A railway freight transportation network vulnerability assessment method based on freight flow data

Abstract

The present invention provides a railway freight transport network vulnerability assessment method based on freight flow data, which constructs an initialized RFTN; uses a pre-interruption model to allocate freight / vehicle flows to the network and maps them to ; calculates the initial network performance indicators and ; allocates freight / vehicle flows to the network again to obtain a failed network; calculates the network performance indicators and after the interruption based on the output results; calculates three vulnerability indicators and a comprehensive vulnerability indicator after normalization; repeats the steps until all interruption scenarios are simulated; obtains the RFTN vulnerability, key stations, sections, and regions under different interruption scenarios and different vulnerability indicators. The present invention introduces four different recovery strategies to reflect the partial elasticity stage and capture the network structure and performance fluctuations for a longer period of time before and after the interruption event. The results and conclusions obtained are helpful in formulating railway infrastructure reinforcement strategies, determining maintenance resource allocation, and formulating emergency response plans.

Description

Technical Field

[0001] The present invention relates to the field of traffic safety assessment, and in particular to a railway freight transportation network vulnerability assessment method based on freight flow data. Background Art

[0002] As China's railway network continues to expand, its railway freight transportation network (RFTN) has become increasingly complex and interconnected. Regional and seasonal variations in freight transport demand have exacerbated system uncertainty and vulnerability. This phenomenon is particularly pronounced in disruption scenarios. Reducing the vulnerability of the RFTN and enhancing its resilience is crucial for maintaining the reliability and sustainability of China's economic and social development.

[0003] RFTN plays an important role in the modern logistics system due to its economic efficiency, safety, convenience, environmental friendliness and large capacity. The extensive railway freight network also brings huge challenges to network management, one of the important challenges is how to manage the disruption of the railway freight network.

[0004] Given the complexity of the rail transport environment, the rail freight network is more susceptible to various events than other modes of transport, resulting in temporary disruptions. These disruptions can last from a few hours to several days, and prolonged and widespread disruptions can even result in significant economic losses. Therefore, to better operate and plan the rail freight network under potential disruption risks, it is imperative to fully understand the performance of the rail freight network under disruptions and analyze its behavior during these periods.

[0005] Over the past decade, extensive research on transportation network vulnerability has led to the development of diverse vulnerability assessment methods. These methods have been used to assess the extent to which performance changes occur in aviation, maritime, rail, and metro networks, as well as in coupled and intermodal networks, under disruptions. While these methods and indicators are interoperable, vulnerability characteristics of the railway network, such as its strict capacity constraints, distinguish it from other modes of transport in case studies of vulnerability. For example, the railway network's transport capacity is strictly constrained, while other networks have relatively looser constraints.

[0006] To date, research methods for railway network vulnerability have primarily focused on topology and systems. The former, rooted in graph theory, describes the railway network as an unweighted network, focusing on analyzing the network's topological characteristics to study its vulnerability, but ignoring the dynamic impact of system performance. The latter describes the railway network as a weighted network weighted by factors such as travel time, passenger flow, and travel demand, focusing on assessing the impact of disruptions from the perspective of system supply and demand. Accordingly, vulnerability assessment indicators can be divided into two categories: one based on complex network theory, such as topological efficiency, maximum connected subgraph size, and global network efficiency; the other based on system dynamic characteristics, such as generalized total travel cost, delay time, and unmet demand. Furthermore, some studies have attempted to combine topological indicators with system performance indicators.

[0007] Railway network vulnerability assessment includes methods such as topology, simulation, optimization, probabilistic models, and data-driven approaches. These assessment methods are not isolated from their evaluation metrics; they are often combined to explore railway network vulnerability from different perspectives. The most commonly used are topology, simulation, and optimization. Topology methods are exhaustive enumeration methods. They remove individual network elements according to certain rules, track changes in assessment metrics, and analyze their vulnerability. However, the exponential growth of network element combinations can lead to excessive computational time. Simulation methods, similar to topology methods, describe vulnerability assessments based on theoretical and / or real-world outage distributions. These methods capture more targeted outage scenarios and tend to analyze dynamic or random network responses. However, they still face limitations due to the exponential growth of multiple network element outage combinations and the high computational requirements of simulation models. Optimization methods, while overcoming the limitations of topology and simulation methods, can address extreme scenarios without exhaustively enumerating all other scenarios. They are suitable for addressing scenarios with simultaneous outages of multiple network elements, but they also impose significant computational demands on large-scale networks. Summary of the Invention

[0008] To address the above issues, the present invention provides a new framework to assess the vulnerability of RFTN. By integrating real China railway freight transport OD data, introducing a method that combines network topology characteristics with functional characteristics, and integrating simulation and mathematical optimization measurement methods, the research on railway freight transport network vulnerability is expanded from the perspective of network services. To achieve the above objectives, the technical solution adopted by the present invention is: a railway freight transport network vulnerability assessment method based on freight flow data, the method includes:

[0009] Step 1: Build and initialize RFTN;

[0010] Step 2: Use the pre-disruption model to allocate freight / vehicle flows to the network and map them to middle;

[0011] Step 3: Calculate the initial network performance indicators based on the network structure and traffic distribution model output before the interruption and ;

[0012] Step 4: Disrupt the network according to a certain disruption simulation scenario, and use the post-disruption model to redistribute the cargo / vehicle flow to the network to obtain a failed network. ;

[0013] Step 5: Calculate the network performance indicators after the interruption based on the output of the network structure and traffic distribution model after the interruption and ;

[0014] Step 6: Based on the indicators obtained in steps 3 and 5, calculate the three vulnerability indicators and the normalized coupled comprehensive vulnerability indicator respectively;

[0015] Step 7: Repeat steps 4-6 until all interruption scenarios are simulated;

[0016] Step 8: Based on the above calculation results, the RFTN vulnerability, key stations, sections and regions under different interruption scenarios and different vulnerability indicators are obtained.

[0017] Furthermore, the interruption simulation scenario is used to simulate common destructive events in transportation, including single network element failure, spatial local network element failure, random failure, and intentional failure.

[0018] Furthermore, the failure of a single network element specifically refers to the complete or incomplete interruption of each station or section in the network one by one, with the interruption level being The discrete values ​​within the range are 25%, 50%, 75% and 100%; the comprehensive vulnerability index values ​​calculated according to the interruption of different stations or sections are ranked to identify the key stations or sections of the railway freight transportation network.

[0019] Furthermore, the spatial local network element failure specifically refers to assuming that the spatial failure area is circular, designing different spatial failure radii, and assuming that all network elements covered by areas corresponding to different radii fail, so as to achieve a complete interruption of multiple stations or sections in the network at the same time; sorting the comprehensive vulnerability index values ​​obtained under different spatial local area failures to identify key areas of different sizes in the railway freight transportation network.

[0020] Furthermore, the random failure specifically refers to the random interruption of stations or sections in the network one by one; the simulation test under the random failure scenario randomly selects stations each time, and in order to eliminate the random influence, multiple tests are required for each interruption probability, and the corresponding vulnerability index value takes the average value of the index values ​​obtained from all tests.

[0021] Furthermore, the intentional failure specifically refers to attacking and interrupting stations or sections in the network one by one according to a given strategy; performing intentional failure simulation based on network centrality indicators from high to low; the network centrality indicators include degree centrality, proximity centerline, betweenness centrality and eigenvector centrality.

[0022] Furthermore, the vulnerability indicators include structural vulnerability indicators,

[0023] Functional vulnerability index and comprehensive vulnerability index.

[0024] Furthermore, the structural vulnerability indicators specifically include, based on the constructed infrastructure layer network and interruption simulation scenarios, using the structural vulnerability indicators of the maximum connected subgraph size change rate and the global efficiency change rate from the perspective of the railway freight transportation network topology to evaluate the network performance when stations and sections are interrupted;

[0025] The maximum connected subgraph size change rate specifically includes: the maximum connected subgraph size is the number of nodes contained in the largest connected subgraph in the network, as shown in formula (1) and formula (2), and the maximum connected subgraph size change index is given by formula (3):

[0026] ;

[0027] ;

[0028] ;

[0029] in, Represent the maximum connected subgraph size in the initial state and after interruption, The larger it is, the more vulnerable the network is and the easier it is to be interrupted and destroyed.

[0030] The global efficiency change rate specifically includes that the global efficiency is the average efficiency between all node pairs in the network. The efficiency between two nodes in the transportation network is expressed as the inverse of the distance between the two points. Therefore, by calculating the average efficiency between all node pairs, the global efficiency of the network is expressed as:

[0031] ;

[0032] Then the change in the global efficiency of the network before and after the interruption can be described as

[0033] ;

[0034] in represents the global efficiency of the railway freight transportation network under normal conditions, The global efficiency of railway freight transport under interruption conditions is shown. The larger it is, the more vulnerable the network is to interruptions, that is, the less robust it is to interruptions.

[0035] Furthermore, the functional vulnerability index specifically includes, based on the functional layer and service layer characteristics of RFTN, the functional vulnerability index is determined as a value reflecting the change in network system performance, that is, the transportation cost change rate , and its calculation formula is shown in formula (6):

[0036] ;

[0037] in, denote the total transportation cost in the initial state and after the interruption, The larger it is, the more vulnerable the network is.

[0038] Furthermore, the comprehensive vulnerability index specifically includes: The four coupling coefficients are used to synthesize the relative changes in the topology and total network transportation cost before and after the interruption.

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] Among them, each vulnerability indicator is normalized to the maximum and minimum using formula (36), so that the value range of the indicator is within the interval [0,1], which is convenient for coupling between indicators. Limited by formulas (33) and (34), The performance is not greater than 1; There are four weight coefficients, which represent the contribution of the three indicators to the overall network vulnerability. This means that the priority of each indicator or the importance in different situations is different in the decision-making process of different stakeholders. The values ​​of the weight coefficients vary according to the actual preferences and personalized management goals of different stakeholders.

[0045] Beneficial effects of this patent:

[0046] 1. The framework proposed in this paper can more comprehensively evaluate the vulnerability of RFTN. By integrating real China railway freight transportation OD data, introducing a method that combines network topology characteristics with functional characteristics, and integrating simulation and mathematical optimization measurement methods, it expands the research on railway freight transportation network vulnerability from the perspective of network services.

[0047] 2. The vulnerability analysis framework proposed in this paper introduces four different recovery strategies (i.e., waiting for repairs before reopening, rerouting freight, and transporting freight using other modes of transportation), reflecting the partial resilience stage and capturing the network structure and performance fluctuations over a longer period of time before and after the disruption event. The results and conclusions obtained are helpful in formulating railway infrastructure reinforcement strategies, determining maintenance resource allocation, and formulating emergency response plans. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention has the following accompanying drawings:

[0049] Figure 1 This is a schematic diagram of a framework of a railway freight transportation network vulnerability assessment method based on freight flow data according to the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to the accompanying drawings.

[0051] like Figure 1 As shown in Figure 1, a railway freight transportation network vulnerability assessment method based on freight flow data is described in detail as follows:

[0052] Step 1: Build and initialize RFTN;

[0053] Step 2: Use the pre-disruption model to allocate freight / vehicle flows to the network and map them to middle;

[0054] Step 3: Calculate the initial network performance indicators based on the network structure and traffic distribution model output before the interruption and ;

[0055] Step 4: Disrupt the network according to a certain disruption simulation scenario, and use the post-disruption model to redistribute the cargo / vehicle flow to the network to obtain a failed network. ;

[0056] Step 5: Calculate the network performance indicators after the interruption based on the output of the network structure and traffic distribution model after the interruption and ;

[0057] Step 6: Based on the indicators obtained in steps 3 and 5, calculate the three vulnerability indicators and the normalized coupled comprehensive vulnerability indicator respectively;

[0058] Step 7: Repeat steps 4-6 until all interruption scenarios are simulated;

[0059] Step 8: Based on the above calculation results, the RFTN vulnerability, key stations, sections and regions under different interruption scenarios and different vulnerability indicators are obtained.

[0060] Among them, the interruption simulation scenario specifically refers to:

[0061] Based on the need for vulnerability analysis from different perspectives in RFTN, this paper designs four types of disruption simulation scenarios to simulate common disruptive events in transportation, such as natural disasters and man-made attacks. Random failures and intentional failures are commonly used simulation scenarios in complex network theory; these failures target only stations within the network. Single network element failures and spatially localized network element failures are commonly used to analyze the criticality of network elements or regions (described in this paper as vulnerability levels). These failures target any station or section within the network.

[0062] (1) Failure of a single network element: Complete or incomplete interruption of each station or section in the network one by one, with the interruption level being The discrete values ​​within the range are 25%, 50%, 75% and 100%. The comprehensive vulnerability index values ​​calculated based on the disruption of different stations or sections are ranked to identify the key stations or sections of the railway freight transportation network.

[0063] (2) Spatial local network element failure: Assuming the spatial failure area is circular, different spatial failure radii are designed, and it is assumed that all network elements covered by the areas corresponding to different radii fail, so as to achieve a complete interruption of multiple stations or sections in the network at the same time. The comprehensive vulnerability index values ​​obtained under different spatial local area failures are ranked to identify key areas of different sizes in the railway freight transportation network.

[0064] (3) Random failure: Stations or sections in the network are randomly interrupted one by one. In this scenario, the simulation test randomly selects stations each time. Therefore, to eliminate the random influence, 100 tests are required for each interruption probability. The corresponding vulnerability index value is the average value of the index values ​​obtained from all the tests.

[0065] (4) Deliberate failure: Attack and disrupt stations or sections in the network one by one according to a given strategy. In graph theory and network analysis, network centrality metrics are used to identify the most important nodes in a graph. This paper simulates deliberate failure based on four network centrality metrics: degree centrality, proximity centrality, betweenness centrality, and eigenvector centrality, ranked from high to low.

[0066] Vulnerability indicators, specifically

[0067] 1. Structural vulnerability indicators

[0068] Based on the constructed infrastructure layer network and interruption simulation scenarios, from the perspective of the railway freight transportation network topology, the study uses two structural vulnerability indicators, namely the maximum connected subgraph size and the global efficiency of the network, to evaluate the network performance when stations and sections are interrupted.

[0069] (1) Maximum connected subgraph size change rate

[0070] The maximum connected subgraph size refers to the number of nodes contained in the largest connected subgraph in the network, as shown in Equation (1) and Equation (2). The maximum connected subgraph size change index is given by Equation (3).

[0071] ;

[0072] ;

[0073] ;

[0074] in, They represent the maximum connected subgraph size in the initial state and after the interruption respectively. The larger it is, the more vulnerable the network is and the easier it is to be interrupted and destroyed.

[0075] (2) Global efficiency change rate

[0076] Global efficiency is often used to analyze the overall connectivity and transportation efficiency of a network. It is defined as the average efficiency between all pairs of nodes in the network. The efficiency between two nodes in a transportation network is generally expressed as the inverse of the distance between the two points. Therefore, by calculating the average efficiency between all pairs of nodes, the global efficiency of the network is expressed as:

[0077] ;

[0078] Then the change in the global efficiency of the network before and after the interruption can be described as

[0079] ;

[0080] in represents the global efficiency of the railway freight transportation network under normal conditions, Represents the global efficiency of railway freight transportation under disruption conditions. The larger it is, the more vulnerable the network is to interruptions, that is, the less robust it is to interruptions.

[0081] 2. Functional Vulnerability Index

[0082] Based on the functional layer and service layer characteristics of RFTN, its functional vulnerability index is determined as the value that reflects the change of network system performance, that is, the transportation cost change rate , and its calculation formula is given by formula (6).

[0083] ;

[0084] in, denote the total transportation cost in the initial state and after the interruption, respectively. The larger it is, the more vulnerable the network is.

[0085] Considering the difficulty and scale of solving point-arc-based models, as well as the difficulty in tracing specific infeasible ODs, the freight flow allocation optimization problem is formulated as an arc-path-based vehicle flow routing optimization model. This reduces the number of variables in advance by removing paths that do not meet additional operational constraints. The symbols used in model construction and their meanings are listed in Table 1.

[0086] Table 1 Marking Overview

[0087]

[0088] (1) Pre-interruption model

[0089] In a given railway freight transport network, the optimization model for calculating the railway traffic routing before the disruption can be used to obtain the traffic routing that minimizes the total railway freight transportation cost under normal conditions. We model this problem as a 0-1 integer programming model:

[0090] ;

[0091] Subject to:

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] The objective function (7) seeks to minimize the total transportation cost of transporting goods by rail from the supply location to the demand location. Part 1 describes that the transportation cost of each feasible route is composed of the total interval mileage and unit mileage transportation cost of the operating route. Taking into account the capacity limitations of the railway freight transportation network and the timeliness constraints of freight transportation, it is allowed that some freight transportation demands cannot be met, which corresponds to the second part of the objective function (7). Constraint (8) describes the principle of indivisibility of traffic in railway traffic allocation, ensuring that each traffic flow has and passes through a feasible route to meet the freight transportation demand. Constraints (9) and (10) describe the interval and station capacity constraints of the network respectively, taking into account the limited interval passing capacity and station capacity in the network. Constraint (11) describes the traffic route mileage constraint, also called the detour rate constraint, and introduces the detour rate threshold. The concept of traffic flow is that for a certain traffic flow, the traffic flow paths available for selection include the shortest path, and also include the physical mileage within the shortest path. Constraint (12) indicates that there must be at least one feasible path to meet each cargo transportation demand before the cargo delivery deadline. Finally, equations (13) and (14) restrict the range of values ​​of the decision variables.

[0100] (2) Post-interruption model

[0101] Considering that network outages at stations and sections will result in a certain degree of capacity loss, we embedded four response strategies into the post-outage model to observe how the RFTN deploys remaining network resources to meet all demands after an outage. Next, we introduce the specific mathematical model.

[0102] ;

[0103] Subject to:

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] When a network interruption occurs, traffic flow needs to be adjusted in a timely manner to meet as many freight transport demands as possible and reduce the impact on the quality of freight transport services. Assuming that only the traffic flow organizations currently remaining in the network are considered during the interruption, the traffic flow allocation optimization model after the interruption is established as shown in Equations (15)-(31). On the basis of seeking to minimize the generalized railway freight transport cost, the objective function (15) considers the distribution of traffic flows that are not affected by the interrupted network elements and traffic flows that are affected by the interrupted network elements. Four response strategies are included in the objective function of the post-interruption model, namely, the waiting for repair strategy, the rerouting strategy, and the strategy of using other transportation modes to meet demand. Traffic flows that are not affected by the interrupted network elements can still use the residual network for transportation. Some traffic flows affected by the interrupted network elements can choose to change the transportation route and participate in the traffic flow allocation that is not affected by the interrupted network elements. These two parts of traffic flows correspond to the first part of the objective function (15). Traffic flows affected by the interrupted network element can choose to continue using the network element for transportation after it is repaired, which corresponds to the second part of the objective function (15); they can choose to switch to other modes of transportation, which corresponds to the third part of the objective function (15); or they can choose to cancel the service, which is included in the infeasible flow in the fourth part of the objective function (15).

[0121] Similar to the constraints of the pre-disruption model, the post-disruption model also contains four types of constraints. The traffic demand is modeled in constraint (16), assuming that the demand can be distributed among the available paths, including transportation through the interrupted network elements under different repair schemes, transportation through other transportation modes, and transportation through virtual arcs for infeasible flows. Constraints (17) and (18) respectively specify the capacity constraints of the normal operating interval and the interval affected by the interruption. Constraints (19) and (20) respectively specify the capacity constraints of the normal operating station and the station affected by the interruption. We consider two types of interruption: partial interruption and complete interruption. Constraints (21) and (22) respectively describe the mileage constraints of the traffic flow paths that pass through and do not pass through the interruption interval or station. This means that even after the interruption, the railway traffic organization should meet the rationality requirements of the path and should not make excessive detours to meet the transportation demand, resulting in a waste of transportation resources. Constraints (23) and (24) indicate that the freight transportation service before and after the interruption must meet the time constraint of the cargo delivery deadline to be considered as a complete transportation service, that is, to meet the freight transportation demand. Constraint (25) ensures that paths through interrupted stations or sections are only accessible after the repair process is complete. Constraint (26) limits the transport capacity of other modes of transport after the interruption to prevent all freight demand from being met by other modes of transport, which would lead to extremely low rail freight service quality that is out of touch with reality. Finally, Equations (27)-(31) specify the sign restrictions of the integer decision variables, corresponding to whether the traffic flow passes through an uninterrupted network element, whether the traffic flow passes through an interrupted network element, whether the interrupted network element is repaired, whether the traffic flow meets the transportation demand through other modes of transport, and whether the traffic flow is infeasible.

[0122] 3. Comprehensive vulnerability index

[0123] From the perspective of the three-layer comprehensive performance of the railway freight transportation network, this application proposes a comprehensive vulnerability index for railway freight network vulnerability assessment , as shown in formula (32), Four coupling coefficients are used to synthesize the relative changes in the topology and total network transportation cost before and after the disruption occurs.

[0124] ;

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] Among them, each vulnerability indicator is normalized to the maximum and minimum using formula (36), so that the value range of each indicator is within the interval [0,1], which is convenient for coupling between indicators. Limited by formulas (33) and (34), The performance is not greater than 1. The four weight coefficients represent the contribution of the three indicators to the overall network vulnerability. This means that the priority of each indicator or the degree of importance in different situations varies in the decision-making process of different stakeholders. The weight coefficient values ​​can be differentiated based on the actual preferences of different stakeholders and personalized management goals.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although this patent is described in detail with reference to the embodiments, ordinary technicians in this field should understand that the technical solutions implemented by the present invention can be modified or replaced by equivalents without departing from the design spirit and scope of the present invention, which should be included in the scope of the claims of the present invention.

[0131] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

Claims

1. A railway freight transportation network vulnerability assessment method based on freight flow data, characterized in that: The method comprises, Step 1: Build and initialize RFTN; Step 2: Use the pre-disruption model to allocate freight / vehicle flows to the network and map them to middle; Step 3: Calculate the initial network performance indicators based on the network structure and traffic distribution model output before the interruption and ; Step 4: Disrupt the network according to a certain disruption simulation scenario, and use the post-disruption model to redistribute the cargo / vehicle flow to the network to obtain a failed network. ; Step 5: Calculate the network performance indicators after the interruption based on the output of the network structure and traffic distribution model after the interruption and ; Step 6: Based on the indicators obtained in steps 3 and 5, calculate the three vulnerability indicators and the normalized coupled comprehensive vulnerability indicator respectively; Step 7: Repeat steps 4-6 until all interruption scenarios are simulated; Step 8: Based on the above calculation results, the RFTN vulnerability, key stations, sections and regions under different interruption scenarios and different vulnerability indicators are obtained. The vulnerability indicators include structural vulnerability indicators, functional vulnerability indicators, and comprehensive vulnerability indicators; The structural vulnerability indicators specifically include, based on the constructed infrastructure layer network and disruption simulation scenarios, using structural vulnerability indicators such as the maximum connected subgraph size change rate and the global efficiency change rate from the perspective of the railway freight transportation network topology to evaluate network performance when stations and sections are disrupted; The maximum connected subgraph size change rate specifically includes: the maximum connected subgraph size is the number of nodes contained in the largest connected subgraph in the network, as shown in formula (1) and formula (2), and the maximum connected subgraph size change index is given by formula (3): ; ; ; in, Represent the maximum connected subgraph size in the initial state and after interruption, The larger it is, the more vulnerable the network is and the easier it is to be interrupted and destroyed. The global efficiency change rate specifically includes that the global efficiency is the average efficiency between all node pairs in the network. The efficiency between two nodes in the transportation network is expressed as the inverse of the distance between the two points. Therefore, by calculating the average efficiency between all node pairs, the global efficiency of the network is expressed as: ; Then the change in the global efficiency of the network before and after the interruption can be described as ; in represents the global efficiency of the railway freight transportation network under normal conditions, represents the global efficiency of railway freight transportation under disruption conditions, The larger it is, the more vulnerable the network is to interruptions, that is, the less robust it is to interruptions. The functional vulnerability index specifically includes, based on the functional layer and service layer characteristics of RFTN, the functional vulnerability index is determined as a value reflecting the change in network system performance, that is, the transportation cost change rate , and its calculation formula is shown in formula (6): ； in, denote the total transportation cost in the initial state and after the interruption, The larger it is, the more vulnerable the network is.

2. The railway freight transportation network vulnerability assessment method based on freight flow data according to claim 1 is characterized in that: The disruption simulation scenario is used to simulate common disruptive events in transportation. Including failure of single network elements, failure of local network elements in space, random failure, and intentional failure.

3. The railway freight transportation network vulnerability assessment method based on freight flow data according to claim 2 is characterized in that: The failure of a single network element specifically refers to the complete or incomplete interruption of each station or section in the network one by one, with the interruption level being The discrete values ​​within the range are 25%, 50%, 75% and 100%; the comprehensive vulnerability index values ​​calculated according to the interruption of different stations or sections are ranked to identify the key stations or sections of the railway freight transportation network.

4. The railway freight transportation network vulnerability assessment method based on freight flow data according to claim 2, characterized in that: The spatial local network element failure specifically refers to assuming that the spatial failure area is circular, designing different spatial failure radii, and assuming that all network elements covered by the areas corresponding to different radii fail, so as to achieve simultaneous and complete interruption of multiple stations or sections in the network; The comprehensive vulnerability index values ​​obtained under different spatial local area failures are ranked to identify key areas of different sizes in the railway freight transportation network.

5. The railway freight transportation network vulnerability assessment method based on freight flow data according to claim 2, characterized in that: The random failure specifically refers to the random interruption of stations or sections in the network one by one. The simulation test under the random failure scenario randomly selects stations each time. To eliminate the random influence, multiple tests are required for each interruption probability, and the corresponding vulnerability index value is the average of the index values ​​obtained from all tests.

6. The railway freight transportation network vulnerability assessment method based on freight flow data according to claim 2, characterized in that: The intentional failure specifically refers to attacking and interrupting stations or sections in the network one by one according to a given strategy; the intentional failure simulation is performed based on network centrality indicators from high to low; the network centrality indicators include degree centrality, closeness centerline, betweenness centrality and eigenvector centrality.

7. The railway freight transportation network vulnerability assessment method based on freight flow data according to claim 1, characterized in that: The comprehensive vulnerability index specifically includes: The four coupling coefficients are used to synthesize the relative changes in the topology and total network transportation cost before and after the interruption. ； ； ； ； ； Among them, each vulnerability indicator is normalized to the maximum and minimum using formula (36), so that the value range of the indicator is within the interval [0,1], which is convenient for coupling between indicators. Limited by formulas (33) and (34), The performance is not greater than 1; There are four weight coefficients, which represent the contribution of the three indicators to the overall network vulnerability. This means that the priority of each indicator or the importance in different situations is different in the decision-making process of different stakeholders. The values ​​of the weight coefficients vary according to the actual preferences and personalized management goals of different stakeholders.

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