E This represents the total number of roads in the network. E c The number of congested and ineffective roads; E f This represents the number of roads that have become submerged and unusable.

[0056] Specifically, the cascading failure impact index, by statistically analyzing the proportion of normally functioning roads in the network, can intuitively reflect the degree of impact of cascading failures on the overall operational status of the network. The cascading failure impact index is directly related to the actual operational status of roads and can provide fundamental support for road network resilience assessment from the perspective of "operational integrity."

[0057] According to one embodiment of this application, step 200 further includes: The formula for calculating network efficiency is: (7) In the formula: N This represents the total number of network nodes. d ij For nodes i and nodes j The shortest path length between them.

[0058] Specifically, network efficiency is a widely used metric in complex network theory, used to measure the overall efficiency of information transmission between all pairs of nodes in a network, and can comprehensively reflect the network's connectivity performance. This metric is highly sensitive to changes in network connectivity; when cascading failures lead to the failure of critical paths, the global network efficiency drops sharply, making it effective in capturing the extent to which cascading failures damage network connectivity.

[0059] According to one embodiment of this application, step 200 further includes: The formula for calculating the average shortest path length is: (8) Specifically, the average shortest path length is directly related to residents' travel distance and time costs in urban road networks. When flooding causes critical roads to fail and triggers cascading failures, vehicles are forced to choose longer detour routes, resulting in a significant increase in the average shortest path length. This indicator can intuitively quantify the impact of cascading failures on residents' travel efficiency.

[0060] According to one embodiment of this application, step 300 further includes: The formula for calculating the road network resilience index is: (9) In the formula: CFII The cascading failure impact index, NE'、APL' These represent the normalized network efficiency and the average shortest path length, respectively. α 1 、α 2 、α 3 represents the weights of different indicators.

[0061] Among them, network efficiency normalization is: the current global network efficiency divided by the baseline network efficiency; Average shortest path length normalization: Baseline average shortest path length divided by the current average shortest path length.

[0062] Preferably, take α 1= α 2= α 3 = 1 / 3.

[0063] Specifically, the average shortest path length is directly related to residents' travel distance and time costs in urban road networks. When flooding causes critical roads to fail and triggers cascading failures, vehicles are forced to choose longer detour routes, resulting in a significant increase in the average shortest path length. This indicator can intuitively quantify the impact of cascading failures on residents' travel efficiency.

[0064] The entire cascading failure process is described as follows: Initially, all roads are normal. Then, rainfall occurs, causing flooding failures on some roads. The load (traffic flow) of the flooded failure roads is distributed to adjacent normal roads. If the capacity of some adjacent roads is less than their load after receiving the load, they are judged as "congestion failures". Congestion failure roads are also redistributed (the portion of the load that is greater than their capacity).

[0065] Taking a certain urban area as an example, this region experienced a severe rainstorm on a certain day. This extreme precipitation event severely paralyzed the urban road traffic system, with the maximum water depth on the main urban roads approaching 2.6 meters, resulting in a complete disruption of road traffic. The research data mainly consists of two parts. The first part is data related to the urban flooding model, mainly including the digital elevation model (DEM), the distribution of rivers, buildings, roads, and pipeline networks; the second part is data related to the city's roads, mainly including the spatial distribution of traffic roads and the service capacity of roads. Among them, the digital elevation model (DEM) comes from the geospatial data cloud platform; the remote sensing image data is selected from the Italian COSMO synthetic aperture radar image data, and the urban building distribution data and river distribution data are manually extracted based on ENVI software. The data also includes river cross-section data, building floor data, drainage network distribution and parameters, urban road related attribute data, and urban road design speed and traffic capacity.

[0066] Using a 200-year return period rainfall event as a typical scenario, a cascading failure model was constructed to simulate and analyze the dynamic evolution of cascading failures in the urban road network under flood impact. In the initial stage of rainfall (1-2 hours), the number of submerged and failed roads increased from 27 to 84, and traffic flow redistribution led to congestion failures on 61 roads, bringing the total number of failed roads to 88. As rainfall continued, the cascading effect accelerated: in the third hour, 121 new congestion failures were added, surging the total number of failed roads to 253; in the fourth hour, the number of submerged and failed roads peaked, with 90 new congestion failures still occurring, indicating that the continuous shift in traffic flow constantly triggered new congestion nodes. Notably, after the rainfall ended (5-6 hours), the number of submerged roads slowly decreased due to the receding water, while the number of congestion failures continued to climb, increasing from 321 to 376, with 74 and 58 new congestion failures respectively. This phenomenon of flooding relief followed by continued worsening of congestion reveals the independence of the cascading failure propagation mechanism: even if external disturbances weaken, the chain reaction triggered by traffic flow redistribution continues to spread throughout the network.

[0067] Spatial evolution characteristics show that cascading failures spread from the initially flooded areas along the river to the densely networked central urban areas. By the 6th hour, a total of 458 roads had failed (64.05%), far exceeding the 82 roads that failed due to flooding, fully demonstrating the amplifying effect of cascading failures on the network. Furthermore, relying solely on natural receding water is insufficient to restore road network function; proactive intervention measures must be taken to break the cascading propagation chain.

[0068] The evolution characteristics of urban road network resilience were analyzed under four rainfall scenarios with return periods of 20, 50, 100, and 200 years. Figure 5 The curves showing the changes in road network resilience under different return periods of rainfall, with and without considering cascading failures, are presented.

[0069] Under all return period scenarios, the road network resilience considering cascading failures was significantly lower than that not considering cascading failures. Under the 200-year return period scenario, at the 6th hour, the road network resilience considering cascading failures was 0.890, while the resilience without considering cascading failures was 0.720, a difference of 0.170, indicating that the traditional method overestimated resilience by 23.6%; even under the 20-year return period scenario, the overestimation was still 4.86%. The road network resilience assessment method that does not consider cascading failures only focuses on flooded roads, ignoring congested roads, which account for more than 80% of the failed roads. Furthermore, the magnitude of the road network resilience loss increased with the return period, from 7.4% under the 20-year return period scenario to 23.8% under the 200-year return period scenario. The greater the rainfall intensity, the wider the scope of congestion failures caused by the cascading effect. This not only directly leads to more roads being flooded due to extreme rainfall, but also amplifies the loss of network resilience exponentially through a chain reaction, making the limitations of assessment methods that do not consider cascading failures increasingly prominent. This demonstrates that incorporating cascading failures into the road network resilience assessment framework is a necessary prerequisite for accurately characterizing the impact of floods on road network performance.

[0070] According to a second aspect of the present invention, a road network resilience assessment system considering cascading failures under the influence of flooding is provided, which corresponds to the road network resilience assessment system considering cascading failures under the influence of flooding described in the above embodiments.

[0071] In some alternative embodiments, a road network resilience assessment system considering cascading failures under flooding conditions includes: The cascading failure modeling module is used to construct cascading failure models for road networks. The calculation module is used to output time-series data based on the road network cascade failure model, and to determine the cascade failure impact index, network efficiency, and average shortest path length based on the time-series data. The resilience assessment module is used to determine the road network resilience index based on the cascading failure impact index, network efficiency, and average shortest path length.

[0072] The present invention provides a road network resilience assessment system considering cascading failures under the influence of flooding, including a road network resilience assessment method considering cascading failures under the influence of flooding in any of the above embodiments.

[0073] According to a third aspect of the present invention, a road network resilience recovery optimization method considering cascading failures under the influence of floods is provided, comprising: constructing a road network resilience recovery optimization model considering cascading failures, wherein the model takes maximizing cumulative road network resilience as the optimization objective, and solves for the optimal road recovery sequence through a genetic algorithm.

[0074] According to one embodiment of this application, it also includes: Determine the objective function. (10)

[0075] In the formula: F This is the cumulative toughness objective function value; K To restore steps; R k The road network resilience index is calculated after restoring k roads.

[0076] Objective Function: This invention aims to maximize the cumulative resilience index. Unlike traditional final-state resilience assessments, cumulative resilience comprehensively reflects the dynamic improvement trajectory of network performance throughout the recovery process. R k Calculate according to formula (9).

[0077] According to one embodiment of this application, it also includes: The decision variables are determined as the priority sequence for the recovery of flooded roads. X ={ x 1, x 2, ... x n},in x i Indicates the first i There are n road numbers to be restored, where n is the total number of flooded and failed roads that need to be restored. The solution space of this sequence is n!, and it grows exponentially with the number of restored roads.

[0078] According to one embodiment of this application, it also includes: Establish constraints such as resource restoration constraints, uniqueness of road restoration, and road condition constraints: (11) (12) (13) In the formula: K max The maximum number of roads that can be restored from flooding failure; E f Set of submerged and failed roads Specifically, to determine a reasonable restoration sequence for submerged and failed roads and improve the disaster resistance capacity of urban road networks, the urban road network resilience restoration analysis should consider the actual resource constraints. Based on the actual conditions of urban roads and the practical problems encountered during the restoration process, constraints such as restoration resource constraints, road restoration uniqueness constraints, and road state constraints should be established. During the restoration process, only submerged and failed roads can have their state changed through restoration measures, while congestion-affected roads need to be alleviated through natural traffic flow dissipation or traffic management measures.

[0079] Another road network resilience recovery optimization method considering cascading failures under flood conditions is also provided. This method includes: a node importance assessment method based on complex network theory, which determines recovery priority by ranking roads from high to low betweenness centrality, prioritizing the recovery of roads with the highest betweenness centrality. Betweenness centrality measures the importance of a node as a "bridge" in the network, reflecting the strategic position of a road in the shortest path network. This strategy is based on the static network topology, assuming that roads with high betweenness centrality have a more significant impact on network connectivity; therefore, prioritizing the recovery of these roads can quickly improve the overall accessibility of the network.

[0080] Based on the relevant data of the aforementioned urban area, Figure 6 This study assesses the road network resilience recovery effects under different return periods for two recovery strategies: one based on optimization algorithms and the other based on betweenness centrality. Figure 6 It is evident that the recovery strategy based on the optimization algorithm (RS1) significantly outperforms the strategy based on betweenness centrality (RS2) under all return period rainfall scenarios. Taking a 200-year return period scenario as an example, when recovering 25 flooded and failed roads, RS1 recovers 27.2% of the resilience loss, while RS2 recovers only 9.9%. Under a 20-year return period scenario, when recovering 7 flooded and failed roads, the two strategies recover 47.5% and 19.6% of the resilience loss, respectively. The advantage of RS1 stems from the optimization algorithm's ability to globally optimize within a vast solution space. At each step of the recovery process, it comprehensively considers the dynamic evolution of cascading failures and network topology characteristics, thereby selecting the road combination that contributes the most to network resilience, rather than relying solely on a single topology indicator for locally optimal decisions.

[0081] Furthermore, the study discovered a critical threshold phenomenon for the optimal number of roads to be restored under different return periods of rainfall: when the number of restored roads reaches approximately 25% of the total number of failed roads, the slope of the resilience curve changes significantly, with the average resilience gain in the first 25% restoration phase being about three times that in the subsequent 75% phase. For example, under a 200-year return scenario, the restoration of the first 21 roads (restored in Table 1, order shown) increased the resilience index from 0.720 to 0.883, an increase of 22.6%; while the restoration of the subsequent 61 roads only brought an additional 7.6%. This pattern remained stable under different return period scenarios, revealing that the restoration of some highly important roads during the road network restoration process has a more significant effect on the network resilience restoration.

[0082] Table 1. Optimal road restoration sequence under a typical 200-year return period.

[0083] By comparing recovery strategies based on optimization algorithms with those based on betweenness centrality, the method with better recovery performance, namely the recovery strategy based on optimization algorithms, is selected.

[0084] According to a fourth aspect of the present invention, a road network resilience recovery system considering cascading failures under the influence of flooding is provided, comprising: constructing a road network resilience recovery optimization model considering cascading failures, wherein the model takes maximizing cumulative road network resilience as the optimization objective and solves for the optimal road recovery sequence through a genetic algorithm.

[0085] According to a fifth aspect of the present invention, a road network resilience assessment and recovery system considering cascading failures under the influence of flooding is provided, comprising: The cascading failure modeling module is used to construct cascading failure models for road networks. The calculation module is used to obtain road network resilience assessment index parameters based on the road network cascade failure model, and to determine the road network resilience assessment index parameters, network efficiency, and average shortest path length based on the road network resilience assessment index parameters. The resilience assessment module is used to determine the road network resilience index based on road network resilience assessment index parameters, network efficiency, and average shortest path length. The recovery optimization module is used to run optimization algorithms and output recovery strategies.

[0086] The recovery optimization module includes constructing a road network resilience recovery optimization model that considers cascading failures. This model aims to maximize the cumulative road network resilience and solves for the optimal road recovery sequence using a genetic algorithm. Alternatively, based on the node importance assessment method in complex network theory, the recovery priority is determined by sorting roads from high to low betweenness centrality, prioritizing the recovery of roads with the highest betweenness centrality.

[0087] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0088] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for assessing road network resilience under the influence of flooding, considering cascading failures, comprising: Step 100: Construct a road network cascading failure model; Step 200: The road network cascade failure model outputs time-series data, and the cascade failure impact index, network efficiency, and average shortest path length are determined based on the time-series data. Step 300: Determine the road network resilience index based on the cascading failure impact index, network efficiency, and average shortest path length.

2. The prediction method as described in claim 1, characterized in that: Step 100 includes: Step 101: Construct a road network topology model based on GIS road network data, abstracting the road network into an undirected network graph G={V, E}, where the node set... V ={?1, ?2, ?3, ..., ? n } represents an intersection, edge set E ={ e ij } represents a road, and road attribute information is obtained; Step 102: Calculate the capacity C of each road based on the ML model. i and initial load L i Set the time step Δt.

3. The prediction method as described in claim 2, characterized in that: Step S100 also includes an iterative process for cascading failure simulation: Step 103, Identification of flooded and failed roads: Extract the flooding depth hi(t) of each road; when hi(t) > the first preset depth threshold, road i is determined to be a flooded and failed road; Step 104, Traffic flow assignment: For failed roads, a local redistribution strategy based on betweenness centrality is used to calculate the assigned flow. Step 105: After traffic redistribution, determine the road status. If there are no congested roads in the network, proceed directly to the next step. If there are congested roads, mark them as "congestion failure" and the load exceeding their capacity on the road needs to be redistributed in the next iteration. Step 106: Proceed the time step to t+Δt, read the flood inundation data for the next moment, and repeat steps 103 to 105 to simulate for the set duration until the flood process ends.

4. The prediction method as described in claim 3, characterized in that: The local redistribution strategy based on betweenness centrality in step S104 includes: Calculate the betweenness centrality of the failed edges: ; Calculate the weighting coefficients for adjacent normal edges: ; Calculate flow allocation: ; In the formula: This refers to the node s To the node t The total number of shortest paths, It refers to passing through the edge i From node s To the node t The number of shortest paths, EBC ( e k () represents adjacent normal edges e k betweenness centrality, ω k Adjacent normal edges e k The weighting coefficients, q k Adjacent normal edges e k The allocated traffic.

5. The prediction method as described in claim 1, characterized in that: Step 200 further includes: The formula for calculating the cascading failure impact index is: ; In the formula: E This represents the total number of roads in the network. E c The number of congested and ineffective roads; E f This represents the number of roads that have become submerged and unusable.

6. The prediction method as described in claim 5, characterized in that: Step 200 further includes: The formula for calculating network efficiency is: ; The formula for calculating the average shortest path length is: ; N This represents the total number of network nodes. d ij For nodes i and nodes j The shortest path length between them.

7. The prediction method as described in claim 6, characterized in that: Step 300 further includes: The formula for calculating the road network resilience index is: ; In the formula: CFII The cascading failure impact index, NE'、APL' These represent the normalized network efficiency and the average shortest path length, respectively. α 1 、α 2 、α 3 represents the weights of different indicators.

8. The prediction method as described in claim 3, characterized in that: The first preset depth threshold is 0.3m.

9. A road network resilience assessment system considering cascading failures under flood conditions, comprising: The cascading failure modeling module is used to construct cascading failure models for road networks. The calculation module is used to obtain road network resilience assessment index parameters based on the road network cascade failure model, and determine the cascade failure impact index, network efficiency, and average shortest path length based on the road network resilience assessment index parameters. The resilience assessment module is used to determine the road network resilience index based on the cascading failure impact index, network efficiency, and average shortest path length.

10. A road network resilience recovery optimization method considering cascading failures under the influence of flooding, comprising: An optimization model for road network resilience recovery considering cascading failures is constructed. The model aims to maximize the cumulative road network resilience index and solves for the optimal road recovery sequence using a genetic algorithm. The road network resilience index is obtained according to the network resilience index formula described in claim 6.

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