Cascade failure analysis method and system for urban rail transit network

Abstract

The invention discloses an urban rail transit network cascade failure analysis method and system, and belongs to the technical field of rail transit and control science. Identifying key stations of the urban rail transit time-varying network of each time step; marking the sites attacked by the key sites as invalid sites; for the unattacked sites, whether the sites fail or not is judged by comparing whether the real-time load of each site of the urban rail transit time-varying network of each time step exceeds the self capacity of the corresponding site or not, and the sites with the real-time loads exceeding the self capacity are marked as failure sites; obtaining the residual capacity of a station adjacent to the failed station, and redistributing the real-time load of the failed station; and analyzing the cascade failure process of the urban rail transit network according to the redistribution result. According to the method, the dynamic change of the key stations of the time-varying network of the urban rail transit in the cascade failure process can be accurately grasped, so that the cascade failure process of the urban rail transit network is better analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit and control science, and more specifically to a method and system for analyzing cascading failures of an urban rail transit network. Background Art

[0002] With the continuous acceleration of urbanization, the status of urban rail transit in public transportation has gradually become prominent, the scale of urban rail transit has continued to expand, and it has begun to enter the network operation stage. The urban rail transit network is usually composed of multiple stations and lines, which are closely coupled in time and space to form a highly complex network. With the continuous expansion of the network scale and passenger flow, the operating load of the urban rail transit network has continued to increase, and the number of operational interruptions caused by emergencies has also continued to increase. In particular, some major operational accidents have had a serious impact on the operation of urban rail transit and even the safety of passengers.

[0003] Urban rail transit networks usually bear a certain load, but the storage and bearing capacity of each station is limited. When the load increases to a certain extent, some stations will fail due to overload. Due to the high coupling and interdependence between the various stations in the network, when a station fails, it may trigger a chain reaction, leading to further failure of the entire network. This phenomenon is called cascading failure. In the urban rail transit network, some stations are more likely to cause cascading failures after failure due to their own location or the importance of their functions, and the failure time is longer and the damage is greater. These stations are critical stations. The network cascading failure caused by the failure of critical stations seriously affects the performance of the entire network. At the same time, due to changes in the network topology and station passenger flow, the importance of the station also changes accordingly, and the key stations in different time periods are not the same. Therefore, it is very important to explore the mechanism of cascading failure of urban rail transit networks and ensure the safe operation and reliability of the network for the network operation of urban rail transit.

[0004] At present, the analysis methods for cascading failures in urban rail transit networks mainly focus on static network models or simple topological structure analysis. These methods usually assume that the stations and lines in the network remain stable and unchanged, and do not fully consider the spatiotemporal heterogeneity of passenger flow distribution, the differences in the importance of different stations, and the actual load changes in network operation. In the key station identification link of cascading failure analysis, it is not fully recognized that the importance of the station will change with the spatiotemporal changes of network topology and passenger flow distribution. Common methods for identifying key stations in urban rail transit networks are mostly based on the topological structure of the network or combined with the static distribution of passenger flow, and the identification of key stations remains at the static level. Existing research methods for cascading failures in urban rail transit networks mostly focus on local failures, and lack a comprehensive analysis of the impact of key stations on cascading failures.

[0005] In summary, the existing analysis method of cascading failure of urban rail transit network cannot effectively identify the key stations of the urban rail transit network when facing the cascading failure occurring in the actual operation of the urban rail transit network, which affects the accurate analysis of the cascading failure. Summary of the invention

[0006] In response to the problems existing in the above-mentioned fields, the present invention proposes a method and system for analyzing cascading failures of urban rail transit networks. Based on the established urban rail transit time-varying network, by determining the comprehensive importance of each station in the urban rail transit time-varying network at the current time step, the key stations in the urban rail transit network can be accurately and dynamically identified, and by simulating different failure scenarios of each station, the impact of each station on cascading failures can be accurately analyzed.

[0007] In order to solve the above technical problems, the present invention discloses a method for analyzing cascading failure of urban rail transit network, comprising the following steps:

[0008] Establish an urban rail transit time-varying network, and obtain the capacity of each station by determining the passenger flow of each station in the urban rail transit time-varying network and the maximum passenger flow of each station at the initial time step;

[0009] Determine the comprehensive importance of each station in the urban rail transit time-varying network at the current time step, and identify the key stations in the urban rail transit time-varying network at each time step;

[0010] The urban rail transit time-varying network at each time step is traversed in a loop, and the stations at the current time step of the urban rail transit time-varying network are judged based on historical data whether they will be attacked by key stations, and the attacked stations are marked as failed stations; for the stations that are not attacked, whether the real-time load of each station in the urban rail transit time-varying network at each time step exceeds the corresponding station's own capacity is compared to judge whether each station is failed, and the stations whose real-time load exceeds their own capacity are marked as failed stations;

[0011] Obtain the remaining capacity of the neighboring sites of the failed site and redistribute the real-time load of the failed site;

[0012] According to the redistribution results, the cascading failure process of the urban rail transit network is analyzed by determining the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step.

[0013] Preferably, the establishment of a time-varying urban rail transit network specifically includes:

[0014] Through the connection relationship between urban rail transit lines and stations, and taking the interval running time as the weight, a weighted network of urban rail transit is established;

[0015] Based on the constructed urban rail transit weighted network at the current time step, the Dijkstra algorithm is used to calculate the shortest path set between each station at the current time step;

[0016] Read the passenger's travel data at the current time step, including the passenger's card number, current station, final station, and arrival time;

[0017] Read the urban rail transit card swiping data of the current time step, including the passenger's card number, starting line, starting station, departure time, terminal line, terminal station and arrival time, and update these data to the passenger travel data of the current time step. The data items include the passenger's card number, current station, terminal station and arrival time.

[0018] Based on the passenger travel data of the current time step, according to the passenger's current station and terminal station, the passenger flow of the OD pairs in the current time step is counted, and the passenger flow OD matrix of the current time step is constructed;

[0019] Get the current station and terminal station of the passenger in the passenger travel data at the current time step, and extract the passenger's travel path from the shortest path set:

[0020] {C L}={c 1 ,c 2 ,K,c i ,K,c L}

[0021] Where L represents the length of the passenger's travel path, c i represents the i-th station that the passenger passes through;

[0022] By judging whether L in the travel path is equal to 1, when L in the travel path is equal to 1, the passenger arrives at the terminal and is deleted from the passenger travel data;

[0023] Otherwise, according to the passenger's travel path, the current station of the passenger and the second station in the travel path are obtained, the interval running time td between the current station and the second station is obtained, and it is determined whether the interval running time td is less than the time-varying network update time difference t;

[0024] When the interval running time td is less than the time-varying network update time difference t, update the passenger travel data, and the current station is updated to the second station in the passenger travel path. Other data remain unchanged. Determine whether the difference between the time difference t and the interval running time td is less than the time threshold TD. If so, do not update the passenger travel data. If not, reduce the interval running time td by the time difference t, and return to the step of constructing the passenger flow OD matrix of the current time step.

[0025] When the interval running time td is greater than or equal to the time-varying network update time difference t, it is determined whether the difference between the time difference td and the running time t is less than the time threshold TD. If so, the passenger travel data is updated, and the current station is updated to the second station in the passenger travel path, and other data remain unchanged; if not, the passenger travel data is not updated;

[0026] The urban rail transit time-varying network is established by using the urban rail transit weighted network at each time step and combining the passenger flow of each OD pair of the urban rail transit network at each time step.

[0027] Preferably, the urban rail transit time-varying network is:

[0028] G t =(V,E t ,W,H t )

[0029] In the formula, is the set of edges in the network at time t, Indicates the time t from site v i To site v j The side of H t ={h i (t)}(i=1,2,3...,N) is the passenger flow set of the station at time t, h i (t) represents the site v at time t i The amount of passenger traffic carried;

[0030]

[0031] In the formula, f ij (t) and f ji (t) represents the time step t at site v i is the cross-sectional passenger flow at the departure and destination, f i (t) represents the path site v in time step t i passenger flow.

[0032] Preferably, the obtaining of the capacity of each site specifically includes:

[0033] Initialize the load of each site:

[0034] L i (0) = h i (t)

[0035] Where, L i (0) is site v i Initial load; h i (t) is the time when the cascading failure starts at site v i The calculation formula of the station load after the cascade failure occurs t′ is:

[0036] L i (t′) = h i (t+t′)

[0037] Where, L i (t′) is the site v i The load after the cascading failure occurs t′ time step; h i (t+t′) is the site v after t′ time step of cascading failure i passenger flow;

[0038] The site capacity is:

[0039] C i =(1+α)h i (max)

[0040] In the formula, C i is the site's own capacity; h i (max) is the maximum passenger flow of the station; α is the capacity parameter.

[0041] Preferably, the identifying of key sites of the urban rail transit time-varying network at each time step specifically includes:

[0042] The identification index of each site is divided into topological structure index, passenger flow index and network connectivity index;

[0043] By determining the subjective weight and objective weight of each indicator, the subjective weight and the objective weight are linearly combined to obtain the comprehensive weight;

[0044] With the goal of minimizing the difference between the comprehensive weight and the subjective weight and objective weight, the linear combination coefficient of the comprehensive weight is optimized to obtain the optimal comprehensive weight;

[0045] Get the time step t site v respectively i The degree centrality index, betweenness centrality index, closeness centrality index, eigenvector centrality index, passenger flow centrality index, and time step t station v i The values ​​of network efficiency loss and maximum connected subgraph change before and after failure;

[0046] According to the optimal comprehensive weight and the corresponding values ​​of each indicator, a standardized weighted decision matrix for each station at time step t is constructed. Matrix Elements The calculation method is as follows:

[0047]

[0048] In the formula, is the constituent element of the standardized weighted decision matrix at time step t, ωj is the optimal comprehensive weight for the j-th index, for site v i is the standardized value of index j at time step t for site v;

[0049] Based on the standardized weighted decision matrix at time step t, obtain the positive and negative ideal solutions of the index values of each site at this time step. Take the maximum value of each column as the positive ideal solution vector, and the minimum value of each column as the negative ideal solution vector;

[0050] Respectively determine the Mahalanobis distance and grey correlation degree between site v i at time step t and the positive and negative ideal solutions. Perform dimensionless processing on the Mahalanobis distance and grey correlation degree, and correspondingly calculate the comprehensive distance between site v i at time step t and the positive and negative ideal solutions;

[0051] Based on the comprehensive distance, calculate the comprehensive importance of site v i at time step t; the larger the comprehensive importance value, the more important the site;

[0052] Sort the comprehensive importance values of each site in the time-varying network of urban rail transit at the same time step, and take the site with the largest value as the key site of the time-varying network of urban rail transit at this time step.

[0053] Preferably, marking the site with real-time load exceeding its own capacity as a failed site specifically includes:

[0054] According to the historical data of the time-varying network of urban rail transit, judge whether each site in the time-varying network of urban rail transit at the current time step will be attacked by the key site through simulation. Mark the site attacked by the key site as a failed site; mark the site not attacked by the key site as a normal site;

[0055] For the site not attacked by the key site, that is, the normal site, judge the status of the site by comparing whether the real-time load of each site in the time-varying network of urban rail transit at the current time step exceeds the site's own capacity;

[0056] When the real-time load of each site in the time-varying network of urban rail transit at the current time step being checked exceeds the site's own capacity, then mark the site as a failed site; otherwise, the site remains a normal site;

[0057] The judgment method is:

[0058]

[0059] In the formula, L i (t′) is the load of site v i at the failure time step t′, and C i is the capacity of site vi own capacity.

[0060] Preferably, the real-time load of the failed site is redistributed, specifically including:

[0061] By checking whether there is a failed station in the urban rail transit time-varying network at the current time step, if there is, the load of the failed station is redistributed, if not, the cascading failure process ends;

[0062] By calculating the remaining capacity of the neighboring sites of the failed site at failure time step t′, the load of the failed site is redistributed;

[0063] Failure time step t′ Failure site v i Assigned to neighboring site v j Load ΔL ij (t′) is:

[0064]

[0065] Where, L j (t′) represents the site v j The load at failure time step t′, L i (t′) is the site v i Load at failure time step t′.

[0066] Preferably, the analysis of the cascading failure process of the urban rail transit network includes:

[0067] According to the redistribution results, the total number of sites in the maximum connected subgraph after the site fails and the load of each site after the site fails are determined;

[0068] Determine the maximum connectivity coefficient based on the total number of sites in the maximum connected subgraph after the site fails and the total number of sites in the initial network;

[0069] The maximum connectivity coefficient is:

[0070]

[0071] Where S is the maximum connectivity coefficient, N' is the total number of sites in the maximum connected subgraph after the site fails, and N is the total number of sites in the initial network;

[0072] Determine the proportion of lost passenger flow based on the load of each station after the station failure and the initial load of each station under normal operation;

[0073] The loss of passenger flow ratio is:

[0074]

[0075] Where LPF is the loss passenger flow ratio, L′(t) is the station load at time t after the station fails, and L(t) is the initial load of the station at time t under normal operation;

[0076] By analogy, the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step are calculated, and the cascading failure process of the urban rail transit time-varying network is analyzed.

[0077] Preferably, the establishment of a weighted urban rail transit network specifically includes:

[0078] According to the connection relationship between sites and lines, an adjacency matrix is ​​established;

[0079] The adjacency matrix is:

[0080]

[0081] The element a in the matrix ij Indicates site v i and v j The connection relationship between them, where a ij The value determination is:

[0082]

[0083] According to the established adjacency matrix, with interval running time as weight, the urban rail transit weighted network is established as follows:

[0084] G=(V,E,W)

[0085] Where, V = {v i}(i=1,2,3...,N) is the set of sites in the network; v i represents the i-th station in the urban rail transit network; E = {e ij}(i,j=1,2,3...,N and i≠j) is the set of edges in the network; e ij Indicates that from site v i To site v j The edge of ij}(i,j=1,2,3...,N and i≠j) is the weight set of the edge; w ij Represents edge e ij The weight of the site v i To site v j interval running time; N is the total number of sites in the initial network.

[0086] Preferably, it also includes a system for analyzing cascading failures of urban rail transit networks, comprising:

[0087] The urban rail transit time-varying network construction module is used to establish the urban rail transit time-varying network, and obtain the capacity of each station by determining the passenger flow of each station in the urban rail transit time-varying network at the initial time step and the maximum passenger flow of each station;

[0088] The key station dynamic identification module is used to determine the comprehensive importance of each station in the urban rail transit time-varying network at the current time step and identify the key stations in the urban rail transit time-varying network at each time step;

[0089] The station status judgment module is used to loop through the urban rail transit time-varying network at each time step, and judge whether each station of the urban rail transit time-varying network at the current time step will be attacked by key stations based on historical data, and mark the attacked stations as failed stations; for the stations that have not been attacked, by comparing whether the real-time load of each station of the urban rail transit time-varying network at each time step exceeds the corresponding station's own capacity, judge whether each station is failed, and mark the station whose real-time load exceeds its own capacity as a failed station;

[0090] A failed site load redistribution module is used to obtain the remaining capacity of the failed site's neighboring sites and redistribute the real-time load of the failed site;

[0091] The cascading failure analysis module is used to analyze the cascading failure process of the urban rail transit network by determining the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step according to the redistribution results.

[0092] Compared with the prior art, the present invention has the following beneficial effects:

[0093] The method for analyzing the cascading failure of the urban rail transit network proposed in the present invention establishes an urban rail transit time-varying network, obtains the comprehensive importance of each station of the urban rail transit time-varying network at the current time step, and the greater the value of the comprehensive importance, the more important the station is, and can dynamically and accurately identify the key stations of the urban rail transit time-varying network. By judging whether each station of the urban rail transit time-varying network at the current time step will be attacked by the key station, the attacked station will be marked as a failed station; the station that has not been attacked is determined by comparing the real-time load of each station of the urban rail transit time-varying network at each time step with the corresponding station's own capacity, and the status of each station is determined, so as to provide theoretical support for further analyzing the cascading failure caused by the failure of the key station in the urban rail transit network under different circumstances. When the current station under inspection is a failed station, the real-time load of the failed station is redistributed, and the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step are determined, and the cascading failure process of the urban rail transit network is analyzed, and the influence of each station on the cascading failure is analyzed, so as to improve the stability and safety of the urban rail transit system, and provide a scientific basis for the planning, design, operation and maintenance and emergency response plan of the urban rail transit system. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 It is a flow chart of the urban rail transit network cascading failure analysis method of the present invention;

[0095] Figure 2 This is a diagram of the architecture of the urban rail transit network cascading failure analysis method of the present invention;

[0096] Figure 3 identifying a hierarchy of indicators for each site of the present invention;

[0097] Figure 4 A topological diagram of a city's rail transit network provided by an embodiment of the present invention;

[0098] Figure 5 A schematic diagram of a time-varying network of urban rail transit provided by an embodiment of the present invention;

[0099] Figure 6 Changes in the loss passenger flow ratio LPF of different attack modes provided in the embodiments of the present invention;

[0100] Figure 7 The changes of the maximum connectivity coefficient S of different attack modes provided in the embodiments of the present invention. DETAILED DESCRIPTION

[0101] The following will be combined with the attached embodiment of the present invention Figure 1-Figure 7, the technical solutions in the embodiments of the present invention are clearly and completely described. It should be understood that the terms described in the present invention are only used to describe specific implementation methods and are not used to limit the present invention.

[0102] like Figure 1 As shown, the present invention proposes a method for analyzing cascading failures of urban rail transit networks, comprising the following steps:

[0103] S1: Based on the connection relationship between urban rail transit lines and station data, the interval running time is used as the weight to establish an urban rail transit weighted network.

[0104] Step S1.1: Establish an adjacency matrix based on the connection relationship between sites and lines;

[0105] The adjacency matrix A is defined as:

[0106]

[0107] Element a in the adjacency matrix ij Indicates site v i and v j The connection relationship between ij The value of is determined according to the following formula:

[0108]

[0109] Step S1.2: Based on the adjacency matrix, the urban rail transit weighted network is established with the interval running time as the weight:

[0110] G=(V,E,W)

[0111] Where, V = {v i}(i=1,2,3...,N) is the set of sites in the network; v i represents the i-th station in the urban rail transit network; E = {e ij}(i,j=1,2,3...,N and i≠j) is the set of edges in the network; e ij Indicates that from site v i To site v j The edge of ij}(i,j=1,2,3...,N and i≠j) is the weight set of the edge; w ij Represents edge e ij The weight of the site v i To site v j The interval running time; N is the total number of sites in the initial network.

[0112] S2: Based on the subway card swiping data and combined with the weighted network of urban rail transit at each time step, the travel volume of the OD pair at each time step, that is, the passenger flow of the OD pair at each time step, is calculated.

[0113] Step S2.1: Based on the urban rail transit weighted network at the current time step, the Dijkstra algorithm is used to calculate the shortest path set between the stations at the current time step.

[0114] Step S2.2: Read the passenger travel data of the current time step, including the passenger's card number, current station, terminal station, and arrival time.

[0115] Step S2.3: Read the urban rail transit card swiping data of the current time step, including the passenger's card number, starting line, starting station, departure time, terminal line, terminal station and arrival time. Update these data to the passenger travel data of the current time step, and the data items include the passenger's card number, current station (i.e. starting station), terminal station and arrival time.

[0116] Step S2.4: Based on the passenger travel data of the current time step, according to the passenger's current station and terminal station, the travel volume of the OD pairs in the current time step is counted, and the passenger flow OD matrix of the current time step is constructed.

[0117] Step S2.5: Obtain the current station and the terminal station of the passenger in the passenger travel data of the current time step, and extract the passenger's travel path from the shortest path set, as shown in the following formula:

[0118] {C L}={c 1 ,c 2 ,K,c i ,K,c L}

[0119] Where L represents the length of the passenger's travel path, c i It represents the i-th station that the passenger passes through.

[0120] Determine whether L in the travel path is equal to 1. If so, the passenger arrives at the terminal and is deleted from the passenger travel data. Otherwise, go to step S2.6.

[0121] Step S2.6: According to the passenger's travel path, obtain the passenger's current station and the second station in the travel path, and obtain the interval running time td between the current station and the second station. Determine whether the interval running time td is less than the time-varying network update time difference t. If so, go to step S2.7; if not, go to step S2.8.

[0122] Step S2.7: Update the passenger travel data, update the current station to the second station in the passenger travel path, and keep other data unchanged. Determine whether the difference between the time difference t and the interval running time td is less than the time threshold TD. If so, do not update the passenger travel data. If not, reduce the interval running time td by the time difference t, and go to step S2.4.

[0123] Step S2.8: Determine whether the difference between the time difference td and the running time t is less than the time threshold TD. If so, update the passenger travel data, and the current station is updated to the second station in the passenger travel path, and other data remain unchanged; if not, do not update the passenger travel data.

[0124] S3: Considering the network topology structure at each time step and the passenger flow of each OD pair, a time-varying network of urban rail transit is established.

[0125] The urban rail transit time-varying network is expressed as:

[0126] G t =(V,E t ,W,H t )

[0127] in, is the set of edges in the network at time t, Indicates the time t from site v i To site v j The side of H t ={h i (t)}(i=1,2,3...,N) is the passenger flow set of the station at time t, h i (t) represents the site v at time t i The amount of passenger traffic carried.

[0128] h i The calculation formula of (t) is as follows:

[0129]

[0130] Among them, f ij (t) and f ji (t) represents the time step t at site v i is the cross-sectional passenger flow at the departure and destination, f i (t) represents the path site v in time step t i passenger flow.

[0131] S4: Use a combination of subjective and objective indicator weight determination methods to determine the identification indicator weights of each station in the urban rail transit time-varying network.

[0132] Step S4.1: Decompose the identification indicators of each site from top to bottom into the target layer, criterion layer, and indicator layer, such as Figure 3 As shown in the figure, it is the hierarchical structure of site identification indicators. The target layer is site identification. The criterion layer includes topological structure indicators, passenger flow indicators and network connectivity indicators. In the indicator layer, the topological structure indicators include degree centrality, betweenness centrality, closeness centrality and eigenvector centrality. The passenger flow indicator is the site passenger flow indicator. The network connectivity indicators include network efficiency loss value and maximum connected subgraph change value.

[0133] Step S4.2: Construct the AHP judgment matrix. According to the “1-9 scale method” shown in Table 1, the judgment matrix B of each level is obtained by pairwise comparison. n×n =(b ij ) n×n , where b ij is the comparison value of two elements, and n is the order of the judgment matrix.

[0134] The judgment matrix is ​​shown as follows:

[0135]

[0136] The matrix element b ij It should have the following properties:

[0137]

[0138] Table 1 Judgment matrix scale and its meaning

[0139] Scale meaning 1 Equally important 2 Between equally important and slightly more important 3 Slightly important 4 Between slightly important and significantly important 5 Clearly important 6 Between obviously important and strongly important 7 Strongly important 8 Between Strongly Important and Absolutely Important 9 Absolutely important

[0140] Step S4.3: Check the consistency of the judgment matrix. When the consistency judgment coefficient CR≤0.1, the judgment matrix meets the consistency requirements. The calculation formula of CR is as follows:

[0141]

[0142] In the formula, CR is the consistency judgment coefficient, CI is the consistency judgment index, RI is the average consistency random index of the judgment matrix, and the value of RI is related to the order of the judgment matrix, as shown in Table 2. max is the maximum eigenvalue of the judgment matrix, and n is the order of the judgment matrix.

[0143] Table 2 Average consistency random index

[0144]

[0145]

[0146] Step S4.4: The weight calculation method is as shown in the following formula, and the weights of the criterion layer and the indicator layer are calculated respectively.

[0147]

[0148] In the formula, ω j is the weight of the jth factor, e=[e 1 ,e 2 ,...,e n ] is the maximum eigenvalue λ of the judgment matrix max The corresponding normalized eigenvector.

[0149] Step S4.5: The subjective weight of each site identification indicator is obtained by multiplying the criterion layer weight and the indicator layer weight accordingly, as shown in the following formula:

[0150]

[0151] In the formula, is the subjective weight of indicator j, is the weight of the criterion layer to which indicator j belongs, is the weight of indicator j under the same criterion layer.

[0152] Step S4.6: Standardize the index values ​​of each site. The standardization method is shown in the following formula:

[0153]

[0154] In the formula, x ij For site v i The value of index j, x′ ij is the index value after standardization.

[0155] Step S4.7: Calculate the standard deviation of each indicator. The calculation method is as follows:

[0156]

[0157] In the formula, σ j is the standard deviation of index j, is the standardized mean of indicator j.

[0158] Step S4.8: Use the Pearson correlation coefficient method to determine the correlation between the indicators. The calculation method is as follows:

[0159]

[0160] In the formula, s jk is the Spearman correlation coefficient between indicator j and indicator k, d i For site v i The level difference of N is the total number of sites, r ij With r ik Site v i The rank of index j and index k.

[0161] Step S4.9: Based on the standard deviation and correlation coefficient, determine the objective weight of each indicator. The calculation method is as follows:

[0162]

[0163] In the formula, is the objective weight of indicator j, I j is the information content of indicator j;

[0164] Step S4.10: Linearly combine the subjective weight and the objective weight, as shown in the following formula:

[0165] W=β 1 W SW +β 2 W OW

[0166] Where W is the comprehensive weight vector, W SW is the subjective weight vector, W OW is the objective weight vector, β 1 With β 2 is the linear combination coefficient.

[0167] The linear combination coefficients are optimized with the goal of minimizing the difference between the comprehensive weight and the subjective weight and the objective weight to obtain the optimal comprehensive weight. The optimization model is shown in the following formula:

[0168] min(||WW SW || 2 +||WW OW || 2 )

[0169] st.β i >0,i=1,2

[0170] Step S4.11: According to the matrix differential theory, the first-order derivative condition for the above linear combination optimization model to achieve the optimal value is as follows:

[0171]

[0172] Step S4.12: Solve the above equation to obtain the optimal linear combination coefficient β 1 With β 2 , normalized according to the following formula:

[0173]

[0174] S5: Determine the starting time step of cascading failure, take the real-time passenger flow of the station as the station load, calculate the maximum number of connected subgraph stations of the urban rail transit network and the passenger flow of each station in the initial time step, and obtain the initial load and self-capacity of each station.

[0175] The initial load calculation method is as follows:

[0176] L i (0) = h i (t)

[0177] Where, L i (0) is site v i Initial load, h i (t) is the time when the cascading failure starts at site v i The site load calculation method after the cascade failure occurs t′ time is as follows:

[0178] L i (t′) = h i (t+t′)

[0179] Where, L i (t′) is the site v i The load after the joint failure occurs t′ time step, h i (t+t′) is the site v after t′ time step of cascading failure i passenger flow.

[0180] The site capacity calculation method is as follows:

[0181] C i =(1+α)h i (max)

[0182] In the formula, C i is the site’s own capacity, h i (max) is the maximum passenger flow of the station, and α is the capacity parameter.

[0183] S6: Based on the urban rail transit time-varying network at the current time step, identify the key stations of the urban rail transit network at the current time step.

[0184] Step S6.1: Time step t site v i The calculation method of the degree centrality index is as follows:

[0185] DC i (t) = k i (t)

[0186]

[0187] Where, DC i(t) is the time step t of site v i The degree centrality of k i (t) is the time step t of site v i The value of a ij (t) represents the time step t of site v i and v j The connection relationship between them.

[0188] Step S6.2: Time step t site v i The calculation method of the betweenness centrality index is as follows:

[0189]

[0190] In the formula, BC i (t) is the time step t of site v i The betweenness centrality of st (t) is the condition of the urban rail transit network at time step t, from station v s To site v t The total number of shortest paths, l sit (t) is the shortest path passing through station v i The number of paths.

[0191] Step S6.3: Time step t site v i The calculation method of the closeness centrality index is as follows:

[0192]

[0193] In the formula, CC i (t) is the time step t of site v i The closeness centrality, d ij (t) is the time step t of site v i With site v j The shortest path length between .

[0194] Step S6.4: Time step t site v i The calculation method of the eigenvector centrality index is as follows:

[0195]

[0196] In the formula, EC i (t) is the time step t of site v i , λ is the maximum eigenvalue of the network adjacency matrix A, and its corresponding eigenvector is e=[e 1 ,e 2 ,...,e N ].

[0197] Step S6.5: Time step t site v i The calculation method of the passenger flow centrality index is as follows:

[0198]

[0199] In the formula, Q i (t) is the time step t of site v i The passenger flow ratio, h i (t) is the time step t of site v i The amount of passenger traffic carried.

[0200] Step S6.6: Time step t site v i The calculation method of network efficiency loss value before and after failure is as follows:

[0201] ΔE i (t) = E(t) - E′(t)

[0202] In the formula, ΔE i (t) is the time step t of site v i The loss value of network efficiency before and after failure, E(t) is the network efficiency at time step t, and E′(t) is the network efficiency at site v at time step t. i Network efficiency after failure.

[0203] The network efficiency is calculated as follows:

[0204]

[0205] Where, d ij For site v i With site v j The shortest path length between .

[0206] Step S6.7: Time step t site v i The calculation method of the maximum connected subgraph change value before and after failure is as follows:

[0207] ΔLCC i (t) = LCC(t) - LCC′(t)

[0208] Where, ΔLCC i (t) is the time step t of site v i The change in the number of sites in the maximum connected subgraph before and after the failure, LCC(t) is the number of sites contained in the maximum connected subgraph at time step t, and LCC′(t) is the number of sites v at time step t. i The number of sites contained in the maximum connected subgraph after failure.

[0209] Step S6.8: Based on the optimal comprehensive weight and the corresponding values ​​of each indicator, construct the standardized weighted decision matrix for each station at time step t Matrix Elements The calculation method is as follows:

[0210]

[0211] In the formula, are the components of the standardized weighted decision matrix at time step t, ω j is the optimal comprehensive weight of the jth indicator, For site v i The normalized value of metric j at time step t.

[0212] Step S6.9: Based on the weighted decision matrix at time step t, obtain the positive and negative ideal solutions of the indicator values ​​of each station at this time step, with the maximum value of each column as the positive ideal solution vector and the minimum value of each column as the negative ideal solution vector, as shown in the following formula:

[0213]

[0214] In the formula, Z + (t) is the positive ideal solution vector at time step t, Z - (t) is the negative ideal solution vector at time step t, is the positive ideal solution of the jth index at time step t, is the negative ideal solution of the jth index at time step t.

[0215] Step S6.10: Calculate the time step t site v i The Mahalanobis distance from the ideal solution is calculated as follows:

[0216]

[0217] In the formula, For time step t, site v i The Mahalanobis distance to the positive ideal solution is, For time step t, site v i The Mahalanobis distance to the negative ideal solution. C(t) is the covariance matrix of the standardized weighted decision matrix at time step t, C -1 (t) is the inverse of the covariance matrix at time step t.

[0218] Step S6.11: Calculate the time step t site v i The grey correlation degree with positive and negative ideal solutions is calculated as follows:

[0219] Time step t site v i Grey correlation degree with positive ideal solution The calculation formula is as follows:

[0220]

[0221] Time step t site v i Grey correlation degree with negative ideal solution The calculation formula is as follows:

[0222]

[0223] In the formula, For time step t, site v i The grey correlation coefficient with the positive ideal solution is For time step t, site v i The grey relational coefficient with the negative ideal solution, ξ is the resolution coefficient, which is usually taken as 0.5.

[0224] Step S6.12: Dimensionless processing of Mahalanobis distance and grey correlation degree, calculation of time step t station v i The overall distance from the ideal solution.

[0225] The dimensionless processing method is shown as follows:

[0226]

[0227]

[0228] In the formula, BD i (t) and BR i (t) are the dimensionless Mahalanobis distance and grey correlation degree respectively.

[0229] Time step t site v i The calculation method of the comprehensive distance from the ideal solution is as follows:

[0230]

[0231] For time step t, site v i The comprehensive distance from the positive ideal solution, For time step t, site v i The comprehensive distance from the negative ideal solution, ρ and λ are taken as 0.5.

[0232] Step S6.13: Based on the integrated distance, calculate the time step t site v i The comprehensive importance of is calculated as follows:

[0233]

[0234] In the formula, m i (t) is the time step t of site v i The greater the value, the more important the site is.

[0235] Step S7: Based on the historical data of the urban rail transit time-varying network at each time step, determine through simulation whether each station of the urban rail transit time-varying network at the current time step will be attacked by the key station, and mark the station attacked by the key station as a failed station; if not, transfer the station that has not been attacked by the key station to step S8.

[0236] Step S8: Otherwise, the status of each station is determined by comparing whether the real-time load of each station in the urban rail transit network at the current time step exceeds the own capacity of the corresponding station.

[0237] When the real-time load of a station of the urban rail transit time-varying network at the current time step checked exceeds the station's own capacity, indicating an attack on the station, the station is marked as a failed station; otherwise, the station is still marked as a normal station.

[0238] The judgment method is as follows:

[0239]

[0240] Where, L i (t′) is site v i The load at failure time step t′, C i For site v i own capacity.

[0241] Step S9: loop through the urban rail transit time-varying network at each time step, and determine whether there is a failed station at the current time step. If so, go to step 10; if not, go to step S12.

[0242] Step S10: Calculate the remaining capacity of the neighboring sites of the failed site at failure time step t′, redistribute the load of the failed site, and calculate the remaining capacity of the neighboring sites of the failed site at failure time step t′. i Assigned to neighboring site v j Load ΔL ij (t′) can be expressed as:

[0243]

[0244] Where, L j (t′) represents the site v j The load at failure time step t′; L i (t′) is site v i Load at failure time step t′.

[0245] Step S11: by calculating the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at this time step, go to step S6 and repeat the process until the cascading failure analysis process is completed.

[0246] The maximum connectivity coefficient calculation method is as follows:

[0247]

[0248] Where S is the maximum connectivity coefficient; N' is the total number of sites in the maximum connected subgraph after site failure; and N is the total number of sites in the initial network.

[0249] The calculation method of loss passenger flow ratio is as follows:

[0250]

[0251] Where LPF is the loss passenger flow ratio; L′(t) is the station load at time t after the station fails; and L(t) is the initial load of the station at time t under normal operation.

[0252] Step S12: The cascading failure analysis process ends. Figure 2 shown.

[0253] The present invention also proposes a system for analyzing cascading failures of urban rail transit networks, comprising:

[0254] The urban rail transit time-varying network construction module is used to establish the urban rail transit time-varying network, and obtain the capacity of each station by determining the passenger flow of each station in the urban rail transit time-varying network at the initial time step and the maximum passenger flow of each station;

[0255] The key station dynamic identification module is used to determine the comprehensive importance of each station in the urban rail transit time-varying network at the current time step and identify the key stations in the urban rail transit time-varying network at each time step;

[0256] The station status judgment module is used to loop through the urban rail transit time-varying network at each time step, and judge whether each station of the urban rail transit time-varying network at the current time step will be attacked by key stations based on historical data, and mark the attacked stations as failed stations; for the stations that have not been attacked, by comparing whether the real-time load of each station of the urban rail transit time-varying network at each time step exceeds the corresponding station's own capacity, judge whether each station is failed, and mark the station whose real-time load exceeds its own capacity as a failed station;

[0257] A failed site load redistribution module is used to obtain the remaining capacity of the failed site's neighboring sites and redistribute the real-time load of the failed site;

[0258] The cascading failure analysis module is used to analyze the cascading failure process of the urban rail transit network by determining the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step according to the redistribution results.

[0259] The urban rail transit network cascading failure analysis method proposed in the present invention can accurately grasp the dynamic changes of key sites in the urban rail transit network during the cascading failure process, thereby better analyzing the cascading failure process of the urban rail transit network.

[0260] Example

[0261] In order to verify the effectiveness of the method proposed in the present invention, this implementation example introduces a cascading failure analysis method for an urban rail transit network based on key site identification, and applies it to a rail transit network in a certain city.

[0262] Step 1: Based on the urban rail transit line and station data, and taking the interval running time as the weight, a weighted rail transit network of a city is established.

[0263] As shown in Table 3, the rail transit network line and station data of a certain city are obtained, and the interval operation time is shown in Table 4.

[0264] Table 3 Data of rail transit lines and stations in a certain city

[0265] Site Number Site Name The line to which the station belongs 1 Apple Orchard Line 1 2 Ancient City Line 1 … … … 328 Terminal 2 Airport Line 329 Terminal 3 Airport Line

[0266] Table 4 Operation time of rail transit network section in a city

[0267] Serial number Starting point Terminal Interval running time (min) 1 Apple Orchard Ancient City 3 2 Ancient City Bajiao Amusement Park 3 … … … … 374 Terminal 3 Terminal 2 14 375 Terminal 2 Sanyuan Bridge 18

[0268] Based on the above data, the Space L method is used to establish a weighted rail transit network for a city. The topological network is as follows: Figure 4 The network adjacency matrix is ​​shown in Table 5.

[0269] Table 5: Adjacency matrix of a city's rail transit network (partial)

[0270]

[0271]

[0272] Based on the above data, a weighted rail transit network of a certain city is established, which contains 329 stations and 375 edges.

[0273] Step 2: Based on a city’s rail transit card swiping data and combined with the urban rail transit weighted network at each time step, calculate the travel volume of the OD pair at each time step.

[0274] The card swiping data of a certain city’s rail transit on a certain day in May 2019 was selected as the data basis, as shown in Table 6.

[0275] Table 6: Rail transit card swiping data in a certain city (partial)

[0276]

[0277] Starting from the earliest data, the passenger travel data is continuously updated, and the passenger travel data in different time periods are counted to obtain the OD travel volume in different time periods, as shown in Table 7.

[0278] Table 7 OD travel volume at a certain time step (partial)

[0279]

[0280]

[0281] Step 3: Considering the network topology structure at each time step and the passenger flow of each OD pair, establish the urban rail transit time-varying network. Figure 5 shown.

[0282] Step 4: Use the subjective and objective indicator weight determination method to determine the weights of key station identification indicators in the urban rail transit network. The results of the weight determination of each indicator are shown in Table 8.

[0283] Table 8 Weights of key station identification indicators for a city's rail transit network

[0284]

[0285] Step 5: Take the morning peak with the largest OD passenger flow as the start time of cascade failure, take the passenger flow borne by the station in real time as the station load, calculate the maximum number of connected subgraph stations of the urban rail transit network and the passenger flow of each station at the initial time step, and determine the initial load and capacity of each station.

[0286] The initial load and capacity of the stations in a city’s rail transit network are shown in Table 9.

[0287] Table 9 Initial load and capacity of a city's rail transit network stations

[0288]

[0289]

[0290] Step 6: Based on the urban rail transit time-varying network at the current time step, identify the key stations of the urban rail transit network at the current time step.

[0291] In the absence of cascading failures, the key sites of a city’s rail transit network are shown in Table 10. Due to cascading failures, the topological structure and passenger flow distribution of the urban rail transit network have changed, resulting in significant changes in key sites, as shown in Table 11.

[0292] Table 10 Key stations of a city's rail transit network under normal operating conditions (part)

[0293]

[0294] Table 11 Key stations of a city's rail transit network during cascading failure (part)

[0295]

[0296]

[0297] Comparing Table 10 with Table 11, it can be found that the changes in key sites are greater during the cascading failure process, indicating that cascading failure has caused tremendous changes in the topological structure of urban rail transit and the temporal and spatial distribution of passenger flow. Cascading failure is closely related to the failure of key sites. Therefore, dynamic identification of key sites is of great significance for cascading failure analysis.

[0298] Step 7: Determine whether to attack the identified key site. If so, make the key site invalid; if not, go to step 8.

[0299] Step S8: By comparing the relationship between the real-time load and capacity of the site, the status of the site is determined. The determination method is shown in the following formula:

[0300]

[0301] Where, L i (t′) is the site v i The load at failure time step t′, C i For site v i Capacity;

[0302] Mark the site whose real-time load exceeds the capacity as a failed site.

[0303] Step 9: Check whether there is a failed site in the current time step. If so, go to step 10; if not, go to step 12.

[0304] Step 10: Calculate the remaining capacity of the neighboring sites of the failed site at failure time step t′ and redistribute the load of the failed site.

[0305] Step 11: Update the urban rail transit time-varying network, calculate the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit network at this time step, go to step 6, and repeat the process until the cascade failure process ends.

[0306] Step 12: Cascading failure ends.

[0307] Compare and analyze the changes in the maximum connectivity coefficient and the loss passenger flow ratio under different attack modes, such as Figure 6 and Figure 7 shown.

[0308] according to Figure 6 and Figure 7 ,It can be seen that the reduction degree of the maximum connected subgraph ratio caused by the static single attack method and the static multiple attack method is roughly the same, while the passenger flow loss caused by the static multiple attack method is greater than that of the static single attack method. This is because the two attack methods attack the same site, so the damage to the topological structure is similar, but the failure duration caused by the static multiple attack method is longer, resulting in greater passenger flow loss. Compared with the static identification attack method, the dynamic identification attack method not only leads to the longest failure duration, but also causes greater damage, indicating that in the process of cascading failure, the site that can cause greater damage is changing, indicating the necessity of dynamic identification of key sites.

[0309] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

[0310] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as commonly understood by those skilled in the art to which the present invention belongs. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In the event of any conflict with any incorporated document, the content of this specification shall prevail.

Claims

1. A method for analyzing cascading failures of urban rail transit networks, characterized in that: The following steps are involved: Establish an urban rail transit time-varying network, and obtain the capacity of each station by determining the passenger flow of each station in the urban rail transit time-varying network and the maximum passenger flow of each station at the initial time step; Determine the comprehensive importance of each station in the urban rail transit time-varying network at the current time step, and identify the key stations in the urban rail transit time-varying network at each time step; The urban rail transit time-varying network at each time step is traversed in a loop, and whether each station of the urban rail transit time-varying network at the current time step will be attacked by key stations is determined based on historical data, and the attacked stations are marked as failed stations; for the stations that are not attacked, whether the real-time load of each station in the urban rail transit time-varying network at each time step exceeds the corresponding station's own capacity is compared to determine whether each station is failed, and the stations whose real-time load exceeds their own capacity are marked as failed stations; Obtain the remaining capacity of the neighboring sites of the failed site and redistribute the real-time load of the failed site; According to the redistribution results, the cascading failure process of the urban rail transit network is analyzed by determining the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step.

2. The urban rail transit network cascading failure analysis method according to claim 1 is characterized in that: The establishment of a time-varying urban rail transit network specifically includes: Through the connection relationship between urban rail transit lines and stations, and taking the interval running time as the weight, a weighted network of urban rail transit is established; Based on the constructed urban rail transit weighted network at the current time step, the Dijkstra algorithm is used to calculate the shortest path set between each station at the current time step; Read the passenger's travel data at the current time step, including the passenger's card number, current station, final station, and arrival time; Read the urban rail transit card swiping data of the current time step, including the passenger's card number, starting line, starting station, departure time, terminal line, terminal station and arrival time, and update these data to the passenger travel data of the current time step. The data items include the passenger's card number, current station, terminal station and arrival time. Based on the passenger travel data of the current time step, according to the passenger's current station and terminal station, the passenger flow of the OD pairs in the current time step is counted, and the passenger flow OD matrix of the current time step is constructed; Get the current station and terminal station of the passenger in the passenger travel data at the current time step, and extract the passenger's travel path from the shortest path set: {C L }={c1,c2,K,c i ,K,c L } Where L represents the length of the passenger's travel path, c i represents the i-th station that the passenger passes through; By judging whether L in the travel path is equal to 1, when L in the travel path is equal to 1, the passenger arrives at the terminal and is deleted from the passenger travel data; Otherwise, according to the passenger's travel path, the current station of the passenger and the second station in the travel path are obtained, the interval running time td between the current station and the second station is obtained, and it is determined whether the interval running time td is less than the time-varying network update time difference t; When the interval running time td is less than the time-varying network update time difference t, update the passenger travel data, and the current station is updated to the second station in the passenger travel path. Other data remain unchanged. Determine whether the difference between the time difference t and the interval running time td is less than the time threshold TD. If so, do not update the passenger travel data. If not, reduce the interval running time td by the time difference t, and return to the step of constructing the passenger flow OD matrix of the current time step. When the interval running time td is greater than or equal to the time-varying network update time difference t, it is determined whether the difference between the time difference td and the running time t is less than the time threshold TD. If so, the passenger travel data is updated, and the current station is updated to the second station in the passenger travel path, and other data remain unchanged; if not, the passenger travel data is not updated; The urban rail transit time-varying network is established by using the urban rail transit weighted network at each time step and combining the passenger flow of each OD pair of the urban rail transit network at each time step.

3. The urban rail transit network cascading failure analysis method according to claim 2 is characterized in that: The urban rail transit time-varying network is: G t =(V,E t ,W,H t ) In the formula, is the set of edges in the network at time t, Indicates the time t from site v i To site v j The side of H t ={h i (t)}(i=1,2,3...,N) is the passenger flow set of the station at time t, h i (t) represents the site v at time t i The amount of passenger traffic carried; In the formula, f ij (t) and f ji (t) represents the time step t at site v i is the cross-sectional passenger flow at the departure and destination, f i (t) represents the path site v in time step t i passenger flow.

4. The urban rail transit network cascading failure analysis method according to claim 3 is characterized in that: The obtaining of the capacity of each site specifically includes: Initialize the load of each site: L i (0)=h i (t) Where, L i (0) is site v i Initial load; h i (t) is the time when the cascading failure starts at site v i passenger flow; The calculation formula for the site load after the cascading failure occurs t′ is: L i (t′)=h i (t+t′) Where, L i (t′) is the site v i The load after the cascading failure occurs t′ time step; h i (t+t′) is the site v after t′ time step of cascading failure i passenger flow; The site capacity is: C i =(1+α)h i (max) In the formula, C i is the site's own capacity; h i (max) is the maximum passenger flow of the station; α is the capacity parameter.

5. The urban rail transit network cascading failure analysis method according to claim 4, characterized in that: The identification of key sites of the urban rail transit time-varying network at each time step specifically includes: The identification index of each site is divided into topological structure index, passenger flow index and network connectivity index; By determining the subjective weight and objective weight of each indicator, the subjective weight and the objective weight are linearly combined to obtain the comprehensive weight; With the goal of minimizing the difference between the comprehensive weight and the subjective weight and objective weight, the linear combination coefficient of the comprehensive weight is optimized to obtain the optimal comprehensive weight; Get the time step t site v respectively i The degree centrality index, betweenness centrality index, closeness centrality index, eigenvector centrality index, passenger flow centrality index, and time step t station v i The values ​​of network efficiency loss and maximum connected subgraph change before and after failure; According to the optimal comprehensive weight and the corresponding values ​​of each indicator, a standardized weighted decision matrix for each station at time step t is constructed. Matrix Elements The calculation method is as follows: In the formula, is the constituent element of the standardized weighted decision matrix at time step t, ω j is the optimal comprehensive weight of the jth indicator, For site v i Normalized value of indicator j at time step t; Based on the standardized weighted decision matrix at time step t, the positive and negative ideal solutions of the indicator values ​​of each station at this time step are obtained, with the maximum value of each column as the positive ideal solution vector and the minimum value of each column as the negative ideal solution vector; Determine the time step t site v separately i The Mahalanobis distance and grey correlation degree of the positive and negative ideal solutions are dimensionless, and the corresponding calculation time step t station v i The combined distance from the positive and negative ideal solutions; Based on the integrated distance, calculate the time step t site v i The greater the comprehensive importance value, the more important the site is. The comprehensive importance values ​​of each station in the urban rail transit time-varying network at the same time step are sorted, and the station with the largest value is regarded as the key station of the urban rail transit time-varying network at that time step.

6. According to the urban rail transit network cascading failure analysis method according to claim 5, it is characterized in that: The process of marking a site whose real-time load exceeds its own capacity as a failed site specifically includes: According to the historical data of the urban rail transit time-varying network, the simulation is used to determine whether each station of the urban rail transit time-varying network at the current time step will be attacked by key stations, and the stations attacked by key stations will be marked as failed stations; the stations not attacked by key stations will be marked as normal stations; For the sites that are not attacked by the key sites, i.e., normal sites, the status of the sites is determined by comparing whether the real-time load of each site in the urban rail transit time-varying network at the current time step exceeds the site's own capacity; When the real-time load of each station in the urban rail transit time-varying network at the current time step exceeds the capacity of the station, the station is marked as a failed station; otherwise, the station remains a normal station; The judgment method is: Where, L i (t′) is the site v i The load at failure time step t′, C i For site v i own capacity.

7. The urban rail transit network cascading failure analysis method according to claim 6, characterized in that: The real-time load redistribution of the failed site specifically includes: By checking whether there is a failed station in the urban rail transit time-varying network at the current time step, if there is, the load of the failed station is redistributed, if not, the cascading failure process ends; By calculating the remaining capacity of the neighboring sites of the failed site at failure time step t′, the load of the failed site is redistributed; Failure time step t′ Failure site v i Assigned to neighboring site v j Load ΔL ij (t′) is: Where, L j (t′) represents the site v j The load at failure time step t′, L i (t′) is the site v i Load at failure time step t′.

8. The urban rail transit network cascading failure analysis method according to claim 7, characterized in that: The analysis of the cascading failure process of the urban rail transit network includes: According to the redistribution results, the total number of sites in the maximum connected subgraph after the site fails and the load of each site after the site fails are determined; Determine the maximum connectivity coefficient based on the total number of sites in the maximum connected subgraph after the site fails and the total number of sites in the initial network; The maximum connectivity coefficient is: Where S is the maximum connectivity coefficient, N' is the total number of sites in the maximum connected subgraph after the site fails, and N is the total number of sites in the initial network; Determine the proportion of lost passenger flow based on the load of each station after the station failure and the initial load of each station under normal operation; The loss of passenger flow ratio is: Where LPF is the loss passenger flow ratio, L′(t) is the station load at time t after the station fails, and L(t) is the initial load of the station at time t under normal operation; By analogy, the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step are calculated, and the cascading failure process of the urban rail transit time-varying network is analyzed.

9. The urban rail transit network cascading failure analysis method according to claim 2, characterized in that: The establishment of a weighted urban rail transit network specifically includes: According to the connection relationship between sites and lines, an adjacency matrix is ​​established; The adjacency matrix is: The element a in the matrix ij Indicates site v i and v j The connection relationship between them, where a ij The value determination is: According to the established adjacency matrix, with interval running time as weight, the urban rail transit weighted network is established as follows: G=(V,E,W) Where, V = {v i }(i=1,2,3...,N) is the set of sites in the network; v i represents the i-th station in the urban rail transit network; E = {e ij }(i,j=1,2,3...,N and i≠j) is the set of edges in the network; e ij Indicates that from site v i To site v j The edge of ij }(i,j=1,2,3...,N and i≠j) is the weight set of the edge; w ij Represents edge e ij The weight of the site v i To site v j interval running time; N is the total number of sites in the initial network.

10. A system for analyzing cascading failures of urban rail transit networks, characterized in that: include: The urban rail transit time-varying network construction module is used to establish the urban rail transit time-varying network, and obtain the capacity of each station by determining the passenger flow of each station in the urban rail transit time-varying network at the initial time step and the maximum passenger flow of each station; The key station dynamic identification module is used to determine the comprehensive importance of each station in the urban rail transit time-varying network at the current time step and identify the key stations in the urban rail transit time-varying network at each time step; The station status judgment module is used to loop through the urban rail transit time-varying network at each time step, and judge whether each station of the urban rail transit time-varying network at the current time step will be attacked by key stations based on historical data, and mark the attacked stations as failed stations; for the stations that have not been attacked, by comparing whether the real-time load of each station of the urban rail transit time-varying network at each time step exceeds the corresponding station's own capacity, judge whether each station is failed, and mark the station whose real-time load exceeds its own capacity as a failed station; A failed site load redistribution module is used to obtain the remaining capacity of the failed site's neighboring sites and redistribute the real-time load of the failed site; The cascading failure analysis module is used to analyze the cascading failure process of the urban rail transit network by determining the maximum connectivity coefficient and the loss passenger flow ratio of the urban rail transit time-varying network at each time step according to the redistribution results.

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