Multi-mode public transportation network dynamic robustness analysis method considering passenger travel behaviors, electronic equipment and storage medium

Abstract

The invention discloses a multi-mode public transport network dynamic robustness analysis method considering passenger travel behaviors, electronic equipment and a storage medium. The method comprises the following steps: establishing a multi-mode public transport topology network and a multi-mode public transport passenger flow network of each time period; calculating the load and capacity of the site based on a nonlinear capacity load model; in consideration of travel mode selection behaviors and path planning behaviors of passengers, a cascade failure process after station failure is simulated, and a multi-mode public transportation network after cascade failure is obtained; and on the basis of the network maximum connection rate, the network operation efficiency and the passenger flow loss rate after each failure station in each time period, calculating the comprehensive robustness of each station in each time period, and evaluating a station area which is easy to cause cascade failure in each time period on the basis of the comprehensive robustness. According to the method, the passenger flow dynamic time-varying characteristics of the stations and the travel behaviors of passengers are comprehensively considered, the method is used for assisting public transport operators in analyzing the dynamic robustness in the multi-mode public transport network, and decision support is provided for making emergency plans under emergencies.

Description

Technical Field

[0001] This invention relates to a method, electronic device, and storage medium for dynamic robustness analysis of multimodal public transport networks that takes into account passenger travel behavior, and belongs to the field of public transport planning and control technology. Background Art

[0002] In my country's large and medium-sized cities, public transportation is the primary mode of transportation to meet the daily travel needs of a large number of residents. Currently, many major cities worldwide are building multimodal public transportation networks with rail transit as the backbone and conventional buses as the main body. As an extremely complex system, this multimodal public transportation network is vulnerable to various unforeseen events, such as extreme weather and surges in passenger flow. When a station or route in the multimodal public transportation network is disrupted, affected passengers are forced to change their travel methods and routes. The redistributed passenger flow may spread to other stations and trigger cascading failures. This not only severely impacts the passenger travel experience but also threatens the overall operational reliability of the network.

[0003] Therefore, accurately describing the failure propagation mechanism of multimodal public transport networks and analyzing the dynamic robustness of multimodal public transport networks after cascading failures is of great significance for formulating emergency management plans and improving the reliability of multimodal public transport networks.

[0004] Existing analytical methods have three main problems:

[0005] First, most existing research focuses on single networks such as subways or buses. However, multimodal public transport networks are typical interdependent networks, where each subsystem can operate independently and interact with passenger flow through pedestrian connections. Therefore, research on single networks is difficult to reveal their complex coupling characteristics.

[0006] Second, existing studies have not considered the impact of spatiotemporal heterogeneity of passenger flow on cascading failures. In reality, passenger flow in multimodal public transport networks exhibits significant spatiotemporal heterogeneity across different types of stations, locations, and time periods. This heterogeneity affects the ability of stations to handle failed passenger transfers, ultimately leading to differentiated propagation patterns of cascading failures.

[0007] Third, existing studies all assume that when a station fails, passengers will not switch to other modes of transportation (such as ride-hailing, taxis, shared bicycles, etc.), and that the proportion of passengers transferring to adjacent stations is only related to the influence of nodes (such as capacity, betweenness, degree, and clustering coefficient). These assumptions ignore passengers' travel mode selection and travel route planning behavior, which may exaggerate the scale of cascading failures and misjudge their propagation range.

[0008] Therefore, those skilled in the art urgently need to start from the actual characteristics of passenger flow and travel behavior, incorporate passenger flow heterogeneity and passenger travel behavior into the analysis of the propagation process of cascading failure, and construct a more realistic multimodal public transport dynamic robustness analysis method. Summary of the Invention

[0009] Objective: To overcome the shortcomings of existing technologies, this invention provides a method, electronic device, and storage medium for dynamic robustness analysis of multimodal public transport networks that considers passenger travel behavior. This method assists public transport operators in analyzing the dynamic robustness of multimodal public transport networks at different times, thereby guiding public transport network planning, station layout, and capacity allocation.

[0010] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0011] Firstly, a method for evaluating the dynamic robustness of a multimodal public transport network includes the following steps:

[0012] Step 1: Obtain subway and bus route and station data, as well as AVL (automated vehicle location) data, and establish a multi-modal public transport topology network.

[0013] Step 2: Obtain passenger flow data for subways and buses, count the origin-destination (OD) travel volume for each time period, and establish a multi-modal public transport passenger flow network for each time period.

[0014] Step 3: Calculate the site load for each time period and calculate the site capacity based on the nonlinear capacity load model.

[0015] Step 4: Based on the constructed multimodal bus topology network, multimodal bus passenger flow network, and station capacity, simulate the cascading failure process after station failure, and establish passenger flow allocation rules that take into account passenger travel behavior to obtain the multimodal bus network after cascading failure in each time period.

[0016] Step 5: Based on the multi-modal bus network after cascading failure, calculate the maximum network connectivity after each station fails in each time period;

[0017] As a preferred option, the following step is also included: Step 6: Based on the multi-mode bus network after cascading failure, calculate the network operation efficiency after each station fails in each time period.

[0018] As a preferred option, the following step is also included: Step 7: Based on the multi-mode bus network after cascading failure, calculate the passenger loss rate after each station fails at each time period.

[0019] As a preferred option, the following steps are also included: Step 8: Calculate the comprehensive robustness index of each site in each time period based on the maximum network connectivity, network operating efficiency, and passenger loss rate after each site fails in each time period, and evaluate the site areas that are prone to cascading failures in each time period based on the comprehensive robustness index.

[0020] As a preferred option, the method for establishing a multi-mode public transport topology network in step 1 is as follows:

[0021] Step 1.1: Based on subway and bus route and station data, establish a bus topology network using the Space L method (a method for modeling physical networks). and subway topology network ,in, , When two stations are adjacent on a subway or bus line, they are considered to have a station segment edge. Represents the subway topology network; Indicates a group of subway stations; Represents the set of station segments and edges in a subway network; Represents the public transport topology network; Indicates a set of bus stops; This represents the set of station segments of a public transport network.

[0022] Step 1.2: Based on the spatial location of subway and bus stations, search for bus stations within walking distance of subway stations. When the distance between a subway station and a bus station is less than R, it is considered that there is a bidirectional transfer edge between the subway station and the bus station. The set of all identified transfer edges is denoted as . , where R is the distance threshold.

[0023] Step 1.3: Based on the AVL data of bus and subway lines, calculate the set of station edges in the subway network. and the station sections of the public transport network The corresponding time weights are denoted as follows: and Time weight represents the average travel time of vehicles between adjacent stations, which can be obtained by subtracting the arrival and departure times between stations in the AVL data.

[0024] Step 1.4: Calculate the transfer edge based on the location data of subway stations and bus stops. Time weight Among them, the site and The formula for calculating the time weight of the transfer edges between them is as follows:

[0025]

[0026] in, Indicates site and Time weights of transfer edges between them; Indicates site and Walking distance between This indicates the passenger's walking speed.

[0027] Step 1.5: Construct a multimodal public transport topology network , .in, V = { V b , V m } = { v i | i ∈ [ 1 , N ]} , Represents a collection of sites. This represents the i-th site in the set of sites. This indicates the number of all stops in a multimodal transit network. , Denotes the set of edges. Indicating the set of edges and The edges connecting them; , This represents the set of weights corresponding to the edges. This represents the weight set of the edges. The corresponding weights i , j ∈ [ 1 , N ], i ≠ j .

[0028] As a preferred option, the method for establishing a multi-modal public transport passenger flow network for each time period in step 2 is as follows:

[0029] Step 2.1: Based on passenger subway and bus card swipe data, calculate passenger flow between stations in different time periods. When at station t in time period t... and When there is passenger flow between them, there is a flow edge. The weight of the flow edge is denoted as , Station t represents time period t and The passenger flow between them.

[0030] Step 2.2: For the flow edge Calculating stations based on multi-mode bus topology network and Travel time between Travel time For the site and The travel time of the shortest path between stations includes travel time and transfer time between stations. The shortest path is calculated using the weighted Dijkstra algorithm.

[0031] Step 2.3: Construct a multimodal public transport passenger flow network for time period t , .in, This represents a set of stations, similar to the multimodal transit topology network. , Represents the set of flow edges in the multi-modal public transport passenger flow network during time period t; , This represents the set of weights corresponding to the flow edges; This represents the set of shortest travel times corresponding to the flow edges. i , j ∈ [ 1 , N ], i ≠ j .

[0032] As a preferred embodiment, step 3 involves calculating the site capacity based on a nonlinear capacity-load model, specifically using the following method:

[0033] Step 3.1: Calculate the stations for each time period t. The site load is calculated using the following formula:

[0034]

[0035] in, Indicates site Site load during time period t.

[0036] Step 3.2: Calculate the site The maximum load for the entire day is calculated using the following formula:

[0037]

[0038] in, This represents a set of time periods that divide the entire day. Indicates site The maximum load throughout the day.

[0039] Step 3.3: Calculate the site based on the nonlinear load model The capacity is calculated using the following formula:

[0040]

[0041] Where α and β are the capacity control coefficients of the nonlinear load model; Indicates site The capacity.

[0042] As a preferred embodiment, step 4 specifically includes:

[0043] Step 4.1: Initialize the multi-mode bus topology network for time period t and multimodal public transport passenger flow network .

[0044] Step 4.2: Obtain the site for time period t Site load and site capacity .

[0045] Step 4.3: Select any site As a failed object, in a multimodal bus topology network Delete the site and its corresponding edges.

[0046] Step 4.4: Targeting the site The destination after failure is Traffic, search sites In multimodal public transport topology network All neighboring sites in the set, denoted as . traversal Calculate the passenger's walking distance to all neighboring stations. any of the sites and from To the destination Total time .

[0047]

[0048] in, Indicates site and Walking distance between; Indicates the passenger's walking speed; Indicates from To the destination The shortest travel time.

[0049] Step 4.5: Calculate passenger transfer to stations based on the multinomial logit model (discrete choice model). probability .

[0050]

[0051] in, Indicates the starting point is a station. Destination is Passenger flow shifted to the station The probability, These are control parameters used to measure passengers' sensitivity to travel time.

[0052] Step 4.6: Based on the transfer probability of each neighboring station, assign the passenger to a neighboring station for transfer, and record the passenger's travel time after being assigned to a specific neighboring station as the updated shortest travel time. .

[0053] Step 4.7: When the updated shortest travel time and the shortest travel time when the multi-modal bus topology network is not attacked The ratio is greater than the passenger's patience threshold TT, that is / > TT, the passenger flow between the OD pairs is lost and is considered to be transferred to other travel modes (such as taxis, online car-hailing, etc.). Conversely, when / < TT, the passenger flow between the OD pairs is assigned to the transferred neighbor stations.

[0054] Step 4.8: Update the site load of the neighbor stations after passenger flow allocation of the site , when the site of the site load is greater than the capacity of the site of the site when the site fails, in delete the site and its corresponding connecting edges;

[0055]

[0056] Step 4.9: Repeat steps 4.4 - 4.8 until no site fails, and output the multi-modal bus network with cascading failures caused by site failures during this period.

[0057] As a preferred solution, the calculation method of the maximum network connectivity rate after the failure of each site in each period in step 5 is expressed as:

[0058]

[0059] Among them: represents the maximum network connectivity rate of the multi-modal bus network after cascading failures in period t; represents the number of sites in the maximum connected subgraph of the multi-modal bus topology network after cascading in period t; N represents the number of sites in the multi-modal bus network when not attacked. The maximum network connectivity rate is used to measure the impact of cascading failures on the topology structure of the multi-modal bus network.

[0060] As a preferred solution, the calculation method of the network operation efficiency after the failure of each site in each period in step 6 is expressed as:

[0061]

[0062] Among them: the network operation efficiency of the multi-modal bus network after cascading failures in period t; Station t represents time period t and Passenger flow between; Indicates the site after the cascading fails during time period t. and The shortest travel time between points; N represents the number of stops in the multimodal transit network when it is not under attack. Network efficiency measures the impact of cascading failures on the overall passenger travel time efficiency of the multimodal transit network.

[0063] As a preferred embodiment, the method for calculating the passenger loss rate after each time period and each station fails in step 7 is expressed as follows:

[0064]

[0065]

[0066] in: Passenger loss rate of multi-modal bus network after time period t cascade failure; Station t represents time period t and Passenger flow between; Indicates from and Does the increase in travel time exceed passengers' tolerance threshold? Indicates the site after the cascading fails during time period t. and The shortest travel time between; This indicates the number of stations in the multi-modal transit network during time period t when they are not under attack. and The shortest travel time between points; TT represents the passenger's tolerance threshold for increased travel time; N represents the number of stops in the multimodal transit network when not under attack. Network efficiency measures the impact of cascading failures on the overall trip volume of the multimodal transit network.

[0067] As a preferred embodiment, step 8 calculates the comprehensive robustness index of each station in each time period, and evaluates the station areas prone to cascading failures in each time period based on the comprehensive robustness index. The specific method is as follows:

[0068] Step 8.1: Based on the maximum network connectivity, network operating efficiency, and passenger churn rate of each site after cascading failures in each time period t, establish a comprehensive robustness evaluation matrix for each site. The comprehensive robustness evaluation matrix can be expressed as:

[0069] X t = [ GC 1 ( t ) OE 1 ( t ) LR 1 ( t ) GC 2 ( t ) ⋮ OE 2 ( t ) ⋮ LR 2 ( t ) ⋮ GC N ( t ) OE N ( t ) LR N ( t ) ]

[0070] in, This represents the maximum network connectivity of the multimodal transit network after the cascading failure at station N during time period t. This represents the network operating efficiency of the multi-mode bus network after the cascading failure of station N during time period t. This represents the passenger loss rate of the multimodal bus network after the cascading failure of station N during time period t.

[0071] Step 8.2: Evaluation of the comprehensive robustness matrix Normalization is performed to convert the absolute values ​​of each indicator into relative values, resulting in a normalized comprehensive evaluation matrix.

[0072] X t ¯ = [ GC 1 ( t ) ¯ OE 1 ( t ) ¯ LR 1 ( t ) ¯ GC 2 ( t ) ¯ ⋮ OE 2 ( t ) ¯ ⋮ LR 2 ( t ) ¯ ⋮ GC N ( t ) ¯ OE N ( t ) ¯ LR N ( t ) ¯ ]

[0073] in, This represents the normalized value of the maximum network connectivity of the multimodal transit network after the cascading failure of station N during time period t. This represents the normalized value of the network operating efficiency of the multimodal transit network after the cascading failure of station N during time period t. This represents the normalized value of the passenger loss rate of the multimodal bus network after the cascading failure of station N during time period t.

[0074] Step 8.3: Calculate the information entropy of three indicators: maximum network connectivity, network operating efficiency, and passenger churn rate. , , .

[0075]

[0076]

[0077]

[0078] Step 8.4: Calculate the weights of the three indicators: maximum network connectivity, network operating efficiency, and passenger churn rate. , , .

[0079]

[0080]

[0081]

[0082] Step 8.5: Calculate the values ​​for each station Comprehensive robustness index for time period t The overall importance of each site was ranked from highest to lowest, with higher-ranked sites being more prone to cascading failures. Among these, the overall robustness index... The expression is as follows:

[0083]

[0084] In a second aspect, a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a dynamic robustness analysis method for a multimodal public transport network that considers passenger travel behavior, as described in any of the first aspects.

[0085] Thirdly, an electronic device includes:

[0086] Memory is used to store instructions.

[0087] A processor is configured to execute the instructions, causing the electronic device to perform operations as described in any of the first aspects of a method for dynamic robustness analysis of multimodal public transport networks that takes into account passenger travel behavior.

[0088] Beneficial Effects: This invention provides a method, electronic device, and storage medium for dynamic robustness analysis of multimodal public transport networks that considers passenger travel behavior. Addressing the shortcomings of current multimodal public transport network dynamic robustness analysis in considering the spatiotemporal heterogeneity of passenger flow and passenger travel behavior, this invention proposes a two-layer network model integrating topological networks and dynamic passenger flow networks. It also incorporates passenger travel mode selection and route planning behavior into a nonlinear capacity load model, constructs a cascading failure propagation mechanism for multimodal public transport networks, and finally proposes dynamic robustness evaluation indicators from three dimensions: network connectivity robustness, travel time robustness, and passenger flow robustness, thus constructing a method for dynamic robustness analysis of multimodal public transport networks.

[0089] This invention can quickly analyze the dynamic robustness of a city's public transportation network at different times based on urban public transportation network data and historical card-swipe travel data, identifying station areas prone to cascading failures. Compared to traditional robustness analysis methods, this method can more accurately characterize passenger travel behavior in multimodal public transportation networks. Furthermore, the dynamic robustness analysis method proposed in this paper comprehensively considers the time-varying characteristics of passenger flow and travel choice characteristics at stations, helping public transportation operators quickly assess station areas in the network prone to cascading failures at different times. Attached Figure Description

[0090] Figure 1 This is a flowchart illustrating a method for dynamic robustness analysis of multimodal public transport networks that considers passenger travel behavior, according to the present invention.

[0091] Figure 2This is a schematic diagram of passenger flow distribution within a day in an embodiment of the present invention.

[0092] Figure 3 This is a schematic diagram of the passenger flow transfer rules of the present invention.

[0093] Figure 4 This is a schematic diagram of the distribution of the top 10% of the comprehensive robustness index of stations during the morning rush hour in an embodiment of the present invention.

[0094] Figure 5 This is a schematic diagram of the distribution of the top 10% of the comprehensive robustness index of the midday peak stations in this embodiment of the invention.

[0095] Figure 6 This is a schematic diagram showing the distribution of the top 10% of the comprehensive robustness index of stations during the evening peak hours in an embodiment of the present invention. Detailed Implementation

[0096] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0097] The present invention will be further described below with reference to specific embodiments.

[0098] Example 1:

[0099] This embodiment describes the specific application of a dynamic robustness analysis method for multimodal public transport networks that considers passenger travel behavior in a certain area. For details, please refer to the following specific embodiment of the multimodal public transport network and the accompanying drawings, which will provide a more detailed explanation of the method of the present invention.

[0100] Step 1: Obtain subway and bus route and station data, as well as AVL data, and establish a multi-modal bus topology network.

[0101] The station data for subways and buses includes the following six attributes: station number, station name, route, station longitude, station latitude, and station type. Specific data examples are shown in Table 1.

[0102] Table 1. Subway and Bus Station Route Data

[0103]

[0104] Based on the above data, a bus topology network and a subway topology network are constructed. as well as Based on this, with the subway station as the center and a buffer zone of 500 meters (R=500 meters), we search for bus stops within walking distance of the subway station. The set of all identified transfer edges is denoted as . .

[0105] Then, based on the AVL data shown in Table 2, the set of edges for each metro segment is calculated. Meet at the bus stop section The corresponding time weights represent the average travel time between adjacent stations, expressed in minutes. These are denoted as... and .

[0106] Table 2 AVL Data Examples

[0107]

[0108] Based on the location data of subway stations and bus stops, the transfer edges are calculated. Time weight The unit is minutes. Table 3 shows examples of the edges and weights of the multimodal bus topology network.

[0109] Table 3. Edges and corresponding weights of the multimodal bus topology network

[0110]

[0111] Based on the above data methods, a multimodal public transport topology network is established. The network contains a total of 911 stations, including 869 bus stations and 42 subway stations. It also contains 2809 edges, including 2275 bus network segments, 86 subway network segments, and 448 transfer edges between the subway and bus networks.

[0112] Step 2: Obtain passenger flow data for subways and buses, count the origin-destination (OD) travel volume for each time period, and establish a multi-modal public transport passenger flow network for each time period.

[0113] The study used bus and subway card swipe data from five working days, from May 17th to May 21st, 2021. Bus data included passenger card numbers, boarding times, boarding stops, boarding routes, and vehicle numbers. Subway data included passenger card numbers, entry times, entry stops, exit times, and exit stops. A total of 3.8 million data entries were collected, with examples shown in Tables 4 and 5.

[0114] Table 4 Example of bus card swiping data

[0115]

[0116] Table 5. Examples of subway card swiping data

[0117]

[0118] like Figure 2 As shown, statistical analysis of OD (Original Departure) travel volume was conducted for each time period, selecting the morning peak (8:00-9:00), midday off-peak (12:00-13:00), and evening peak (17:00-18:00) as the research subjects. A multimodal public transport passenger flow network was established for each time period. The flow networks for the three time periods are denoted as follows: , , The weights of the edges in the traffic flow network represent the passenger flow during that time period, and the shortest travel time represents the travel time of the shortest path calculated using the weighted Dijkstra algorithm, including travel time and transfer time between stations. Examples of the edges and weights of the three multimodal public transport traffic flow networks are shown in Tables 6-8.

[0119] Table 6. Network Edges and Corresponding Weights of Multimodal Public Transport Flow During Morning Peak

[0120]

[0121] Table 7. Network Edges and Corresponding Weights of Multimodal Bus Traffic Flow During Off-Peak Hours

[0122]

[0123] Table 8. Network Edges and Corresponding Weights of Multi-Mode Public Transport Flow During Evening Peak

[0124]

[0125] Step 3: Calculate the site load for each time period and calculate the site capacity based on the nonlinear capacity load model.

[0126] The load of each site in three time periods is calculated based on the nonlinear capacity-load model proposed in this paper. , , and capacity The values ​​of α and β are set to 0.5. Example results are shown in Table 9.

[0127] Table 9. Site load and capacity for each time period

[0128]

[0129] Step 4: Based on the constructed multimodal bus topology network, multimodal bus passenger flow network, and station capacity, simulate the cascading failure process after station failure, and establish passenger flow allocation rules that take into account passenger travel behavior to obtain the multimodal bus network after cascading failure in each time period.

[0130] Taking the multimodal bus network during the morning rush hour as an example, Nanjing Station was selected as the ineffective station.

[0131] (1) Initialize the multi-mode bus topology network based on steps 1 and 2. and multimodal public transport passenger flow network .

[0132] (2) Obtain the load of each site based on step 3. and site capacity .

[0133] (3) Select Nanjing Station as the failed station, in Delete the node corresponding to Nanjing Station and the corresponding edge connected to it.

[0134] (4) For example Figure 3 As shown, the destination after Nanjing Station becomes unavailable is... (The following example uses the destination station, Dingshan Hotel, to analyze passenger flow and search the site.) exist All neighboring stations in the network. Iterate through all neighboring stations and calculate the total time it takes for the passenger to walk to any neighboring station in the network and from that neighboring station to the destination station. The results are shown in Table 10.

[0135] Table 10 Walking time from the failed site to neighboring nodes and total time to the destination

[0136]

[0137] (5) Calculate the transfer probability of passengers moving to all neighboring stations based on the multinomial logit model, where, Set it to 20. The calculation results are shown in Table 11.

[0138] Table 11. Transfer probability of passengers moving to all neighboring stations

[0139]

[0140] (6) Assign passengers to transfer stations based on the transfer probabilities of each neighboring station. In this case, the assigned neighboring station is Nanjing Station South Square West, and the updated shortest travel time is 22.08 minutes.

[0141] (7) Determine when the ratio of the updated shortest travel time to the original network's shortest travel time is greater than the passenger's tolerance threshold TT. In this case, the original network's shortest travel time is 20.75 minutes, and TT is set to 1.5. Since 22.08 / 20.75 < 1.5, the passenger flow that originally started at Nanjing Station and ended at Dingshan Hotel was transferred to Nanjing Station South Square West.

[0142] (8) Update the load of neighboring stations after passenger flow allocation. In this case, due to the failure of Nanjing Station, the passenger flow allocated to Nanjing Station South Square West is 488. The load and capacity of Nanjing Station South Square West are 344 and 393, respectively.

[0143] The Nanjing Railway Station South Square West Plaza is inoperable due to its own passenger load exceeding its allocated capacity. Delete the corresponding node of Nanjing Station South Square West and the corresponding edge connected to it.

[0144] (9) Repeat steps 4-8 until no more sites fail.

[0145] The results showed that the failure of Nanjing Station caused a cascading failure of 262 other stations.

[0146] Step 5: Based on the multi-mode bus network after cascading failure, calculate the maximum network connectivity after each station fails in each time period.

[0147] Based on the network status of the multi-mode bus network after cascading failure, the maximum network connectivity after the failure of different stations in different time periods is calculated. The results are shown in Table 12.

[0148] Table 12 Maximum network connectivity after different sites fail during different time periods

[0149]

[0150] Step 6: Based on the multi-mode bus network after cascading failure, calculate the network operation efficiency after each station fails in each time period.

[0151] Based on the network status of the multi-mode bus network after cascading failure, the network operation efficiency after the failure of different stations in different time periods is calculated, and the results are shown in Table 13.

[0152] Table 13 Network operating efficiency after different sites fail at different times

[0153]

[0154] Step 7: Based on the multi-mode bus network after cascading failure, calculate the passenger loss rate after each station fails at each time period.

[0155] Based on the network status of the multi-mode bus network after cascading failure, the passenger loss rate after the failure of different stations in different time periods is calculated. The results are shown in Table 14.

[0156] Table 14 Passenger Loss Rate After Different Stations Failed During Different Time Periods

[0157]

[0158] Step 8: Based on the maximum network connectivity, network operating efficiency, and passenger loss rate after each site fails in each time period, calculate the comprehensive robustness index of each site in each time period, and evaluate the site areas that are prone to cascading failures in each time period based on the comprehensive robustness index.

[0159] Based on the maximum network connectivity, network operating efficiency, and passenger churn rate after each site failure in each time period, a comprehensive robustness evaluation matrix for each site is first established. This matrix is ​​then normalized to obtain a normalized comprehensive evaluation matrix. Next, the information entropy of the maximum network connectivity, network operating efficiency, and passenger churn rate for each time period is calculated, and the results are shown in Table 15. Based on this, the weights of the maximum network connectivity, network operating efficiency, and passenger churn rate for each time period are calculated, and the results are shown in Table 16. Finally, the comprehensive robustness index for each site in each time period is calculated, and the results are shown in Table 17.

[0160] Table 15 Information Entropy of Maximum Network Connectivity, Network Operating Efficiency, and Passenger Loss Rate for Each Time Period

[0161]

[0162] Table 16 Weights of Maximum Network Connectivity, Network Operating Efficiency, and Passenger Loss Rate for Each Time Period

[0163]

[0164] Table 17 Comprehensive Robustness Index of Different Sites in Different Time Periods

[0165]

[0166] The stations are ranked in descending order of their comprehensive robustness index. The higher the ranking of a station, the greater the impact of its cascading failure on the multimodal public transport network. Figure 4 , Figure 5 , Figure 6 The distribution of the comprehensive robustness index of stations in each time period is plotted based on the calculation results in Table 17.

[0167] This invention discloses a dynamic robustness analysis method for multimodal public transport networks considering passenger travel behavior. First, a multimodal public transport topology network and a multimodal public transport passenger flow network for each time period are established. Second, station load and capacity are calculated based on a nonlinear capacity-load model. Then, considering passenger travel mode selection and route planning behavior, the cascading failure process after station failure is simulated to obtain the multimodal public transport network after cascading failure. Finally, based on the maximum network connectivity, network operating efficiency, and passenger loss rate after each failed station in each time period, the comprehensive robustness of each station in each time period is calculated. Based on the comprehensive robustness, station areas prone to cascading failures in each time period are assessed. This invention comprehensively considers the dynamic time-varying characteristics of station passenger flow and passenger travel behavior, and can be used to assist public transport operators in analyzing the dynamic robustness of multimodal public transport networks, thereby providing decision support for emergency response plan development under sudden events.

[0168] Example 2:

[0169] This embodiment describes a computer-readable storage medium storing a computer program that, when executed by a processor, implements a dynamic robustness analysis method for a multimodal public transport network that considers passenger travel behavior, as described in any of Embodiment 1.

[0170] Example 3:

[0171] This embodiment describes an electronic device, including:

[0172] Memory is used to store instructions.

[0173] A processor is configured to execute the instructions, causing the electronic device to perform operations as described in any of Embodiment 1 of a method for dynamic robustness analysis of multimodal public transport networks that considers passenger travel behavior.

[0174] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0175] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0176] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0177] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0178] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A dynamic robustness analysis method for multimodal public transport networks considering passenger travel behavior, characterized in that: Includes the following steps: Step 1: Obtain subway and bus route and station data, as well as AVL data, and establish a multi-modal bus topology network; Step 2: Obtain passenger flow data for subways and buses, count the origin-destination (OD) travel volume for each time period, and establish a multi-modal public transport passenger flow network for each time period; Step 3: Calculate the site load for each time period and calculate the site capacity based on the nonlinear capacity load model; Step 4: Based on the constructed multimodal bus topology network, multimodal bus passenger flow network and station capacity, simulate the cascading failure process after station failure, and establish passenger flow allocation rules that take into account passenger travel behavior to obtain the multimodal bus network after cascading failure in each time period. Step 5: Based on the multi-modal bus network after cascading failure, calculate the maximum network connectivity after each station fails in each time period; Step 6: Based on the multi-mode bus network after cascading failure, calculate the network operation efficiency after each station fails in each time period; Step 7: Based on the multi-mode bus network after cascading failure, calculate the passenger loss rate after each station fails at each time period.

2. The method for dynamic robustness analysis of multimodal public transport networks considering passenger travel behavior as described in claim 1, characterized in that: Also includes: Step 8: Based on the maximum network connectivity, network operating efficiency, and passenger loss rate after each site fails in each time period, calculate the comprehensive robustness index of each site in each time period, and evaluate the site areas that are prone to cascading failures in each time period based on the comprehensive robustness index.

3. A dynamic robustness analysis method for multimodal public transport networks considering passenger travel behavior, as described in claim 1 or 2, is characterized in that: The establishment of the multi-modal public transport topology network specifically includes: Step 1.1: Based on subway and bus route and station data, establish a bus topology network using a physical network modeling method. and subway topology network ,in, , When two stations are adjacent on a subway or bus line, they are considered to have a station segment edge between them; among them, Represents the subway topology network; Indicates a group of subway stations; Represents the set of station segments and edges in a subway network; Represents the public transport topology network; Indicates a set of bus stops; Represents the set of station segments and edges in a public transport network; Step 1.2: Based on the spatial location of subway and bus stations, search for bus stations within walking distance of subway stations. When the distance between a subway station and a bus station is less than R, it is considered that there is a bidirectional transfer edge between the subway station and the bus station. The set of all identified transfer edges is denoted as . Where R is the distance threshold; Step 1.3: Based on the AVL data of bus and subway lines, calculate the set of station edges in the subway network. and the station sections of the public transport network The corresponding time weights are denoted as follows: and Time weighting represents the average travel time of vehicles between adjacent stations. Step 1.4: Calculate the transfer edge based on the location data of subway stations and bus stops. Time weight Among them, the site and The formula for calculating the time weight of the transfer edges between them is as follows: ； in, Indicates site and Time weights of transfer edges between them; Indicates site and Walking distance between Indicates the passenger's walking speed; Step 1.5: Construct a multimodal public transport topology network , ;in, , Represents a collection of sites. This represents the i-th site in the set of sites. This indicates the number of all stops in a multimodal transit network. , Denotes the set of edges. Indicating the set of edges and The edges connecting them; , This represents the set of weights corresponding to the edges. This represents the weight set of the edges. The corresponding weights .

4. A dynamic robustness analysis method for multimodal public transport networks considering passenger travel behavior, as described in claim 1 or 2, characterized in that: The establishment of a multi-modal public transport passenger flow network for different time periods specifically includes: Step 2.1: Based on passenger subway and bus card swipe data, calculate passenger flow between stations in different time periods. When at station t in time period t... and When there is passenger flow between them, there is a flow edge. The weight of the flow edge is denoted as , Station t represents time period t and Passenger flow between; Step 2.2: For the flow edge Calculating stations based on multi-mode bus topology network and Travel time between Travel time For the site and The travel time of the shortest path between stations, including travel time and transfer time between stations; Step 2.3: Construct a multimodal public transport passenger flow network for time period t , ;in, Represents a collection of sites; , Represents the set of flow edges in the multi-modal public transport passenger flow network during time period t; , This represents the set of weights corresponding to the flow edges; This represents the set of shortest travel times corresponding to the flow edges. .

5. A dynamic robustness analysis method for multimodal public transport networks considering passenger travel behavior, as described in claim 1 or 2, characterized in that: The calculation of site capacity based on the nonlinear capacity-load model specifically includes: Step 3.1: Calculate the stations for each time period t. The site load is calculated using the following formula: ； in, Indicates site Site load during time period t; Step 3.2: Calculate the site The maximum load for the entire day is calculated using the following formula: ； in, This represents a set of time periods that divide the entire day. Indicates site Maximum daily load; Step 3.3: Calculate the site based on the nonlinear load model The capacity is calculated using the following formula: ； Where α and β are the capacity control coefficients of the nonlinear load model; Indicates site The capacity.

6. A method for dynamic robustness analysis of multimodal public transport networks considering passenger travel behavior, as described in claim 1 or 2, characterized in that: Step 4 specifically includes: Step 4.1: Initialize the multi-mode bus topology network for time period t and multimodal public transport passenger flow network ; Step 4.2: Obtain the site for time period t Site load and site capacity ; Step 4.3: Select any site As a failed object, in a multi-modal bus topology network Delete the site and its corresponding edges; Step 4.4: Targeting the site The destination after failure is Traffic, search sites In multimodal public transport topology network All neighboring sites in the set, denoted as . traversal Calculate the passenger's walking distance to all neighboring stations. any of the sites and from To the destination Total time ; ； in, Indicates site and Walking distance between; Indicates the passenger's walking speed; Indicates from To the destination The shortest travel time; Step 4.5: Calculate passenger transfer to stations based on discrete choice model probability ; ； in, Indicates the starting point is a station. Destination is Passenger traffic shifted to the station The probability of These are control parameters used to measure passengers' sensitivity to travel time. Step 4.6: Based on the transfer probability of each neighboring station, assign the passenger to a neighboring station for transfer, and record the passenger's travel time after being assigned to a specific neighboring station as the updated shortest travel time. ; Step 4.7: When the updated shortest travel time and the shortest travel time when the multi-modal transit topology network is not attacked The ratio is greater than the passenger tolerance threshold TT, that is / > TT, the passenger flow between OD pairs is lost and is considered to be transferred to other travel modes; conversely, when / < TT, the passenger flow between this OD pair is assigned to the transferred neighbor stations; Step 4.8: Update neighboring sites after passenger flow allocation Site load When the site Site load Larger than the site capacity At that time, the site Failure, in Deleting a site and its corresponding connecting edges; ； Step 4.9: Repeat steps 4.4-4.8 until no station fails, and output the multi-mode bus network that caused cascading failures due to station failures during this period.

7. A method for dynamic robustness analysis of multimodal public transport networks considering passenger travel behavior, as described in claim 1 or 2, characterized in that: The method for calculating the maximum network connectivity after each site fails in each time period is expressed as follows: ； in: This represents the maximum network connectivity of the multimodal bus network after the cascading failure in time period t. N represents the number of stations in the largest connected subgraph of the multimodal bus topology network after cascading occurs in time period t; N represents the number of stations in the multimodal bus network when it is not under attack. The method for calculating network operating efficiency after each site fails in each time period is expressed as follows: ； in: Network operation efficiency of multi-mode bus network after time period t cascade failure; Station t represents time period t and Passenger flow between; Indicates the site after the cascading fails during time period t. and The shortest travel time between; N represents the number of stops in the multimodal transit network when it is not under attack; The method for calculating the passenger loss rate after each station fails in each time period is expressed as follows: ； In the formula: ; in: Passenger loss rate of multi-modal bus network after time period t cascade failure; Station t represents time period t and Passenger flow between; Indicates from and Does the increase in travel time exceed passengers' tolerance threshold? Indicates the site after the cascading fails during time period t. and The shortest travel time between; This indicates the number of stations in the multi-modal transit network during time period t when they are not under attack. and The shortest travel time between; TT represents the passenger's tolerance threshold for increased travel time; N represents the number of stops in the multimodal transit network when it is not under attack.

8. The method for dynamic robustness analysis of multimodal public transport networks considering passenger travel behavior as described in claim 7, characterized in that: Step 8 is specifically described as follows: Step 8.1: Based on the maximum network connectivity, network operating efficiency, and passenger churn rate of each site after cascading failures in each time period t, establish a comprehensive robustness evaluation matrix for each site. The comprehensive robustness evaluation matrix is ​​expressed as follows: ； in, This represents the maximum network connectivity of the multimodal transit network after the cascading failure at station N during time period t. This represents the network operating efficiency of the multi-mode bus network after the cascading failure of station N during time period t. This represents the passenger loss rate of the multimodal bus network after the cascading failure of station N during time period t. Step 8.2: Evaluation of the comprehensive robustness matrix Normalization is performed to convert the absolute values ​​of each indicator into relative values, resulting in a normalized comprehensive evaluation matrix. ; ； in, This represents the normalized value of the maximum network connectivity of the multimodal transit network after the cascading failure of station N during time period t. This represents the normalized value of the network operating efficiency of the multimodal transit network after the cascading failure of station N during time period t. This represents the normalized value of the passenger loss rate of the multimodal bus network after the failure of the cascading system at station N during time period t. Step 8.3: Calculate the information entropy of three indicators: maximum network connectivity, network operating efficiency, and passenger churn rate. , , ; ； ； ； in, This represents the normalized value of the maximum network connectivity of the multimodal transit network after the cascading failure at station i during time period t. This represents the normalized value of the network operating efficiency of the multimodal bus network after the cascading failure at station i during time period t. This represents the normalized value of the passenger loss rate of the multimodal bus network after the cascading failure of station i in time period t. Step 8.4: Calculate the weights of the three indicators: maximum network connectivity, network operating efficiency, and passenger churn rate. , , ; ； ； ； Step 8.5: Calculate the values ​​for each station Comprehensive robustness index for time period t The overall importance of each site was ranked from highest to lowest, with higher-ranked sites being more prone to cascading failures. Among these, the overall robustness index... The expression is as follows: 。 9. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed by a processor, implements a dynamic robustness analysis method for multimodal public transport networks that considers passenger travel behavior, as described in any of claims 1 to 8.

10. An electronic device, characterized in that: include: Memory, used to store instructions; A processor is configured to execute the instructions, causing the electronic device to perform operations as described in any one of claims 1 to 8, a method for dynamic robustness analysis of multimodal public transport networks that takes into account passenger travel behavior.

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