A multi-stage and multi-dimensional resilience assessment method and system for subway networks

Abstract

The present invention relates to the technical field of traffic resilience assessment, and in particular to a multi-stage and multi-dimensional resilience assessment method and system for a subway network. The method includes: Step S1: Based on the dynamic performance of the directed subway network system before and after interference occurs, construct a multi-stage resilience assessment framework, which includes an assessment model in the preparation stage, an assessment model in the absorption stage, an assessment model in the recovery stage, and an assessment model in the improvement stage. Any assessment model includes at least one evaluation index; Step S2: Calculate the resilience assessment values of the directed subway network system in different stages according to the at least one evaluation index; Step S3: According to the resilience assessment values, guide the operator to optimize the allocation of subway traffic resources and formulate emergency response strategies. The present invention can more comprehensively evaluate the dynamic performance of the subway network system during the entire interference cycle, and guide the operator to optimize resource allocation and emergency response strategies.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic resilience assessment, and particularly to a multi-stage and multi-dimensional resilience assessment method and system for subway networks. Background Art

[0002] As a core component of the modern urban public transportation system, the subway has become an important tool for alleviating urban traffic congestion due to its powerful carrying capacity, fast running speed, and significant environmental protection advantages. However, the operation of the subway system is not invulnerable. It is vulnerable to various factors, including human factors (such as the peak travel season during holidays and the surge in passenger flow caused by large-scale sports events), systematic problems (such as power outages and train delays), and natural disasters (such as floods and earthquakes). These interferences not only bring inconvenience to passengers but may also cause a wider range of traffic paralysis and even affect the normal operation of the entire urban function.

[0003] To address these challenges, the resilience research of the subway system has gradually attracted the attention of the academic and industrial communities. Resilience is defined as the ability of the subway system to maintain or quickly resume normal operation in the face of various interferences. Traditional resilience assessment methods mainly rely on topological characteristic indicators and evaluate the resilience by analyzing the performance changes of the system before and after the interference. However, these methods are usually limited to static assessment and are difficult to comprehensively describe the full-cycle performance of the subway system from the initial state before the interruption to the absorption, recovery, and even optimization and improvement after the interference.

[0004] In the existing technology, most of the subway network resilience assessment models are for undirected networks or partially directed networks. The undirected network model represents the subway system through undirected nodes (platforms) and undirected arcs (tracks), but it cannot reflect the directional characteristics of the two-way running tracks and passenger flow in the subway system. Therefore, some studies have introduced partially directed network models. Although they have improved the deficiencies of the undirected model to a certain extent, it is still difficult to accurately evaluate the dynamic characteristics of the actual subway system, especially the system resilience when interference occurs at a one-way platform.

[0005] In addition, the existing resilience assessment methods often focus on a specific stage after the system is interfered, such as the vulnerability assessment during the interference or the partial recovery analysis after the interference, while ignoring the system performance in the preparation stage before the interference and the ability of optimization and improvement after the interference. This single-stage resilience assessment method cannot comprehensively reflect the dynamic performance of the subway system in the full cycle.

[0006] In terms of the selection of resilience assessment indicators, existing methods also have obvious shortcomings. Most assessment methods are still based on static topological indicators, such as network connectivity and topological efficiency, which are difficult to reflect the actual performance of the subway system under the dynamic supply and demand balance. Although some studies have begun to introduce functional indicators such as passenger flow distribution and passenger demand, they have not considered the structural and functional characteristics of the system at the same time, resulting in the evaluation results often ignoring the actual needs of passengers.

[0007] Therefore, constructing a comprehensive, multi-stage resilience assessment framework that takes into account both the structural and functional characteristics of the system has become a key issue that needs to be urgently addressed in the current technological field. Summary of the invention

[0008] In order to solve the above technical problems, the present invention provides a multi-stage and multi-dimensional resilience assessment method and system for a subway network, the method comprising the following steps:

[0009] Step S1: Based on the dynamic performance of the directed subway network system before and after the disturbance, a multi-stage resilience assessment framework is constructed, wherein the multi-stage resilience assessment framework includes an assessment model for the preparation stage, an assessment model for the absorption stage, an assessment model for the recovery stage, and an assessment model for the enhancement stage, and any assessment model includes at least one evaluation indicator;

[0010] Step S2: calculating the resilience evaluation value of the directional subway network system at different stages according to the at least one evaluation index;

[0011] Step S3: guiding the operator to optimize subway traffic resource allocation and formulate emergency response strategies according to the resilience assessment value;

[0012] Among them, the evaluation model in the preparation stage is used to evaluate the initial performance index value of the directional subway network system before the interference occurs, the evaluation model in the absorption stage is used to calculate the performance index value of the directional subway network system when it decreases after the interference occurs, the evaluation model in the recovery stage is used to calculate the performance index value of the directional subway network system in the stage of taking recovery measures, and the evaluation model in the improvement stage is used to calculate the performance index value of the directional subway network system after the interference is restored.

[0013] In one embodiment of the present invention, the network topology diagram of the directed subway network system includes a plurality of directed nodes and a plurality of directed edges, wherein the directed nodes represent directed platforms, and the directed edges represent directed sections connecting the directed nodes.

[0014] In one embodiment of the present invention, the evaluation model in the preparation phase is used to evaluate the initial performance index value of the directional subway network system before the interference occurs, including:

[0015] On the premise that all the directed nodes and the edges are fully connected before interference occurs, the number of nodes pointing to the directed node i is denoted as the in-degree d in (i), and the number of nodes that the directed node i points to other nodes is denoted as the out-degree d out (i). Respectively, normalize d in (i) and d out (i) to obtain the in-degree centrality D in (i) and the out-degree centrality D out (i);

[0016] Calculate the full-load rate P i,k of each directed node, and normalize the P i,k to obtain the normalized full-load rate

[0017]

[0018] Based on the normalized full-load rate the in-degree centrality D in (i) and the out-degree centrality D out (i), obtain the initial performance index value R p of the directed subway network system before interference occurs:

[0019]

[0020] where k is the train number passing through the directed node i, and (P i,k ) max represents the maximum value among the full-load rates of all directed nodes, and (P i,k ) min represents the minimum value among the full-load rates of all directed nodes.

[0021] In an embodiment of the present invention, the method for calculating the full-load rate P i,k of each directed node is as follows:

[0022] Calculate the full-load rate P i,k of each directed node according to the ratio of the remaining number of passengers of each train at each directed node to the rated capacity of the train:

[0023]

[0024] where, represents the remaining number of passengers of train k at the directed node i, and its value is determined by the number of passengers at the previous node (i - 1) of the directed node i and the number of passengers getting on and off at the directed node i, Indicates the number of passengers getting off at the directed node i. Indicates the number of passengers getting on at the directed node i, and N represents the total number of nodes in the subway network; c i,k Indicates the rated capacity of train k.

[0025] In an embodiment of the present invention, the evaluation model in the absorption stage is used to calculate the performance index values when the directed subway network system declines after a disturbance occurs, including:

[0026] Calculate the removal rate f of the directed platform in the directed subway network system after a disturbance occurs r :

[0027] f r = f 1 (S = 0.1)

[0028]

[0029] Calculate the failure rate f of the directed platform in the directed subway network system after a disturbance occurs c :

[0030] f c = f 2 (I = 0.9)

[0031]

[0032] Take the ratio of the efficiency difference V between the directed subway network system before and after the disturbance and the initial efficiency E e to obtain the vulnerability rate f v :

[0033]

[0034] According to the removal rate f r , the failure rate f c and the vulnerability rate f v , obtain the performance index value R when the directed subway network system declines after a disturbance occurs a :

[0035] R a = f r + f c + f v

[0036] where S represents the relative size of the largest connected subgraph, N represents the total number of directed platforms in the subway network, N' represents the number of directed platforms in the largest connected subgraph after the directed subway network system is disturbed, f 1(S = 0.1) represents the removal rate when S = 0.1; I represents the degree value of the interference suffered by the directed subway network system; M represents the number of paths from an origin platform O to a destination platform D before the interference occurs; Q ij represents the number of passengers between the directed platform i and the directed platform j before the interference occurs; M' represents the number of paths from an origin platform O to a destination platform D after the interference occurs; Q' ij represents the number of passengers between the directed platform i and the directed platform j after the interference occurs; f 2 (I = 0.9) represents the failure rate when I = 0.9; V = ΔE e = E e - E e ', E e represents the network efficiency of the directed platform before the interference, E e ' represents the network efficiency of the directed platform after the interference.

[0037] In an embodiment of the present invention, the network efficiency E of the directed platform before the interference e :

[0038]

[0039] wherein, d ij represents the shortest path between the directed platform i and the directed platform j before the interference occurs, and Q represents the total number of passengers of all directed platforms in the network before the interference occurs.

[0040] In an embodiment of the present invention, the network efficiency E of the directed platform after the interference e ':

[0041]

[0042] wherein, d' ij represents the shortest path between the directed platform i and the directed platform j after the interference occurs, and Q' represents the total number of passengers of all directed platforms in the network after the interference occurs.

[0043] In an embodiment of the present invention, the evaluation model in the recovery stage is used to calculate the performance index value of the directed subway network system in the stage of taking recovery measures, including:

[0044] After the interference occurs, for each train k and each directed platform i, based on the rated capacity c of the train k i,k and the remaining number of passengers of the train k at the directed platform i calculate the available capacity of the carriage of the train k at the directed platform i; k ∈ {1, 2, 3,...., K}, K represents the total number of trains, i ∈ {1, 2, 3,...., N}, N represents the total number of platforms;

[0045] The number of passengers waiting for train k at the directed platform i is denoted as the instantaneous demand. According to the available capacity of the carriage and the instantaneous demand, calculate the instantaneous supply-demand ratio ρ of each train k arriving at each directed platform i i,k ;

[0046] Since the total number of platforms is N and the total number of trains is K, there are N×K cases of all instantaneous supply-demand ratios. Furthermore, construct an instantaneous supply-demand ratio matrix P with a dimension of N×K i,k :

[0047]

[0048] Traverse each instantaneous supply-demand ratio ρ i,k in the instantaneous supply-demand ratio matrix P i,k , obtain the quantity card of the instantaneous supply-demand ratio ρ i,k less than or equal to 1, and take the ratio R r of the card to the total quantity NK of all instantaneous supply-demand ratios as the performance index value in the recovery stage:

[0049]

[0050] In an embodiment of the present invention, the evaluation model in the improvement stage is used to calculate the performance index value of the directed subway network system after interference recovery, including:

[0051] After interference recovery, for each train k and each directed platform i, based on the rated capacity c i,k of train k and the remaining number of passengers of train k at the directed platform i calculate the available capacity of the carriage of train k at the directed platform i; k∈{1,2,3,....,K}, K represents the total number of trains, i∈{1,2,3,....,N}, N represents the total number of platforms;

[0052] The number of passengers waiting for train k at the directed platform i is denoted as the instantaneous demand. According to the available capacity of the carriage and the instantaneous demand, calculate the instantaneous supply-demand ratio ρ' of each train k arriving at each directed platform i i,k ;

[0053] Since the total number of platforms is N and the total number of trains is K, there are N×K cases of all instantaneous supply-demand ratios. Furthermore, construct an instantaneous supply-demand ratio matrix P' with a dimension of N×K i,k :

[0054]

[0055] Based on the instantaneous supply-demand ratio matrix P'i,k , calculate the instantaneous supply-demand ratio ρ' after interference recovery i,k of the average value E(ρ' i,k ), and at the same time calculate the instantaneous supply-demand ratio ρ during the recovery stage i,k of the average value E(ρ i,k ). Denote η as the number of the platform with passenger flow congestion. According to E(ρ i,k ) and E(ρ' i,k ), obtain the performance index value R of the directed subway network system after interference recovery η :

[0056]

[0057] Based on the same inventive concept, the present invention also provides a subway network multi-stage multi-dimensional resilience evaluation system for implementing the steps of the subway network multi-stage multi-dimensional resilience evaluation method. The subway network multi-stage multi-dimensional resilience evaluation system includes the following modules:

[0058] A multi-stage resilience evaluation framework construction module for constructing a multi-stage resilience evaluation framework based on the dynamic performance of the directed subway network system before and after interference occurs. The multi-stage resilience evaluation framework includes an evaluation model in the preparation stage, an evaluation model in the absorption stage, an evaluation model in the recovery stage, and an evaluation model in the improvement stage. Any evaluation model includes at least one evaluation index;

[0059] A resilience evaluation value calculation module for calculating the resilience evaluation value of the directed subway network system in different stages according to the at least one evaluation index;

[0060] An operation optimization module for guiding the operator to optimize the allocation of subway traffic resources and formulate emergency response strategies according to the resilience evaluation value;

[0061] Among them, the evaluation model in the preparation stage is used to evaluate the initial performance index value of the directed subway network system before interference occurs. The evaluation model in the absorption stage is used to calculate the performance index value when the directed subway network system decreases after interference occurs. The evaluation model in the recovery stage is used to calculate the performance index value of the directed subway network system in the stage of taking recovery measures. The evaluation model in the improvement stage is used to calculate the performance index value of the directed subway network system after interference recovery.

[0062] The above technical solution of the present invention has the following advantages compared with the prior art:

[0063] (1)Enhanced the applicability of the resilience assessment model. Based on the fully directed subway network model, the present invention can effectively analyze the performance changes of the system before and after the unidirectional platform is subjected to external interference, thus more accurately reflecting the operating characteristics of the actual subway system and solving the deficiencies of traditional models in characterizing the characteristics of actual systems.

[0064] (2)Achieved full-cycle resilience assessment. The phased resilience assessment framework proposed by the present invention divides the resilience of the subway system into a preparation stage, an absorption stage, a recovery stage, and a promotion stage, comprehensively covering the dynamic change process of the system from before the interference to after the interference. This method overcomes the limitation of traditional assessment methods that only focus on a single stage and can more comprehensively evaluate the dynamic performance of the system during the entire interference cycle.

[0065] (3)Comprehensively considered the system structure and functional characteristics. The present invention formulates resilience assessment indicators by combining the structural characteristics of the system (such as network connectivity, node degree) and functional characteristics (such as passenger flow distribution, supply-demand ratio). The introduction of such multi-dimensional indicators makes the assessment results closer to the actual operation scenario and can provide a scientific basis for resource allocation optimization and emergency response strategies for the operator. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in combination with the drawings, where

[0067] Figure 1 is a schematic flow chart of a multi-stage and multi-dimensional resilience assessment method for a subway network provided in an embodiment of the present invention;

[0068] Figure 2 is a schematic work flow chart of a multi-stage resilience assessment framework provided in an embodiment of the present invention;

[0069] Figure 3 is the average relative size of the largest connected subgraph in the network when simulating the interference of the platform in the subway network by randomly attacking the platform during the absorption stage;

[0070] Figure 4 is the result of the change in the degree of network interference with the change in the failure ratio of the directed platform when simulating the failure scenario of the directed platform by using the method of randomly removing the platform;

[0071] Figure 5 is the simulation result of the subway network vulnerability rate, where (a) represents the simulation result of the vulnerability rate of the up-platform and (b) represents the simulation result of the vulnerability rate of the down-platform;

[0072] Figure 6 is a schematic structural diagram of a multi-stage and multi-dimensional resilience assessment system for a subway network provided in an embodiment of the present invention;

[0073] Description of the reference numerals in the drawings: 100, multi-stage resilience assessment framework construction module; 200, resilience assessment value calculation module; 300, operation optimization module. Specific embodiments

[0074] The present invention will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited are not intended to limit the present invention.

[0075] Embodiment 1

[0076] The present invention provides a multi-stage and multi-dimensional resilience assessment method for a subway network. This method constructs a multi-stage resilience assessment framework, comprehensively considers the structural characteristics and functional characteristics of the system, and comprehensively evaluates the dynamic performance of the subway system before and after interference. Specifically, referring to Figure 1 and Figure 2 as shown, the method includes the following steps:

[0077] Step S1: Based on the dynamic performance of the directed subway network system before and after interference, construct a multi-stage resilience assessment framework. The multi-stage resilience assessment framework includes an assessment model in the preparation stage, an assessment model in the absorption stage, an assessment model in the recovery stage, and an assessment model in the enhancement stage. Any assessment model includes at least one evaluation index;

[0078] Step S2: Calculate the resilience assessment value of the directed subway network system at different stages according to the at least one evaluation index;

[0079] Step S3: According to the resilience assessment value, guide the operator to optimize the allocation of subway traffic resources and formulate emergency response strategies;

[0080] Among them, the assessment model in the preparation stage is used to evaluate the initial performance index value of the directed subway network system before interference occurs. The assessment model in the absorption stage is used to calculate the performance index value when the directed subway network system declines after interference occurs. The assessment model in the recovery stage is used to calculate the performance index value of the directed subway network system in the stage of taking recovery measures. The assessment model in the enhancement stage is used to calculate the performance index value of the directed subway network system after interference recovery.

[0081] Based on the above multi-stage resilience assessment framework, specific technical features and evaluation indicators are introduced in each stage to ensure the accuracy and comprehensiveness of the assessment results. Specifically as follows:

[0082] Furthermore, the network topology diagram of the directed subway network system includes a plurality of directed nodes and a plurality of directed edges. The directed nodes represent directed platforms, and the directed edges represent directed sections connecting the directed nodes.

[0083] In the preparation stage, use the evaluation model of the preparation stage to evaluate the initial performance index values of the directed subway network system before the occurrence of interference, including:

[0084] On the premise that all the directed nodes and the edges are fully connected before the occurrence of interference, denote the number of nodes pointing to the directed node i as the in-degree d in (i), and denote the number of nodes that the directed node i points to other nodes as the out-degree d out (i). If the node j points to the node i, then A ji = 1; otherwise A ji = 0. Similarly, if the node i points to the node j, then A ij = 1; otherwise A ij = 0. The expressions of d in (i) and d out (i) are as follows:

[0085]

[0086] To obtain a unified metric, use the total number of nodes N in the subway network to normalize d in (i) and d out (i) respectively, and obtain the in-degree centrality D in (i) and the out-degree centrality D out (i) with a value range between 0 and 1:

[0087]

[0088] However, only considering the impact of the topological structure on the system performance is limited and one-sided. Since the full-load rate directly reflects the travel comfort of passengers, therefore, according to the ratio of the remaining number of passengers in each train of each directed node to the rated capacity of the train, calculate the full-load rate P i,k :

[0089]

[0090] Normalize the P i,k to obtain the normalized full-load rate

[0091]

[0092] Based on the normalized full-load rate the in-degree centrality D in (i) and the out-degree centrality D out (i), obtain the initial performance index value R p :

[0093]

[0094] Among them, k is the train number passing through the directed node i, indicating the remaining number of passengers of train k at the directed node i, and its value is determined by the number of passengers at the previous node (i - 1) of the directed node i and the number of passengers getting on and off at the directed node i. indicating the number of passengers getting off at the directed node i, indicating the number of passengers getting on at the directed node i; N represents the total number of nodes in the subway network, and c i,k represents the rated capacity of train k; (P i,k ) max represents the maximum value among the full-load rates of all directed nodes, (P i,k ) min represents the minimum value among the full-load rates of all directed nodes.

[0095] During the absorption stage, use the evaluation model of the absorption stage to calculate the performance index values when the directed subway network system declines after the occurrence of interference, including:

[0096] Use the removal rate f r of the directed platform in the directed subway network system after the occurrence of interference as one of the indicators of the absorption capacity of the directed subway network system, indicating the connectivity of the network under different degrees of interference. As the removal rate of the platform increases, the network connectivity decreases, and the relative size of the largest connected subgraph becomes smaller. By simulating different removals of directed platforms, the performance of the system under interference can be evaluated. For example, when S = 0.1, the subway network is almost paralyzed, and the removal rate f 1 at this time is one of the indicators of the absorption stage, denoted as f r :

[0097] f r = f 1 (S = 0.1),

[0098]

[0099] The interference of the directed platform affects both the network topology and the passenger flow distribution. The failure rate f c of the directed platform in the directed subway network system after the occurrence of interference is another indicator to measure the absorption capacity, used to measure the degree of network failure. As the degree of interference increases (i.e., the failure rate of the directed platform rises), the number of paths connecting the origin platform (O) to the destination platform (D) in the network will decrease, and the number of passengers between the directed platforms i and j will also decrease.

[0100] When the degree value I of the interference on the directed subway network system reaches 90%, the subway network is close to collapse. The failure rate f at this time 2 is one of the indicators in the absorption stage, denoted as f c :

[0101] f c = f 2 (I = 0.9),

[0102]

[0103] The ratio of the efficiency difference V between the directed subway network system before and after interference to the initial efficiency E e gives the vulnerability rate f v :

[0104]

[0105] According to the removal rate f r and the failure rate f c and the vulnerability rate f v , the performance index value R when the directed subway network system declines after the interference occurs is obtained a :

[0106] R a = f r + f c + f v

[0107] where S represents the relative size of the largest connected subgraph of the directed subway network system after the interference occurs, N represents the total number of directed platforms in the subway network, N' represents the number of directed platforms in the largest connected subgraph of the directed subway network system after the interference; I represents the degree value of the interference on the directed subway network system; M represents the number of paths from an origin platform O to a destination platform D before the interference occurs; Q ij represents the number of passengers between the directed platform i and the directed platform j before the interference occurs; M' represents the number of paths from an origin platform O to a destination platform D after the interference occurs; Q' ij represents the number of passengers between the directed platform i and the directed platform j after the interference occurs; V = ΔE e = E e - E e ', E e represents the network efficiency of the directed platform before the interference, and E e ' represents the network efficiency of the directed platform after the interference.

[0108] Furthermore, the network efficiency E of the directed platform before the interference e :

[0109]

[0110] Among them, d ij represents the shortest path between the directed platform i and the directed platform j before interference occurs, and Q represents the total number of passengers on all directed platforms in the network.

[0111] Furthermore, the network efficiency E e ' of the directed platform after interference is:

[0112]

[0113] Among them, d' ij represents the shortest path between the directed platform i and the directed platform j after interference occurs, and Q' represents the total number of passengers on all directed platforms in the network after interference occurs.

[0114] During the recovery stage, use the evaluation model in the recovery stage to calculate the performance index values of the directed subway network system during the recovery measure stage, including:

[0115] After interference occurs, for each train k and each directed platform i, based on the rated capacity c i,k of train k and the remaining number of passengers of train k at the directed platform i calculate the available capacity of the carriages of train k at the directed platform i; k ∈ {1, 2, 3,...., K}, K represents the total number of trains, i ∈ {1, 2, 3,...., N}, N represents the total number of platforms;

[0116] Record the number of passengers waiting for train k at the directed platform i as the instantaneous demand. According to the available capacity of the carriage and the instantaneous demand, calculate the instantaneous supply-demand ratio ρ i,k of each train k arriving at each directed platform i;

[0117] Since the total number of platforms is N and the total number of trains is K, there are N×K cases of all instantaneous supply-demand ratios. Furthermore, construct an instantaneous supply-demand ratio matrix P i,k with a dimension of N×K:

[0118]

[0119] Traverse each instantaneous supply-demand ratio ρ i,k in the instantaneous supply-demand ratio matrix P i,k , obtain the quantity card of the instantaneous supply-demand ratio ρ i,k less than or equal to 1, and take the ratio R r of the card and the total quantity NK of all instantaneous supply-demand ratios as the performance index value in the recovery stage:

[0120]

[0121] During the improvement stage, use the evaluation model of the improvement stage to calculate the performance index values of the directed subway network system after interference recovery, including:

[0122] After interference recovery, for each train k and each directed platform i, based on the rated capacity c of train k i,k and the remaining number of passengers of train k at the directed platform i calculate the available capacity of the carriages of train k at the directed platform i; k ∈ {1, 2, 3,...., K}, where K represents the total number of trains, and i ∈ {1, 2, 3,...., N}, where N represents the total number of platforms;

[0123] Record the number of passengers waiting for train k at the directed platform i as the instantaneous demand. According to the available capacity of the carriages and the instantaneous demand, calculate the instantaneous supply-demand ratio ρ' of each train k arriving at each directed platform i i,k ;

[0124] Since the total number of platforms is N and the total number of trains is K, there are N×K cases of all instantaneous supply-demand ratios. Furthermore, construct an instantaneous supply-demand ratio matrix P' with a dimension of N×K i,k :

[0125]

[0126] Based on the instantaneous supply-demand ratio matrix P' i,k , calculate the average value E(ρ' i,k ) of the instantaneous supply-demand ratio ρ' after interference recovery. At the same time, calculate the average value E(ρ i,k ) of the instantaneous supply-demand ratio ρ during the recovery stage. Denote η as the number of the platform with passenger backlog. According to E(ρ i,k ) and E(ρ' i,k ), obtain the performance index value R of the directed subway network system after interference recovery i,k : i,k : η :

[0127]

[0128] Next, in order to further verify the effectiveness of the method described in the present invention, apply the method to the fully directed Shenzhen subway network. As of October 2013, the Shenzhen subway network included 5 lines and 131 stations, with a total of 252 directed platforms. Use the above resilience evaluation method to evaluate and analyze the system performance in the preparation stage, absorption stage, recovery stage, and improvement stage respectively.

[0129] (1) Preparation stage

[0130] In the preparation stage, as analyzed from Table 1, the resilience value of Metro Line 4 is the highest, which is 0.214, about five times that of the minimum resilience value. In addition, the full-load rate of Shenzhen North Station is 7.468, and the resilience value is the highest, which is 1.016, the largest among all stations. The stations with resilience values higher than the average are mostly transfer stations, indicating that the key nodes in the network, especially the transfer stations, have a significant impact on the overall resilience value of the subway system.

[0131] Table 1 Evaluation results in the preparation stage

[0132]

[0133] (2) Absorption stage

[0134] In the absorption stage, the interference suffered by the platforms in the subway network is simulated by randomly attacking the platforms. The initial number of network nodes is set as N = 252, and the number of remaining nodes N' after each attack is obtained through simulation calculation. To effectively reduce the deviation of the simulation results, 10 repeated experiments are carried out under the same experimental conditions. Subsequently, the average relative size of the largest connected subgraph in the network is calculated, and the final result is as Figure 3 shown. When the proportion of removed nodes is less than 10%, the overall network performance remains above 70%. When the proportion of removed nodes reaches 40%, the relative size of the largest connected subgraph will drop below 0.1, and at this time, the network is determined to be in a collapsed state.

[0135] In the Shenzhen subway network, the initial number of paths from an origin platform (O) to a destination platform (D) is 63,252, and the weekday passenger flow reaches 4,752,462 person-times. As the number of interferences suffered by the directed platforms increases, the number of connected OD pairs gradually decreases, and the passenger flow is also affected accordingly. As Figure 4 shown, the present invention calculates the network failure level by using the same method of randomly removing platforms. The results show that when the proportion of interfered platforms is between 15% and 20%, the network failure rate shows a sharp upward trend. When the failure rate of the directed platforms reaches 75%, the degree of network interference reaches 90%, and at this time, the network is regarded as collapsed.

[0136] Then, Figure 5 (a) and (b) of respectively show the simulation results of the vulnerability rates in the up and down directions of the Shenzhen subway network. The results show that there are obvious differences between the up and down results. Compared with ordinary stations, key stations, especially transfer stations, have a more significant impact on the network performance.

[0137] (3) Recovery stage

[0138] During the recovery stage, the present invention simulates the interference situation of each line to strengthen practical applications. These scenarios are based on the accidents that have occurred in the history of the Shenzhen Metro and the corresponding recovery measures. Compared with ordinary platforms, the impact of interference on high-passenger-flow platforms is greater. Therefore, the present invention simulates the interference situation of the platform with the largest passenger flow up and down throughout the day based on a fully directed network, that is, the passenger flow is doubled. When interference occurs, an additional train is directly dispatched to the interfered platform without stopping at intermediate stations. Table 2 details the instantaneous supply-demand ratio results of each line under the above interference scenarios.

[0139] Table 2 Instantaneous supply-demand ratio during the evaluation stage

[0140]

[0141] The average instantaneous supply-demand ratio of each line of the Shenzhen Metro is 0.171. The results show that although the supply-demand ratio values of some key platforms, especially transfer platforms, are less than or equal to 1, the proportion of these platforms in the total number of stations along the whole line is less than 20%. This indicates that the Shenzhen Metro network can quickly respond to interference and effectively resume normal operation.

[0142] (4) Enhancement stage

[0143] During the enhancement stage, the instantaneous supply-demand ratio when the system resumes to the normal operation state is calculated again. Taking the evaluation results in Table 3 as an example, the proportion of the average supply-demand ratio of the up line of Line 4 being 1 or less is 0.208.

[0144] Table 3 Average instantaneous supply-demand ratio during the enhancement stage (Note: x w represents the number of supply-demand ratios being 1 or less at each time period throughout the day)

[0145]

[0146] In summary, the present invention applies the proposed resilience evaluation method to the actual Shenzhen Metro system to evaluate the resilience of the fully directed Shenzhen Metro network; the proposed resilience evaluation method evaluates the performance of the Shenzhen Metro system in stages, covering each state and process before and after the network is interfered; the resilience evaluation method proposed by the present invention provides multi-dimensional evaluation indicators, considering the performance of both the structure and function of the system.

[0147] Embodiment 2

[0148] Based on the same inventive concept as in Embodiment 1, the present invention also provides a multi-stage and multi-dimensional resilience evaluation system for the subway network, which is used to implement the steps of the multi-stage and multi-dimensional resilience evaluation method for the subway network described in Embodiment 1. As Figure 6 shown, the multi-stage and multi-dimensional resilience evaluation system for the subway network includes the following modules:

[0149] The multi-stage resilience assessment framework construction module 100 is used to construct a multi-stage resilience assessment framework based on the dynamic performance of the directed subway network system before and after interference. The multi-stage resilience assessment framework includes an assessment model in the preparation stage, an assessment model in the absorption stage, an assessment model in the recovery stage, and an assessment model in the improvement stage. Any assessment model includes at least one evaluation index;

[0150] The resilience assessment value calculation module 200 is used to calculate the resilience assessment value of the directed subway network system in different stages according to the at least one evaluation index;

[0151] The operation optimization module 300 is used to guide the operator to optimize the allocation of subway traffic resources and formulate emergency response strategies according to the resilience assessment value;

[0152] Among them, the assessment model in the preparation stage is used to evaluate the initial performance index value of the directed subway network system before interference occurs. The assessment model in the absorption stage is used to calculate the performance index value when the directed subway network system declines after interference occurs. The assessment model in the recovery stage is used to calculate the performance index value of the directed subway network system in the stage of taking recovery measures. The assessment model in the improvement stage is used to calculate the performance index value of the directed subway network system after interference recovery.

[0153] A multi-stage and multi-dimensional resilience assessment system for subway network proposed in this embodiment is used to implement the foregoing multi-stage and multi-dimensional resilience assessment method for subway network. Therefore, the specific implementation manners in the system can be seen in the embodiment part of the foregoing multi-stage and multi-dimensional resilience assessment method for subway network. For example, the multi-stage resilience assessment framework construction module 100, the resilience assessment value calculation module 200, and the operation optimization module 300 are respectively used to correspondingly implement steps S1, S2, and S3 in the multi-stage and multi-dimensional resilience assessment method for subway network in Embodiment 1. Therefore, the specific implementation manners can be referred to the descriptions of the corresponding various part embodiments. To avoid redundancy, they will not be elaborated here.

[0154] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, such that the instructions executed by the processors of the computer or other programmable data processing devices produce means for implementing the functions specified in one or more flows Figure 1 one or more flows and / or blocks Figure 1 or means for implementing the functions specified in one or more blocks.

[0156] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means for implementing the functions specified in one or more flows Figure 1 one or more flows and / or blocks Figure 1 or means for implementing the functions specified in one or more blocks.

[0157] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more flows Figure 1 one or more flows and / or blocks Figure 1 or means for implementing the functions specified in one or more blocks.

[0158] Obviously, the above embodiments are merely examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to enumerate all implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A multi-stage and multi-dimensional resilience assessment method for a subway network, characterized in that: The following steps are involved: Step S1: Based on the dynamic performance of the directed subway network system before and after the disturbance, a multi-stage resilience assessment framework is constructed, wherein the multi-stage resilience assessment framework includes an assessment model for the preparation stage, an assessment model for the absorption stage, an assessment model for the recovery stage, and an assessment model for the enhancement stage, and any assessment model includes at least one evaluation indicator; Step S2: calculating the resilience evaluation value of the directional subway network system at different stages according to the at least one evaluation index; Step S3: guiding the operator to optimize subway traffic resource allocation and formulate emergency response strategies according to the resilience assessment value; The evaluation model in the preparation phase is used to evaluate the initial performance index value of the directional subway network system before the interference occurs, the evaluation model in the absorption phase is used to calculate the performance index value of the directional subway network system when it decreases after the interference occurs, the evaluation model in the recovery phase is used to calculate the performance index value of the directional subway network system in the stage of taking recovery measures, and the evaluation model in the improvement phase is used to calculate the performance index value of the directional subway network system after the interference is restored; The evaluation model in the absorption phase is used to calculate the performance index value of the directional subway network system when it decreases after the interference occurs, including: Calculate the removal rate f of directional platforms in a directional subway network system after interference occurs r : f r =f1(S=0.1) Calculate the failure rate f of directional platforms in a directional subway network system after interference occurs c : f c =f2(I=0.9) The efficiency difference V of the directional subway network system before and after the interference is compared with the initial efficiency E e The ratio of v : According to the removal rate f r , the failure rate f c and the fragility rate f v , we get the performance index value R of the directional subway network system when it decreases after the interference occurs a : R a =f r +f c +f v Where S represents the relative size of the largest connected subgraph, N represents the total number of directed platforms in the subway network, N' represents the number of directed platforms in the largest connected subgraph after the directed subway network system is disturbed, f1(S=0.1) represents the removal rate when S is 0.1; I represents the degree of disturbance of the directed subway network system; M represents the number of paths from a starting platform O to a destination platform D before the disturbance occurs; Q ij represents the number of passengers between directional platform i and directional platform j before the interference occurs; M' represents the number of paths from an origin platform O to a destination platform D after the interference occurs; Q' ij represents the number of passengers between directional platform i and directional platform j after the interference occurs; f2(I=0.9) represents the failure rate when I is 0.9; V=ΔE e =E e -E e ', E e represents the network efficiency before directional station interference, E e 'Indicates the network efficiency after directional station interference.

2. The multi-stage and multi-dimensional resilience assessment method for subway networks according to claim 1 is characterized in that: The network topology diagram of the directed subway network system includes a plurality of directed nodes and a plurality of directed edges, wherein the directed nodes represent directed platforms, and the directed edges represent directed sections connecting the directed nodes.

3. The multi-stage and multi-dimensional resilience assessment method for subway networks according to claim 2 is characterized in that: The evaluation model in the preparation phase is used to evaluate the initial performance index values ​​of the directional subway network system before the interference occurs, including: Assuming that all directed nodes and edges are fully connected before interference occurs, the number of nodes pointing to directed node i is recorded as in-degree d in (i), the number of other nodes pointed to by directed node i is denoted as degree d out (i), respectively for d in (i) and d out (i) Perform normalization to obtain the in-degree centrality D in (i) and out-degree centrality D out (i); Calculate the full load rate P of each directed node i,k , for the P i,k Perform normalization to obtain the normalized full load rate Based on the normalized full load factor The in-degree centrality D in (i) and the out-degree centrality D out (i) The initial performance index value R of the directional subway network system before the interference occurs is obtained. p : Where k is the train number passing through directed node i, (P i,k ) max represents the maximum value of the full load rate of all directed nodes, (P i,k ) min Indicates the minimum value of the full load rate of all directed nodes.

4. The multi-stage and multi-dimensional resilience assessment method for a subway network according to claim 3 is characterized in that: Calculate the full load rate P of each directed node i,k The method is as follows: According to the ratio of the number of remaining passengers of each train at each directed node to the rated capacity of the train, the full load rate P of each directed node is calculated. i,k : in, Represents the number of remaining passengers of train k at directed node i, whose value is the number of passengers at the previous node (i-1) of directed node i and the number of passengers getting on and off at directed node i, represents the number of passengers getting off at directed node i, represents the number of passengers boarding at directed node i, N represents the total number of nodes in the subway network; c i,k represents the rated capacity of train k.

5. The multi-stage and multi-dimensional resilience assessment method for subway networks according to claim 1 is characterized in that: The network efficiency E before the directional station interference e : Among them, d ij It represents the shortest path between directed platform i and directed platform j before the interference occurs, and Q represents the total number of passengers before the interference occurs in all directed platforms in the network.

6. The multi-stage and multi-dimensional resilience assessment method for subway networks according to claim 1 is characterized in that: The network efficiency after the directional station interference is E e ': Among them, d' ij It represents the shortest path between directed platform i and directed platform j after the interference occurs, and Q' represents the total number of passengers after the interference occurs at all directed platforms in the network.

7. The multi-stage and multi-dimensional resilience assessment method for subway networks according to claim 1 is characterized in that: The evaluation model of the recovery phase is used to calculate the performance index values ​​of the directional subway network system in the recovery measure phase, including: After the interference occurs, for each train k and each directional platform i, based on the rated capacity c of train k i,k and the remaining number of passengers of train k at directional platform i Calculate the available capacity of the carriages of train k at the directional platform i; k∈{1,2,3,....,K}, K represents the total number of trains, i∈{1,2,3,....,N}, N represents the total number of platforms; The number of passengers who will wait for train k at directional platform i Recorded as instantaneous demand, according to the available capacity of the carriage and the instantaneous demand, calculate the instantaneous supply-demand ratio ρ of each train k arriving at each directional platform i i,k ; Since the total number of platforms is N and the total number of trains is K, there are N×K cases for all instantaneous supply-demand ratios, and thus an instantaneous supply-demand ratio matrix P with a dimension of N×K is constructed. i,k : Traverse the instantaneous supply-demand ratio matrix P i,k Each instantaneous supply-demand ratio ρ i,k , obtain the instantaneous supply-demand ratio ρ i,k The number of cards less than or equal to 1, the ratio R of the card to the total number NK of all instantaneous supply and demand ratios r As performance indicator values ​​for the recovery phase:

8. The multi-stage and multi-dimensional resilience assessment method for a subway network according to claim 1 is characterized in that: The evaluation model in the improvement phase is used to calculate the performance index values ​​of the directional subway network system after the interference recovery, including: After the disturbance is restored, for each train k and each directional platform i, based on the rated capacity c of train k i,k and the remaining number of passengers of train k at directional platform i Calculate the available capacity of the carriages of train k at the directional platform i; k∈{1,2,3,....,K}, K represents the total number of trains, i∈{1,2,3,....,N}, N represents the total number of platforms; The number of passengers who will wait for train k at directional platform i Recorded as instantaneous demand, according to the available capacity of the carriage and the instantaneous demand, calculate the instantaneous supply-demand ratio ρ' of each train k arriving at each directional platform i i,k ; Since the total number of platforms is N and the total number of trains is K, there are N×K cases for all instantaneous supply-demand ratios, and thus a dimension N×K instantaneous supply-demand ratio matrix P' is constructed. i,k : Based on the instantaneous supply-demand ratio matrix P' i,k , calculate the instantaneous supply-demand ratio ρ' after the disturbance is restored i,k The average value E(ρ' i,k ), and calculate the instantaneous supply-demand ratio ρ during the recovery phase i,k The average value E(ρ i,k ), let η be the number of the platform with accumulated passenger flow, according to E(ρ i,k ) and E(ρ' i,k ), and obtain the performance index value R of the directional subway network system after interference recovery η :

9. A multi-stage and multi-dimensional resilience assessment system for a subway network, characterized in that: The steps for implementing the multi-stage and multi-dimensional resilience assessment method for a subway network as claimed in any one of claims 1 to 8, wherein the multi-stage and multi-dimensional resilience assessment system for a subway network comprises the following modules: A multi-stage resilience assessment framework construction module is used to construct a multi-stage resilience assessment framework based on the dynamic performance of the directed subway network system before and after the disturbance occurs, wherein the multi-stage resilience assessment framework includes an assessment model for the preparation stage, an assessment model for the absorption stage, an assessment model for the recovery stage, and an assessment model for the enhancement stage, and any assessment model includes at least one evaluation indicator; A resilience evaluation value calculation module, used to calculate the resilience evaluation value of the directional subway network system at different stages according to the at least one evaluation index; An operation optimization module, used to guide the operator to optimize the allocation of subway traffic resources and formulate emergency response strategies according to the resilience assessment value; Among them, the evaluation model in the preparation stage is used to evaluate the initial performance index value of the directional subway network system before the interference occurs, the evaluation model in the absorption stage is used to calculate the performance index value of the directional subway network system when it decreases after the interference occurs, the evaluation model in the recovery stage is used to calculate the performance index value of the directional subway network system in the stage of taking recovery measures, and the evaluation model in the improvement stage is used to calculate the performance index value of the directional subway network system after the interference is restored.

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