A pre-disaster-post-disaster two-stage optimization method for urban metro network resilience under flood disasters

Abstract

The application provides a kind of urban subway network resilience pre-disaster-post-disaster two-stage optimization method under flood disaster, comprising: obtaining urban subway network information, road network information and flood disaster information;Build urban subway topology network and road topology network;Simulate flood depth spatio-temporal variation in subway and road network during flood disaster duration, and determine subway network failure site set based on water depth;Based on the number of stations, platform type and flood depth of each site in the failure site set, calculate the demand for flood control resources;Establish and solve the pre-disaster-post-disaster two-stage optimization model of urban subway network resilience to obtain the optimal pre-disaster closing site decision, flood control resource warehouse location decision and post-disaster repair decision;Wherein, the two-stage optimization model is a bi-level programming model;The upper model and the lower model are coupled and optimized through the pre-disaster closing site set and the post-disaster repair process.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of data processing and disaster emergency decision-making, and specifically relates to a pre-disaster and post-disaster double-stage optimization method for urban subway network resilience under flood disasters. BACKGROUND

[0002] As the core public transportation carrier of high-density cities, the network continuity and operation safety of urban subway directly relate to the stable operation of urban transportation systems. Subway stations are mostly distributed in low-lying areas of cities, and the underground platforms and tunnel structures have weak resistance to floods. Once water intrusion occurs, not only will it cause equipment damage and line shutdown, but also may cause secondary risks such as difficult evacuation of personnel. In history, many cities have experienced large-scale paralysis of subway networks due to flood disasters, highlighting the urgent need to improve the flood resilience of subway networks.

[0003] Currently, the academic and industrial communities have formed a certain foundation in the study of subway network resilience under flood disasters, mainly focusing on three directions: network resilience evaluation, pre-disaster prevention measures, and post-disaster repair strategies. In the field of pre-disaster resource planning, existing researches mostly take the static attributes of subway stations (such as station size, passenger flow level) as the core basis, and estimate the demand for flood prevention resources through empirical formulas or simple linear models. For example, some schemes only determine the configuration scale of resources such as sandbags and water pumping equipment according to the station building area or platform number, but fail to fully consider the differentiated impact of dynamic changes in flood depth on resource demand. In fact, when the flood depth is lower than the height of the subway station entrance steps, only local blocking measures are needed to prevent risks; when the flood depth exceeds the height of the steps and invades the platform area, additional resources such as water blocking, drainage, and equipment protection are needed, and the resource demand will show a non-linear growth trend with the increase of flood depth. This static resource estimation method often leads to the problem of "resource redundancy in low-risk stations and resource shortage in high-risk stations" in actual disasters, seriously affecting the effectiveness of pre-disaster prevention and control.

[0004] In the aspect of post-disaster repair and optimization model construction, the existing technology generally has the limitation of "subway network independence". Most optimization models regard the subway network as a closed system and only focus on the connectivity recovery of stations and lines, ignoring the key supporting role of the external road network in post-disaster rescue. The repair of subway stations depends on the timely delivery of rescue personnel, equipment and materials, while the flood disaster can significantly reduce the capacity of the road network: when the water depth of the road is small, it will cause the vehicle speed to decrease; when the water depth exceeds the critical value, some road sections will even be completely interrupted. Existing models mostly use fixed road traffic speed or pre-set path parameters for repair scheduling planning, and fail to dynamically couple the decline law of road traffic capacity with flood depth, resulting in a serious disconnection between the calculated repair timing, resource transportation path and actual scene. For example, the model plans to "complete resource delivery from a certain warehouse to the failed station within 1 hour", but in the actual flood, the vehicle speed will be reduced due to road waterlogging, which may take more than 3 hours to arrive, ultimately causing the repair strategy to fail to land, further prolonging the downtime of the subway network.

[0005] In addition, the existing subway network resilience research also has the problem of "disaster-pre-disaster and post-disaster stage separation": some schemes only focus on pre-disaster risk assessment and resource reservation, failing to form synergy with post-disaster repair scheduling; another part of the scheme focuses on post-disaster recovery path optimization, but lacks pre-disaster high-risk station prediction and pre-control design. This stage separation research paradigm makes it difficult to form a "prevention-response-recovery" full-cycle closed loop for subway network resilience improvement, and further highlights the importance of building a systematic scheme that can integrate the dynamic changes of flood depth and the decline law of road traffic capacity, and link pre-disaster prevention and post-disaster recovery. SUMMARY

[0006] In view of the defects and deficiencies of the existing technology, the present application provides a two-stage optimization method for urban subway network resilience before and after flood disasters, aiming to solve the problems of insufficient pre-disaster resource estimation accuracy, optimization model ignoring dynamic decline of road traffic capacity, pre-disaster and post-disaster stage separation in the prior art, and realize full-cycle closed loop optimization of subway network resilience improvement.

[0007] The method first acquires urban subway network information (including station line, station number and type, passenger AFC card data, entrance step height, etc.), road network information (including intersection node, design speed, surrounding elevation, etc.) and flood disaster information (including rainfall intensity, duration, spatial distribution, etc.), constructs the topological network of subway and road based on Space L method, generates the adjacency matrix representing the connection relationship between stations / nodes and the edge weight matrix representing the travel time, then simulates the temporal and spatial variation of flood depth in subway and road network during the disaster by using the runoff curve method, determines the set of failed subway stations according to the entrance step height of the subway station, and determines the set of failed road lines according to the preset flooding threshold; then, the demand for flood control resources is calculated in stages according to the number of aboveground / underground stations of the failed station and the flood depth, wherein the demand is calculated in a linear manner when the flood depth does not exceed the preset threshold, and is calculated in a nonlinear exponential growth manner when the threshold is exceeded, and the demand for underground station resources adopts a higher weight coefficient to match the higher demand for flood control; finally, the performance measurement index of urban subway network (combined with the passenger flow between stations and the passenger utility function within the period, the utility function is associated with the time delay caused by the failure of the station and the maximum acceptable delay time of the passenger, and the shortest travel time is calculated by using Dijkstra algorithm), a double-stage double-layer optimization model before and after the disaster is constructed, and a genetic algorithm is used for solving.

[0008] In the double-stage double-layer optimization model, the upper model maximizes the network resilience during the whole flood disaster process, and the decision variables include the set of stations closed before the disaster (which is a subset of the set of failed subway stations), the set of flood control resource warehouses selected (selected from road intersection nodes, and when selected, the priority score is calculated first to associate the network performance loss caused by the failure of the station, and then the node selection evaluation value is calculated to associate the priority score and the shortest distance from the node to the station), and the total amount of resources in each warehouse; the lower model maximizes the passenger flow of the stations successfully repaired during the disaster as a constraint, and the decision variables include the resource allocation amount from the warehouse to the failed station and the repair scheme; the upper and lower models are coupled through the topological dynamic adjustment of the stations closed before the disaster (removing the station node of the closed station and building a new edge between adjacent stations) and the time sequence accessibility constraint after the disaster (the road speed nonlinearly decays according to the hyperbolic tangent function with the flood depth, and the complete repair time of the station needs to be combined with the failure start time, resource transportation time and repair time, and the resource allocation is stopped if the time exceeds); finally, the optimal pre-disaster closing station decision, flood control resource warehouse location decision and post-disaster repair decision are output, and the system improvement of the anti-disaster and recovery ability of the subway network is realized.

[0009] The technical solution adopted by the application to solve the technical problems is:

[0010] A pre-disaster-post-disaster double-stage optimization method for urban subway network resilience under flood disaster, comprising the following steps:

[0011] obtain urban metro network information, road network information and flood disaster information;

[0012] construct urban metro topology network and road topology network;

[0013] simulate the spatial and temporal variation of flood depth in the metro and road network during the duration of the flood disaster, and determine the set of failed metro network sites based on the accumulated water depth;

[0014] based on the number of platforms, platform types and flood depth of each site in the set of failed sites, calculate the amount of flood control resources required;

[0015] establish and solve a pre-disaster-post-disaster two-stage optimization model of urban metro network resilience to obtain optimal pre-disaster closing site decisions, flood control resource warehouse location decisions and post-disaster repair decisions;

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

[0017] Further, the urban metro network information includes urban metro sites and lines, metro station-to-station travel time, metro station-to-station transfer time, metro passenger AFC card data, metro station entrance step height, metro station surrounding elevation, metro platform number and location; the road network information includes urban road network information and road network line surrounding elevation data, wherein the urban road network information includes urban road intersection nodes, road line layout, road node-to-node travel time and road design speed; the flood disaster information includes rainfall intensity, duration and spatial distribution data of the rainstorm.

[0018] Further, the construction of urban metro topology network and road topology network uses Space L method, and the specific process is as follows:

[0019] Based on the station and line, the number and location of the platform in the urban subway network information, and the intersection and line data in the road network information, a subway topology network containing a subway network node set, a subway platform set, and a subway network edge set, and a road topology network containing a road network node set and a road network edge set are constructed; spatial connection is performed using ArcGIS to generate a subway topology network adjacency matrix and a road topology network adjacency matrix, and define a subway network edge weight matrix and a road network edge weight matrix; wherein, the adjacency matrix elements represent whether there is a starting line, a transfer route or a road connection between the platforms or nodes, and if there is, the value is 1, otherwise it is 0, and the weight matrix elements represent the travel time or transfer time between platforms or the travel time between road nodes.

[0020] Further, the spatial and temporal variation of the flood depth in the subway and road network during the duration of the flood disaster is simulated, and the subway network failure station set is determined based on the accumulated water depth, which specifically comprises:

[0021] The spatial and temporal variation of the flood depth is simulated by using the runoff curve method: based on the rainfall data in the flood disaster information, the runoff of each location in the subway and road network is calculated; wherein, the calculation rule of the runoff is: when the rainfall at the location is less than the initial loss of the basin at the location, the runoff is 0; when the rainfall is not less than the initial loss of the basin, the runoff is the ratio of the square of the difference between the rainfall and the initial loss of the basin to the difference between the rainfall and the initial loss of the basin plus the potential maximum retention capacity at the location; the initial loss of the basin is determined based on the potential maximum retention capacity; the potential maximum retention capacity is calculated by the runoff curve method;

[0022] The rainfall accumulation process is simulated by time period to obtain the depth variation curve of the flood on the subway network and the road network;

[0023] The failure state of the subway network and the road network is determined based on the flood depth variation curve: for the subway network, the flood depth at the entrance coordinate of the subway station is used as the determination standard to determine the subway network failure station set; for the road network, the flood depth at any position of the road line is used as the determination standard to determine the road network failure line set.

[0024] Further, based on the number of platforms, the type of platforms and the flood depth of each station in the failure station set, the demand for flood control resources is calculated by using a staged calculation method:

[0025] When the entrance flood depth of the failure station does not exceed the preset depth threshold, the demand for flood control resources = unit submerged depth ground platform resource coefficient x flood depth x (number of ground platforms + number of underground platforms x underground platform resource weight coefficient);

[0026] When the flood depth exceeds the depth threshold, the flood control resource demand = unit inundation depth overground platform resource coefficient × (nonlinear exponential multiple of flood depth) × (number of overground platforms + number of underground platforms × underground platform resource weight coefficient);

[0027] Wherein, the nonlinear index is greater than 1, and the underground platform resource weight coefficient is greater than 1.

[0028] Further, the post-disaster repair process integrates the time sequence accessibility constraint, which is determined based on the dynamic change of road network traffic capacity:

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

[0030] Further, the specific process of the flood control resource warehouse site selection is:

[0031] Calculate the priority score of each site in the subway failed site set: priority score = network performance loss caused by assuming that the site is completely failed ÷ flood control resource demand of the site; calculate the site selection evaluation value of each node in the road network intersection node set: site selection evaluation value = sum of "priority score ÷ shortest road distance from the node to the site" of all failed sites within the service range of the node, provided that the distance from the node to the failed site is not more than the maximum rescue radius of the warehouse; sort the nodes in descending order according to the site selection evaluation value, and select the first several nodes as the flood control resource warehouse site selection set.

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

[0033] Randomly generate an initial population, and each individual encodes the pre-disaster closed site set and the warehouse site selection scheme; under the constraint of total flood control resource amount, the individual is modified for feasibility; call the lower model under each candidate solution to calculate the protected site passenger flow and the whole network performance index, and determine the individual fitness; evolve the population through selection, crossover and mutation operations, introduce constraint correction mechanism and elite preservation strategy in each generation; when the optimal solution does not improve continuously for several generations or reaches the maximum iteration number, output the optimization result.

[0034] Further, the coupling of the upper model and the lower model further includes dynamic adjustment of the subway topological network:

[0035] Pre-disaster stage: after determining the closed station set, all platform nodes corresponding to the closed stations are removed from the subway topology network, and new edges are established between the adjacent two platform nodes of the removed platforms;

[0036] Post-disaster stage: after determining the failed station set, all platform nodes and edges corresponding to the failed stations are removed from the subway topology network; when the failed stations are repaired, all platform nodes and edges of the stations are restored.

[0037] Further, the network resilience index is calculated in the following manner:

[0038] City subway network performance measurement index = (sum of the product of passenger flow and passenger utility function between stations in period t) ÷ (sum of passenger flow between stations in period t);

[0039] Passenger utility function = max [1 - (time delay caused by station failure ÷ maximum acceptable delay time of passengers), 0], time delay = shortest travel time between stations in the presence of partial station failure calculated by Dijkstra algorithm - shortest travel time between stations in normal state;

[0040] Network resilience index = (integrated value of network performance measurement index during disaster duration) ÷ (disaster duration × network performance in normal state).

[0041] And a pre-disaster-post-disaster two-stage optimization system for urban subway network resilience under flood disasters, comprising:

[0042] A data acquisition module for acquiring urban subway network information, road network information and flood disaster information;

[0043] A topology network construction module for constructing an urban subway topology network and a road topology network based on the urban subway network information and road network information obtained by the data acquisition module;

[0044] A flood simulation and failure determination module for simulating the spatiotemporal variation of flood depth in the subway and road networks during the duration of the flood disaster based on the flood disaster information obtained by the data acquisition module, and determining a failed station set of the subway network based on the accumulated water depth;

[0045] A flood control resource calculation module for calculating the demand for flood control resources based on the failed station set obtained by the flood simulation and failure determination module, in combination with the number of platforms, platform types and flood depth of each failed station;

[0046] An optimization model construction and solving module is configured to establish a pre-disaster-post-disaster two-stage optimization model of the urban subway network resilience and solve the model to output optimal pre-disaster closed station decisions, flood control resource warehouse location decisions and post-disaster repair decisions.

[0047] The two-stage optimization model constructed by the optimization model construction and solving module is a bi-level programming model, the decision variables of the upper model of the bi-level programming model include a pre-disaster closed station set, flood control resource warehouse location and total resource quantity of each warehouse, and the objective function is to maximize the network resilience index in the whole process of the flood disaster; the decision variables of the lower model include resource allocation from the warehouse to the failed station and a repair time sequence scheme, and the objective function is to maximize the passenger flow of the successfully repaired station during the disaster duration given the upper layer decision; and the upper model and the lower model are coupled and optimized with each other through the pre-disaster closed station set and the post-disaster repair process.

[0048] Further, a computer device includes a memory, a processor and a computer program stored in the memory, and the processor implements the method as described above when executing the computer program.

[0049] A non-transitory computer readable storage medium has a computer program stored thereon, and the computer program is executed by a processor to implement the method as described above.

[0050] Compared with the prior art, the present application and the preferred schemes thereof at least have the following beneficial effects:

[0051] The accuracy and rationality of pre-disaster flood control resource estimation are effectively improved. Instead of using the static and extensive resource estimation method in the prior art, the present application distinguishes the flood control demand difference between the aboveground platform and the underground platform, and calculates the flood control resource demand in stages in combination with the dynamic change of the flood depth: when the flood depth does not exceed a preset threshold, the resource scale is matched in a linear relationship; when the flood depth exceeds the threshold, the rapid increase of the resource demand is adapted through nonlinear growth design, which not only avoids resource redundancy of low-risk stations, but also ensures sufficient resource supply of high-risk stations, and significantly optimizes the scientificity of pre-disaster resource preparation and resource utilization efficiency.

[0052] The problem of unfeasible repair strategy caused by ignoring the dynamic change of road traffic capacity in the existing optimization model is solved. The present application deeply couples the attenuation law of road network traffic capacity with the flood depth into the optimization model, dynamically calculates the road driving speed of the repair personnel and the resource transportation, and constructs a time sequence accessibility constraint based on the same, adjusts the resource allocation and repair priority by judging whether the complete repair time (including the failure start time, transportation time and repair time) of the station is within the disaster duration cycle, so that the planned repair scheduling scheme is highly consistent with the road traffic condition under the actual flood scenario, and the operability of the repair strategy is greatly improved.

[0053] The whole cycle collaborative optimization of pre-disaster prevention and post-disaster recovery is realized, and the limitation of the existing technology stage is broken. The two-stage double-layer optimization model constructed by the application maximizes the subway network resilience in the whole disaster process as the target, determines the set of closed stations before the disaster and the location of the flood control resource warehouse (the optimal position is selected by combining the network performance loss of the failed station and the node distance when locating the warehouse), and maximizes the passenger flow of the repaired station as the constraint in the lower layer. The upper and lower layers are coupled with each other through the topological dynamic adjustment (removing the closed station platform and connecting the adjacent platform) of the closed station before the disaster and the time sequence constraint of the post-disaster repair, forming a closed loop optimization of “prevention-response-recovery”, avoiding the limitation of single-stage optimization.

[0054] A network performance evaluation system and a resilience optimization scheme more suitable for actual operation demand are constructed. The network performance measurement index established by the application is no longer only based on network connectivity, but also combines the passenger flow between stations in the period and the passenger utility function (associated with the time delay caused by station failure and the passenger acceptable delay threshold), which more accurately reflects the actual service capacity of the subway network. At the same time, the optimization model is solved by genetic algorithm, and the constraint correction and elite reservation strategy are introduced to ensure that the pre-disaster closing decision, warehouse location and post-disaster repair scheme output are globally optimal, and finally the anti-disaster ability and rapid recovery ability of the subway network under the flood disaster are systematically enhanced. BRIEF DESCRIPTION OF DRAWINGS

[0055] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0056] Figure 1 is a flowchart of the pre-disaster-post-disaster two-stage optimization method of urban subway network resilience under flood disaster provided by the embodiments of the application;

[0057] Figure 2 is a flowchart of constructing a time-weighted topological network of urban subway and road in the embodiments of the application;

[0058] Figure 3 is a flowchart of determining the set of failed stations of urban subway network and the set of failed lines of road network in the embodiments of the application;

[0059] Figure 4 is a flowchart of calculating the demand amount of flood control resources based on urban subway information in the embodiments of the application;

[0060] Figure 5 is a flowchart of establishing network performance index and constructing resilience two-stage optimization model in the embodiments of the application. DETAILED DESCRIPTION

[0061] In order to make the features and advantages of the application more obvious and easy to understand, the following embodiments are described in detail as follows:

[0062] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0063] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0064] As shown in Figure 1 The embodiment provides a specific implementation process of a pre-disaster and post-disaster two-stage optimization method for urban subway network resilience under a flood disaster, and the specific implementation process comprises the following steps:

[0065] S1, acquiring urban subway, road network line and flood disaster information;

[0066] S2, constructing an urban subway topology network and a road topology network by using a Space L method;

[0067] S3, simulating flood depth changes in the urban subway and road network during a disaster by using a runoff curve method, and determining failed sites of the urban subway network and failed lines of the road network;

[0068] S4, calculating a flood control resource demand based on the number of platforms, the types of platforms and the flood depth of each site in the failed sites;

[0069] S5, establishing an urban subway network performance measurement index, constructing a pre-disaster and post-disaster two-stage optimization model for urban subway network resilience, and solving the model by using a genetic algorithm.

[0070] As a preferred scheme of the embodiment, in the step S1, the urban subway information comprises urban subway sites and lines, travel time between subway stations, transfer time in a subway station, AFC card swiping data of subway passengers, step height, elevation around a subway station, the number and positions of platforms;

[0071] The road network line information comprises urban road network information and elevation data around road network lines; wherein the urban road network information comprises urban road intersection nodes, road line layout and travel time between road nodes;

[0072] The flood disaster information comprises rainfall intensity, duration and spatial distribution data of a rainstorm.

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

[0074] Step S21: Based on the urban subway station and line, subway platform quantity and position and urban road network intersection and line data obtained in step S1, a subway topology network is constructed by using Space L method and road topology network The formula is as follows:

[0075]

[0076] In the formula, , respectively represent the node set of the subway and road network, , are respectively the nodes in the subway and road network, and m and n are the number of nodes in the subway and road network, represents the platform set of the subway, represents the station of the th platform of the station, , respectively represent the edge set of the subway and road network, , are respectively the physical relationship of the station in the subway network and the node in the road network, , is the serial number of any node in the network; l and c in the above formula refer to the serial number of any platform in the station;

[0077] Step S22: Based on the subway topology network and road topology network constructed in step S21, spatial connection is performed by using ArcGIS to obtain the adjacency matrix of the subway topology network and road topology network respectively , , define the network edge weight matrix , The matrix form is as follows:

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, , respectively represent the connection relationship of the platform in the subway network and the node in the road network, or its adjacent nodes or there is an open line or transfer route between them, then , otherwise 0; in the matrix , is the weight of the edge , representing the travel time or transfer time between the station platform and ; in the matrix , is the weight of the edge , representing the travel time between the node and .

[0083] As a preferred scheme of the present embodiment, as shown in Figure 3 , 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, the runoff at each location of the subway and road network is calculated using the runoff curve method , the formula is as follows:

[0085]

[0086]

[0087] In the formula, is the runoff (mm) at the location ; is the rainfall (mm) at the location ; is the potential maximum retention (mm) at the location , is the curve runoff number of the location , which can be determined by comprehensively considering the land use mode of the basin, the characteristics of hydrological soil group and hydrological conditions, and looking up the applicable value in the table proposed by the Soil Conservation Service of the U.S. Department of Agriculture, is the initial loss (mm) of the basin, which is taken as ;

[0088] Step S32: The subway and road network area is divided into several regions. Based on the runoff at each location obtained in step S31, the total volume of accumulated water in each sub-region is calculated, 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 to 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 to station The shortest travel time For normal operation from the site Arrive at the 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 provide.

[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 warehouses 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 For road network intersection nodes To the shortest road distance of failure sites.

[0135] In summary, the present application provides a kind of urban subway network resilience pre-disaster-post-disaster two-stage optimization method under flood disaster, the flood disaster urban subway network resilience pre-disaster-post-disaster two-stage optimization method of the present application is by constructing the time weighted topological network of city subway and road, uses runoff curve method to simulate the flood depth variation in city subway and road network during disaster duration, determines the invalid station set of city subway network and invalid road set, based on the number of platforms matching invalid station in city subway information and flood depth, calculate the demand of flood control resources, establish city subway network performance measure index, and adopt genetic algorithm to construct city subway network resilience pre-disaster-post-disaster two-stage optimization model;Through the present application, the pre-disaster-post-disaster two-stage resilience strategy of subway network can be optimized, and the disaster resistance and recovery ability of subway network under flood disaster can be enhanced.

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

[0137] (1) the present application establishes the relationship between flood depth and repair resource demand, realizes the phased estimation of resource type and quantity, overcomes the defects of extensive and static resource evaluation in the prior art, and significantly improves the scientificity of pre-disaster preparation and the utilization efficiency of post-disaster repair resources.

[0138] (2) the present application takes the dynamic change of external road network capacity into the subway network resilience optimization model, solves the decision deviation problem caused by ignoring the accessibility of rescue path in traditional method, and makes the repair scheduling scheme more practical.

[0139] (3) the two-stage optimization method provided by the present application can generate globally optimal resilience improvement strategy, provides whole-process decision support from strategic preparation to tactical execution for coping with flood disaster, and makes up for the shortcomings of stage fragmentation and system deficiency in existing schemes.

[0140] ​Based on the same inventive concept, the present application further provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the program comprises program instructions, and the processor is configured to execute the program instructions stored in the memory. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, and are configured to implement one or more instructions, and are specifically configured to load and execute one or more instructions in the computer storage medium to implement the above method.

[0141] It needs to be further explained that, based on the same inventive concept, the present application further provides a computer storage medium, which stores a computer program, and the computer program is executed by the processor to perform the above method. The storage medium can adopt any combination of one or more computer readable media. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium may, for example, be but is not limited to an electrical, magnetic, optical, infrared, or semiconductor system, device or apparatus, or any combination of the above. More specific examples (non-exhaustive list) of the computer readable storage medium include: an electrical connection with one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the 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, device or apparatus.

[0142] It should be noted that, unless otherwise defined, technical terms or scientific terms used in the present application shall have the common meaning understood by one of ordinary skill in the art to which the present application pertains. The terms "first", "second", and similar terms used in the present application do not denote any order, quantity, or importance, but are used to distinguish different components. The terms "comprise", "include", and similar terms mean that the elements or objects before the terms encompass the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "upper", "lower", "left", "right", and the like are used only to indicate relative positional relationships, and when the absolute positions of the described objects are changed, the relative positional relationships can also be changed accordingly.

[0143] The above description is only the preferred embodiments of the present application, and is not intended to limit the present application in other forms. Any person skilled in the art can modify or change the above-mentioned disclosed technology into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change, and modification of the above-mentioned embodiments made without departing from the technical solution of the present application and in accordance with the technical essence of the present application shall still fall within the protection scope of the present application.

[0144] The present application is not limited to the above-mentioned preferred embodiments, and anyone can derive other various forms of the present application under the inspiration of the present application. Any equivalent change and modification made in accordance with the scope of the present application shall fall within the scope of the present application.

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. 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. The post-disaster recovery process integrates temporal accessibility constraints, which are determined based on dynamic changes in road network capacity. 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 failed site ÷ travel speed. The complete repair time of the site = 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. 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.

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: 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 failed site" of all failed sites within the service range of the node that 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 several nodes as the site selection set for the flood control resource warehouse.

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: 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.

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 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).

7. A pre-disaster and post-disaster dual-stage optimization system for the resilience of urban subway networks under flood disasters, used to implement the method as described in claim 1, 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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