Urban subway network toughness pre-disaster and post-disaster dual-stage optimization method under flood disaster

Abstract

The invention provides an urban subway network toughness pre-disaster and post-disaster dual-stage optimization method under flood disasters. The method comprises the following steps: acquiring urban subway network information, road network information and flood disaster information; constructing an urban subway topology network and a road topology network; simulating flood depth space-time change in the subway and road network during the duration of the flood disaster, and determining a subway network failure station set based on the accumulated water depth; calculating flood control resource demand quantity based on the platform number, the platform type and the flood depth of each station in the failure station set; establishing and solving a pre-disaster-post-disaster dual-stage optimization model of urban subway network toughness to obtain an optimal pre-disaster site closing decision, an optimal flood control resource warehouse site selection decision and an optimal post-disaster restoration decision; wherein the double-stage optimization model is a double-layer planning model; and the upper-layer model and the lower-layer model are mutually coupled and optimized through a pre-disaster closing site set and a post-disaster repairing process.

Description

Technical Field

[0001] This invention belongs to the field of data processing and disaster emergency decision-making technology, specifically involving a two-stage optimization method for the resilience of urban subway networks under flood disasters, from pre-disaster to post-disaster. Background Technology

[0002] As the core public transportation carrier in high-density cities, the continuity and operational safety of urban subway networks directly affect the stable operation of the urban transportation system. Subway stations are mostly located in low-lying areas of the city, and the underground platforms and tunnel structures are relatively weak in their ability to withstand floods. Once floodwaters intrude, it can not only lead to equipment damage and line shutdowns, but also potentially cause secondary risks such as difficulties in evacuating people. Historically, many cities have experienced large-scale subway network paralysis due to floods, highlighting the urgent need to improve the flood resilience of subway networks.

[0003] Currently, academic and industry research on the resilience of subway networks under flood disasters has established a certain foundation, mainly focusing on three major directions: network resilience assessment, pre-disaster prevention measures, and post-disaster recovery strategies. In the field of pre-disaster resource planning, existing research mostly relies on the static attributes of subway stations (such as station size and passenger flow level) as the core basis, using empirical formulas or simple linear models to predict flood control resource requirements. For example, some plans determine the scale of resources such as sandbags and pumping equipment based solely on the station building area or the number of platforms, failing to fully consider the differentiated impact of dynamic changes in flood depth on resource requirements. In fact, when the flood depth is lower than the height of the subway station entrance steps, only local sealing measures are needed to control the risk; however, when the flood depth exceeds the step height and intrudes into the platform area, not only are additional waterproofing and sealing resources required, but also additional resources such as drainage and equipment protection. Moreover, resource requirements show a non-linear growth trend with the increase of flood depth. This static resource prediction method often leads to the problem of "resource redundancy at low-risk stations and resource shortage at high-risk stations" in actual disasters, seriously affecting the effectiveness of pre-disaster prevention and control.

[0004] In terms of post-disaster recovery and optimization model construction, existing technologies generally suffer from the limitation of "isolizing the subway network." Most optimization models treat the subway network as a closed system, focusing only on restoring the connectivity of stations and lines, while neglecting the crucial supporting role of the external road network in post-disaster relief. The repair of subway stations depends on the timely delivery of rescue personnel, equipment, and supplies, while floods significantly reduce the traffic capacity of the road network: when the water depth is shallow, it leads to a decrease in vehicle speed; when the water depth exceeds a critical value, some sections may even be completely blocked. Existing models mostly use fixed road traffic speeds or preset path parameters for repair scheduling planning, failing to dynamically couple the attenuation law of road traffic capacity with flood depth, resulting in a serious disconnect between the calculated repair sequence and resource transportation routes and the actual scenario. For example, the model's plan of "delivering resources from a warehouse to a failed station within 1 hour" may take more than 3 hours in actual floods due to reduced vehicle speed caused by road flooding, ultimately rendering the repair strategy unfeasible and further prolonging the subway network's downtime.

[0005] Furthermore, existing research on subway network resilience suffers from a disconnect between the pre-disaster and post-disaster phases: some solutions focus solely on pre-disaster risk assessment and resource reserves, failing to coordinate with post-disaster repair and scheduling; others emphasize post-disaster recovery path optimization but lack prediction and proactive prevention design for high-risk stations before the disaster. This fragmented research paradigm makes it difficult to form a complete "prevention-response-recovery" closed loop for improving subway network resilience, further highlighting the importance of constructing a systematic solution that integrates the dynamic changes in flood depth and the attenuation patterns of road capacity, connecting pre-disaster prevention and post-disaster recovery. Summary of the Invention

[0006] To address the shortcomings and deficiencies of existing technologies, this invention provides a two-stage optimization method for the resilience of urban subway networks under flood disasters, encompassing pre-disaster and post-disaster phases. This method aims to solve problems such as insufficient accuracy in pre-disaster resource forecasting, neglect of dynamic decay of road capacity in optimization models, and the disconnect between pre-disaster and post-disaster phases in existing technologies, thereby achieving a closed-loop optimization throughout the entire lifecycle of improving subway network resilience.

[0007] This method first acquires urban subway network information (including station lines, number and type of platforms, passenger AFC card swipe data, entrance step height, etc.), road network information (including intersection nodes, design speed, surrounding elevation, etc.), and flood disaster information (including rainfall intensity, duration, spatial distribution, etc.), based on Space... The L-method is used to construct the topological network of subway and roads, generating an adjacency matrix representing the connection relationship between platforms / nodes and an edge weight matrix representing travel time. Then, the runoff curve method is used to simulate the spatiotemporal changes in flood depth within the subway and road network during disaster periods. The set of failed subway stations is determined by combining the height of the steps at subway station entrances, and the set of failed road lines is determined by combining a preset inundation threshold. Next, the flood control resource demand is calculated in stages based on the number of above-ground / underground platforms at failed stations and the flood depth. When the flood depth does not exceed the preset threshold, the calculation is linear; when it exceeds the threshold, it is calculated using a non-linear exponential growth method. The resource demand for underground platforms uses a higher weighting coefficient to match their higher flood control requirements. Finally, a performance measurement index for the urban subway network is established (combining passenger flow between stations and passenger utility functions within a time period; the utility function is related to the time delay caused by station failures and the maximum acceptable delay time for passengers; the shortest travel time is calculated using Dijkstra's algorithm). A two-stage, two-layer optimization model is constructed for pre-disaster and post-disaster periods and solved using a genetic algorithm.

[0008] In this two-stage, two-layer optimization model, the upper-layer model aims to maximize network resilience throughout the entire flood disaster process. Decision variables include the pre-disaster closed station set (a subset of the failed subway station set), the flood control resource warehouse site selection set (selected from road intersection nodes; during selection, the priority score of failed stations is first calculated to correlate with network performance loss caused by the complete failure of these stations, and then the node site selection evaluation value is calculated to correlate the priority score with the shortest distance from the node to the station), and the total resources of each warehouse. The lower-layer model, constrained by the upper-layer decisions, aims to maximize passenger flow at successfully repaired stations during the disaster. Decision variables include... This includes resource allocation and repair plans from warehouses to failed stations; the upper and lower layer models are coupled through dynamic topology adjustment of pre-disaster closed stations (removing station platform nodes of closed stations and creating new connections between adjacent stations) and time-series reachability constraints for post-disaster repair (road travel speed decreases nonlinearly with flood depth according to the hyperbolic tangent function, and the time for complete station repair needs to be combined with the failure start time, resource transportation time and repair time, and resource allocation stops if the time is exceeded). Finally, the optimal pre-disaster closed station decision, flood control resource warehouse site selection decision and post-disaster repair decision are output, so as to realize the systematic improvement of the subway network's disaster resistance and recovery capabilities.

[0009] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0010] A two-stage optimization method for the resilience of urban subway networks under flood disasters, comprising the following steps:

[0011] Obtain information on the city's subway network, road network, and flood disasters;

[0012] Constructing urban subway topology networks and road topology networks;

[0013] The study simulates the spatiotemporal changes of flood depth within the subway and road network during a prolonged flood disaster, and determines the set of failed subway network stations based on the water depth.

[0014] Based on the number of stations, station type, and flood depth of each station in the set of failed stations, the demand for flood control resources is calculated.

[0015] Establish and solve a two-stage pre-disaster and post-disaster optimization model for the resilience of urban subway networks to obtain optimal pre-disaster station closure decisions, flood control resource warehouse site selection decisions, and post-disaster repair decisions.

[0016] The dual-stage optimization model is a two-level programming model. The decision variables of the upper-level model include the pre-disaster closure site set, the location of flood control resource warehouses, and the total resources of each warehouse. The objective function is to maximize the network resilience index throughout the entire flood disaster process. The decision variables of the lower-level model include the resource allocation and repair sequence scheme from warehouses to failed sites. The objective function is to maximize the passenger flow of successfully repaired sites during the disaster duration, given the upper-level decisions. The upper-level model and the lower-level model are coupled and optimized through the pre-disaster closure site set and the post-disaster repair process.

[0017] Furthermore, the urban subway network information includes urban subway stations and lines, travel time between subway stations, transfer time within subway stations, subway passenger AFC card swipe data, subway station entrance step height, surrounding elevation of subway stations, and the number and location of subway platforms; the road network information includes urban road network information and elevation data around road network lines, wherein the urban road network information includes urban road intersection nodes, road line layout, travel time between road nodes, and road design speed; the flood disaster information includes rainfall intensity, duration, and spatial distribution data of rainstorms.

[0018] Furthermore, the construction of the urban subway topology network and road topology network adopts the Space L method, and the specific process is as follows:

[0019] Based on the station and line data, platform number and location data in the urban subway network information, and the intersection and line data in the road network information, a subway topology network containing a set of subway network nodes, a set of subway platform nodes, and a set of subway network edges, and a road topology network containing a set of road network nodes and a set of road network edges are constructed. ArcGIS is used for spatial connection to generate the adjacency matrix of the subway topology network and the adjacency matrix of the road topology network, respectively, and the weight matrices of the subway network edges and the road network edges are defined. The elements of the adjacency matrix represent whether there are operating lines, transfer routes, or road connections between platforms or nodes; a value of 1 indicates a connection, and a value of 0 indicates a connection. The elements of the weight matrix represent the travel time or transfer time between platforms and the travel time between road nodes.

[0020] Furthermore, the simulation of the spatiotemporal changes in flood depth within the subway and road network during the duration of the flood disaster, and the determination of the set of subway network failure stations based on the water depth, specifically include:

[0021] The runoff curve method is used to simulate the spatiotemporal variation of flood depth: Based on rainfall data from flood disaster information, the runoff at various locations in the subway and road network is calculated. The calculation rules for runoff are as follows: when the rainfall at a location is less than the initial watershed loss at that location, the runoff value is 0; when the rainfall is not less than the initial watershed loss, the runoff is the ratio of "the square of the difference between rainfall and initial watershed loss" to "the difference between rainfall and initial watershed loss plus the potential maximum retention capacity at that location"; the initial watershed loss is determined based on the potential maximum retention capacity, which is calculated using the runoff curve method.

[0022] The rainfall accumulation process was simulated in different time periods to obtain the depth variation curves of floodwater in the subway network and road network;

[0023] The failure status of the metro network and the road network is determined based on the flood depth variation curve: for the metro network, the failure site set is determined by whether the flood depth at the entrance coordinate of the metro station is greater than the height of the entrance steps of the metro station; for the road network, the failure route set is determined by whether the flood depth at any location of the road line exceeds the preset flooding threshold.

[0024] Furthermore, based on the number of stations, station type, and flood depth of each station in the set of failed stations, the flood control resource demand is calculated using a phased calculation method:

[0025] When the inlet flood depth of a failed site does not exceed the preset depth threshold, the flood control resource demand = above-ground platform resource coefficient per unit inundation depth × flood depth × (number of above-ground platforms + number of underground platforms × underground platform resource weight coefficient).

[0026] When the flood depth exceeds the aforementioned depth threshold, the flood control resource demand = above-ground platform resource coefficient per unit inundation depth × (non-linear exponential multiple of flood depth) × (number of above-ground platforms + number of underground platforms × underground platform resource weight coefficient).

[0027] Among them, the nonlinearity index is greater than 1, and the weight coefficient of underground platform resources is greater than 1.

[0028] Furthermore, the post-disaster recovery process integrates temporal reachability constraints, which are determined based on the dynamic changes in road network capacity:

[0029] The road travel speed of maintenance personnel decreases nonlinearly with flood depth. Travel speed = (half of the road design speed × hyperbolic tangent function value) + half of the road design speed. The independent variable of the hyperbolic tangent function is the ratio of "-flood depth + median critical water depth causing vehicle stagnation" to the attenuation elasticity coefficient. The transportation time from the warehouse to the failed site = the shortest road distance between the warehouse and the site ÷ travel speed. The complete repair time of the site = the site failure start time + transportation time + site repair time. If the complete repair time exceeds the disaster end time, resource allocation to the site will be stopped.

[0030] Furthermore, the specific process for selecting the site for the flood control resource warehouse is as follows:

[0031] Calculate the priority score for each station in the set of failed subway stations: Priority score = Network performance loss assuming the station fails completely ÷ Flood control resource demand of the station; Calculate the site selection evaluation value for each node in the set of road network intersection nodes: Site selection evaluation value = The sum of the "priority scores ÷ shortest road distances from nodes to stations" of all failed stations within the node's service range that do not exceed the maximum rescue radius of the warehouse; Sort the nodes in descending order according to the site selection evaluation values, and select the top few nodes as the site selection set for the flood control resource warehouse.

[0032] Furthermore, in the process of establishing and solving the pre-disaster-post-disaster two-stage optimization model for the resilience of urban subway networks, a genetic algorithm is used for solving, including:

[0033] An initial population is randomly generated, and each individual simultaneously encodes the pre-disaster site closure set and warehouse site selection scheme. Under the constraint of total flood control resources, the feasibility of individuals is modified. Under each candidate solution, the lower-level model is called to calculate the passenger flow of the protected sites and the overall network performance index to determine the fitness of individuals. The population evolves through selection, crossover, and mutation operations, and a constraint modification mechanism and elite retention strategy are introduced in each generation. When the optimal solution does not improve for several consecutive generations or reaches the maximum number of iterations, the optimization result is output.

[0034] Furthermore, the coupling between the upper-layer model and the lower-layer model also includes the dynamic adjustment of the subway topology network:

[0035] Pre-disaster phase: After determining the set of stations to be closed before the disaster, remove all platform nodes corresponding to the closed stations in the subway topology network, and establish new connections between the two adjacent platform nodes of the removed stations;

[0036] Post-disaster phase: After identifying the set of failed stations, remove all platform nodes and edges corresponding to the failed stations from the subway topology network; when the failed stations are repaired, restore all original platform nodes and edges of the stations.

[0037] Furthermore, the network resilience index is calculated as follows:

[0038] The performance measurement index of urban subway network = (sum of the products of passenger flow and passenger utility function between stations within time period t) ÷ (sum of passenger flow between stations within time period t).

[0039] Passenger utility function = max[1 - (time delay caused by station failure ÷ maximum acceptable delay time for passengers), 0], time delay = shortest travel time between stations when some stations fail (calculated using Dijkstra's algorithm) - shortest travel time between stations under normal conditions;

[0040] Network resilience index = (integral value of network performance measurement index during the disaster duration) ÷ (disaster duration × network performance under normal conditions).

[0041] And, a pre-disaster and post-disaster dual-stage optimization system for the resilience of urban subway networks under flood disasters, including:

[0042] The data acquisition module is used to acquire information on the urban subway network, road network, and flood disasters.

[0043] The topology network construction module is used to construct urban subway topology networks and road topology networks based on the urban subway network information and road network information obtained by the data acquisition module.

[0044] The flood simulation and failure determination module is used to simulate the spatiotemporal changes of flood depth in the subway and road network during the duration of flood disaster based on the flood disaster information obtained by the data acquisition module, and to determine the set of failed subway network stations based on the water depth.

[0045] The flood control resource calculation module is used to calculate the flood control resource demand based on the set of failed stations obtained by the flood simulation and failure determination module, combined with the number of stations, station type and flood depth of each failed station.

[0046] The optimization model construction and solution module is used to establish a two-stage optimization model for the resilience of urban subway networks before and after disasters, and to solve the model to output the optimal decisions for pre-disaster station closure, flood control resource warehouse site selection, and post-disaster repair.

[0047] The optimization model constructed by the optimization model construction and solution module is a two-level programming model. The upper-level model decision variables of the two-level programming model include the pre-disaster closure site set, the location of flood control resource warehouses, and the total resources of each warehouse. The objective function is to maximize the network resilience index of the entire flood disaster process. The lower-level model decision variables include the resource allocation and repair sequence scheme from warehouses to failed sites. The objective function is to maximize the passenger flow of successfully repaired sites during the disaster duration, given the upper-level decisions. The upper-level model and the lower-level model are coupled and optimized with each other through the pre-disaster closure site set and the post-disaster repair process.

[0048] And a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method described above.

[0049] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0050] Compared with the prior art, the present invention and its preferred embodiments have at least the following beneficial effects:

[0051] This invention effectively improves the accuracy and rationality of pre-disaster flood control resource forecasting. Instead of employing the static and crude resource estimation methods of existing technologies, it differentiates the flood control needs of above-ground and underground flood control stations, and calculates flood control resource requirements in stages based on the dynamic changes in flood depth: when the flood depth does not exceed a preset threshold, resource scale is matched according to a linear relationship; when the flood depth exceeds the threshold, a non-linear growth design is used to adapt to the rapid increase in resource demand. This avoids resource redundancy at low-risk sites while ensuring sufficient resource supply at high-risk sites, significantly optimizing the scientific nature and efficiency of pre-disaster resource preparation.

[0052] This invention addresses the problem of infeasible repair strategies caused by existing optimization models neglecting the dynamic changes in road capacity. It deeply couples the attenuation pattern of road network capacity with flood depth into the optimization model, dynamically calculates the road travel speeds of maintenance personnel and resource transport, and constructs temporal reachability constraints based on this. By determining whether the complete repair time of a site (including failure start time, transport time, and repair time) falls within the disaster duration, resource allocation and repair priorities are adjusted. This ensures that the planned repair scheduling scheme highly matches the road traffic conditions in actual flood scenarios, significantly improving the practicality of the repair strategy.

[0053] This invention achieves full-cycle collaborative optimization of pre-disaster prevention and post-disaster recovery, overcoming the limitations of existing technologies that separate stages. The invention constructs a two-stage, two-layer optimization model. The upper layer aims to maximize the resilience of the subway network throughout the disaster process, determining the set of stations to be closed before the disaster and the location of flood control resource warehouses (the optimal location for the warehouses is selected by combining the network performance loss of failed stations with node distance). The lower layer uses the decisions of the upper layer as constraints to maximize the passenger flow of the repaired stations. Furthermore, the upper and lower layers are coupled through dynamic topology adjustments of pre-disaster closed stations (removing closed station platforms and connecting adjacent platforms) and the temporal constraints of post-disaster recovery, forming a closed-loop optimization of "prevention-response-recovery," avoiding the limitations of single-stage optimization.

[0054] This invention constructs a network performance evaluation system and resilience optimization scheme that better meets actual operational needs. The network performance measurement index established in this invention no longer focuses solely on network connectivity, but combines passenger flow between stations within a time period with passenger utility functions (time delays caused by associated station failures and passenger-acceptable delay thresholds), more accurately reflecting the actual service capacity of the subway network. Simultaneously, by solving the optimization model using a genetic algorithm and introducing constraint correction and elite retention strategies, it ensures that the output pre-disaster closure decisions, warehouse site selection, and post-disaster repair schemes are globally optimal, ultimately systematically enhancing the subway network's disaster resistance and rapid recovery capabilities under flood conditions. Attached Figure Description

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0056] Figure 1 This is a flowchart illustrating the pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters provided in an embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram illustrating the process of constructing a time-weighted topology network for urban subways and roads in an embodiment of the present invention;

[0058] Figure 3 This is a flowchart illustrating the process of determining the set of failed stations in the urban subway network and the set of failed lines in the road network in an embodiment of the present invention.

[0059] Figure 4 This is a schematic diagram of the process for calculating flood control resource demand based on urban subway information in an embodiment of the present invention;

[0060] Figure 5 This is a schematic diagram of the process for establishing network performance indicators and constructing a resilient two-stage optimization model in an embodiment of the present invention. Detailed Implementation

[0061] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0062] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0063] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0064] like Figure 1 As shown, this embodiment provides a specific implementation process for a two-stage pre-disaster and post-disaster optimization method for the resilience of urban subway networks under flood disasters, including:

[0065] S1. Obtain information on urban subway and road network lines and flood disasters;

[0066] S2. Construct urban subway topology network and road topology network using the Space L method;

[0067] S3. Use the runoff curve method to simulate the changes in flood depth within the urban subway and road networks during the duration of the disaster, and determine the failed stations in the urban subway network and the failed lines in the road network.

[0068] S4. Calculate the flood control resource demand based on the number of stations, station type, and flood depth of each station in the failed station set;

[0069] S5. Establish performance measurement indicators for urban subway networks, construct a pre-disaster and post-disaster dual-stage optimization model for urban subway network resilience, and solve it using a genetic algorithm.

[0070] As a preferred embodiment, in step S1, the urban subway information includes: urban subway stations and lines, travel time between subway stations, transfer time within subway stations, subway passenger AFC card swiping data, step height, elevation around subway stations, number and location of subway platforms.

[0071] Road network information includes: urban road network information and elevation data around the road network routes; among which, urban road network information includes urban road intersection nodes, road route layout, and travel time between each road node;

[0072] Information on flood disasters includes: rainfall intensity, duration, and spatial distribution data of rainstorms.

[0073] As a preferred embodiment, such as Figure 2 As shown, the specific process of step S2 is as follows:

[0074] Step S21: Based on the data obtained in Step S1 regarding urban subway stations and lines, the number and location of subway platforms, and urban road network intersections and lines, construct the subway topology network using the Space L method. and road topology network The formula is as follows:

[0075]

[0076] In the formula, , These represent the sets of nodes in the subway and road networks, respectively. , Let m and n be the nodes in the subway and road networks, respectively, and m and n be the number of nodes in the subway and road networks, respectively. This represents a set of subway platforms. Indicates site The One platform, , These represent the edge sets of the subway and road networks, respectively. , These refer to the physical relationships between stations in the subway network and nodes in the road network, respectively. , Let l be the sequence number of any node in the network; l and c in the above formula refer to the sequence number of any station in the station.

[0077] Step S22: Based on the subway topology network and road topology network constructed in step S21, use ArcGIS to perform spatial connection to obtain the adjacency matrices of the subway topology network and road topology network respectively. , Define the network edge weight matrix. , The matrix form is:

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, , These represent the connection relationships between platforms in the subway network and nodes in the road network, respectively. or Its neighboring nodes or If there are operating routes or transfer routes between them, then Otherwise, it is 0; in the matrix middle, Connecting edges The weight of the station platform and Travel time or transfer time between locations; in the matrix middle, Connecting edges The weight of the node represents the node's weight. and Travel time between.

[0083] As a preferred embodiment, such as Figure 3 As shown, the specific process of step S3 is as follows:

[0084] Step S31: Based on the rainfall intensity, duration, and spatial distribution data of the rainstorm obtained in Step S1, calculate the runoff at various locations along the subway and road network using the runoff curve method. The formula is as follows:

[0085]

[0086]

[0087] In the formula, For position Runoff volume at point (mm); For position Rainfall at location (mm); For position The maximum potential retention (mm) at the location. For position The curve runoff number can be obtained by comprehensively considering watershed land use patterns, hydrological and soil group characteristics, and hydrological conditions, based on the data proposed by the USDA Soil Conservation Service. Find and determine the applicable ones in the table. value, The initial watershed loss (mm) is taken as... ;

[0088] Step S32: Divide the subway and road network area into several regions. Based on the runoff at each location obtained in Step S31, calculate the runoff for each sub-region. Total volume of water inside The formula is as follows:

[0089]

[0090] In the formula, Represents the unit element within a sub-region. For position The drainage capacity of the drainage system per unit time; It refers to the duration of the rainfall;

[0091] Step S33: Based on the sub-region obtained in step S1 The ground elevation is determined by filling sub-regions. The depression within the depression is used to calculate the water surface elevation in reverse, and then the location is determined. The formula for the water depth at a given location is as follows:

[0092]

[0093]

[0094] In the formula, sub-region ground elevation, This refers to the water surface elevation. For position The depth of the accumulated water at that location;

[0095] Step S34: Determine the failure status of subway stations and road routes based on the water depth. For the road network, extract the locations of each road network route. The depth of the water at that location If any position Exceeding the flood threshold If the road segment is invalid, then the road segment is deemed invalid; for the subway network, extract the coordinates of each subway station entrance. The depth of the water at that location Height of the subway station entrance steps Calculate the inlet flood depth ,when At that time, the subway station and its corresponding platform were determined to be ineffective; by simulating the rainfall accumulation process in different time periods, the depth variation curve of the flood on the network was obtained, and the set of subway stations that failed under the influence of flood disasters was determined. And a set of road failure routes.

[0096] As a preferred embodiment, such as Figure 4 As shown, the specific process of step S4 is as follows:

[0097] Step S41: Based on the set of failed subway stations obtained in step S3 Extracting invalid sites Number of ground-level platforms Number of underground platforms and the flood depth at the station entrance ;

[0098] Step S42: Considering the higher flood protection requirements of underground platforms compared to above-ground platforms, and using different calculation methods in stages according to flood depth, the formulas are as follows:

[0099]

[0100] In the formula, For the site The demand for flood control resources, γ is a coefficient representing the resource requirement for above-ground platforms per unit flood depth, and γ is a weighting coefficient representing the resource requirement for underground platforms compared to above-ground platforms. It is a non-linear exponent. The flood depth threshold is adjusted according to resource demand.

[0101] As a preferred embodiment, such as Figure 5 As shown, the specific process of step S5 is as follows:

[0102] Step S51: Based on the metro topology network constructed in Step S2 and the metro passenger AFC card swiping data, inter-metro station travel time, and intra-metro station transfer time obtained in Step S1, establish urban metro network performance measurement indicators. The formula is as follows:

[0103]

[0104]

[0105]

[0106] In the formula, For time period From the site Arrive at the station Customer traffic, For passenger utility function, Time delays caused by site failure or closure For time period When some sites are unavailable or closed, access from the site Arrive at the station The shortest travel time For normal operation from the site to station The shortest travel time is calculated using Dijkstra's algorithm. The maximum acceptable delay time for passengers;

[0107] Step S52: Construct a two-stage pre-disaster and post-disaster optimization model for the urban subway network resilience. The model consists of an upper-layer model and a lower-layer model. The upper-layer model aims to maximize network resilience during floods. The objective function of the upper-level model The formula is as follows:

[0108]

[0109] In the formula, As a resilience indicator, For upper-level decision variables, including the location of flood control resource warehouses, the first Total flood control resources of each warehouse and the collection of sites closed before the disaster The decision, In order to make decisions at the top The optimal response scheme is given by the lower-level model. The time when the flood disaster began. The end time of the flood disaster. This represents network performance under normal conditions.

[0110] The lower-level model uses maximizing passenger flow at protected sites during the duration of the flood disaster as its objective function. The formula is as follows:

[0111]

[0112] In the formula, For lower-level decision variables, It's a warehouse. To the invalid site The flood control resources transported Deactivated site Passenger traffic during the duration of the disaster;

[0113] Simultaneously, constraints are established, including total warehouse resource constraints:

[0114]

[0115] In the formula, M represents the total flood control resources, and M represents the site selection set.

[0116] Warehouse service radius constraints:

[0117]

[0118] In the formula, It's a warehouse. To the invalid site The flood control resources transported It's a warehouse. To the invalid site distance, This is the maximum rescue radius that the warehouse can serve;

[0119] Warehouse inventory constraints:

[0120]

[0121] Site requirements satisfy constraints:

[0122]

[0123] Timing reachability constraints:

[0124]

[0125]

[0126]

[0127]

[0128] In the formula, For warehouse Arrival at the invalid site The delivery time For the speed at which maintenance personnel travel on the road, Design speed for roads (km / h) Flood depth (cm) The median (cm) of the critical water depth that causes vehicles to stop. The damping elasticity coefficient characterizes the rate at which vehicle speed decreases with increasing water depth on a road. For the site The time required for a complete repair For the site The start time of failure For the site Required repair time This refers to the time when the flood disaster will end;

[0129] Step S53: Solve the two-stage optimization model using a genetic algorithm. First, an initial population containing pre-disaster site closure decisions and warehouse location schemes is randomly generated. Each individual simultaneously encodes the set of closed sites and the set of warehouse locations, and undergoes feasibility adjustments under a given total resource constraint to ensure that the individual meets the resource allocation conditions. Then, for each candidate solution, the lower-level model is invoked to calculate the passenger flow of the protected sites and the overall network performance indicators based on the coverage relationship between the warehouse and the failed sites and the repair sequence, thereby obtaining the individual's fitness. Subsequently, the population is continuously evolved through selection, crossover, and mutation operations. After each generation of evolution, a constraint-based correction mechanism and an elite retention strategy are introduced to avoid infeasibility of solutions and to prevent the loss of the optimal solution. As iterations proceed, when the optimal solution no longer improves within several consecutive generations or reaches the maximum number of iterations, the final optimization results are output, including the pre-disaster site closure set, the warehouse location set, and the post-disaster repair scheme, thereby obtaining a pre-disaster–post-disaster two-stage optimization strategy that maximizes the resilience of the urban subway network.

[0130] In the pre-disaster-post-disaster dual-stage optimization model for urban subway network resilience, the dual-stage refers to the pre-disaster stage and the post-disaster stage. The pre-disaster stage identifies the set of stations to be closed in advance during floods. In the model calculation, all station nodes corresponding to pre-closed stations are removed, but new connections are established between two adjacent station nodes of the removed stations. In the post-disaster phase, the set of stations to be repaired is determined. The final failure site set and the site selection set of flood control resource warehouses In the model calculation, all station nodes and connections corresponding to the failed station are removed. After the failed station is repaired, all original stations and connections are restored.

[0131] Among these steps, the site selection for flood control resource warehouses first requires pre-screening the set of intersection nodes in the road network, and then calculating the set of all failed subway stations. Internal site priority score For nodes within the intersection node set of the road network Calculate its site selection evaluation value ,according to Sort the values ​​in descending order and select the top [values]. The candidate nodes are selected as the final site set for the flood control resource warehouse. The formula is as follows:

[0132]

[0133]

[0134] In the formula, Assuming a failed site Network performance loss due to complete failure Road network intersection nodes To the invalid site The shortest road distance.

[0135] In summary, this invention provides a two-stage pre- and post-disaster optimization method for urban subway network resilience under flood disasters. This method constructs a time-weighted topology network of urban subway and roads, uses runoff curves to simulate flood depth changes within the urban subway and road networks during the disaster period, determines the set of failed subway stations and road lines, calculates flood control resource requirements based on the number of platforms and flood depth at the failed stations matched in the urban subway information, establishes performance measurement indicators for the urban subway network, and uses a genetic algorithm to construct a two-stage pre- and post-disaster optimization model for urban subway network resilience. This invention enhances the disaster resistance and recovery capabilities of subway networks under flood disasters by optimizing the two-stage pre- and post-disaster resilience strategy.

[0136] Compared with the prior art, the present invention has the following beneficial effects:

[0137] (1) By establishing the relationship between flood depth and the demand for restoration resources, this invention enables phased prediction of resource types and quantities, overcomes the shortcomings of the extensive and static resource assessment in the prior art, and significantly improves the scientific nature of pre-disaster preparation and the utilization efficiency of post-disaster restoration resources.

[0138] (2) This invention incorporates the dynamic changes in the capacity of the external road network into the subway network resilience optimization model, which solves the decision-making bias problem caused by neglecting the accessibility of rescue routes in traditional methods, making the repair and scheduling scheme more practical.

[0139] (3) The dual-stage optimization method provided by the present invention can generate the globally optimal resilience enhancement strategy, providing full-process decision support from strategic preparation to tactical execution for dealing with flood disasters, and making up for the shortcomings of stage fragmentation and system inadequacy in the existing scheme.

[0140] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0141] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0142] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0143] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0144] This invention is not limited to the above-described preferred embodiments. Anyone inspired by this invention can derive other pre- and post-disaster dual-stage optimization methods for the resilience of urban subway networks under various forms of flood disasters. All equivalent variations and modifications made within the scope of the patent applications of this invention shall fall within the scope of this invention.

Claims

1. A two-stage optimization method for the resilience of urban subway networks under flood disasters, characterized in that: Includes the following steps: Obtain information on the city's subway network, road network, and flood disasters; Constructing urban subway topology networks and road topology networks; The study simulates the spatiotemporal changes of flood depth within the subway and road network during a prolonged flood disaster, and determines the set of failed subway network stations based on the water depth. Based on the number of stations, station type, and flood depth of each station in the set of failed stations, the demand for flood control resources is calculated. Establish and solve a two-stage pre-disaster and post-disaster optimization model for the resilience of urban subway networks to obtain optimal pre-disaster station closure decisions, flood control resource warehouse site selection decisions, and post-disaster repair decisions. The dual-stage optimization model is a two-level programming model. The decision variables of the upper-level model include the pre-disaster closure site set, the location of flood control resource warehouses, and the total resources of each warehouse. The objective function is to maximize the network resilience index throughout the entire flood disaster process. The decision variables of the lower-level model include the resource allocation and repair sequence scheme from warehouses to failed sites. The objective function is to maximize the passenger flow of successfully repaired sites during the disaster duration, given the upper-level decisions. The upper-level model and the lower-level model are coupled and optimized through the pre-disaster closure site set and the post-disaster repair process.

2. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: The construction of the urban subway topology network and road topology network adopts the Space L method, and the specific process is as follows: Based on the station and line data, platform number and location data in the urban subway network information, and the intersection and line data in the road network information, a subway topology network containing a set of subway network nodes, a set of subway platform nodes, and a set of subway network edges, and a road topology network containing a set of road network nodes and a set of road network edges are constructed. ArcGIS is used for spatial connection to generate the adjacency matrix of the subway topology network and the adjacency matrix of the road topology network, respectively, and the weight matrices of the subway network edges and the road network edges are defined. The elements of the adjacency matrix represent whether there are operating lines, transfer routes, or road connections between platforms or nodes; a value of 1 indicates a connection, and a value of 0 indicates a connection. The elements of the weight matrix represent the travel time or transfer time between platforms and the travel time between road nodes.

3. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: The simulation examines the spatiotemporal changes in flood depth within the subway and road network during a prolonged flood disaster, and determines the set of subway network failure stations based on the water depth. Specifically, this set includes: The runoff curve method is used to simulate the spatiotemporal variation of flood depth: Based on rainfall data from flood disaster information, the runoff at various locations in the subway and road network is calculated. The calculation rules for runoff are as follows: when the rainfall at a location is less than the initial watershed loss at that location, the runoff value is 0; when the rainfall is not less than the initial watershed loss, the runoff is the ratio of "the square of the difference between rainfall and initial watershed loss" to "the difference between rainfall and initial watershed loss plus the potential maximum retention capacity at that location"; the initial watershed loss is determined based on the potential maximum retention capacity, which is calculated using the runoff curve method. The rainfall accumulation process was simulated in different time periods to obtain the depth variation curves of floodwater in the subway network and road network; The failure status of the metro network and the road network is determined based on the flood depth variation curve: for the metro network, the failure site set is determined by whether the flood depth at the entrance coordinate of the metro station is greater than the height of the entrance steps of the metro station; for the road network, the failure route set is determined by whether the flood depth at any location of the road line exceeds the preset flooding threshold.

4. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: Based on the number of stations, station types, and flood depth of each station in the set of failed stations, the flood control resource demand is calculated using a phased calculation method: When the inlet flood depth of a failed site does not exceed the preset depth threshold, the flood control resource demand = above-ground platform resource coefficient per unit inundation depth × flood depth × (number of above-ground platforms + number of underground platforms × underground platform resource weight coefficient). When the flood depth exceeds the aforementioned depth threshold, the flood control resource demand = above-ground platform resource coefficient per unit inundation depth × (non-linear exponential multiple of flood depth) × (number of above-ground platforms + number of underground platforms × underground platform resource weight coefficient). Among them, the nonlinearity index is greater than 1, and the weight coefficient of underground platform resources is greater than 1.

5. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: The post-disaster recovery process integrates temporal accessibility constraints, which are determined based on dynamic changes in road network capacity. The road driving speed of maintenance personnel decreases nonlinearly with the flood depth. The driving speed = (half of the road design speed × hyperbolic tangent function value) + half of the road design speed. The independent variable of the hyperbolic tangent function is the ratio of "-flood depth + median critical water depth that causes vehicles to stop" to the attenuation elastic coefficient. Transportation time from warehouse to failed site = shortest road distance between warehouse and site ÷ travel speed; site full repair time = site failure start time + transportation time + site repair time; If the complete restoration time exceeds the disaster end time, resource allocation to the site will be suspended.

6. The pre-disaster and post-disaster two-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: The specific process for selecting the site for the flood control resource warehouse is as follows: Calculate the priority score of each station in the set of failed subway stations: Priority score = Network performance loss assuming the station fails completely ÷ Flood control resource requirement of the station; Calculate the site selection evaluation value of each node in the road network intersection node set: Site selection evaluation value = the sum of the "priority score ÷ shortest road distance from node to site" of all failed sites within the service range of the node and the distance from the node to the failed site does not exceed the maximum rescue radius of the warehouse; Sort the nodes in descending order according to the site selection evaluation value, and select the top few nodes as the site selection set for flood control resource warehouses.

7. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: In the process of establishing and solving the pre-disaster and post-disaster two-stage optimization model for the resilience of urban subway networks, a genetic algorithm is used for solving the problem, including: An initial population is randomly generated, and each individual simultaneously encodes the pre-disaster site closure set and warehouse site selection scheme. Under the constraint of total flood control resources, the feasibility of individuals is modified. Under each candidate solution, the lower-level model is called to calculate the passenger flow of the protected sites and the overall network performance index to determine the fitness of individuals. The population evolves through selection, crossover, and mutation operations, and a constraint modification mechanism and elite retention strategy are introduced in each generation. When the optimal solution does not improve for several consecutive generations or reaches the maximum number of iterations, the optimization result is output.

8. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: The coupling between the upper-layer model and the lower-layer model also includes the dynamic adjustment of the subway topology network: Pre-disaster phase: After determining the set of stations to be closed before the disaster, remove all platform nodes corresponding to the closed stations in the subway topology network, and establish new connections between the two adjacent platform nodes of the removed stations; Post-disaster phase: After identifying the set of failed stations, remove all platform nodes and edges corresponding to the failed stations from the subway topology network; when the failed stations are repaired, restore all original platform nodes and edges of the stations.

9. The pre-disaster and post-disaster dual-stage optimization method for urban subway network resilience under flood disasters as described in claim 1, characterized in that: The network resilience index is calculated as follows: The performance measurement index of urban subway network = (sum of the products of passenger flow and passenger utility function between stations within time period t) ÷ (sum of passenger flow between stations within time period t). Passenger utility function = max[1 - (time delay caused by station failure ÷ maximum acceptable delay time for passengers), 0], time delay = shortest travel time between stations when some stations fail (calculated using Dijkstra's algorithm) - shortest travel time between stations under normal conditions; Network resilience index = (integral value of network performance measurement index during the disaster duration) ÷ (disaster duration × network performance under normal conditions).

10. A pre-disaster and post-disaster dual-stage optimization system for the resilience of urban subway networks under flood disasters, characterized in that: include: The data acquisition module is used to acquire information on the urban subway network, road network, and flood disasters. The topology network construction module is used to construct urban subway topology networks and road topology networks based on the urban subway network information and road network information obtained by the data acquisition module. The flood simulation and failure determination module is used to simulate the spatiotemporal changes of flood depth in the subway and road network during the duration of flood disaster based on the flood disaster information obtained by the data acquisition module, and to determine the set of failed subway network stations based on the water depth. The flood control resource calculation module is used to calculate the flood control resource demand based on the set of failed stations obtained by the flood simulation and failure determination module, combined with the number of stations, station type and flood depth of each failed station. The optimization model construction and solution module is used to establish a two-stage optimization model for the resilience of urban subway networks before and after disasters, and to solve the model to output the optimal decisions for pre-disaster station closure, flood control resource warehouse site selection, and post-disaster repair. The optimization model constructed by the optimization model construction and solution module is a two-level programming model. The upper-level model decision variables of the two-level programming model include the pre-disaster closure site set, the location of flood control resource warehouses, and the total resources of each warehouse. The objective function is to maximize the network resilience index of the entire flood disaster process. The lower-level model decision variables include the resource allocation and repair sequence scheme from warehouses to failed sites. The objective function is to maximize the passenger flow of successfully repaired sites during the disaster duration, given the upper-level decisions. The upper-level model and the lower-level model are coupled and optimized with each other through the pre-disaster closure site set and the post-disaster repair process.

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