Method for measuring connectivity of air-railway combined transportation network

Abstract

The invention relates to the technical field of transportation network model processing, in particular to a method for measuring connectivity of an air-railway combined transportation network, which comprises the following steps of: constructing an air-railway combined transportation network matrix, and constructing connectivity evaluation indexes of the air-railway combined transportation network based on network node centrality. And based on the connectivity evaluation index system of the air-railway combined transportation network matrix, solving a connectivity comprehensive evaluation value of the airport and the railway station. The built air-railway combined transportation network covers an air transportation and railway transportation multilayer complex transportation network, the public transportation service condition between an airport and a railway station is also considered while air transportation characteristics and railway transportation characteristics are considered respectively, and mathematical expression and description of the air and railway multilayer complex transportation are effectively realized.

Description

Technical Field

[0001] The present invention relates to the technical field of transportation network model processing, and in particular to a method for measuring connectivity of an air-rail combined transportation network. Background Art

[0002] With the development of the railway transportation network, it plays an important role in serving domestic short-distance passenger transportation, while the air transportation of hub airports focuses on international transportation and domestic long-distance transportation. By connecting airports with railway stations to form an air-rail combined transportation network, the speed advantages of air transportation and railway transportation can be fully utilized, and the radiation range of transportation services can be expanded, thereby improving the overall transportation efficiency and service quality. The connectivity of the transportation network is an important concept and service indicator in transportation science, which is used to evaluate the transportation resources and convenience of the transportation network. Specifically, the better the connectivity of the air-rail combined transportation network, the wider the coverage of the route resources and railway line resources of the transportation unit, the greater the market resources, and at the same time reflects that the number of transfers for transportation travelers is less and the degree of convenience is higher.

[0003] The connectivity of airports and railway stations in the air-rail combined transport network is defined as the connectivity of transportation nodes. Focusing on the connectivity of transportation nodes will help evaluate their status and role in the air-rail combined transport network, help optimize the resource allocation of the air-rail combined transport network, and help improve the travel convenience and satisfaction of travelers.

[0004] However, the current research on the connectivity of transportation nodes has the following main deficiencies: (1) The traffic scenarios involved are often single traffic, such as limited to air transport networks or railway transport networks, and do not take into account the multi-layered complex traffic network formed by combining multiple transportation modes.

[0005] (2) It is only characterized by simple mathematical statistics, mainly including the number of connected transportation stations, geographical distribution and passenger volume. The essence of its description is the direct coverage of transportation routes rather than connectivity.

[0006] (3) Some studies tend to use artificial intelligence or complex mathematical optimization algorithms, which require large amounts of computation and have many constraints, and often result in significant discrepancies between theoretical results and actual operations. Summary of the invention

[0007] The purpose of the present invention is to provide a method for measuring the connectivity of an air-rail combined transport network to solve the above-mentioned problems in the prior art.

[0008] The embodiments of the present invention are implemented by the following technical solutions: A method for measuring the connectivity of air-rail combined transportation networks, including: Obtain airport flight operation information and railway shuttle operation information, and establish the aviation transportation network adjacency matrix and the railway transportation network adjacency matrix respectively; Establish the air-rail combined transport network matrix through the air transport network adjacency matrix and the railway transport network adjacency matrix; According to the network centrality of each node in the air-rail combined transport network matrix, the connectivity evaluation index is obtained, and the connectivity evaluation index matrix of the air-rail combined transport network is constructed; The comprehensive evaluation value of the connectivity of airports and railway stations is obtained through the connectivity evaluation index matrix.

[0009] Preferably, the connectivity evaluation indicators include degree centrality, betweenness centrality, closeness centrality, eigenvector centrality and clustering coefficient.

[0010] Preferably, the degree centrality includes:

[0011] in, For traffic nodes The degree centrality of is the total number of transportation nodes in the air-rail combined transportation network, For traffic nodes and traffic nodes The total volume of transportation between and is a natural number.

[0012] Preferably, the betweenness centrality includes:

[0013] in, For traffic nodes The betweenness centrality of From the traffic node To the traffic node The total number of all shortest paths, For traffic nodes To the traffic node The shortest path passes through the traffic node The number of shortest paths.

[0014] Preferably, the closeness centrality includes:

[0015] in, For traffic nodes The closeness centrality, Indicates a traffic node To the traffic node The shortest distance.

[0016] Preferably, the eigenvector centrality includes:

[0017] in, For traffic nodes The eigenvector centrality of represents a constant, For traffic nodes Traffic nodes The number of flights or traffic between For traffic nodes The number of direct connections to other nodes, is the element of the feature vector, i.e., the traffic node The eigenvector centrality measure of .

[0018] Preferably, the clustering coefficient includes:

[0019] In the formula, For traffic nodes The clustering coefficient, For traffic nodes The number of transportation nodes directly accessible to navigation or traffic, for The number of navigable or traffic routes that actually exist between the nodes.

[0020] Preferably, the method of solving the comprehensive evaluation value of connectivity of the airport and the railway station comprises: Obtain the mean and standard deviation of the connectivity evaluation index samples, standardize the connectivity evaluation index matrix, and obtain the connectivity evaluation index correlation coefficient matrix; The matrix eigenvalue is obtained by the correlation coefficient matrix of the connectivity evaluation index, and the The variance contribution rate of each indicator variable and each connectivity evaluation index; from Select from the indicator variables As the principal component, The correlation coefficient of the connectivity evaluation index corresponding to the principal component is used as the weight, and the linear weighting is used to obtain the first The evaluation function of the principal components; Before calculation The contribution ratio of each connectivity evaluation index is calculated, and the comprehensive connectivity evaluation value is obtained based on the contribution ratio and evaluation function.

[0021] Preferably, the variance contribution rate of each connectivity evaluation index includes:

[0022] In the formula, is the variance contribution rate, is the correlation coefficient matrix of connectivity evaluation indicators No. matrix eigenvalues, is the correlation coefficient matrix of connectivity evaluation indicators No. matrix eigenvalues, is the number of indicator variables; The evaluation function includes:

[0023] In the formula, For traffic nodes No. The evaluation function of the connectivity evaluation of the indicators corresponding to the principal components is: Connectivity evaluation index and connectivity evaluation indicators The correlation coefficient of For the principal components.

[0024] Preferably, obtaining a comprehensive connectivity evaluation value based on the contribution ratio and the evaluation function includes:

[0025]

[0026] In the formula, is the contribution ratio, For traffic nodes The comprehensive connectivity evaluation value.

[0027] The technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects: The method provided by the present invention mainly includes constructing an air-rail combined transport network matrix based on the air transport network and the railway transport network, constructing a connectivity evaluation index of the air-rail combined transport network based on the network node centrality, and solving the comprehensive evaluation value of the connectivity of airports and railway stations based on the connectivity evaluation index system of the air-rail combined transport network matrix.

[0028] The constructed air-rail combined transportation network covers the multi-layer complex transportation network of air transportation and rail transportation. While considering the characteristics of air transportation and rail transportation respectively, it also considers the public transportation service conditions between airports and railway stations, effectively realizing the mathematical expression and characterization of the multi-layer complex transportation of air and rail.

[0029] The proposed fusion method for comprehensive evaluation of connectivity of airports and railway stations is based on multiple network node centrality measurement methods and effectively integrates the connectivity role of transportation nodes in different network topological structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0033] Please refer to Figure 1 The present invention provides a method for measuring connectivity of an air-rail combined transport network, comprising: S101: Acquire airport flight operation information and railway shuttle operation information, and establish an aviation transportation network adjacency matrix and a railway transportation network adjacency matrix respectively; Based on the obtained flight schedule, the airport flight operation information is obtained, and according to the air traffic conditions between airports, the aviation transportation network adjacency matrix is ​​constructed.

[0034] Assume that the total number of airports is , then the size of the adjacency matrix of the air transport network is , where the elements are:

[0035] in, is the adjacency matrix of the air transport network No. Line The elements of the column, For Airport To the Airport The total number of flights, 0 represents the airport To the Airport No flights.

[0036] Then the adjacency matrix of the air transport network is It is expressed as:

[0037] According to the obtained railway timetable, the railway operation information is obtained, and the railway transportation network adjacency matrix is ​​constructed according to the traffic conditions between railway stations. . Assume that the total number of train stations is , then the size of the railway transportation network adjacency matrix is , where the elements are:

[0038] In the formula, is the adjacency matrix of the railway transportation network No. Line The elements of the column, For the train station To the train station The total number of trains, 0 is the train station To the train station There are no trains in between.

[0039] Then the adjacency matrix of the railway transportation network is It is expressed as:

[0040] S102: Establish an air-rail combined transport network matrix through the air transport network adjacency matrix and the railway transport network adjacency matrix; Combining the airport construction and railway construction in the same city, the nodes of the aviation transport network and the railway transport network are connected to construct an air-rail combined transport network matrix.

[0041] Among them, one of the matrix elements formed by the airport and the railway station is:

[0042] In the formula, The connection matrix No. Line The elements of the column, For Airport To the train station The total number of public transportation trips, 0 is the airport To the train station There is no public transportation.

[0043] Then the connection relationship matrix between the airport and the railway station is for:

[0044] The second is:

[0045] In the formula, The connection matrix No. Line The elements of the column, For the train station To the Airport The total number of public transportation trips, 0 is the train station To the Airport There is no public transportation.

[0046] Then the connection relationship matrix between the airport and the railway station is for:

[0047] So the above aviation transportation network adjacency matrix , Railway transportation network adjacency matrix The connection matrix between the airport and the railway station After combining, we get the air-rail combined transport network matrix :

[0048] S103: Obtaining connectivity evaluation indexes according to the network centrality of each node in the air-rail combined transport network matrix, and constructing a connectivity evaluation index matrix of the air-rail combined transport network; S104: Obtain the comprehensive connectivity evaluation value of the airport and the railway station through the connectivity evaluation index matrix.

[0049] The method provided by the present invention mainly includes constructing an air-rail combined transport network matrix based on the air transport network and the railway transport network, constructing a connectivity evaluation index of the air-rail combined transport network based on the network node centrality, and solving the comprehensive evaluation value of the connectivity of airports and railway stations based on the connectivity evaluation index system of the air-rail combined transport network matrix.

[0050] The constructed air-rail combined transportation network covers the multi-layer complex transportation network of air transportation and rail transportation. While considering the characteristics of air transportation and rail transportation respectively, it also considers the public transportation service conditions between airports and railway stations, effectively realizing the mathematical expression and characterization of the multi-layer complex transportation of air and rail.

[0051] The proposed fusion method for comprehensive evaluation of connectivity of airports and railway stations is based on multiple network node centrality measurement methods and effectively integrates the connectivity role of transportation nodes in different network topological structures.

[0052] In an exemplary embodiment of the present invention, the connectivity evaluation indicators include degree centrality, betweenness centrality, closeness centrality, eigenvector centrality and clustering coefficient.

[0053] Specifically, airports and railway stations are transportation nodes in the air-rail combined transportation network. Their degree centrality refers to the sum of the weights of the transportation node's neighbors. It reflects that the larger the degree centrality value, the more transportation stations that have direct navigation or traffic with this transportation node, indicating that the greater the connectivity in the transportation network. Degree centrality includes:

[0054] in, For traffic nodes The degree centrality of is the total number of transportation nodes in the air-rail combined transportation network, For traffic nodes and traffic nodes The total volume of transportation between and is a natural number.

[0055] In the air-rail combined transport network, among the shortest paths of all traffic node pairs, if the number of shortest paths that transfer through a traffic node is greater, the connectivity of the traffic node is greater. The betweenness centrality of the air-rail combined transport network includes:

[0056] in, For traffic nodes The betweenness centrality of From the traffic node To the traffic node The total number of all shortest paths, For traffic nodes To the traffic node The shortest path passes through the traffic node The number of shortest paths.

[0057] The proximity centrality of a transportation node represents the reciprocal of the sum of the shortest paths between the transportation node and all other transportation nodes in the air-rail combined transportation network. The smaller the average distance between a node and other nodes, the greater the proximity centrality of the node and the greater the connectivity. The proximity centrality includes:

[0058] in, For traffic nodes The closeness centrality, Indicates traffic node To the traffic node The shortest distance.

[0059] The eigenvector centrality of a transportation node not only considers the number of its neighboring nodes, but also the importance of each neighbor of the node. It shows that if the connectivity of the transportation nodes with which the transportation node is open to navigation or traffic is greater, the connectivity of the transportation node is greater. The eigenvector centrality in the air-rail combined transportation network includes:

[0060] in, For traffic nodes The eigenvector centrality of represents a constant, For traffic nodes Traffic nodes The number of flights or traffic between is the element of the feature vector, i.e., the traffic node The eigenvector centrality measure of the traffic node For traffic nodes Neighbor nodes, traffic nodes Traffic nodes Directly connected, Can be understood as a traffic node The number of direct connections to other nodes.

[0061] remember , then the above formula can be written as the eigenvector equation:

[0062] Solve to get the elements of the eigenvector Traffic Node The eigenvector centrality of yes Order square array, for A characteristic value of for The corresponding eigenvalue of The feature vector of .

[0063] Nodes in a transportation network usually have clustering properties, that is, the next navigable or accessible point of a node that is connected to a transportation node is also connected to the original transportation node. The larger the value of the transportation node clustering coefficient, the higher the connectivity of the local area where the transportation node is located. Assuming that the transportation node and If a transportation node is directly accessible to navigation or traffic, then this The maximum possible navigation or traffic routes between the traffic nodes is If this The number of routes that actually exist between nodes is The clustering coefficient includes:

[0064] In the formula, For traffic nodes The clustering coefficient, For traffic nodes The number of transportation nodes directly accessible to navigation or traffic, for The number of navigable or traffic routes that actually exist between the nodes.

[0065] Using traffic nodes The degree centrality, betweenness centrality, closeness centrality, eigenvector centrality and clustering coefficient of the network are used to construct a connectivity evaluation index system. .

[0066] The degree centrality, betweenness centrality, closeness centrality, eigenvector centrality and clustering coefficient of all transportation nodes in the air-rail combined transportation network are obtained respectively to obtain the connectivity evaluation matrix ,in , For the Traffic nodes, For the The connectivity evaluation indicators are degree centrality, betweenness centrality, closeness centrality, eigenvector centrality and clustering coefficient, that is, . is the connectivity evaluation matrix Line The elements of the column, and is a constant.

[0067] In an exemplary embodiment of the present invention, obtaining the comprehensive evaluation value of connectivity between airports and railway stations includes: S201: obtaining the mean and standard deviation of the connectivity evaluation index samples, standardizing the connectivity evaluation index matrix, and obtaining the connectivity evaluation index correlation coefficient matrix; Among them, the mean and standard deviation of the samples of connectivity evaluation indicators include:

[0068] in, After standardization , For traffic nodes In the The mean value of the connectivity evaluation index, For traffic nodes In the The standard deviation of an indicator.

[0069] Calculate each two connectivity evaluation indicators and Correlation coefficient between :

[0070] In the formula, For traffic nodes Evaluation indicators The evaluation value of For traffic nodes Evaluation indicators The evaluation value.

[0071] Standardized connectivity evaluation index matrix :

[0072] Connectivity evaluation index correlation coefficient matrix :

[0073] in, , correlation coefficient matrix of general index and connectivity evaluation index matrix The meanings of the elements in the corresponding positions are the same and will not be explained one by one.

[0074] S202: Obtain matrix eigenvalues ​​through the connectivity evaluation index correlation coefficient matrix, and obtain The variance contribution rate of each indicator variable and each connectivity evaluation index; Calculate the correlation coefficient matrix of connectivity evaluation indicators The matrix eigenvalues ​​of , in, For the 1st to matrix eigenvalues ​​and corresponding eigenvectors ,in, Equivalent to ,and ,in, is the transpose of a vector, for The eigenvalues ​​of the eigenvectors, is the feature vector The vector-valued, consisting of eigenvectors New indicator variables:

[0075] In the formula, is the first indicator variable, is the second indicator variable, For the indicator variables, For the The standardized indicator variable of each indicator.

[0076] S203: From Select from the indicator variables As the principal component, The correlation coefficient of the connectivity evaluation index corresponding to the principal components is used as the weight, and the traffic node is obtained by linear weighting. No. The evaluation function of the principal components; Before calculation The contribution ratio of each connectivity evaluation index is calculated, and the comprehensive connectivity evaluation value is obtained based on the contribution ratio and evaluation function.

[0077] Specifically, the variance contribution rate of each connectivity evaluation index includes:

[0078] In the formula, Connectivity evaluation index The variance contribution rate of is the correlation coefficient matrix of connectivity evaluation indicators No. matrix eigenvalues, is the correlation coefficient matrix of connectivity evaluation indicators No. matrix eigenvalues, is the number of indicator variables; Regarding the selection of principal components, the cumulative contribution rate of indicator variables is further obtained:

[0079] in, For the The cumulative contribution rate of indicator variables is When it is close to 1, select the current indicator variables As principal components, replacing the original indicator variable.

[0080] The evaluation function includes:

[0081] In the formula, For traffic nodes No. The evaluation function of the connectivity evaluation of the indicators corresponding to the principal components is: Connectivity evaluation index and connectivity evaluation indicators The correlation coefficient of For the principal components.

[0082] The comprehensive connectivity evaluation values ​​obtained based on the contribution ratio and evaluation function include:

[0083]

[0084] In the formula, is the contribution ratio, For traffic nodes The comprehensive connectivity evaluation value.

[0085] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0086] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. The computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0087] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for measuring the connectivity of an air-rail combined transport network, characterized in that: include: Obtain airport flight operation information and railway shuttle operation information, and establish the aviation transportation network adjacency matrix and the railway transportation network adjacency matrix respectively; Establish the air-rail combined transport network matrix through the air transport network adjacency matrix and the railway transport network adjacency matrix; According to the network centrality of each node in the air-rail combined transport network matrix, the connectivity evaluation index is obtained, and the connectivity evaluation index matrix of the air-rail combined transport network is constructed; The comprehensive evaluation value of the connectivity of airports and railway stations is obtained through the connectivity evaluation index matrix.

2. The method for measuring connectivity of an air-rail combined transport network according to claim 1, characterized in that: The connectivity evaluation indicators include degree centrality, betweenness centrality, closeness centrality, eigenvector centrality and clustering coefficient.

3. The method for measuring the connectivity of an air-rail combined transport network according to claim 2, characterized in that: The degree centrality includes: in, For traffic nodes The degree centrality of is the total number of transportation nodes in the air-rail combined transportation network, For traffic nodes and traffic nodes The total volume of transportation between and is a natural number.

4. The method for measuring connectivity of an air-rail combined transport network according to claim 3, characterized in that: The betweenness centrality includes: in, For traffic nodes The betweenness centrality of From the traffic node To the traffic node The total number of all shortest paths, For traffic nodes To the traffic node The shortest path passes through the traffic node The number of shortest paths.

5. The method for measuring connectivity of an air-rail combined transport network according to claim 4, characterized in that: The closeness centrality includes: in, For traffic nodes The closeness centrality, Indicates a traffic node To the traffic node The shortest distance.

6. The method for measuring connectivity of an air-rail combined transport network according to claim 5, characterized in that: The eigenvector centrality includes: in, For traffic nodes The eigenvector centrality of represents a constant, For traffic nodes Traffic nodes The number of flights or traffic between For traffic nodes The number of direct connections to other nodes, is the element of the feature vector, i.e., the traffic node The eigenvector centrality measure of .

7. The method for measuring connectivity of an air-rail combined transport network according to claim 6, characterized in that: The clustering coefficient includes: In the formula, For traffic nodes The clustering coefficient, For traffic nodes The number of transportation nodes directly accessible to navigation or traffic, for The number of navigable or traffic routes that actually exist between the nodes.

8. The method for measuring connectivity of air-rail combined transport network according to claim 1, characterized in that: The comprehensive evaluation values ​​of connectivity of airports and railway stations obtained by solving the above problems include: Obtain the mean and standard deviation of the connectivity evaluation index samples, standardize the connectivity evaluation index matrix, and obtain the connectivity evaluation index correlation coefficient matrix; The matrix eigenvalue is obtained by the correlation coefficient matrix of the connectivity evaluation index, and the The variance contribution rate of each indicator variable and each connectivity evaluation index; from Select from the indicator variables As the principal component, The correlation coefficient of the connectivity evaluation index corresponding to the principal component is used as the weight, and the linear weighting is used to obtain the first The evaluation function of the principal components; Before calculation The contribution ratio of each connectivity evaluation index is calculated, and the comprehensive connectivity evaluation value is obtained based on the contribution ratio and evaluation function.

9. The method for measuring connectivity of air-rail combined transport network according to claim 8, characterized in that: The variance contribution rates of the connectivity evaluation indicators include: In the formula, is the variance contribution rate, is the correlation coefficient matrix of connectivity evaluation indicators No. matrix eigenvalues, is the correlation coefficient matrix of connectivity evaluation indicators No. matrix eigenvalues, is the number of indicator variables; The evaluation function includes: In the formula, For traffic nodes No. The evaluation function of the connectivity evaluation of the indicators corresponding to the principal components is: Connectivity evaluation index and connectivity evaluation indicators The correlation coefficient of For the principal components.

10. The method for measuring connectivity of air-rail combined transport network according to claim 9, characterized in that: The comprehensive connectivity evaluation value obtained based on the contribution ratio and the evaluation function includes: In the formula, is the contribution ratio, For traffic nodes The comprehensive connectivity evaluation value.

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