Urban rail transit network toughness evaluation method considering passenger flow dynamics

Abstract

The invention discloses an urban rail transit network toughness evaluation method considering passenger flow dynamics, and relates to the technical field of urban rail transit network evaluation. Comprising the following steps: modeling an urban rail transit network by using a complex network theory; calculating traffic demands among stations in the urban rail transit network to obtain passenger flow demand data; passenger flow distribution is obtained by adopting a user balance model according to passenger flow demand data from a starting place to a destination among the nodes; establishing an urban rail transit network cascade failure model considering station overload; establishing an urban rail transit network recovery model considering passenger flow redistribution and station state recovery; through three indexes of nodes, lines and topology, the recovery capability of the urban rail transit network is quantified, and the toughness of the urban rail transit network is evaluated. According to the method, the performance evaluation indexes are constructed from the three aspects of nodes, lines and topology, and the changes of the operation performance of the urban rail transit network in all aspects can be comprehensively grasped.

Description

Technical Field

[0001] The present invention relates to the technical field of urban rail transit network assessment, and in particular to an urban rail transit network resilience assessment method considering the dynamics of passenger flow. Background Art

[0002] Due to rapid urbanization, rail transit networks (URTNs) play a vital role in ensuring efficient, sustainable, and reliable travel for millions of passengers. However, these networks are vulnerable to disruptions caused by natural disasters, random failures, and malicious sabotage, which can lead to massive congestion and economic losses. Given the critical role of URTNs in public transportation systems, analyzing the effective performance recovery of URTNs has become a frontier issue for transportation stakeholders. Resilience reflects the ability of a system to withstand, adapt to, and recover from disturbances and is an important concept for quantifying the overall performance changes at different stages. For URTNs, the research phase of resilience can generally be divided into two stages: failure and recovery, to analyze the performance degradation caused by failures and the system's ability to recover from failures.

[0003] In existing technologies, the effects of line impedance and station capacity are ignored. Furthermore, in URTNs, there are significant differences in passenger flow between stations and lines, but the impact of these variations on resilience during the recovery process has not been studied in previous models. Furthermore, existing studies have not considered key factors, such as the state of the repaired node. This is because a faulty node may be unable to resume function after repair due to excessive load. Furthermore, during the recovery phase, the redistribution of passenger flow caused by the restoration of the faulty node and the impact of key parameters (such as capacity) on recovery capabilities have not been explored in depth.

[0004] Therefore, it is an urgent problem for those skilled in the art to propose an urban rail transit network resilience assessment method that takes into account the dynamics of passenger flow to solve the difficulties existing in the existing technology. Summary of the Invention

[0005] In view of this, the present invention provides an urban rail transit network resilience assessment method that takes into account the dynamics of passenger flow, which can construct performance evaluation indicators from three aspects: nodes, lines and topology, and can comprehensively grasp the changes in various aspects of the operational performance of the urban rail transit network.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for assessing the resilience of urban rail transit networks considering the dynamics of passenger flow is proposed, including:

[0008] S1. Use complex network theory to model urban rail transit networks;

[0009] S2. Calculate the traffic demand between stations in the urban rail transit network to obtain passenger flow demand data;

[0010] S3. Based on the passenger flow demand data from the origin to the destination between each node, the user equilibrium model is used to obtain the passenger flow distribution;

[0011] S4. Establish a cascading failure model for urban rail transit networks considering station overload;

[0012] S5. Establish an urban rail transit network restoration model that considers passenger flow redistribution and repair station status;

[0013] S6. Quantify the recovery capacity of the urban rail transit network through the three indicators of nodes, lines and topology, and evaluate the resilience of the urban rail transit network.

[0014] In the above method, optionally, the urban rail transit network is modeled in S1, where stations are modeled as nodes and tracks between stations are modeled as edges. The rail transit network is G(V,E), where V represents a node set and E represents an edge set.

[0015] The above method is optional. In S2, the traffic demand between stations in the urban rail transit network is calculated as follows:

[0016] The proportion f of individual commutes from origin o to destination d od for:

[0017]

[0018] Among them, D d and D i is the total traffic demand of site d and site i, l od is the distance between the originating station o and the destination d, in km, p(l od ) is the distance factor between the originating station o and the destination d, p(l oi ) is the distance factor between the origin o and the destination i;

[0019] The distance factor p(l od )for:

[0020]

[0021] Traffic demand F from origin o to destination d od The calculation is as follows:

[0022] F od =D o f od ψ,

[0023] Where ψ is the parameter that controls the intensity of inter-station traffic demand, D o is the total traffic demand of station o.

[0024] In the above method, optionally, S3 uses a user equilibrium model to obtain the passenger flow distribution, specifically:

[0025] The user equilibrium model is:

[0026]

[0027] Where: Indicates that edge u has flow x u Driving time under the condition of represents the flow on path m from the starting point o to the destination d; when edge u belongs to the path m from the starting point o to the destination d, Otherwise

[0028] Use the BPR function to represent the edge u when the flow is x u Driving time

[0029]

[0030] Where v is the train speed; lu is the actual length of edge u; cu is the design capacity of edge u; α and β are the coefficients of the line.

[0031] In the above method, optionally, a cascading failure model of an urban rail transit network is established in S4, specifically:

[0032] S401. Calculate the passenger flow p of node i based on the flow of the adjacent lines of node i. i :

[0033]

[0034] Among them, Φ i is the set of neighboring edges of node i;

[0035] S402, design capacity C of node i i for:

[0036] C i =(1+μ)p i ,

[0037] Among them, μ is the capacity parameter, which controls the value of the design capacity;

[0038] S403, maximum capacity of node i for:

[0039]

[0040] Wherein, η is the overload parameter that controls the maximum capacity value;

[0041] S404. Based on the relationship between passenger flow and capacity at simulation time step τ, a rule for determining the state of node i is proposed:

[0042]

[0043] Where r is a random number uniformly distributed between 0 and 1;

[0044] When p i (τ)≤C i When , the status of the station is normal;

[0045] when When , the station status is faulty;

[0046] When node i satisfies When the condition is met, the site may not be able to operate and is considered to be failed, with a probability θ i (τ) is:

[0047]

[0048] S405. In each iteration step, the total traffic demand value of all stations remains unchanged;

[0049] In the iterative step τ, the traffic demand D of node j, one of the neighboring nodes of failed node i, is updated j (τ):

[0050]

[0051] Where Δ represents the set of remaining nodes except the failed node, and the traffic demand D of the failed node i is i (τ) is set to 0;

[0052] S406. Based on the updated remaining node traffic demand and network topology, the user balance model is solved to recalculate the site and line traffic. If there are no more faulty nodes, the cascading failure stops at iterative step τ; otherwise, repeat the above steps S404 to S406.

[0053] In the above method, optionally, an urban rail transit network restoration model is established in S5, specifically:

[0054] S501. Repairing a faulty node in the urban rail transit network, including:

[0055] Degree-based repair strategy: sort the faulty nodes in descending order of their degree values and repair them;

[0056] Betweenness-based repair strategy: sort the faulty nodes in descending order of their betweenness values and repair them;

[0057] Repair strategy based on traffic demand: sort the faulty nodes in descending order of their initial traffic demand values and repair them;

[0058] Repair strategy based on passenger flow: sort the faulty nodes in descending order of initial passenger flow and repair them;

[0059] S502: The repaired node reconnects with the adjacent nodes according to the initial network structure and re-receives the traffic demand allocated by other normal nodes. The traffic demand D of the repaired node i in any iterative step τ is i (τ) is:

[0060]

[0061] S503: Traffic demand D of other nodes k k (τ) is updated as:

[0062]

[0063] The above method is optional. In S6, the resilience of the urban rail transit network is evaluated as follows:

[0064] S601, evaluate the recovery capability of the urban rail transit network by the status of the repaired nodes, and the operating efficiency of node i at the simulation time step τ for:

[0065]

[0066] At the simulation time step τ, the average operating efficiency E of each station in the urban rail transit network is N for:

[0067]

[0068] The node operation efficiency resilience index is:

[0069]

[0070] Among them, τ s The time step when all nodes are attacked is τ f The simulation time step when all failed nodes are repaired; (1-E N (τ s ))N f Optimal toughness value;

[0071] S602. Use line operation efficiency to construct the resilience index of the urban rail transit network, quantify the performance recovery results after the implementation of repair measures, and the operating efficiency of line u at the simulation time step τ for:

[0072]

[0073] in, is the travel time of line u in the traffic equilibrium state at the simulation time step τ; at any simulation time step τ, the line operation efficiency of the urban rail transit network is:

[0074]

[0075] The line operation efficiency resilience index is:

[0076]

[0077] S603. Quantify the resilience level of urban rail transit network through topological performance, and the network efficiency E of urban rail transit network U (τ) at the simulation time step τ is:

[0078]

[0079] Among them, d ij (τ) represents the shortest path distance between node i and node j at simulation time step τ;

[0080] The ability to restore the topological performance of urban rail transit networks is:

[0081]

[0082] It can be seen from the above technical solutions that, compared with the prior art, the present invention provides an urban rail transit network resilience assessment method that takes into account the dynamics of passenger flow, which has the following beneficial effects:

[0083] The present invention establishes a cascading failure model and a recovery model for the urban rail transit network, taking into account the redistribution of traffic demand due to normal node failure or fault node recovery. By solving the user equilibrium model under the updated traffic demand and topological structure, an accurate and reasonable passenger flow distribution can be obtained. In the failure and recovery stages, the three states of the node are taken into account, namely the normal state, the overload state and the failure state, and a practical cascading failure model and a recovery model for the rail transit network can be constructed. In the failure and recovery stages, the dynamics of the passenger flow in the urban rail transit network are taken into account, and from the three aspects of stations, lines and networks, loss and recovery indicators for quantifying the efficiency of stations, lines and networks are proposed respectively, which accurately reflect the overall resilience level of the urban rail transit network. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0085] Figure 1 A flowchart of a method for evaluating the resilience of an urban rail transit network taking into account the dynamics of passenger flow, provided by the present invention;

[0086] Figure 2 This is a schematic diagram of the cascading failure and recovery process of the urban rail transit network provided by the present invention. DETAILED DESCRIPTION

[0087] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0088] In this application, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. The terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or apparatus comprising the element.

[0089] Reference Figure 1 As shown, the present invention discloses a method for evaluating the resilience of an urban rail transit network taking into account the dynamics of passenger flow, comprising:

[0090] S1. Use complex network theory to model urban rail transit networks;

[0091] S2. Calculate the traffic demand between stations in the urban rail transit network to obtain passenger flow demand data;

[0092] S3. Based on the passenger flow demand data from the origin to the destination between each node, the user equilibrium model is used to obtain the passenger flow distribution;

[0093] S4. Establish a cascading failure model for urban rail transit networks considering station overload;

[0094] S5. Establish an urban rail transit network restoration model that considers passenger flow redistribution and repair station status;

[0095] S6. Quantify the recovery capacity of the urban rail transit network through the three indicators of nodes, lines and topology, and evaluate the resilience of the urban rail transit network.

[0096] Furthermore, the urban rail transit network is modeled in S1, where stations are modeled as nodes and tracks between stations are modeled as edges. The rail transit network is G(V,E), where V represents the node set and E represents the edge set.

[0097] Furthermore, S2 calculates the traffic demand between stations in the urban rail transit network, specifically:

[0098] Assume that the commuting flow from the starting station o to the destination d is equal to the traffic demand D at the destination d. d is proportional to the cost function of the distance between the two stations and inversely proportional to the cost function of the distance between the two stations. In general, the traffic demand at each station can be determined by the number of passengers entering and leaving the station. Using these assumptions, the proportion f of individuals commuting from the origin station o to the destination d is od for:

[0099]

[0100] Among them, D d and D i is the total traffic demand of site d and site i, l od is the distance between the originating station o and the destination d, in km, p(l od ) is the distance factor between the originating station o and the destination d, p(l oi ) is the distance factor between the origin o and the destination i;

[0101] The distance factor p(l od )for:

[0102]

[0103] Traffic demand F from origin o to destination d od The calculation is as follows:

[0104] F od =D o f od ψ,

[0105] Where ψ is the parameter that controls the intensity of inter-station traffic demand, D o is the total traffic demand of station o.

[0106] Furthermore, in a transportation network, due to different traffic impedance values, there are significant differences in the flow on each line. To better characterize this characteristic, a user equilibrium model is used to obtain the passenger flow distribution based on the passenger flow demand data from the origin to the destination between each node. At the same time, according to a specific selection mechanism, the OD demand is allocated to each edge within the path. Specifically, if passengers can obtain all information about a path and choose the path with the shortest travel time, the transportation network can reach a state of equilibrium. The result can be regarded as the flow distribution data of the urban rail transit network.

[0107] Furthermore, S3 uses a user equilibrium model to obtain the passenger flow distribution, specifically:

[0108] The user equilibrium model is:

[0109]

[0110]

[0111] Where: Indicates that edge u has flow x u Driving time under the condition of represents the flow on path m from the starting point o to the destination d; when edge u belongs to the path m from the starting point o to the destination d, Otherwise

[0112] Use the BPR function to represent the edge u when the flow is x u Driving time

[0113]

[0114] Where, v is the train speed; l u is the actual length of side u; c u is the design capacity of edge u, and α and β are the coefficients of the line.

[0115] Furthermore, passenger flow fluctuations generally cause station congestion or even station failures, which in turn changes the routes chosen by passengers. In this case, as other stations receive more additional passenger flow, they may experience congestion or failures one after another. To reflect the above cascading failure mechanism, a cascading failure model for urban rail transit networks considering station overload is proposed.

[0116] Furthermore, a cascading failure model of urban rail transit network is established in S4, specifically:

[0117] S401. Calculate the passenger flow p of node i based on the flow of the adjacent lines of node i. i :

[0118]

[0119] Among them, Φ i is the set of neighboring edges of node i;

[0120] S402, design capacity C of node i i for:

[0121] C i =(1+μ)p i ,

[0122] Among them, μ is the capacity parameter, which controls the value of the design capacity;

[0123] S403. Once the load of a station exceeds its capacity, it will fail. However, if a station carries a relatively high passenger flow, it may not fail because it has a strong ability to handle a certain amount of additional load. Therefore, unlike the existing research on the normal state and fault state of stations in urban rail transit networks, we define the overload state of a station to describe the station's ability to bear the additional flow; the maximum capacity of station i for:

[0124]

[0125] Wherein, η is the overload parameter that controls the maximum capacity value;

[0126] S404. Based on the relationship between passenger flow and capacity at simulation time step τ, a rule for determining the state of node i is proposed:

[0127]

[0128] Where r is a random number uniformly distributed between 0 and 1;

[0129] When p i (τ)≤C i When , the status of the station is normal;

[0130] when When , the station status is faulty;

[0131] When node i satisfies When the condition is met, the site may not be able to operate and is considered to be failed, with a probability θ i (τ) is:

[0132]

[0133] Obviously, the greater the value of load exceeding capacity, the higher the probability of failure of the overloaded node;

[0134] S405. In the fault phase, the faulty node and its line are removed from the urban rail transit network, while normal nodes and overloaded nodes are retained. In the urban rail transit network, random faults and intentional damage often occur, such as extreme weather and failures of lines or equipment within the station. Therefore, it is assumed that in each iteration step, a node in the urban rail transit network will be attacked. Considering that if a station is closed after the attack, passengers may choose to travel at another station, we assume that the total traffic demand value of all stations remains unchanged;

[0135] In the iterative step τ, the traffic demand D of node j, one of the neighboring nodes of failed node i, is updated j (τ):

[0136]

[0137] Where Δ represents the set of remaining nodes except the failed node, and the traffic demand D of the failed node i is i (τ) is set to 0;

[0138] S406. Based on the updated remaining node traffic demand and network topology, the user balance model is solved to recalculate the site and line traffic. If there are no more faulty nodes, the cascading failure stops at iterative step τ; otherwise, repeat the above steps S404 to S406.

[0139] Furthermore, the urban rail transit network was attacked multiple times (the number of attacks is represented by N a ), how to effectively repair the failed site determines the recovery of network operation performance, so resilience assessment is a problem that decision makers and researchers are very concerned about. In this paper, the total number of failed sites after the failure process is recorded as N f (N f ≥N a ), then, assuming that in each iteration of the recovery phase, the failed nodes are repaired one by one until all N f All faulty nodes have been repaired. Generally speaking, topological indicators (such as degree, betweenness, etc.) can reflect the role of nodes in the topological structure, while the traffic demand and passenger flow of the station determine the operating efficiency of the urban rail transit network;

[0140] Furthermore, an urban rail transit network restoration model is established in S5, specifically:

[0141] S501. Repairing a faulty node in the urban rail transit network, including:

[0142] Degree-based repair strategy: sort the faulty nodes in descending order of their degree values and repair them;

[0143] Betweenness-based repair strategy: sort the faulty nodes in descending order of their betweenness values and repair them;

[0144] Repair strategy based on traffic demand: sort the faulty nodes in descending order of their initial traffic demand values and repair them;

[0145] Repair strategy based on passenger flow: sort the faulty nodes in descending order of initial passenger flow and repair them;

[0146] S502: The repaired node reconnects with the adjacent nodes according to the initial network structure and re-receives the traffic demand allocated by other normal nodes. The traffic demand D of the repaired node i in any iterative step τ is i (τ) is:

[0147]

[0148] S503. Traffic demand D of other functional nodes k (including normal, overloaded and repaired nodes) k (τ) is updated as:

[0149]

[0150] Specifically, for a repaired node, if its adjacent nodes are normal, the edge between them will also resume function. Otherwise, the edge will remain in a faulty state unless the faulty adjacent node is repaired. To update the traffic demand of the repaired node and other normal nodes, there are obviously two situations that need to be considered for the node status:

[0151] (1) If the repaired node does not have any functional edges, that is, its adjacent nodes are faulty, the repaired node is considered to be temporarily faulty and does not participate in the evaluation of the site metric but is retained in the network. Passenger flow is redistributed by solving the user equilibrium model until one of the adjacent nodes is also repaired and its load is no greater than its maximum capacity. Only then is its function and the edges between the repaired node and the adjacent nodes restored.

[0152] (2) After redistributing passenger flow, if the load of the repaired node is higher than the maximum capacity, its status remains invalid. Only when the load does not exceed the maximum capacity can the node resume its function and be included in the calculation of the site metric again.

[0153] In order to more clearly illustrate the failure and recovery process, the network reference at simulation time step τ = 0 Figure 2As shown in the figure; assuming that node 1 is attacked when the iteration step τ = 1, node 1 and its edges are removed from the network, and traffic demands are redistributed to other nodes. The node load is calculated based on the updated topology and traffic demands. Assuming that the load of node 2 exceeds its maximum capacity, or is between the design capacity and the maximum capacity and the random number is less than its failure probability, due to the higher load of node 2 and the fact that node 3 is an isolated node, these two nodes and their edges are removed, and traffic demands are redistributed. At the same time, we assume that the load of node 5 is between the design capacity and the maximum capacity and the random number is greater than its failure probability, then the node is considered to be overloaded. Since there are no new failed nodes, the cascading failure stops at τ = 1. In the recovery phase, assuming a repair order of 3-1-2, at τ = 2, failed node 3 is repaired, and some traffic demand is redirected from other functional nodes to it. However, since its neighboring nodes are also failed, repaired node 3 remains failed at τ = 2. At τ = 3, node 1 is repaired, and traffic demand is redistributed from node 1. Passenger flow is then redistributed based on user equilibrium. Since repaired node 3 is reconnected to repaired node 1, node 3 regains functionality. Furthermore, assuming the load on node 1 is greater than its maximum capacity, node 1 is considered temporarily down. At τ = 4, failed node 2 is repaired, traffic demand is redirected to it, and passenger flow is recalculated. Assuming that after passenger flow redistribution, the load on each node is below its design capacity, both repaired nodes 1 and 2 are functional. Finally, the recovery process ends.

[0154] Furthermore, since the dynamic nature of passenger flow in the urban rail transit network is taken into account during the failure and recovery stages, it is necessary to use flow-related indicators to quantify the recovery of the urban rail transit network's operational performance; in addition, as a complex network system, topology also plays a vital role in the urban rail transit network; in summary, in order to reflect various aspects of the recovery capability of the urban rail transit network, we considered three indicators, including nodes, lines, and topology, to reflect the overall resilience level of the urban rail transit network.

[0155] At the station, when passenger flow remains at a low level, congestion will not occur and passengers can get on and off the train efficiently. Conversely, if the passenger flow exceeds the design capacity, the excessive passenger flow will cause station congestion and affect boarding and transfers. Therefore, when evaluating the operating efficiency of the station, the status of the repaired nodes must be considered to define the recovery capacity.

[0156] Furthermore, S6 evaluates the resilience of urban rail transit networks, specifically:

[0157] S601, evaluate the recovery capability of the urban rail transit network by the status of the repaired nodes, and the operating efficiency of node i at the simulation time step τ for:

[0158]

[0159] At the simulation time step τ, the average operating efficiency E of each station in the urban rail transit network is N for:

[0160]

[0161] In order to reflect the ability of the urban rail transit network to recover its performance after interference, the node operation efficiency resilience index is proposed as follows:

[0162]

[0163] Among them, τ s The time step when all nodes are attacked is τ f The simulation time step when all failed nodes are repaired; (1-E N (τ s ))N f The optimal resilience value indicates that repairing only one fault node can ensure the complete recovery of the operating efficiency of all stations. According to the definition, R N The higher the value, the more significant the recovery of the station's operational performance.

[0164] S602. The travel time of a line is an important indicator reflecting the operating efficiency of the urban rail transit network. Due to the recovery of the faulty node, the travel time between stations will be greatly shortened, which shows that the urban rail transit network has a high recovery capability. Therefore, the line operation efficiency is used to construct the resilience index of the urban rail transit network, and the performance recovery results after the implementation of the repair measures are quantified. The operating efficiency of line u at the simulation time step τ is for:

[0165]

[0166] in, is the travel time of route u in the traffic equilibrium state at the simulation time step τ;

[0167] Taking into account the operating efficiency of all lines, at any simulation time step τ, the line operating efficiency of the urban rail transit network is:

[0168]

[0169] Taking into account the changes in the line operation efficiency of the urban rail transit network with the simulation time step, the line operation efficiency resilience index is proposed as follows:

[0170]

[0171] Obviously, during the fault and restoration phases, higher line operation efficiency reflects the higher level of resilience of the urban rail transit network in the face of disturbances;

[0172] S603. As a complex network system, the topology of the urban rail transit network can measure the connectivity between nodes. Strong connectivity can often ensure the accessibility of passengers between the departure and destination points. Therefore, the connectivity of the urban rail transit network should be considered in order to quantify the resilience level of the urban rail transit network through topological performance. The network efficiency E of the urban rail transit network U (τ) at the simulation time step τ is:

[0173]

[0174] Among them, d ij (τ) represents the shortest path distance between node i and node j at simulation time step τ;

[0175] The ability to restore the topological performance of urban rail transit networks is:

[0176]

[0177] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple. For relevant parts, refer to the partial description of the method embodiment. The system and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without expending creative work.

[0178] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for evaluating the resilience of urban rail transit networks considering the dynamics of passenger flow, characterized in that: include: S1. Use complex network theory to model urban rail transit networks; S2. Calculate the traffic demand between stations in the urban rail transit network to obtain passenger flow demand data; S3. Based on the passenger flow demand data from the origin to the destination between each node, the user equilibrium model is used to obtain the passenger flow distribution; S4. Establish a cascading failure model for urban rail transit networks considering station overload; S5. Establish an urban rail transit network restoration model that considers passenger flow redistribution and repair station status; S6. Quantify the recovery capacity of the urban rail transit network through the three indicators of nodes, lines and topology, and evaluate the resilience of the urban rail transit network.

2. The urban rail transit network resilience assessment method considering passenger flow dynamics according to claim 1 is characterized in that: In S1, the urban rail transit network is modeled, stations are modeled as nodes, tracks between stations are modeled as edges, and the rail transit network is G(V,E), where V represents the node set and E represents the edge set.

3. The urban rail transit network resilience assessment method considering passenger flow dynamics according to claim 2 is characterized in that: S2 calculates the traffic demand between stations in the urban rail transit network, specifically: The proportion f of individual commutes from origin o to destination d od for: Among them, D d and D i is the total traffic demand of site d and site i, l od is the distance between the originating station o and the destination d, in km, p(l od ) is the distance factor between the originating station o and the destination d, p(l oi ) is the distance factor between the origin o and the destination i; The distance factor p(l od )for: Traffic demand F from origin o to destination d od The calculation is as follows: F od =D o f od ψ, Where ψ is the parameter that controls the intensity of inter-station traffic demand, D o is the total traffic demand of station o.

4. The urban rail transit network resilience assessment method considering passenger flow dynamics according to claim 3 is characterized in that: S3 uses the user equilibrium model to obtain the passenger flow distribution, specifically: The user equilibrium model is: Where: Indicates that edge u has flow x u Driving time under the condition of represents the flow on path m from the starting point o to the destination d; when edge u belongs to the path m from the starting point o to the destination d, Otherwise Use the BPR function to represent the edge u when the flow is x u Driving time Where, v is the train speed; l u is the actual length of side u; c u is the design capacity of edge u, and α and β are the coefficients of the line.

5. The urban rail transit network resilience assessment method considering passenger flow dynamics according to claim 4 is characterized in that: In S4, a cascading failure model of urban rail transit network is established, specifically: S401. Calculate the passenger flow p of node i based on the flow of the adjacent lines of node i. i : Among them, Φ i is the set of neighboring edges of node i; S402, design capacity C of node i i for: C i =(1+μ)p i Among them, μ is the capacity parameter, which controls the value of the design capacity; S403, maximum capacity of node i for: Wherein, η is the overload parameter that controls the maximum capacity value; S404. Based on the relationship between passenger flow and capacity at simulation time step τ, a rule for determining the state of node i is proposed: Where r is a random number uniformly distributed between 0 and 1; When p i (τ)≤C i When , the status of the station is normal; when When , the station status is faulty; When node i satisfies When the condition is met, the site may not be able to operate and is considered to be failed, with a probability θ i (τ) is: S405. In each iteration step, the total traffic demand value of all stations remains unchanged; In the iterative step τ, the traffic demand D of node j, one of the neighboring nodes of failed node i, is updated j (τ): Where Δ represents the set of remaining nodes except the failed node, and the traffic demand D of the failed node i is i (τ) is set to 0; S406. Based on the updated remaining node traffic demand and network topology, the user balance model is solved to recalculate the site and line traffic. If there are no more faulty nodes, the cascading failure stops at iterative step τ; otherwise, repeat the above steps S404 to S406.

6. The urban rail transit network resilience assessment method considering passenger flow dynamics according to claim 5 is characterized in that: In S5, an urban rail transit network restoration model is established, specifically: S501. Repairing a faulty node in the urban rail transit network, including: Degree-based repair strategy: sort the faulty nodes in descending order of their degree values and repair them; Betweenness-based repair strategy: sort the faulty nodes in descending order of their betweenness values and repair them; Repair strategy based on traffic demand: sort the faulty nodes in descending order of their initial traffic demand values and repair them; Repair strategy based on passenger flow: sort the faulty nodes in descending order of initial passenger flow and repair them; S502: The repaired node reconnects with the adjacent nodes according to the initial network structure and re-receives the traffic demand allocated by other normal nodes. The traffic demand D of the repaired node i in any iterative step τ is i (τ) is: S503: Traffic demand D of other nodes k k (τ) is updated as:

7. The urban rail transit network resilience assessment method considering passenger flow dynamics according to claim 6 is characterized in that: S6 evaluates the resilience of urban rail transit networks, specifically: S601, evaluate the recovery capability of the urban rail transit network by the status of the repaired nodes, and the operating efficiency of node i at the simulation time step τ for: At the simulation time step τ, the average operating efficiency E of each station in the urban rail transit network is N for: The node operation efficiency resilience index is: Among them, τ s is the time step when all nodes are attacked, τ f The simulation time step when all failed nodes are repaired; (1-E N (τ s ))N f Optimal toughness value; S602. Use line operation efficiency to construct the resilience index of the urban rail transit network, quantify the performance recovery results after the implementation of repair measures, and the operating efficiency of line u at the simulation time step τ for: in, is the travel time of line u in the traffic equilibrium state at the simulation time step τ; at any simulation time step τ, the line operation efficiency of the urban rail transit network is: The line operation efficiency resilience index is: S603. Quantify the resilience level of urban rail transit network through topological performance, and the network efficiency E of urban rail transit network U (τ) at the simulation time step τ is: Among them, d ij (τ) represents the shortest path distance between node i and node j at simulation time step τ; The ability to restore the topological performance of urban rail transit networks is:

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