Dynamic risk assessment method and system for regional rail transit road network

Abstract

The invention relates to the technical field of network robustness analysis, in particular to a dynamic risk assessment method and system for a regional rail transit road network. According to the method, multiple factors such as train departure time, inter-station buffer time and operation supplement time are comprehensively considered, and the change of the network state can be analyzed under different initial delay situations, so that more accurate dynamic risk assessment is provided. Meanwhile, the invention further provides an optimization objective function based on a dynamic risk assessment index, and an optimal capacity increasing scheme can be solved according to different initial delay conditions, so that the network robustness is improved to the maximum extent, the node vulnerability is reduced, and the negative influence of fault spreading on the whole traffic system is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of network robustness analysis, and particularly relates to a method and system for dynamically evaluating risks of a regional rail transit road network. Background Art

[0002] The rapid development of high-speed railways in China has made ensuring the safe operation of the railway system an important practical task, and this task occupies an indispensable position in the national security strategy. As an inherent attribute for measuring the ability of a network to respond to disasters and risks, the core of network risk performance lies in revealing the stability and reliability of the network under emergencies. For the high-speed railway system, network riskiness not only reflects its ability to respond to risks such as natural disasters, human sabotage, or technical failures, but also reflects the resilience and recovery ability of the system structure. Existing methods for evaluating high-speed railway network risks usually ignore the delay propagation and cascading effects between multi-layer networks, and thus cannot accurately evaluate the global impact of faults on the entire network and its vulnerability. At the same time, most traditional methods rely on static models and fail to reflect the dynamic risks of the road network in different operating states in real time, which greatly reduces the support effect for fault prevention and emergency dispatching decisions. It can be seen that existing regional rail transit road networks lack efficient and accurate means for risk assessment in case of faults or delays. Summary of the Invention

[0003] The present invention provides a method and system for dynamically evaluating risks of a regional rail transit road network, aiming to solve the problem that existing regional rail transit road networks lack efficient and accurate means for risk assessment in case of faults or delays.

[0004] To solve the above technical problems, the technical solutions proposed by the present invention are as follows:

[0005] In a first aspect, the present invention provides a method for dynamically evaluating risks of a regional rail transit road network, including:

[0006] S1: Construct a delay model for each train at each station of the regional rail transit road network according to relevant information of the regional rail transit road network;

[0007] S2: Obtain the initial train timetable information, and calculate the running supplementary time of each train at each station and the buffer time between two trains according to the arrival and departure time relationships of each train at different stations and the arrival and departure time relationships of different trains at the same station;

[0008] S3: Based on the network delay model, construct a multi-layer network delay model under the initial delay of the regional rail transit road network;

[0009] S4: According to the multi-layer network delay model, construct a multi-layer network delay propagation model and a multi-layer network cascading failure model under the initial delay of the regional rail transit road network;

[0010] S5: Construct dynamic risk assessment indicators for the regional rail transit network based on the multi-layer network delay propagation model and the multi-layer network cascading failure model, and calculate the risk assessment results of the regional rail transit network under cascading failures with different initial delays according to the dynamic risk assessment indicators;

[0011] S6: Calculate the total capacity after increasing the capacity of the operation supplementary time and the buffer time between two trains based on the operation supplementary time of each train at each station, the buffer time between two trains, and the risk assessment results of the regional rail transit network under cascading failures with different initial delays, construct an optimization objective function, and determine the optimal solution under the initial delay based on the total capacity and the optimization objective function.

[0012] In a second aspect, the present invention provides a dynamic risk assessment system for a regional rail transit network, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the steps of the method described in the first aspect above are implemented.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] The dynamic risk assessment method for a regional rail transit network provided by the present invention combines a multi-layer network delay model, a delay propagation model, and a cascading failure model, and can comprehensively evaluate the risks of the regional rail transit network from multiple dimensions. Specifically, the method comprehensively considers multiple factors such as train departure time, buffer time between stations, and operation supplementary time, and can analyze the changes in the network state under different initial delay scenarios, thereby providing a more accurate dynamic risk assessment. At the same time, the present invention also proposes an optimization objective function based on dynamic risk assessment indicators, which can solve the optimal capacity increase solution for different initial delay conditions, thereby maximizing the network robustness, reducing node vulnerability, and reducing the negative impact of fault spread on the entire traffic system. Brief Description of the Drawings

[0015] Figure 1 It is a flowchart of a dynamic risk assessment method for a regional rail transit network according to a preferred embodiment of the present invention;

[0016] Figure 2 It is a schematic diagram of the high-speed railway network modeling process from the perspective of a multi-layer network according to a preferred embodiment of the present invention;

[0017] Figure 3 It is a schematic diagram of the cascading failure process in a multi-layer high-speed railway network according to a preferred embodiment of the present invention;

[0018] Figure 4 It is a partial high-speed railway network diagram within the jurisdiction of the Shanghai Railway Bureau according to a preferred embodiment of the present invention;

[0019] Figure 5 Schematic diagram of the change of network vulnerability with the initial delay in the preferred embodiment of the present invention;

[0020] Figure 6 Schematic diagram of the change of the remaining unaffected nodes with the initial delay in the preferred embodiment of the present invention;

[0021] Figure 7 Schematic diagram of the change of network vulnerability with the initial delay under different redundant time increments in the preferred embodiment of the present invention;

[0022] Figure 8 Schematic diagram of the change of the proportion of remaining nodes with the initial delay under different redundant time increments in the preferred embodiment of the present invention. Detailed implementation manners

[0023] The technical solutions of the present invention will be described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0024] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the art to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. Similarly, the terms such as "a" or "one" do not denote a quantity limitation, but mean that there is at least one. The term "connected" or "coupled" and the like are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms "upper", "lower", "left", "right" and the like are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship also changes accordingly. Please refer to Figure 1 , the present invention provides a method for dynamically assessing the risks of an urban rail transit network, including:

[0025] S1: Construct a delay model of each train at each station in the urban rail transit network according to the relevant information of the urban rail transit network;

[0026] S2: Obtain the initial train timetable information, and calculate the running supplementary time of each train at each station and the buffer time between two trains according to the arrival and departure time relationships of each train at different stations and the arrival and departure time relationships of different trains at the same station;

[0027] S3: Based on the network delay model, construct a multi-layer network delay model under the initial delay of the urban rail transit network;

[0028] S4: Construct a multi-layer network delay propagation model and a multi-layer network cascading failure model under the initial delay of the regional rail transit road network according to the multi-layer network delay model;

[0029] S5: Construct dynamic risk assessment indicators for the regional rail transit road network based on the multi-layer network delay propagation model and the multi-layer network cascading failure model, and calculate the risk assessment results of the regional rail transit road network under cascading failures under different initial delays according to the dynamic risk assessment indicators;

[0030] S6: Calculate the total capacity after increasing the capacity of the operation supplementary time and the buffer time based on the operation supplementary time of each train at each station, the buffer time between two trains, and the risk assessment results of the regional rail transit road network under cascading failures under different initial delays, construct an optimization objective function, and determine the optimal solution under the initial delay based on the total capacity and the optimization objective function.

[0031] The above-mentioned dynamic risk assessment method for the regional rail transit road network combines a multi-layer network delay model, a delay propagation model, and a cascading failure model, and can comprehensively evaluate the risks of the regional rail transit road network from multiple dimensions. Specifically, the method comprehensively considers multiple factors such as the train departure time, the buffer time between stations, and the operation supplementary time, and can analyze the changes in the network state under different initial delay scenarios, so as to provide a more accurate dynamic risk assessment. At the same time, the present invention also proposes an optimization objective function based on dynamic risk assessment indicators, which can solve the optimal capacity increase plan for different initial delay conditions, so as to maximize the network robustness, reduce the node vulnerability, and reduce the negative impact of fault spread on the entire traffic system.

[0032] In a preferred embodiment of the present invention, a part of the high-speed rail network under the jurisdiction of the Shanghai Railway Bureau is taken as an example for illustration. The topological diagram of this high-speed network is as Figure 4 shown, and the shortest running time of trains in each section of the network is shown in Table 1.

[0033] Table 1 The shortest running time of trains in each section of the high-speed rail network

[0034]

[0035] Furthermore, based on the above parameters, the steps of a dynamic risk assessment method for a regional rail transit road network provided by the present invention are described in detail as follows:

[0036] Optionally, step 1 specifically includes:

[0037] Collect information such as the number of trains, the number of stations in the regional rail transit road network, and the actual departure and planned departure times of each train at each station. According to this information, construct a delay model for train α at station i in the regional rail transit road network. The formula is:

[0038]

[0039] wherein, represents the delay time of train α at station i, represents the actual departure time of train α at station i, represents the planned departure time of train α at station i, α = 1, 2, …, A, i = 1, 2, …, I, where A and I are the total numbers of trains and stations in the regional rail transit network respectively.

[0040] The set of delay times of all trains at all stations in the entire regional rail transit network is

[0041] Optionally, step 2 specifically includes:

[0042] Calculate the running supplementary time of train α between station i and station j, expressed as:

[0043]

[0044]

[0045]

[0046] wherein, represents the running supplementary time of train α in the section (i, j] (including at station j), represents the running supplementary time of train α in the section (i, j), represents the stop supplementary time of train α at station j, respectively represent the planned arrival times of train α at stations j and i, represents the planned departure time of train α at station i, represents the running time of train α in the section (i, j), represents the minimum stop time of train α at station j, u r and u d respectively represent the minimum running supplementary time and minimum stop supplementary time of the trains in operation, and their values are u r = u d = 3 min;

[0047] The set of running supplementary times of all trains between all stations in the entire regional rail transit network is

[0048] Calculate the buffer time between train α and train β at station i, expressed as:

[0049]

[0050] Among them, represents the buffer time between train α and train β at station i, respectively represent the planned departure times of train α and train β at station i, represents the minimum interval time between train α and train β at station i, b r represents the minimum buffer time between trains during operation.

[0051] The set of buffer times between train α and train β at all stations in the entire regional rail transit network is

[0052] Optionally, step 3 specifically includes:

[0053] See Figure 2 , construct the initial delay of the regional rail transit network The α-layer network delay model under is:

[0054]

[0055] Among them, represents the initial delay time of train γ at station k, that is, the initial delay time in the set of delay times of all trains at all stations in the entire regional rail transit network in, γ ∈ α = 1, 2, …, A, k ∈ i = 1, 2, …, I, represents the α-layer network delay model with the initial delay time in the entire regional rail transit network as the independent variable, represents the α-layer network directed weighted graph, and represents the occurrence of the initial delay The node set of the α-layer network directed weighted graph formed by the stations where train α passes and stops in the α-layer under represents the node of the α-layer network directed weighted graph formed by the stop station i, reflects that the network node where the initial delay occurs is located at the node in the γ-layer network directed weighted graph represents the occurrence of the initial delay The set of intra-layer connection edges (directed edges) of the α-layer network directed weighted graph formed by any two consecutive stop stations passed by train α in the α-layer under represents the occurrence of the initial delay The intra-layer connection edge (directed edge) of the α-layer network directed weighted graph formed by train α passing through the i-th and j-th consecutive stop stations in the α-layer under. Indicates the occurrence of an initial delay The set of inter-layer connection edges (directed edges) between the α-th layer and other layers below, and Indicates the occurrence of an initial delay The set of inter-layer connection edges (directed edges) between the α-th layer and the β-th layer below, and Indicates the occurrence of an initial delay The inter-layer connection edge (directed edge) between the α-th layer and the β-th layer formed by train α in the α-th layer and train β in the β-th layer continuously passing through the same station i

[0056] Construct a multi-layer network delay model under the initial delay of the regional rail transit network, and the formula is:

[0057]

[0058] Wherein, Indicates the multi-layer network delay model constructed with the initial delay time in the entire regional rail transit network as the independent variable, and Indicates the occurrence of an initial delay The next set of multi-layer delay network directed weighted graphs, and Indicates the occurrence of an initial delay The set of inter-layer connection edges between different layers below, and

[0059] Wherein, the multi-layer network delay model under the initial delay Indicates a multi-layer (total of A layers) network directed weighted graph (delay model) constructed with the initial delay time in the entire regional rail transit network as the independent variable and the directed weighted graph of the α-th layer network (α = 1, 2,..., A) formed by the running track of train α; in layer α, if train α passes through and stops at station i, then there is a node in the directed weighted graph (delay model) of the α-th layer network In layer α, if train α continuously stops at stations i and j, then there is an intra-layer connection edge in the directed weighted graph (delay model) of the α-th layer network In different layers α and β, if train α and train β continuously pass through the same station i, then there is an inter-layer connection edge

[0060] The multi-layer network model Indicates a multi-layer (total of A layers) network directed weighted graph (model) constructed with the directed weighted graph of the α-th layer network (α = 1, 2,..., A) formed by the running track of train α, Denote a set of multi - layer network directed weighted graphs under normal operation, and Denote the set of inter - layer connection edges between different layers under normal operation, and In layer α, if train α passes through and stops at station i, then there exists a node in the directed weighted graph (model) of the α - th layer network In layer α, if train α stops continuously at stations i and j, then there exists an intra - layer connection edge in the directed weighted graph (model) of the α - th layer network In different layers α and β, if trains α and β pass through the same station i continuously, then there exists an inter - layer connection edge

[0061] The running supplementary time of train α between stations i and j described in step 2 Denote the capacity (running supplementary time) of the intra - layer connection edge between stations i and j in the α - th layer of the constructed multi - layer (total A layers) network directed weighted graph (model), denoted as The buffer time between train α and train β at station i Denote the capacity (buffer time) of the inter - layer connection edge at station i in the directed weighted graph of the α - th layer in the constructed multi - layer (total A layers) network directed weighted graph (model) between different layers α and β, denoted as

[0062] Optionally, step 4 specifically includes:

[0063] Refer to Figure 3 to respectively construct the delay propagation models of train γ at station k + 1 (intra - layer adjacent node ) and train γ + 1 at station k (inter - layer adjacent layer node ) when the initial delay occurs in the regional rail transit road network. The formulas are respectively:

[0064]

[0065]

[0066] In the formula respectively represent the delay times of train γ at station k + 1 (intra - layer adjacent node ) and train γ + 1 at station k (inter - layer adjacent layer node ) when the initial delay ) occurs, ​​​respectively represent the supplementary time (capacity) for train γ to run in the section (k, k + 1] (including at station k + 1), and the buffer time (capacity) between train γ and train γ + 1 at station k. If respectively indicate the intra-layer connection edges inter-layer connection edges are unable to accommodate more capacity trains passing through, resulting in the node failure.

[0067] Construct the delay propagation models for the intra-layer adjacent nodes adjacent to the node and the inter-layer adjacent nodes adjacent to the node or the intra-layer adjacent nodes adjacent to the node and the inter-layer adjacent nodes adjacent to the node or the intra-layer adjacent nodes adjacent to the node and the inter-layer adjacent nodes adjacent to the node and the inter-layer adjacent nodes adjacent to the node respectively. The formulas are as follows: In the formula

[0068]

[0069]

[0070]

[0071] where represents the delay propagation model of the intra-layer adjacent nodes adjacent to the node that is, the delay time for the following train γ to propagate from station k + 1 to the adjacent station k + 2 after the initial delay occurs; represents the delay propagation model of the inter-layer adjacent nodes adjacent to the node or the intra-layer adjacent nodes adjacent to the node that is, the delay time for the following train γ to propagate from station k + 1 to train γ + 1 passing through station k + 1 after the initial delay occurs, or the delay time for the following train γ + 1 to propagate from station k to station k + 1 after the initial delay represents the delay propagation model of the inter-layer adjacent nodes adjacent to the node that is, the delay time for the following train γ + 1 to propagate from station k to train γ + 2 passing through station k after the initial delay occurs; represents the supplementary time (capacity) for train γ to run in the section (k + 1, k + 2] (including at station k + 2), Indicates the supplementary time (capacity) for train γ+1 to run in the section (k, k+1] (including at station k+1). Indicates the buffer time (capacity) between train γ and train γ+1 at station k+1. Indicates the buffer time (capacity) between train γ+1 and train γ+2 at station k. If Respectively indicate the intra-layer connection edge Inter-layer connection edge Or the intra-layer connection edge Inter-layer connection edge Cannot accommodate more capacity trains passing through, resulting in the node Failure.

[0072] Let γ = γ+1, k = k+1, repeat formulas (10), (11), (12), traverse all nodes in the multi-layer network until γ = A, k = I, and obtain the initial delay Of all nodes in the delay propagation model

[0073]

[0074] Combine the delay propagation models of all nodes Construct a multi-layer network cascading failure model, the formula is:[[]]END]]

[0075]

[0076] Among them, Indicates the initial delay Of the multi-layer network cascading failure model of all nodes Indicates the initial delay Of the node Status, Then the initial delay Of the node Fails, Then the initial delay Of the node Runs normally, α = 1, 2,..., A, i = 1, 2,..., I, Satisfies the following formula:

[0077]

[0078] At the node In the multi-layer network model M, a failure occurs, causing an initial delay of train γ at station k This initial delay propagates in the multi-layer network model M, constituting the initial delay Multi - layer network delay model under In the multi - layer network model M, the nodes The initial delays are respectively propagated to the adjacent nodes within the layer (operation supplement time), and to the adjacent nodes between layers (buffer time), and then to the adjacent nodes within the layer and adjacent nodes between layers and through the nodes propagate to all nodes (all trains at all stations) in the entire multi - layer network, forming a multi - layer network delay propagation model under the initial delay and a multi - layer network cascading failure model

[0079] Optionally, step 5 specifically includes:

[0080] Construct a global network efficiency index, and the calculation formula is:

[0081]

[0082] where E0 represents the global network efficiency of the multi - layer network under normal operation, N is the total number of nodes in the multi - layer network model M, represents the distance from node to node in the multi - layer network model M, β≠α, α = 1, 2, …, A, β = 1, 2, …, A, i≠j, i = 1, 2, …, I, j = 1, 2, …, I. The larger the value of the global network efficiency, the higher the overall performance of the multi - layer network under normal operation, the higher the utilization rate of the operation supplement time of each station and each train and the buffer time between two trains in the entire multi - layer network, and the higher the connection effectiveness between nodes in the entire multi - layer network.

[0083] Combined with the multi - layer network cascading failure model constructed under the occurrence of the initial delay Construct a global network efficiency index under the propagation of fault delays, and the formula is:

[0084]

[0085] In the formula, represents the global network efficiency of the multi - layer network delay model under the occurrence of the initial delay (propagation of fault delays), represents the multi - layer network delay model from node to node in, β≠α, α = 1, 2, …, A, β = 1, 2, …, A, i≠j, i = 1, 2, …, I, j = 1, 2, …, I.

[0086] Construct a node vulnerability metric, and the calculation formula is as follows:

[0087]

[0088] Where, represents the occurrence of an initial delay (fault delay propagation) in the multi-layer network delay model of the node vulnerability. The node vulnerability reflects the performance degradation when a fault occurs at the node ; if the global network efficiency remains unchanged under the initial delay (fault delay propagation), that is then represents that the node fault (initial delay and fault delay propagation) has a relatively small risk impact on the regional rail transit network.

[0089] By setting faults at different nodes in the multi-layer network model M, that is, setting γ = 1, 2,..., A, k = 1, 2,..., I, compare the vulnerabilities of nodes in all multi-layer network delay models to obtain the measurement of the vulnerabilities of all nodes in the multi-layer network.

[0090] Construct a network robustness metric, and the calculation formula is as follows:

[0091]

[0092] Where, represents the robustness of the multi-layer network delay model under the occurrence of an initial delay , represents the number of remaining normally operating nodes in the multi-layer network delay model when a fault occurs at the node (initial delay and fault delay propagation). The network robustness reflects the ability of the network to operate normally when a fault occurs at the node ; if the number of remaining normally operating nodes is larger (the number of failed nodes is smaller) under the initial delay and fault delay propagation, that is the value is larger, it means that the robustness of the multi-layer network delay model is greater, and the risk impact of the node fault (initial delay and fault delay propagation) on the regional rail transit network is smaller.

[0093] Formulas (15), (16), (17), and (18) constitute the dynamic risk assessment indicators for the regional rail transit network.

[0094] Set different initial delays γ = 1, 2, ..., A, k = 1, 2, ..., I. According to the constructed dynamic risk assessment indicators, calculate the risk assessment results of the regional rail transit network under different initial delays, and obtain the results of the impact of different initial delays on the risk of the regional rail transit network. See the experimental results in Figure 5 and Figure 6 .

[0095] Optionally, step 6 specifically includes:

[0096] Calculate the total capacity of the in-layer connection edges (operation supplementary time) and the inter-layer connection edges (buffer time) after adding the new capacity respectively. The expressions are as follows:

[0097]

[0098]

[0099] Where respectively represent the total capacity of the in-layer connection edges (operation supplementary time) and the inter-layer connection edges (buffer time) after increasing the capacity, and β ≠ α, α = 1, 2, …, A, β = 1, 2, …, A, i ≠ j, i = 1, 2, …, I, j = 1, 2, …, I; respectively represent the new capacity of the operation supplementary time (the capacity of the in-layer connection edge ) and the buffer time (the capacity of the inter-layer connection edge ), and there are η u 、η b are respectively the upper bounds of the new capacity of the operation supplementary time (the capacity of the in-layer connection edge ) and the buffer time (the capacity of the inter-layer connection edge ).

[0100] For a given initial delay Construct an optimization objective function, and the formula is:

[0101]

[0102] Among them, p1 and p2 represent the penalty coefficients of the optimization objective function, and η represents the total capacity (total operation supplementary time and buffer time) that the road network can bear; the optimization objective represents minimizing node vulnerability, enhancing the network's ability to resist potential failures or attacks, and reducing network risk; the optimization objective represents maximizing network robustness, enhancing the stability and recovery ability of the entire network when encountering train delay failures, and reducing the risk impact of node failures on the regional rail transit road network; the constraint conditions ensure that the newly added operation supplementary time and buffer time are within the acceptable range (ensuring that all optimization adjustments are carried out within the minimum time unit (minute) of the train timetable), and will not significantly affect the overall operation efficiency of the regional rail transit road network.

[0103] Find the optimal solution of the newly added capacity that satisfies equation (21) By optimally increasing the operation supplementary time and buffer time (the capacity of intra-layer connection edges and inter-layer connection edges of each node) of all trains at all stations in the regional rail transit road network, obtain the optimal solution for minimizing the overall risk of the regional rail transit road network and enhancing network stability under a given initial delay (or when this initial delay occurs during actual operation) The optimal solution with the lowest overall risk of the regional rail transit road network and enhanced network stability. See the experimental results in Figure 7 and Figure 8 .

[0104] In summary, a dynamic risk assessment method for a regional rail transit road network provided by the present invention combines a multi-layer network delay model, a delay propagation model, and a cascading failure model, and can comprehensively evaluate the risks of a regional rail transit road network from multiple dimensions. Specifically, the method comprehensively considers various factors such as train departure time, buffer time between stations, and operation supplementary time, and can analyze the changes in network status under different initial delay scenarios, thereby providing a more accurate dynamic risk assessment. At the same time, the present invention also proposes an optimization objective function based on dynamic risk assessment indicators, which can solve the optimal capacity increase scheme for different initial delay conditions, thereby maximizing network robustness, reducing node vulnerability, and reducing the negative impact of fault spread on the entire transportation system.

[0105] The present invention also provides a dynamic risk assessment system for a regional rail transit road network, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method described in the first aspect above. This dynamic risk assessment system for a regional rail transit road network can implement each embodiment of the above-mentioned dynamic risk assessment method for a regional rail transit road network and achieve the same beneficial effects, which will not be elaborated here.

[0106] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field according to the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art shall fall within the protection scope determined by the claims.

Claims

1. A dynamic risk assessment method for a regional rail transit network, characterized in that, Including: S1: Construct a delay model for each train at each station in the regional rail transit network based on relevant information of the regional rail transit network; S2: Obtain the initial train timetable information, and calculate the running supplementary time for each train at each station and the buffer time between two trains according to the arrival and departure time relationships of each train at different stations and the arrival and departure time relationships of different trains at the same station; S3: Construct a multi-layer network delay model under the initial delay of the regional rail transit network based on the network delay model; S4: Construct a multi-layer network delay propagation model and a multi-layer network cascading failure model under the initial delay of the regional rail transit network according to the multi-layer network delay model; S5: Construct dynamic risk assessment indicators for the regional rail transit network based on the multi-layer network delay propagation model and the multi-layer network cascading failure model, and calculate the risk assessment results of the regional rail transit network under cascading failures under different initial delays according to the dynamic risk assessment indicators; S6: Calculate the total capacity after increasing the capacity of the running supplementary time and the buffer time based on the running supplementary time for each train at each station, the buffer time between two trains, and the risk assessment results of the regional rail transit network under cascading failures under different initial delays, construct an optimization objective function, and determine the optimal solution under the initial delay based on the total capacity and the optimization objective function.

2. The dynamic risk assessment method for the regional rail transit network according to claim 1, wherein The S1 includes: Collect relevant information of the regional rail transit network, where the relevant information includes the number of trains, the number of stations, and the actual departure and planned departure times of each train at each station; Construct a delay model for train α at station i in the regional rail transit network according to the relevant information, and the formula is: wherein, represents the delay time of train α at station i, represents the actual departure time of train α at station i, represents the planned departure time of train α at station i, α = 1, 2,..., A, i = 1, 2,..., I, where A and I are the total numbers of trains and stations in the regional rail transit network respectively; Among them, the set of delay times of all trains at all stations in the entire regional rail transit network is 3. The dynamic risk assessment method for the regional rail transit network according to claim 1, characterized in that The S2 includes: Calculate the running supplementary time for train α between station i and station j, which is expressed as: Among them, represents the additional running time of train α in the interval (i, j]; represents the additional running time of train α in the interval (i, j); represents the additional stop time of train α at station j; respectively represent the planned arrival times of train α at stations j and i; represents the planned departure time of train α at station i; represents the running time of train α in the interval (i, j); represents the minimum stop time of train α at station j, u r and u d respectively represent the minimum additional running time and the minimum additional stop time of the trains in operation; The set of running supplementary times of all trains between all stations in the entire regional rail transit network is Calculate the buffer time between train α and train β at station i, which is expressed as: Among them, represents the buffer time between train α and train β at station i, respectively represent the planned departure times of train α and train β at station i, represents the minimum interval time between train α and train β at station i, b r represents the minimum buffer time between trains during operation; The set of buffer times between train α and train β at all stations in the entire regional rail transit network is 4. The dynamic risk assessment method for the regional rail transit network according to claim 1, characterized in that The S3 includes: Construct the initial delay of the regional rail transit network The α-layer network delay model under the following conditions, and the formula is: Among them, represents the initial delay time of train γ at station k, represents the α-th layer network delay model with the initial delay time in the entire regional rail transit network as the independent variable, represents the α-th layer network directed weighted graph, and represents the occurrence of the initial delay the node set of the α-th layer network directed weighted graph formed by the stations where train α passes through and stops in the α-th layer under the initial delay represents the node in the α-th layer network directed weighted graph formed by station i, reflects that the position of the network node where the initial delay occurs is at the node in the γ-th layer network directed weighted graph represents the occurrence of the initial delay the intra-layer connection edge set of the α-th layer network directed weighted graph formed by any two consecutive stations where train α passes through and stops in the α-th layer under the initial delay represents the occurrence of the initial delay the intra-layer connection edge of the α-th layer network directed weighted graph formed by the i-th and j-th consecutive stations where train α passes through and stops in the α-th layer under the initial delay represents the occurrence of the initial delay the set of inter-layer connection edges between the α-th layer and other layers under the initial delay, and represents the occurrence of the initial delay the set of inter-layer connection edges between the α-th layer and the β-th layer under the initial delay, and represents the occurrence of the initial delay the inter-layer connection edge between the α-th layer and the β-th layer formed by train α in the α-th layer and train β in the β-th layer passing continuously at the same station i under the initial delay; Construct a multi-layer network delay model under the initial delay of the regional rail transit network, and the formula is: Among them, represents a multi-layer network delay model constructed with the initial delay time as the independent variable, and represents the occurrence of an initial delay the next set of multi-layer delay network directed weighted graphs, and represents the occurrence of an initial delay the set of inter-layer connection edges between different layers below, and 5. The dynamic risk assessment method for regional rail transit network according to claim 4, characterized in that Multi - layer Network Delay Model under Initial Delay Denote the initial delay time in the entire regional rail transit network as the independent variable, and the multi - layer network directed weighted graph constructed from the directed weighted graph of the α - th layer network formed by the running track of train α, where α = 1, 2,..., A; in layer α, if train α passes through and stops at station i, then there is a node in the directed weighted graph of the α - th layer network In layer α, if train α continuously stops at stations i and j, then there is an intra - layer connection edge in the directed weighted graph of the α - th layer network In different layers α and β, if trains α and β continuously pass through the same station i, then there is an inter - layer connection edge Multi - layer network model It represents a multi - layer network directed weighted graph constructed from the α - th layer network directed weighted graph formed by the running track of train α. It represents a set of multi - layer network directed weighted graphs under normal operation, and It represents the set of inter - layer connection edges between different layers under normal operation, and: In level α, if train α passes through and stops at station i, then there exists a node V in the directed weighted graph of the α-level network i α ; In layer α, if train α stops continuously at stations i and j, there is an intra-layer connection edge in the layer-α network directed weighted graph In different layers α and β, if trains α and β pass continuously through the same station i, there is an inter-layer connection edge (V i α , V i β ) ∈ E α,β ; The additional running time of train α between station i and station j Indicates that in the α - th level of the constructed multi - layer network directed weighted graph, the capacity of the intra - layer connection edge between station i and station j is regarded as the additional running time, denoted as The buffer time between train α and train β at station i Indicates that in different levels α and β of the constructed multi - layer network directed weighted graph, in the α - th layer network directed weighted graph, the capacity of the inter - layer connection edge (V i α , V i β ) at station i is regarded as the buffer time, denoted as 6. The dynamic risk assessment method for the regional rail transit network according to claim 1, wherein The S4 includes: Construct the initial delay of the regional rail transit network separately The delay propagation models of train γ at station k + 1 and train γ + 1 at station k are as follows, where station k + 1 is regarded as an adjacent node within the layer Station k is regarded as an adjacent node between adjacent layers The formulas are as follows: In the formula, respectively represent the occurrence of the initial delay of train γ at adjacent nodes within the layer and of train γ + 1 at adjacent layer nodes between layers The delay time, respectively represent the additional running time of train γ in the interval (k, k + 1], and the buffer time between train γ and train γ + 1 at station k. If respectively indicate that the in-layer connection edge and the inter-layer connection edge cannot accommodate more trains with capacity passing through, resulting in the node failure; Construct delay propagation models for the in-layer adjacent nodes adjacent to node , the inter-layer adjacent nodes adjacent to node , or the in-layer adjacent nodes adjacent to node and the inter-layer adjacent nodes adjacent to node , or the in-layer adjacent nodes adjacent to node and the inter-layer adjacent nodes adjacent to node . The formulas are respectively as follows: , and ​ In the formula, represents the delay propagation model of adjacent nodes within a layer adjacent to node ; represents the delay propagation model of adjacent nodes between layers adjacent to node or the delay propagation model of adjacent nodes within a layer adjacent to node ; represents the delay propagation model of adjacent nodes between layers adjacent to node ; represents the additional running time of train γ in the section (k + 1, k + 2]; represents the additional running time of train γ + 1 in the section (k, k + 1]; represents the buffer time between train γ and train γ + 1 at station k + 1; represents the buffer time between train γ + 1 and train γ + 2 at station k, if respectively indicates that the intra-layer connection edge the inter-layer connection edge or the intra-layer connection edge the inter-layer connection edge is unable to accommodate more trains with capacity passing through, resulting in the failure of node ; is unable to accommodate more trains with capacity passing through, resulting in the failure of node ; fails. Let γ = γ + 1, k = k + 1, repeat formulas (10), (11), and (12), traverse all nodes in the multi-layer network until γ = A and k = I to obtain the initial delay of the regional rail transit network The delay propagation models of all nodes below are as follows: Delay propagation model integrating all nodes Construct a multi-layer network cascading failure model, with the formula: Among them, represents the initial delay of the multi-layer network cascade failure model of all nodes, represents the initial delay of node V i α status, then the initial delay of node fails, then the initial delay of node operates normally, satisfies the following formula:

7. The dynamic risk assessment method for the regional rail transit network according to claim 1, wherein At node in the multi - layer network model M, a fault occurs, causing an initial delay of train γ at station k This initial delay propagates in the multi - layer network model M, forming a multi - layer network delay model under the initial delay The initial delays of nodes in the multi - layer network model M are respectively propagated to adjacent intra - layer nodes and inter - layer adjacent nodes through intra - layer connection edges and inter - layer connection edges and are propagated through nodes to all nodes in the entire multi - layer network, forming a multi - layer network delay propagation model under the initial delay and a multi - layer network cascading fault model 8. The dynamic risk assessment method for regional rail transit network according to claim 1, characterized in that The dynamic risk assessment indicators for the regional rail transit network in S5 include: global network efficiency, global network efficiency under fault delay propagation, node vulnerability, and network robustness; The S5 includes: Construct a global network efficiency indicator, and the calculation formula is: Among them, E0 represents the global network efficiency of the multi-layer network under normal operation, N is the total number of nodes in the multi-layer network model M, represents the distance from node V i α to node in the multi-layer network model M, β≠α, α = 1, 2, …, A, β = 1, 2, …, A, i≠j, i = 1, 2, …, I, j = 1, 2, …, I. The larger the value of the global network efficiency, the higher the overall performance of the multi-layer network under normal operation, the higher the utilization rate of the operation supplement time of each station and each train and the buffer time between two trains in the whole multi-layer network, and the higher the connection effectiveness between nodes in the whole multi-layer network; Combined with the occurrence of an initial delay Based on the multi-layer network cascade failure model constructed below, a global network efficiency index under the propagation of fault delays is constructed. The formula is as follows: In the formula, represents the occurrence of the initial delay the multi - layer network delay model of the global network efficiency, represents the multi - layer network delay model from node to node the distance, β≠α, α = 1, 2, …, A, β = 1, 2, …, A, i≠j, i = 1, 2, …, I, j = 1, 2, …, I; Construct a node vulnerability metric indicator, and the calculation formula is: Among them, indicates the occurrence of an initial delay the multi-layer network delay model below the nodes in vulnerability; node vulnerability reflects the node when a failure occurs at the performance degradation; if the initial delay the global network efficiency remains unchanged, that is then indicates that the node the failure of the regional rail transit network has a relatively small risk impact; By setting different nodes in the multi-layer network model M to have a failure, that is, setting to compare all multi-layer network delay models for the vulnerability of nodes in it, a measure of the vulnerability of all nodes in the multi-layer network is obtained; Construct a network robustness metric indicator, and the calculation formula is: Among them, indicates the occurrence of an initial delay The multi - layer network delay model robustness, indicates at the node When a fault occurs in the multi - layer network delay model the number of remaining normally operating nodes in the network, the network robustness reflects the ability of the network to operate normally when a fault occurs at the node ; If the initial delay and the number of remaining normally operating nodes under the propagation of fault delay are more, the larger the value, it indicates that the robustness of the multi - layer network delay model is greater, and the risk impact of the node fault on the regional rail transit road network is smaller; Constitute the dynamic risk assessment indicators for the regional rail transit network according to formulas (15), (16), (17), and (18); Set different initial delays According to the constructed dynamic risk assessment indicators, the risk assessment results of the regional rail transit network under different initial delays are calculated, and the results of the impact of different initial delays on the risk of the regional rail transit network are obtained.

9. The dynamic risk assessment method for the regional rail transit network according to claim 1, characterized in that The S6 includes: Regarding the running supplementary time as the in-layer connection edge and the buffering time as the inter-layer connection edge, calculate the in-layer connection edge inter-layer connection edge (V i α , V i β ) The total capacity after adding the new capacity is as follows: Among them, respectively represent the intra-layer connection edges inter-layer connection edges (V i α , V i β ), and the total capacity after increasing the capacity, and β≠α, α = 1, 2, …, A, β = 1, 2, …, A, i≠j, i = 1, 2, …, I, j = 1, 2, …, I; respectively represent the intra-layer connection edges the capacity of, the inter-layer connection edges (V i α , V i β ) the newly added capacity, and there is η u 、η b respectively are the upper bounds of the capacity of the intra-layer connection edges the capacity of, the inter-layer connection edges (V i α , V i β ) the newly added capacity; For a given initial delay Construct an optimization objective function, the formula of which is: Among them, p1 and p2 represent the penalty coefficients of the optimization objective function, and η represents the total capacity that the road network can withstand; the optimization objective represents minimizing node vulnerability, and the optimization objective represents maximizing network robustness. The constraint conditions are used to keep the newly added operation supplement time and buffer time within the tolerable range; Find the optimal solution for the new capacity that satisfies equation (21). By optimally increasing the intra-layer connection edge capacity and inter-layer connection edge capacity of each node of all trains at all stations in the regional rail transit network, an optimal solution is obtained for minimizing the overall delay of the regional rail transit network to the greatest extent under the given initial delay.

10. A dynamic risk assessment system for a regional rail transit network, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method described in any one of the above claims 1-9.

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