Subway network key station identification method considering cascade failure, electronic equipment and storage medium

Abstract

The invention discloses a subway network key station identification method considering cascade failure, an electronic device and a storage medium, and the method comprises the steps: simulating a cascade failure process after station failure based on a constructed subway weighted time-varying network and the initial state and degree value of each station in each time period, building a passenger flow distribution rule based on the consideration of origin and destination of passengers, and carrying out the identification of the subway network key station. And obtaining the metro weighted time-varying network after cascade failure caused by failure of each time period and each station. And based on the node failure rate, the network maximum connection rate and the network passenger flow intensity entropy after each station loses efficacy in each time period, calculating the comprehensive importance of each station in each time period, and identifying the key subway station in each time period based on the comprehensive importance. The method is used for assisting a public transport operator to identify key stations in each time period in a subway network, so that decision support is provided for emergency plan making under emergencies, and a scientific basis is provided for emergency operation scheduling and management of the subway network.

Description

Technical Field

[0001] The invention relates to a method for identifying key sites in a subway network taking cascading failure into consideration, electronic equipment and a storage medium, and belongs to the technical field of public transportation planning and control. Background Art

[0002] With the acceleration of my country's urbanization process, the population density and travel demand of large and medium-sized cities have increased sharply. With the characteristics of high capacity, high timeliness and strong reliability, the subway has become the backbone network for medium and long-distance travel in the city. However, with the increase in the density of subway lines and the enhancement of the interaction between stations, higher requirements are also placed on the robustness of its network. The failure of local stations or operating sections may trigger cascading failures of the network through dynamic redistribution of passenger flow, resulting in a sharp drop in the transportation efficiency of the subway network or even paralysis, which will seriously affect the daily travel of residents. Especially during peak hours in the morning and evening or in emergency scenarios, the chain reaction of key station failures will aggravate the vulnerability of the network. Therefore, identifying key stations in the subway network that may cause large-scale cascading failures in different time periods can provide decision support for the formulation of emergency support plans under public emergencies, such as the operation plan of small routes of subway lines, the operation route and dispatching plan of shuttle vehicles, etc.

[0003] There are three main problems with existing key site identification methods: First, most existing studies evaluate the importance of sites based on static network topology structures (such as degree centrality and betweenness centrality), ignoring the cascading failure phenomenon caused by the dynamic transfer of actual passenger flow between sites, and it is difficult to capture the cascading propagation path caused by site failure in real scenarios.

[0004] Second, most existing studies assume that the network is a static one, without considering the temporal heterogeneity of passenger flows in actual networks, and thus cannot reflect the time-varying characteristics of key stations in subway networks.

[0005] Third, most existing studies assume that when a key station fails, passenger flow will be transferred to surrounding stations with greater influence (influence is measured by degree, betweenness, flow intensity, etc.), without considering passengers' travel mode selection and travel path selection behavior, resulting in an inadequate description of the scale and propagation process of cascading failures.

[0006] Therefore, those skilled in the art urgently need to improve the identification of key sites in the subway network from the perspective of actual passenger flow. Summary of the invention

[0007] Objective: To overcome the deficiencies in the existing methods for identifying current critical stations, which do not adequately consider the spatio-temporal heterogeneity of the actual passenger flow in the subway network and the cascading failure phenomenon caused by station failures in real scenarios, the present invention provides a method, an electronic device, and a storage medium for identifying critical stations in the subway network considering cascading failures. Starting from the actual passenger flow perspective, a method for identifying critical stations in the subway network that integrates the characteristics of "weighted-dynamic-cascading" is constructed, and the global impact of station failures is quantified from the perspective of the spatio-temporal evolution of passenger flow, which is used to assist public transportation operators in identifying critical stations in the subway network at different times, thereby providing decision support for formulating emergency plans in the event of emergencies and providing a scientific basis for the emergency operation scheduling and management of the subway network.

[0008] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows: In the first aspect, a method for identifying critical stations in the subway network considering cascading failures includes the following steps: Obtain subway line data and station data, and establish an unweighted subway network.

[0009] Based on the card-swipe data, obtain the OD pair travel volumes in each time period of the unweighted subway network.

[0010] Taking the OD pair travel volumes in each time period as the input and the shortest passenger travel path length as the goal, based on the unweighted subway network, obtain the passenger flow volume of each edge in the network in each time period, and establish a weighted time-varying subway network.

[0011] For the weighted time-varying subway network, calculate the degree value, flow intensity, and capacity upper limit of each station in each time period.

[0012] Based on the flow intensity and capacity upper limit of each station in each time period, calculate the initial state value of each station in each time period.

[0013] Based on the constructed weighted time-varying subway network and the initial state and degree value of each station in each time period, simulate the cascading failure process after station failures, and establish a passenger flow distribution rule considering the origin and destination of passengers, to obtain the weighted time-varying subway network after cascading failures caused by each failed station in each time period.

[0014] Based on the weighted time-varying subway network after cascading failures, calculate the node failure rate of each failed station in each time period.

[0015] Based on the weighted time-varying subway network after cascading failures, calculate the maximum network connectivity rate of each failed station in each time period.

[0016] Based on the weighted time-varying subway network after cascading failures, calculate the network passenger flow intensity entropy of each failed station in each time period.

[0017] Based on the node failure rate, network maximum connectivity rate and network passenger flow intensity entropy after the failure of each station in each time period, the comprehensive importance of each station in each time period is calculated, and the key subway stations in each time period are identified based on the comprehensive importance.

[0018] In a second aspect, a computer-readable storage medium is provided, characterized in that a computer program is stored thereon, and when the computer program is executed by a processor, a method for identifying key sites in a subway network taking into account cascading failures as described in any one of the first aspects is implemented.

[0019] According to a third aspect, a computer device includes: Memory, used to store instructions.

[0020] The processor is used to execute the instructions so that the computer device performs the operations of the method for identifying key sites in a subway network considering cascading failures as described in any one of the first aspects.

[0021] Beneficial effect: The present invention provides a method for identifying key sites in a subway network taking cascading failure into consideration, an electronic device and a storage medium. By deeply mining subway passenger flow data, a subway weighted time-varying network is constructed. On this basis, an improved coupled map lattice (CML) model is used to characterize the cascading failure process caused by the failure of the site. The node failure rate, the maximum network connectivity rate and the network passenger flow intensity entropy are introduced to use the minimum entropy weight method to evaluate the network after the final cascading failure, and a method for identifying key sites in the network is constructed.

[0022] The key site identification method proposed in the present invention comprehensively considers the time-varying passenger flow characteristics and dynamic propagation characteristics of the site passenger flow. Compared with the traditional key site identification method based on static network topology structure, it can more accurately describe the cascading fault propagation process and dynamic evolution law of the network under actual emergency situations. In addition, compared with other cascading failure propagation models, the present invention considers the impact of the heterogeneity of passengers' travel origin and destination points on passenger flow distribution, and more accurately describes the passengers' travel mode selection behavior and travel path selection behavior. It can provide decision support for the determination of emergency plans for subway networks under public emergencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flow chart of the key site identification method of the present invention.

[0024] Figure 2 Schematic diagram of a subway network in an embodiment of the present invention Figure 3 It is a passenger flow distribution diagram within one day in an embodiment of the present invention.

[0025] Figure 4It is a schematic diagram of the passenger flow distribution rule in the present invention, where: Figure 4 In (a), it is the schematic diagram of the station at s being affected by failure at a certain moment; Figure 4 In (b), it is the schematic diagram of the passenger flow distribution when the network is removed at at s +1 moment; Figure 4 In (c), it is the schematic diagram of the network topology structure after the station removes the network.

[0026] Figure 5 It is the distribution map of the top 50 stations with comprehensive importance from 8:00 to 9:00 in the embodiment of the present invention.

[0027] Figure 6 It is the distribution map of the top 50 stations with comprehensive importance from 12:00 to 13:00 in the embodiment of the present invention.

[0028] Figure 7 It is the distribution map of the top 50 stations with comprehensive importance from 17:00 to 18:00 in the embodiment of the present invention. Specific implementation manner

[0029] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the present invention.

[0030] Next, the present invention will be further described in combination with specific embodiments.

[0031] Embodiment 1:

[0032] This embodiment introduces a method for identifying key stations in the subway network considering cascading failures. As Figure 1 shown, it includes the following steps: Step 1: Obtain the subway line data and station data within the research scope, and establish an unweighted subway network.

[0033] Step 2: Based on the historical card swiping data, obtain the travel volume of each OD (ORIGIN - DESTINATION) pair in the unweighted subway network for each time period.

[0034] Step 3: Taking the travel volume of each OD pair as the input and the shortest travel path length of passengers as the goal, based on the established unweighted subway network, obtain the passenger flow of each edge in the network for each time period, and establish a weighted time - varying subway network.

[0035] Step 4: For the subway weighted time-varying network, calculate the degree value, traffic intensity, and capacity limit of each station in each time period.

[0036] Step 5: Based on the traffic intensity and capacity limit of each station in each time period, calculate the initial state value of each station in each time period.

[0037] Step 6: Based on the constructed subway weighted time-varying network, the initial state and degree value of each station in each time period, use the improved coupled map lattice (CML) model to simulate the cascading failure process after station failure, and establish a passenger flow distribution rule considering the origin-destination of passengers to obtain the subway weighted time-varying network after cascading failure of each failed station in each time period.

[0038] Step 7: Based on the subway weighted time-varying network after cascading failure, calculate the node failure rate of each failed station in each time period.

[0039] Step 8: Based on the subway weighted time-varying network after cascading failure, calculate the maximum network connectivity rate of each failed station in each time period.

[0040] Step 9: Based on the subway weighted time-varying network after cascading failure, calculate the network passenger flow intensity entropy of each failed station in each time period.

[0041] Step 10: Based on the node failure rate, maximum network connectivity rate, and network passenger flow intensity entropy of each failed station in each time period, use the entropy weight method to calculate the comprehensive importance of each station in each time period, and identify the key subway stations in each time period based on the comprehensive importance.

[0042] Furthermore, Step 1 specifically includes: Step 1.1: Based on the subway line and station data, establish an unweighted subway network using the method of constructing an entity network (such as: Space L method) .

[0043] Among them, represents the unweighted subway network; represents the set of subway stations, N is the total number of stations in the subway network; represents the set of edges of the subway network. The adjacency matrix corresponding to the edge set E can be expressed as: (1) Among them, represents that station is directly connected to station , otherwise .

[0044] Furthermore, Step 2 specifically includes: Step 2.1: Read the historical subway card - swiping data, which includes the passenger's card number, entry time, entry station, exit time, and exit station.

[0045] Step 2.2: According to the historical card - swiping data, count the travel volume of OD pairs with the same origin and destination within each time period t and construct the travel volume matrix of passengers . Among them, is matrix, is the number of stations in the unweighted subway network. The elements in the travel volume matrix are denoted as , represents that the boarding time is within the time period t , the boarding station is station , and the alighting station is station 's travel volume.

[0046] Furthermore, the specific steps of step 3 are as follows: Step 3.1: For the travel volume matrix in each time period, based on the constructed unweighted subway network G , use Dijkstra's algorithm to calculate the shortest path.

[0047] Step 3.2: Count the passenger flow volume passing through each edge in the subway network for each time period, denoted as , represents that the boarding time is within the time period t , and the passenger flow volume passing through the link in the subway network.

[0048] Step 3.3: Based on the unweighted subway network G and the passenger flow volume on each link in each time period, establish a weighted time - varying subway network , where represents t the passenger flow volume of the subway network link in the time period, and its matrix can be expressed as: (2) Furthermore, the specific steps of step 4 are as follows: Step 4.1: According to the established weighted time - varying subway network , calculate the degree value of the network stations, and its calculation formula is as follows: (3) Step 4.2: According to the established weighted time - varying subway network , calculate the flow intensity of the network stations, and its calculation formula is as follows: (4) (5) (6) Among them: represents the traffic intensity passing through the station t during the period, which is the sum of the inbound passenger flow t and the outbound passenger flow during the period.

[0049] Step 4.3: According to the established weighted time-varying subway network , calculate the capacity upper limit of each station in the subway network. The calculation formula is as follows: (7) (8) Among them: is the maximum traffic intensity of station during all time periods ; is the last selected time period; and are the adjustment coefficients of the capacity upper limit, .

[0050] Furthermore, the said Step 5 specifically includes: Step 5.1: According to the traffic intensity and the capacity upper limit of each station in each time period, calculate the initial state value of each station in each time period. The calculation formula is as follows: (9) Furthermore, the said Step 6, as Figure 4 shown, specifically includes: Step 6.1: Set the maximum iteration period T , and the initial state of all stations.

[0051] Step 6.2: Select any station as the failure object, and apply an external perturbation R ( R ≥1) to the failed station at time step 1 to make it fail. Then the state of station at the next moment can be expressed by formula (10). When station fails at time step 1, the failed station is removed from the subway network at time step 1, and the state of the station is set to 0 for all subsequent times starting from time step 1.

[0052] (10) Step 6.3: The stations directly connected to the station will be affected by the station at time step 1. Subsequently, the station status value may exceed 1, triggering a new round of station failures. This process will repeat continuously until no more stations fail. Here, the state values of all stations in the network at s +1 time step are updated using the improved coupled map lattice (CML) model of formula (11).

[0053] (11) Where: represents the state value of station t at during the s +1 time step, which can be used to determine whether the station can provide travel services at the current moment. If , then station is in normal operation; if , then the station is in a congested or failed state; represents the topological connection relationship between stations; represents t the passenger flow weight flowing into station at s +1 time step during the period; represents t the total passenger flow flowing into station s +1 time step during the period; is the topological coupling coefficient, is the passenger flow coupling coefficient, and ; s represents the time step, that is, the iteration times of the station status value under cascading failure propagation; is a non-linear mapping function used to describe the change of the element state value in the chaotic dynamic system. Select as this non-linear mapping function to describe the dynamic behavior of stations in the subway network. When , .

[0054] Step 6.4: During the iteration process of the CML model, after the failure of station is removed from the network, the passenger flow flowing into the failed station will reselect the next inflow station according to the needs of the passenger flow itself. When the failed station In time step s +1 When removed from the subway network, from the station Inflow site Passenger flow Will be assigned to the site Other neighboring sites of . s +1 moment from the site Flow to site The passenger flow weight allocation and update process is shown in formulas (12)-(13): (12) St. (13) in, Indicates the site remove Other neighboring sites other than express s +1 moment from the site Flow to site passenger flow weight; express s Time from site Flow to site passenger flow weight; express s Time from site Flow to site passenger flow weight; yes s +1 time station After expiration You can pass through the site The passenger flow weight of the detour to the destination is calculated as follows: Network Current site Starting point The passenger flow destination in is the end point, and the Dijkstra algorithm is used to calculate the shortest path between two stations. There will be a shortest path and the stations on the shortest path The next stop is of The passenger flow in is allocated to , there will be no shortest path The passenger flow in the network is removed. The specific allocation process is as follows Figure 3 shown.

[0055] Step 6.5: According to s +1 moment from the site Flow to site The passenger flow weight and failed sites , update the network , time step s Increment by 1, and repeat steps 6.3 - 6.4. If the time step , then the iteration terminates, and output the weighted time - varying subway network after cascade failure .

[0056] Furthermore, the node failure rate after the failure of each station in each time period in step 7 is calculated as follows: (14) Where: represents t the failed stations in the time period the node failure rate of the weighted time - varying subway network after cascade failure; represents t the failed stations in the time period the weighted time - varying subway network after cascade failure the number of failed stations.

[0057] Furthermore, the maximum connectivity rate of the network after the failure of each station in each time period in step 8 is calculated as follows: (15) Where: represents t the failed stations in the time period the maximum connectivity rate of the weighted time - varying subway network after cascade failure; represents the number of nodes in the largest connected sub - graph of the weighted time - varying subway network after the failure of stations in the t - th time period the weighted time - varying subway network after cascade failure after cascade failure.

[0058] Furthermore, the entropy of the network passenger flow intensity after the failure of each station in each time period in step 9 is calculated as follows: (16) (17) Where: represents the entropy of the network passenger flow intensity of the weighted time - varying subway network after the failure of stations in the t - th time period after cascade failure.

[0059] Furthermore, step 10 specifically includes: Step 10.1: Based on the node failure rate, the maximum connectivity rate of the network, and the entropy of the network passenger flow intensity after the failure of each station in each time period, establish a comprehensive evaluation matrix of the stations , and the calculation formula is as follows: (18) Step 10.2: For the comprehensive evaluation matrix Perform normalization processing to obtain a normalized comprehensive evaluation matrix , and the calculation formula is as follows: (19) Step 10.3: Calculate the information entropy of the three indicators of node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy , , , and the calculation formula is as follows: (20) (21) (22) Step 10.4: Calculate the weights of the three indicators of node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy , , , and the calculation formula is as follows: (23) (24) (25) Step 10.5: Calculate the comprehensive importance of each site at each time period ; Sort the comprehensive importance of each site in descending order. The site with a higher ranking is a key site in the subway network. Among them, the comprehensive importance The calculation formula is as follows: (26) Example 2: This example introduces a computer-readable storage medium with a computer program stored thereon. When the computer program is executed by a processor, it implements a method for identifying key sites in a subway network considering cascading failures as described in any one of Example 1.

[0060] Example 3: This example introduces a computer device, including: A memory for storing instructions.

[0061] A processor for executing the instructions, so that the computer device performs the operations of a method for identifying key sites in a subway network considering cascading failures as described in any one of Example 1.

[0062] Example 4: This embodiment introduces a method for dynamically identifying key stations in a subway network considering cascading failures, specifically the process of applying it to a certain city's subway network to identify key stations, which is as follows.

[0063] 1: Obtain subway line data and station data within the research scope, and establish an unweighted subway network.

[0064] Obtain subway line data and station data within the research scope. Among them, the subway station and line data include the following attributes: station number, station name, station longitude, station latitude, and line name. Specific data examples are shown in Table 1.

[0065] Table 1 Example of subway station and line data

[0066] Based on the above data, use the Space L method to establish an unweighted directed bus network and an unweighted directed subway network . Among them, G represents the unweighted subway network; V represents the set of subway stations; E represents the edge set of the subway network; During the establishment of the subway network, stations with the same name but belonging to different lines are regarded as the same station. This network is an undirected network, which contains 159 stations and 328 edges in total. The unweighted directed subway network is as shown in Figure 2 .

[0067] 2: Based on historical card - swiping data, obtain the travel volume of each OD pair in the unweighted subway network for each time period; As shown in Figure 3 , select the subway card - swiping data for three time periods: the morning rush hour (8:00 - 9:00), the mid - day flat peak (12:00 - 13:00), and the evening rush hour (17:00 - 18:00) on April 12, 2019 as the research object. The subway card - swiping data includes OD number, entry time, entry station, exit time, and exit station, with a total of 381,120 data records. Specific data examples are shown in Table 2, Table 3, and Table 4.

[0068] Table 2 Example of morning rush - hour subway card - swiping data

[0069] Table 3 Example of mid - day flat - peak subway card - swiping data

[0070] Table 4 Example of evening rush - hour subway card - swiping data

[0071] According to the historical card - swiping data, count the travel volume within a certain time periodt The travel volumes of OD pairs with the same origin and destination are shown in Tables 5, 6, and 7. Based on Tables 5 - 7, establish the travel volume matrix of OD pairs within each time period t .

[0072] Table 5 Example of OD pair travel volumes during the morning peak

[0073] Table 6 Example of OD pair travel volumes during the midday flat peak

[0074] Table 7 Example of OD pair travel volumes during the evening peak

[0075] 3: Taking the travel volumes of OD pairs in each time period as input and the shortest passenger travel path length as the objective, based on the established unweighted subway network, obtain the passenger flow of each edge in the network during each time period, and establish a weighted time-varying subway network; For all OD pairs in each time period, calculate the shortest path on the constructed unweighted subway network G using Dijkstra's algorithm. The obtained shortest paths are shown in Tables 8, 9, and 10.

[0076] Table 8 Example of the shortest paths of OD pairs during the morning peak

[0077] Table 9 Example of the shortest paths of OD pairs during the midday flat peak

[0078] Table 10 Example of the shortest paths of OD pairs during the evening peak

[0079] Distribute the travel volumes of OD pairs in each time period evenly to each edge on the obtained shortest paths. Taking the OD pair numbered 1 during the morning peak as an example, the shortest path of this OD pair has only one section. Therefore, distribute all 98 passengers to the edge from Zhonghuamen to Sanshanjie, and record the origin and destination of the distributed passenger flow.

[0080] Based on the unweighted subway network G and the passenger flow distributed to the edges of each station, establish a weighted time-varying subway network for each time period: morning peak , midday flat peak , evening peak .

[0081] 4: For the weighted time-varying subway network, calculate the degree value, flow intensity, and capacity limit of each station, where the adjustment coefficient of the capacity limit​ , . The degree values, flow intensities, and capacity limits of each station at each time period are shown in Tables 11, 12, and 13.

[0082] Table 11 Example of Degree Values of Each Station

[0083] Table 12 Example of Flow Intensities of Each Station

[0084] Table 13 Example of Capacity Limits of Each Station

[0085] 5: Based on the flow intensities and capacity limits of each station at each time period, calculate the initial state values of each station at each time period. The initial values of each station are shown in Table 14.

[0086] Table 14 Example of Initial States of Each Station

[0087] 6: Based on the constructed weighted time-varying subway network and the initial states of each station, use the improved coupled map lattice (CML) model to simulate the cascading failure process after a station failure, and establish a passenger flow distribution rule considering the origin and destination of passengers.

[0088] Select the failure network as , select the failure station to apply the failure simulation for the cascading failure process after the station failure, set the maximum iteration period T = 50, apply an external perturbation R = 4, the topological coupling coefficient , the passenger flow coupling coefficient . Use formula (10) to apply a perturbation to the failure station to make it fail.

[0089] s At time Figure 2 , the failure station is removed from the weighted time-varying subway network, and the edges connected to the failure station are removed. According to the passenger flow distribution rule, use formula (12) to re-distribute the passenger flow flowing into the failure station. The specific distribution process is as shown. Use formula (10) to update the states of other stations in the network, let s increment by 1, and repeat the above steps until

[0090] s , end this process. becomes s fails, sAt time s = 1, the Maigaoqiao station is removed from the network. The passenger flow that flows into the Maigaoqiao station from the adjacent Hongshan Zoo station (number: 2) leaves the subway network because it cannot reach the destination by detour, resulting in the number of passengers changing from 172 at s = 0 to 0 at s = 1 and not increasing subsequently.

[0091] The interference suffered by the Maigaoqiao station radiates from the center to the surrounding areas, affecting the surrounding stations, resulting in the state of the Hongshan Zoo station changing from to failure. The surrounding stations are also interfered to varying degrees, thus triggering a new round of station failures. This process will continue continuously with the change of s until no more stations fail and the network returns to stability. When this condition is met, the iterative process ends.

[0092] 7: For the weighted time-varying subway network, calculate the node failure rate after each station fails in each time period.

[0093] According to the network state after the evolution of the CML model, calculate the node failure rate after different stations fail in each time period through formula (14) , and the results are shown in Table 15.

[0094] Table 15 Node failure rates after different stations fail in each time period Example

[0095] 8: For the weighted time-varying subway network, calculate the maximum network connectivity rate after each station fails in each time period; According to the network state after the evolution of the CML model, calculate the maximum network connectivity rate after different stations fail in each time period through formula (15) , and the results are shown in Table 16.

[0096] Table 16 Maximum network connectivity rates after different stations fail in each time period Example

[0097] 9: For the weighted time-varying subway network, calculate the entropy of network passenger flow intensity after each station fails in each time period; According to the network state after the evolution of the CML model, calculate the entropy of network passenger flow intensity after different stations fail in each time period through formula (16) , and the results are shown in Table 17.

[0098] Table 17 Entropy of network passenger flow intensity after different stations fail in each time period Example

[0099] Step 10: Based on the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy of each station in each time period, use the entropy weight method to calculate the comprehensive importance of each station in each time period, and identify the key subway stations in each time period based on the comprehensive importance.

[0100] Based on the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy of each station in each time period, first establish a comprehensive evaluation matrix as shown in Equation (18). Then, normalize this matrix to obtain the normalized comprehensive evaluation matrix. Next, use Equations (20)-(22) to calculate the information entropy of the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy in each time period, and the calculation results are shown in Table 18. On this basis, calculate the weights of the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy in each time period through Equations (23)-(25), and the calculation results are shown in Table 19. Finally, calculate the comprehensive importance of each station in each time period based on Equation (26), and the example results are shown in Table 20. Sort the comprehensive importance of each station in descending order. The higher the ranking of the station, the larger the scale of cascading failure caused to the subway network and the more affected passenger flow. Figure 5 、 Figure 6 、 Figure 7 Figure 50 shows the distribution map of the top 50 stations with comprehensive importance in each time period based on the calculation results in Table 20.

[0101] Table 18 Information entropy of node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy in each time period

[0102] Table 19 Weights of node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy in each time period

[0103] Table 20 Comprehensive importance of stations in each time period in the subway network

[0104] The present invention discloses a method for dynamically identifying key stations in a subway network considering cascading failures. Based on subway card-swipe data, the OD pair travel volumes at different times in the subway network are obtained. Taking the OD travel volumes at each time period as input and the shortest travel path length of passengers as the optimization goal, the passenger flow volume on each edge in the subway network at each time period is obtained, and a weighted time-varying subway network model is constructed. For the weighted time-varying subway network, the flow intensity and capacity limit of each station at each time period are calculated, so as to quantify the initial state of each station at each time period. An improved coupled map lattice (CML) model is introduced to simulate the cascading propagation process after station failures, and a dynamic reassignment rule based on passenger origin-destination is embedded to characterize the coupling effect of fault propagation and passenger flow time-varying characteristics. Through multi-dimensional indicators such as node failure rate, network maximum connectivity rate, and passenger flow intensity entropy, combined with the entropy weight method, the comprehensive importance of each station at each time period is calculated, and finally the dynamic identification of key stations is realized. The present invention can help subway operation enterprises quickly identify key stations that may trigger large-scale cascading failures at each time period, and provide decision-making support for the formulation of emergency plans under emergencies.

[0105] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for identifying key sites in a subway network considering cascading failures, characterized in that: The following steps are involved: Obtain subway line data and station data to build a subway permissionless network; Based on the card swiping data, the OD pair travel volume in each period in the subway unweighted network is obtained; Taking the OD pair travel volume in each time period as input and the shortest passenger travel path length as the goal, based on the subway unweighted network, the passenger flow of each edge in each time period in the network is obtained to establish a subway weighted time-varying network; For the subway weighted time-varying network, the degree value, flow intensity and capacity limit of each station in each time period are calculated; Based on the traffic intensity and capacity upper limit of each site in each time period, calculate the initial state value of each site in each time period; Based on the constructed subway weighted time-varying network and the initial state and degree value of each station in each time period, the cascading failure process after the station failure is simulated, and the passenger flow allocation rule based on the passenger's starting and ending points is established to obtain the subway weighted time-varying network after the cascading failure caused by the failure of each station in each time period; Based on the subway weighted time-varying network after cascading failure, the node failure rate after each station fails in each period is calculated; Based on the subway weighted time-varying network after cascading failure, the maximum network connectivity rate after the failure of each station in each period is calculated; Based on the subway weighted time-varying network after cascade failure, the network passenger flow intensity entropy after the failure of each station in each period is calculated; Based on the node failure rate, network maximum connectivity rate and network passenger flow intensity entropy after the failure of each station in each time period, the comprehensive importance of each station in each time period is calculated, and the key subway stations in each time period are identified based on the comprehensive importance.

2. The method for identifying key sites in a subway network considering cascading failures according to claim 1, characterized in that: The obtaining of the OD pair travel volume in each period in the subway unweighted network in each period specifically includes: Read subway card swiping data, which includes the passenger's card number, entry time, entry station, exit time, and exit station; According to the card swiping data, the travel volume of OD pairs with the same starting and ending points in each time period t is counted to construct the passenger travel volume matrix ;in, for matrix, is the number of stations in the subway unweighted network; the travel volume matrix The element is denoted by , Indicates that the boarding time is within time period t and the boarding station is station , the alighting point is the station of travel volume.

3. The method for identifying key sites in a subway network considering cascading failures according to claim 1 is characterized in that: The establishment of a subway weighted time-varying network specifically includes: Travel volume matrix for each time period ,Based on the constructed subway unweighted network G, the Dijkstra algorithm is used to calculate the shortest path; Count the passenger flow of the shortest path through each side of the subway network in each time period, recorded as , Indicates that when the boarding time is within time period t, the edges through the subway network passenger flow; According to the subway unweighted network G and the passenger flow of each link in each time period, a subway weighted time-varying network is established. , represents the set of subway stations, N is the total number of stations in the subway network; represents the edge set of the subway network, where The passenger flow of the subway network edge during period t is expressed as: 。 4. The method for identifying key sites in a subway network considering cascading failures according to claim 1, characterized in that: The calculation of the degree value, traffic intensity and capacity upper limit of each site in each time period specifically includes: According to the subway weighted time-varying network established , calculate the degree value of the network site The expression is as follows: ； in, is the element of the adjacency matrix corresponding to the edge set E, , N is the total number of stations in the subway network; According to the subway weighted time-varying network established , calculate the traffic intensity of the network site The expression is as follows: ； ； ； in: is the edge of the subway network that passes through the boarding time within time period t of passenger flow, Indicates passing the station within the t period The flow intensity, is the passenger flow in period t, is the outflow passenger flow in period t; According to the subway weighted time-varying network established , calculate the upper capacity limit of each station in the subway network The expression is as follows: ； ； in: For Site In all time periods The maximum flow intensity, The last time period selected, and is the adjustment factor for the upper capacity limit.

5. The method for identifying key sites in a subway network considering cascading failures according to claim 1, characterized in that: The calculating of the initial state value of each site in each time period specifically includes: According to the traffic intensity of each site in each period and capacity limit , calculate the initial state value of each station in each period The expression is as follows: 。 6. The method for identifying key sites in a subway network considering cascading failures according to claim 1, characterized in that: The method of obtaining a weighted time-varying subway network after cascading failures caused by failures of various stations in various time periods specifically includes: Step 6.1: Set the maximum iteration period T and the initial state of all sites ; Step 6.2: Select any site As the failed object, an external disturbance R is applied to the failed station at time step 1 to make it fail. In the next state ; When the time step is 1 station After failure, the failed site Remove it from the subway network at time step 1, and set the status of the station to 0 from time step 1 onwards; Step 6.3: With the site Directly connected stations will be affected by station The impact of s+1 triggers a new round of site failures. The site failure process will be repeated until no more sites fail. The state values ​​of all sites at the s+1 time step are obtained. , the expression is as follows: ； in: Indicates the site in time period t The state value at the s+1 time step, if , then the site In normal operation; if , then the site In a congested or out-of-service state; Indicates the topological connection relationship between sites; Indicates the station in period t Inflow station at time step s+1 passenger flow weight; Indicates the inflow station at time step s+1 in period t Total passenger flow; is the topological coupling coefficient, is the passenger flow coupling coefficient; s represents the time step; is a nonlinear mapping function, , N is the total number of stations in the subway network; Indicates the site The degree value, Indicates the site in time period t The state value at the s+1 time step, Indicates the site in time period t The state value at the time step s; Step 6.4: During the iteration of the state values ​​of all stations in the s+1 time step, when the failed station At time step s+1, when removed from the subway network, Inflow site Passenger flow Will be assigned to the site Other adjacent sites of , get the time s+1 from site Flow to site The passenger flow weight , the expression is as follows: ； St. ; in, Indicates the site remove Other neighboring sites other than Indicates that the time s+1 is from the station Flow to site passenger flow weight; Indicates the time s from the station Flow to site passenger flow weight; Indicates the time s from the station Flow to site passenger flow weight; It is the station at time s+1 After expiration You can pass through the site The passenger flow weight of detouring to the destination; in, The method of obtaining is as follows: Network Current site Starting point The passenger flow destination in is the end point, and the shortest path between two stations is calculated. There will be a shortest path and the stations on the shortest path The next stop is of The passenger flow in is allocated to ; Step 6.5: According to the time s+1, the Flow to site The passenger flow weight and failed sites , update the network , the time step s increases by 1, and steps 6.3-6.4 are repeated. If the time step , then the iteration is terminated, and the subway weighted time-varying network after the cascade failure is output .

7. The method for identifying key sites in a subway network considering cascading failures according to claim 1, characterized in that: The node failure rate expression after each site fails in each time period is as follows: ； in: Indicates the failed site in period t The failure rate of subway weighted time-varying network nodes after cascading failures; Indicates the failed site in period t Subway weighted time-varying network after cascading failure The number of failed stations, N is the total number of stations in the subway network; The expression of the maximum network connectivity rate after each site fails in each time period is as follows: ； in: Indicates the failed site in period t Maximum connectivity rate of subway weighted time-varying network after cascading failure; Indicates the failed site in period t Subway weighted time-varying network after cascading failure The number of nodes in the maximum connected subgraph; The network passenger flow intensity entropy after the failure of each station in each period is calculated as follows: ； ； in: Indicates the failed site in period t The weighted time-varying network passenger flow intensity entropy of the subway after the final cascade failure, Indicates passing the station within the t period The flow intensity.

8. The method for identifying key sites in a subway network considering cascading failures according to claim 1, characterized in that: The identification of key subway stations in each period based on comprehensive importance specifically includes: Based on the node failure rate, network maximum connectivity rate and network passenger flow intensity entropy after failure of each station in each period, a comprehensive evaluation matrix of the station is established. ; Comprehensive evaluation matrix Perform normalization to obtain the normalized comprehensive evaluation matrix ; Calculate the information entropy based on three indicators: node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy , , ; Calculate the weights of the three indicators: node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy , , , the expression is as follows: ； ； ； Calculate the time period and each station The overall importance of ; Sort the comprehensive importance of each station from high to low. The higher the ranking, the more critical the station in the subway network. The expression is as follows: 。 9. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, a method for identifying key sites in a subway network taking into account cascading failures as described in any one of claims 1 to 8 is implemented.

10. A computer device, characterized in that: include: A memory for storing instructions; The processor is used to execute the instructions so that the computer device performs the operations of the method for identifying key sites in a subway network considering cascading failures as described in any one of claims 1 to 8.

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