Airport group network connectivity analysis method and system based on relative entropy theory

Abstract

The invention provides an airport group network connectivity analysis method and system based on a relative entropy theory. The method comprises the following steps: constructing an airport group network topology model; calculating the node degree and the node flow intensity of each node; calculating route connection strength and passenger demand strength between airport networks based on the node degree of each node, node flow strength, route opening condition between airports, flight frequency data and route passenger volume data; based on the airline connection strength between the airport networks and the airport network passenger demand strength, calculating an airline direct navigation rate and a passenger direct navigation rate; the method comprises the following steps: constructing an airline direct navigation connectivity influence degree measurement index ACI based on a relative entropy value and an airline direct navigation rate, constructing a passenger direct navigation connectivity influence degree measurement index PCI based on the relative entropy value and a passenger direct navigation rate, and constructing an airport group network connectivity index NCI based on the ACI and the PCI so as to comprehensively evaluate the network connectivity of the airport group. According to the invention, the accuracy and effectiveness of airport group network connectivity analysis are improved.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of transportation, and in particular to a method and system for analyzing the connectivity of an airport cluster network based on relative entropy theory. Background Art

[0002] With the rapid development of my country's aviation transportation industry, airport clusters, as aviation hubs with multiple airports, are increasingly becoming the core of modern aviation networks. Connectivity analysis of airport cluster networks is an important means to evaluate transportation efficiency, aviation resource sharing and emergency response capabilities among airport clusters. At present, some airport cluster connectivity analysis methods have been applied to air traffic management, mainly relying on network topology analysis, graph theory, network flow analysis and other methods. By abstracting airports and routes into nodes and edges in the network, the route network structure and connectivity between airports are evaluated.

[0003] In the existing technology, common connectivity analysis methods include connectivity assessment based on network topology, complex network theory and hierarchical analysis of airport groups:

[0004] (1) Connectivity evaluation based on network topology: The network topology analysis method describes the connectivity relationship between nodes (airports) in the airport network and uses some basic characteristics in graph theory (such as degree, connectivity, centrality, etc.) to evaluate the connectivity of the airport network. Specifically, the connectivity of the airport network is usually measured by the following indicators: Node degree: measures the number of direct connections between an airport and other airports. The larger the degree, the more connections the airport has with other airports. Connectivity: measures whether an airport network is connected, that is, whether there is a path between any two airports. Centrality: measures the importance of an airport in the network. Airports with high centrality are usually hub airports connecting other airports, with higher flight frequencies and more important transportation status. Shortest path length: measures the number of steps required to connect any two airports through the shortest path. This indicator can reflect the overall compactness of routes within the airport group. Network density: measures the ratio of actual routes to possible routes in the network. A network with high density indicates that the connections between airports are denser.

[0005] (2) Complex network theory: In the framework of complex network theory, the airport network can be viewed as a complex scale-free network in which different airports have very different numbers of connections to other airports. This theory holds that in a complex network, some airports will become "super nodes", that is, hubs with high flight frequencies and connections to other airports. In this way, it is possible to identify which airports are key nodes that play a decisive role in the connectivity of the entire network. For example, some hub airports may play a core role with fewer flight connections (but more connecting flights), while other smaller airports may rely on the flight connections of these hub airports.

[0006] (3) Hierarchical analysis of airport clusters: Some scholars have proposed a hierarchical airport cluster model that divides airport clusters into different levels and functional categories. For example, the core area of ​​some airport clusters is composed of major hub airports with high connectivity, while the peripheral area may be composed of some smaller airports that usually rely on hub airports for transfers or connect to other regions through indirect routes. Through this analysis, researchers can identify the roles of different airports within the airport cluster and their role in the entire airport network.

[0007] The above methods mostly focus on the connectivity indicators of a single airport, which can reflect the connectivity of the airport network to a certain extent, but often ignore the importance and stability of the airport cluster as a whole in the aviation network. At the same time, they ignore the coordinated development and resource sharing effects among the airports within the airport cluster, as well as the impact of passenger flow and direct connectivity between airports on the overall connectivity of the airport cluster.

[0008] In summary, the prior art has the following disadvantages:

[0009] (1) Single perspective, ignoring the integrity and synergy of airport clusters

[0010] Existing studies have mostly focused on the connectivity analysis of a single airport or a single route, ignoring the synergy of the airport cluster as a whole system. The interaction and overall layout between airports have an important impact on connectivity, but these factors are often ignored in existing studies.

[0011] (2) Ignoring the impact of passenger flow and direct routes

[0012] Traditional analysis methods mainly rely on static indicators such as the number of flights and frequency, ignoring the impact of passenger flow and direct routes on airport connectivity. Although some airports have fewer flight connections, their actual passenger flow may be very large due to their role as transit airports; at the same time, the existence of direct routes plays an important role in improving connectivity.

[0013] (3) Lack of comprehensive connectivity evaluation indicators, ignoring the relationship between airport clusters

[0014] Existing studies usually focus on single-dimensional network indicators, lacking comprehensive indicators that can comprehensively evaluate the connectivity of airport cluster networks and the importance of airport nodes in the network. In addition, there is a relative lack of research on connectivity between airport clusters, ignoring the relationship between different airport clusters and the impact of aviation network layout. Summary of the invention

[0015] In view of this, the embodiment of the present invention provides an airport cluster network connectivity analysis method and system based on the relative entropy theory. The scheme of the present invention aims to solve the problems existing in the prior art when evaluating the airport cluster network connectivity, especially the problems of ignoring the integrity of the airport cluster, ignoring passenger flow, ignoring the impact of direct flights between airports, ignoring the relationship between airport clusters, and lacking comprehensive indicators for stability evaluation. By introducing the relative entropy theory, the present invention provides a method and system for quantitatively evaluating the importance and stability of each airport node in the airport cluster in the network, so as to more accurately analyze the network connectivity of the airport cluster.

[0016] According to the first aspect of an embodiment of the present invention, a method for analyzing the connectivity of an airport cluster network based on the relative entropy theory is provided, including: S1, constructing an airport cluster network topology model: based on the route opening status, flight frequency data and route passenger volume data between each airport, taking each airport in the airport cluster as a node and the route as an edge, constructing an airport cluster network model, taking the airports outside the airport cluster as nodes and the route as an edge, constructing an airport network model, and constructing an airport cluster network topology model based on the airport cluster network model and the airport network model; S2, calculating the node degree and node flow intensity: based on the constructed airport cluster network topology model, calculating the node degree and node flow intensity of each node to reflect the connection relationship and intensity between airports; S3, calculating the route connection strength and passenger demand intensity between airport networks: based on the node degree and node flow intensity of each node, the route opening status, flight frequency data and route passenger volume data between each airport, calculating the route connection strength and passenger demand intensity between airport networks; S4, calculating the direct access of routes Flight rate, passenger direct flight rate: Based on the route connection strength between airport networks and the passenger demand strength of airport networks, calculate the route direct flight rate and passenger direct flight rate; S5. Calculate the relative entropy value: define probability distribution P and probability distribution Q, probability distribution P is the complete network connectivity state distribution including a specific airport, and probability distribution Q is the network connectivity state distribution assuming that the specific airport has lost its function. By calculating the relative entropy value between probability distribution P and probability distribution Q, quantitatively evaluate the importance and stability of the specific airport in the network; S6. Construct an airport cluster network connectivity analysis model: Based on the relative entropy value and route direct flight rate, construct the route direct flight connectivity impact measurement index ACI, based on the relative entropy value and passenger direct flight rate, construct the passenger direct flight connectivity impact measurement index PCI, and at the same time, construct the airport cluster network connectivity index NCI based on the route direct flight connectivity impact measurement index ACI and the passenger direct flight connectivity impact measurement index PCI to comprehensively evaluate the network connectivity of the airport cluster.

[0017] In one implementation, in step S1, in constructing the airport cluster network topology model, the airport cluster network model is composed of a weighted matrix G P (V P ,E P) indicates that It's G P A set of nodes representing the airports in the airport cluster. It's G P The edge set represents the routes connecting the airports. The number of network nodes in the airport cluster network model is N1, and the number of edges in the airport cluster network model is M1. The airport network model is represented by G W (V W ,E W ), where V W It's G W The node set of E represents the airports outside the airport cluster. W It's G W The edge set represents the routes between airports outside the airport cluster. The number of network nodes in the airport network model is N2, and the number of edges in the airport network model is M2. The airport cluster network topology model is expressed as G(V,E), where V is the node set of G, E is the edge set of G, the number of network nodes in the airport cluster network topology model is N, and the number of edges is M. The relationship between the airport cluster network model, the airport network model and the airport cluster network topology model is expressed as:

[0018] G=G P +G W (1)

[0019] The adjacency matrix of the airport cluster network topology model G is represented by A. When the node v i and v j When connecting, the element in the adjacency matrix A is a ij =1, otherwise, the element in the adjacency matrix A is a ij =0, airport cluster network model G P The adjacency matrix is ​​represented as A P , Airport Network Model G W The adjacency matrix is ​​represented as A W .

[0020] In another implementation, in step S2, when calculating the node degree and node traffic intensity, the node v i The node degree D(v i ) is the node v in the network i The number of nodes with edges, node degree D(v i ) is expressed as:

[0021]

[0022] Node v i The node traffic intensity S(v i ) is the total passenger volume of all direct flights connected to the node, and the node flow intensity S(v i ) is expressed as:

[0023]

[0024] Among them, w ij Indicates airport v i With Airport v j The number of passengers between.

[0025] In another implementation, in step S3, in calculating the route connection strength and passenger demand strength between airport networks, for the connection strength between airport clusters, all airports in the airport cluster are regarded as a whole, and the connection strength between two airport clusters is the sum of the connection strengths from each airport in one airport cluster to each airport in the other airport cluster. The route OD pair refers to the starting and ending point pair of the route, which is used to describe the route combination from a specific starting point to a specific destination. Assuming there are two airport clusters, in the OD pair, the airport network formed by the airports in one of the airport clusters is regarded as a whole and recorded as O. The network is defined as G O In the OD pair, the airport network formed by the airports of another airport group is regarded as a whole, denoted as D, and the network is defined as G D , Airport Network G O With Airport Network G D The total number of edges between them is expressed as the connection strength between OD pairs, denoted as S(G O -G D ), the formula for calculating the route connection strength between airport networks is as follows:

[0026]

[0027] Among them, S(G O -G D ) represents the strength of route connections between airport networks;

[0028] Airport Network G O With Airport Network G D The passenger demand intensity S w (G O -G D ) is expressed as:

[0029]

[0030] Among them, w ij Representative Airport i With Airport v j The number of passengers between.

[0031] In another implementation, in step S4, when calculating the route direct access rate and the passenger direct access rate, the airport network G O With Airport Network G D The calculation formula of the direct navigation rate δ between the routes is:

[0032]

[0033] Among them, N O Airport Network G O The number of airports in D Indicates the airport network G D The number of airports in, at the same time, δ∈(0,1], the maximum value δ max =1;

[0034] Airport Network G O With Airport Network G D The direct passenger rate between w The calculation formula is:

[0035]

[0036] Among them, NW O Airport Network G O Total number of passengers, NW D Airport Network G D The total number of passengers, at the same time, δ w ∈(0,1], maximum value δ wmax =1.

[0037] In another implementation, in step S5, in calculating the relative entropy value, the relative entropy D(P||Q) is defined as:

[0038] D(P||Q)=∑P(i)log(P(i) / Q(i)) (8)

[0039] Among them, i represents the value of the random variable, P and Q represent two probability distributions respectively. When P=Q, the relative entropy takes the minimum value of 0. At this time, the probability distribution P and the probability distribution Q are exactly the same. The greater the difference between P and Q, the greater the value of the relative entropy.

[0040] In another implementation, S6 constructs an airport cluster network connectivity analysis model. When flights are normal, the airport network G O and Airport Network G D When the direct air traffic rate between the two airports is δ, the airport network G O and Airport Network G D The direct air traffic rate between the two routes is δ′. According to the relative entropy theory, the calculation formula of the direct air connectivity impact index ACI is as follows:

[0041]

[0042] Due to δ max =δ′ max=1, so the ACI of the direct flight connectivity between the final airport network can be expressed as:

[0043]

[0044] When flights are normal, the airport network G O and Airport Network G D The direct passenger traffic rate between them is that when an airport is disrupted and temporarily stops operating, the airport network G O and Airport Network G D The direct passenger traffic rate between w ′, according to the relative entropy theory, the calculation formula of the passenger direct flight connectivity impact measurement index PCI is as follows:

[0045]

[0046] The calculation formula of airport cluster network connectivity index NCI is:

[0047] NCI=α1·ACI+α2·PCI (12)

[0048] Among them, α1+α2=1, and the parameters α1 and α2 are determined according to the importance of the direct flight connectivity of routes and the direct flight connectivity of passengers on the connectivity of the entire airport cluster.

[0049] According to a second aspect of an embodiment of the present invention, there is provided an airport cluster network connectivity analysis system based on relative entropy theory, comprising: a data processing module for processing the collected route opening conditions, flight frequency data and route passenger volume data between the airport cluster and its external airports to obtain processed data; a network construction module for constructing an airport cluster network topology model based on the processed data; a network index calculation module for calculating the node degree, node flow intensity, route connection intensity, passenger demand intensity, route direct flight rate and passenger direct flight rate of each node in the airport cluster network topology model to obtain network index calculation results; a relative entropy calculation module for calculating the relative entropy value between the actual connectivity state of each airport in the airport network and the network connectivity state after assuming that the airport has lost its function based on the relative entropy theory and the network index calculation results; a connectivity analysis module for calculating the route direct flight connectivity influence measurement index and the passenger direct flight connectivity influence measurement index based on the relative entropy value, and calculating the airport cluster network connectivity index to obtain the airport cluster network connectivity analysis result.

[0050] According to a third aspect of an embodiment of the present invention, there is provided an electronic device, comprising a processor and a memory storing a program, wherein the program comprises instructions, and when the instructions are executed by the processor, the processor executes the steps executed by the method of the first aspect.

[0051] According to a fourth aspect of an embodiment of the present invention, there is provided a computer storage medium on which a computer program is stored. When the program is executed by a processor, the method of the first aspect described above is implemented.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) Improve the accuracy of analysis

[0054] In the present invention, relative entropy, as a method to measure the difference between two probability distributions, plays a key role in the analysis of airport cluster network connectivity. By calculating the relative entropy value between the actual connectivity state of the airport in the network and the network connectivity state after the airport is assumed to be out of function, the present invention can more accurately quantify the degree of connection between airports and the importance of each airport in the airport cluster network, reveal the bottlenecks and weak links in the airport network, and thus capture the characteristics of airport cluster connectivity that may not be obtained by traditional single airport connectivity analysis methods, further improving the accuracy and depth of analysis.

[0055] (2) Enhance the effectiveness of analysis

[0056] The application of the relative entropy theory of the present invention makes the analysis process more systematic and scientific. By constructing a connectivity analysis model based on relative entropy and combining the passenger volume data of each route, the present invention not only realizes the dynamic monitoring of the connectivity of the airport cluster network, but also can timely discover and respond to potential airport network risks. It also provides a solid scientific basis for the network optimization of the airport cluster, effectively guides resource allocation and route adjustment strategies, and thus comprehensively improves the operating efficiency and reliability of the entire network.

[0057] (3) Strong technical adaptability

[0058] The analysis method based on relative entropy of the present invention has wide applicability and can adapt to airport cluster networks of different sizes and structures. Whether it is a large airport cluster or a small and medium-sized airport cluster, effective connectivity analysis can be achieved through this method. More importantly, the method of the present invention can be flexibly adjusted to meet actual needs, such as considering changes in flight flow and route density in different time periods, ensuring that the analysis results are closer to the actual situation and enhancing the practicality and accuracy of the analysis.

[0059] (4) Easy to understand and implement

[0060] In the present invention, relative entropy is a mathematical tool with a broad application basis in the fields of statistics and information theory. Therefore, the airport cluster network connectivity analysis method based on relative entropy is easy to understand and accept in theory. In terms of implementation, the method can be implemented through existing data processing and computing tools, reducing technical barriers and costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0062] Figure 1 It is a flowchart of the steps of the airport group network connectivity analysis method based on relative entropy theory of the present invention;

[0063] Figure 2 This is a schematic diagram of the airport cluster network topology model structure;

[0064] Figure 3 For Figure 1 The corresponding flowchart of the specific steps of the airport cluster network connectivity analysis method based on relative entropy theory;

[0065] Figure 4 It is a structural schematic diagram of the airport cluster network connectivity analysis system based on relative entropy theory of the present invention. DETAILED DESCRIPTION

[0066] In order to have a clearer understanding of the technical features, purposes and effects of the embodiments of the present invention, the specific implementation of the embodiments of the present invention is now described with reference to the accompanying drawings.

[0067] In this document, “exemplary” means “serving as an example, instance or illustration”, and any illustration or implementation described in this document as “exemplary” should not be construed as a more preferred or more advantageous technical solution.

[0068] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, 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 only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in the field based on the embodiments in the embodiments of the present invention should fall within the scope of protection of the embodiments of the present invention.

[0069] The specific implementation of the embodiment of the present invention is further described below in conjunction with the accompanying drawings of the embodiment of the present invention.

[0070] See also Figure 1 , Figure 2 , Figure 3 The embodiment of the present invention provides an airport cluster network connectivity analysis method based on relative entropy theory, which mainly includes the following steps:

[0071] S1. Constructing the network topology model of the airport cluster: Based on the route opening situation, flight frequency data and route passenger volume data between the airports, the airports in the airport cluster are taken as nodes and the routes as edges to construct the airport cluster network model. The airports outside the airport cluster are taken as nodes and the routes as edges to construct the airport network model. The airport cluster network topology model is constructed based on the airport cluster network model and the airport network model.

[0072] S2. Calculate node degree and node flow intensity: Based on the constructed airport cluster network topology model, calculate the node degree and node flow intensity of each node to reflect the connection relationship and intensity between airports;

[0073] S3. Calculate the route connection strength and passenger demand strength between airport networks: Based on the node degree of each node, node traffic intensity, route opening status between airports, flight frequency data and route passenger volume data, calculate the route connection strength and passenger demand strength between airport networks;

[0074] S4. Calculate the direct air route rate and the direct passenger air route rate: Calculate the direct air route rate and the direct passenger air route rate based on the air route connection strength between airport networks and the passenger demand strength of airport networks;

[0075] S5. Calculate the relative entropy value: define probability distribution P and probability distribution Q , the probability distribution P is the complete network connectivity state distribution including the specific airport, and the probability distribution Q is the network connectivity state distribution after assuming that the specific airport has lost its function. By calculating the relative entropy value between the probability distribution P and the probability distribution Q, the importance and stability of the specific airport in the network are quantitatively evaluated;

[0076] S6. Construct an airport cluster network connectivity analysis model: Based on the relative entropy value and the direct flight rate, construct the route direct connectivity impact measurement index ACI; based on the relative entropy value and the direct passenger flight rate, construct the passenger direct connectivity impact measurement index PCI; at the same time, based on the route direct connectivity impact measurement index ACI and the passenger direct flight connectivity impact measurement index PCI, construct the airport cluster network connectivity index NCI to comprehensively evaluate the network connectivity of the airport cluster.

[0077] Specifically, the scheme of the present invention is further described according to the following examples:

[0078] The working principle of the present invention is based on the relative entropy theory. The relative entropy value is calculated by comparing the actual connectivity state of the airport in the network with the network connectivity state after the airport is assumed to be out of service. The larger the relative entropy value, the higher the importance of the airport in the network and the greater its connectivity. The specific process includes:

[0079] (1) Constructing an airport cluster network topology model: Based on the route opening status, flight frequency data, and route passenger volume data between airports, the airports in the airport cluster are taken as nodes and the routes as edges to construct the airport cluster network model G. P (V P ,E P ) ; Taking the external airports of the airport cluster as nodes and the routes as edges, the airport network model G is constructed W (V W ,E W ), the overall airport cluster network topology model is composed of G = G P +G W express.

[0080] (2) Calculation of node degree and node traffic intensity: Based on the constructed airport cluster network topology model, the node degree D (v i ), node traffic intensity S(v i ) to reflect the connection relationship and strength between airports.

[0081] (3) Calculate the route connection strength and passenger demand strength between airport networks: Based on the node degree and node flow intensity of each node, combined with the route opening status, flight frequency data and route passenger volume data between airports, calculate the route connection strength S(G O -G D ), passenger demand intensity S w (G O -G D );

[0082] (4) Calculation of route direct access rate and passenger direct access rate: Based on the route connection strength between airport networks and the passenger demand strength of airport networks, the route direct access rate δ and passenger direct access rate δ are calculated. w ;

[0083] (5) Calculate the relative entropy value: Define two probability distributions P and Q, one is the complete network connectivity state distribution including a specific airport, and the other is the network connectivity state distribution after assuming that the airport has lost its function. By calculating the relative entropy value D(P||Q) between these two distributions, the importance and stability of the airport in the network can be quantitatively evaluated.

[0084] (6) Construct an airport cluster network connectivity analysis model: Based on the relative entropy value and the direct flight rate, construct the route direct connectivity impact measurement index ACI; based on the relative entropy value and the direct passenger flight rate, construct the passenger direct flight connectivity impact measurement index PCI; at the same time, based on the route direct flight connectivity impact measurement index and the passenger direct flight connectivity impact measurement index, construct the airport cluster network connectivity index NCI to comprehensively evaluate the network connectivity of the airport cluster.

[0085] 1. Constructing the airport cluster network topology model

[0086] With the rapid development of the aviation industry, the aviation network between airport clusters has become increasingly complex, and measuring the connectivity of aviation networks has become an important research topic in the field of aviation transportation. From the perspective of network topology, the structural characteristics of the aviation network between airport clusters can be effectively analyzed, and then the level of connectivity can be evaluated. The principle of network topology is the basis for studying the relationship between nodes and edges in the network and their spatial distribution patterns. When analyzing the airport aviation network, the airport or airport cluster as a whole is regarded as a node, and the routes are regarded as the edges connecting these nodes. By analyzing topological indicators such as node degree, node flow intensity, and edge connection intensity, the connectivity and other characteristics of the aviation network can be revealed.

[0087] The network between airport clusters, namely the airport cluster network model, is composed of a weighted matrix G P (V P ,E P ) indicates that It's G P The node set (airports in the airport cluster), It's G P The number of network nodes is N1, and the number of edges is M1. This network is composed only of airports in different airport clusters and routes between airports, which is called an airport cluster network. Similarly, the network formed by the remaining airports outside the airport cluster is the airport network model, which is represented by G W (V W ,E W ), where V W It's G W The node set of E W It's G W The number of network edges (routes between airports outside the airport cluster) is N2, and the number of edges is M2. This network consists only of airports outside the airport cluster and the routes between the airports, and is called an airport network. The entire airport network that includes all airports in the airport cluster and all external airports, that is, the airport cluster network topology model, is represented by G(V,E), where V is the node set of G, E is the edge set of G, the number of nodes in the network is N, and the number of edges is M. The above network has the following relationship:

[0088] G=G P +G W (1)

[0089] The adjacency matrix of the entire airport network G is represented by A, where when node v i and v j When connecting, the element of the adjacency matrix A is a ij =1, otherwise, the element of the adjacency matrix A is aij = 0. Accordingly, network G P The adjacency matrix is ​​represented as A P , Network G W The adjacency matrix is ​​represented as A W .

[0090] 2. Calculate node degree and node traffic intensity

[0091] (1) Node degree

[0092] Node v i The node degree D(v i ) is the node v in the network i The number of nodes with connected edges reflects the direct flights between an airport and other airports. It also indicates the local importance of the airport in the airport network.

[0093]

[0094] (2) Node traffic intensity

[0095] Node v i The flow intensity S(v i ) is the sum of passenger traffic of all direct flights connected to the node, that is,

[0096]

[0097] Among them, w ij Indicates airport v i With Airport v j The number of passengers between.

[0098] 3. Calculate the route connection strength and passenger demand strength between airport networks

[0099] (1) Route connection strength

[0100] For the connection strength between airport clusters, all airports in the airport cluster are regarded as a whole. The connection strength between two airport clusters is the sum of the connection strengths from the airports in one airport cluster to the airports in the other airport cluster (if there are routes between the airports). Route OD pairs refer to the starting and ending point pairs of routes. Therefore, route OD pairs are used to describe the combination of routes from a specific starting point to a specific destination. Route OD pairs are an important concept in the field of air transportation and transportation planning, which is used to analyze route traffic, optimize route networks and predict flight demand. Suppose there are two airport clusters. In the OD pairs, the airport network formed by the airports in one of the airport clusters is regarded as a whole, denoted as O. The network is defined as G O In the OD pair, the airport network formed by the airports of the other airport group is regarded as a whole, denoted as D, and the network is defined as G D. Airport Network G O With Airport Network G D The total number of edges between them is expressed as the connection strength between OD pairs, denoted as S(G O -G D ). This connection strength reflects the aviation connectivity between the two airport networks, that is, the direct connecting routes between the two airport clusters. The route connection strength between the airport clusters is calculated as follows:

[0101]

[0102] (2) Passenger demand intensity

[0103] Similarly, the airport network G O With Airport Network G D The passenger demand intensity between w (G O -G D ), which reflects the passenger flow between two airport clusters. Unlike the route connection strength between airport networks, what is considered here is the passenger flow of each route, that is, the total number of passengers on each route. Its expression is:

[0104]

[0105] Among them, w ij Representative Airport i With Airport v j The number of passengers between.

[0106] 4. Calculate the direct air traffic rate of routes and the direct air traffic rate of passengers

[0107] (1) Direct air traffic rate

[0108] Airport Network G O With Airport Network G D The direct flight rate between the two airports is defined as δ, which is expressed as the ratio of the total number of direct routes between the two airport clusters to the total number of all possible connecting routes, where the total number of all possible connecting routes means that if there are routes between the airports of the two airport clusters, then the total number of all possible connecting routes is the total number of all possible connecting routes. For example, if the two airport clusters have 4 and 5 airports respectively, then the total number of all possible connecting routes between the two airport clusters is 20. Therefore, the calculation formula for the direct flight rate is:

[0109]

[0110] Among them, N O Airport Network G O The number of airports in D Represents the airport network G DThe number of airports in. At the same time, δ∈(0,1], the maximum value δ max =1.

[0111] (2) Passenger direct flight rate

[0112] Airport Network G O With Airport Network G D The direct passenger traffic rate between w , which is expressed as the ratio of the total number of direct flight passengers to the total number of passengers between two airport clusters. The formula for calculating the direct passenger rate is:

[0113]

[0114] Among them, NW O Airport Network G O Total number of passengers, NW D Airport Network G D The total number of passengers. At the same time, δ w ∈(0,1], maximum value δ wmax =1.

[0115] 5. Calculate relative entropy

[0116] Entropy is a physical concept that can be used to measure the degree of disorder within a system. Relative entropy, also known as Kullback-Leibler (KL) divergence or information divergence, is a basic concept in probability theory and information theory.

[0117] The definition of relative entropy is based on the difference in expected values ​​of probability distributions P and Q. Specifically, for discrete random variables, the relative entropy D(P||Q) is defined as:

[0118] D(P||Q)=∑P(i)log(P(i) / Q(i)) (8)

[0119] Where i represents the value of a random variable, and P and Q represent two probability distributions. Relative entropy is a measure of the difference between two probability distributions. It describes the efficiency of using one distribution to describe another distribution. When P = Q, the relative entropy takes the minimum value of 0, and the two distributions are exactly the same. The greater the difference between P and Q, the greater the value of relative entropy.

[0120] Relative entropy is a method in information theory to measure the difference between two probability distributions. It can be effectively applied to the evaluation of the connectivity of airport route networks. In an airport network, each airport can be regarded as a node, and the routes constitute the edges between the nodes. When relative entropy theory is applied to this situation, the impact of the airport on the connectivity of the entire network can be measured by comparing the actual connectivity status of the airport in the network with the network connectivity status after assuming that the airport has lost its function.

[0121] Specifically, two probability distributions can be defined: one is the distribution of the connectivity state of the complete airport network including a specific airport, and the other is the distribution of the network connectivity state after the airport is assumed to be out of service. By calculating the relative entropy between these two distributions, the importance of the airport to maintaining the connectivity of the entire network can be quantified. The higher the relative entropy value, the more critical the role of the airport in the network, and its loss of service will lead to a significant decrease in network connectivity.

[0122] Therefore, the index based on relative entropy can not only reflect the connectivity level of airports in the aviation network, but also reveal the importance of different airports in the network and their mutual influence. This index helps to more accurately evaluate the connectivity of the airport cluster aviation network and provide strong support for route planning, network optimization and risk control. Therefore, the relative entropy theory has important application value in the evaluation of airport route network connectivity. Next, an airport cluster network connectivity analysis model will be established based on the relative entropy theory.

[0123] 6. Constructing an airport cluster network connectivity analysis model

[0124] (1) Index of direct flight connectivity impact

[0125] When flights are normal, the airport network G O and Airport Network G D The direct air traffic rate between the two airports is δ. However, when the airport is disturbed and temporarily stops operating, the integrity of the airport network will also be affected. At this time, the direct air traffic rate between the airport network is δ′. According to the relative entropy theory, the calculation formula of the route direct connectivity impact measurement index (expressed as ACI) is as follows:

[0126]

[0127] Due to δ max =δ′ max =1, so the impact index of direct flight connectivity between airport networks can be expressed as:

[0128]

[0129] (2) Passenger direct flight connectivity impact measurement index

[0130] When flights are normal, the airport network G O and Airport Network G D The direct passenger traffic rate between w However, when airports are disrupted and temporarily stop operating, the integrity of the airport network is also affected, and the direct passenger traffic rate between the airport networks is δ w ′. According to the relative entropy theory, the calculation formula of the passenger direct flight connectivity impact measurement index (expressed by PCI) is as follows:

[0131]

[0132] (3) Airport cluster network connectivity index

[0133] The direct flight connectivity impact measurement index based on relative entropy has the characteristics of entropy change and can effectively reflect the changes in the traffic rate between airport networks. As a measure of the difference between two probability distributions, relative entropy has ideal properties such as non-negativity, symmetry and additivity. In the airport network, the application of relative entropy can effectively and accurately measure the changes in the traffic rate between airports.

[0134] Specifically, the direct flight connectivity impact measurement index based on relative entropy can reflect the flight changes between airports in the airport network. When the number of flights between two airports changes, the relative entropy will also change accordingly. If the value of this indicator is large, it means that the flight rate between the two airport networks has changed greatly, which has a greater impact on the airport route connectivity. Conversely, if the value of this indicator is small, it means that the flight rate between the two airport networks has changed little, and the impact on the airport route connectivity is also relatively small.

[0135] Therefore, the application of the direct air traffic impact index based on relative entropy can help airports better understand flight changes and provide an important reference for flight planning and operation management. By using this index, the impact of different flight changes on route connectivity can be better evaluated, so as to formulate more reasonable and efficient flight plans.

[0136] Therefore, the calculation formula of the airport cluster network connectivity index (expressed as NCI) is:

[0137] NCI=α1·ACI+α2·PCI (12)

[0138] Among them, α1+α2=1.

[0139] In this embodiment, in step 6, parameters α1 and α2 need to be determined based on the importance of the direct route connectivity and direct passenger flight connectivity on the connectivity of the entire airport cluster. For example, if it is considered that the direct route connectivity and direct passenger flight connectivity are equally important to the connectivity of the entire airport cluster, then α1 and α2 are taken as 0.5 and 0.5 respectively.

[0140] See also Figure 4 The embodiment of the present invention further provides an airport cluster network connectivity analysis system based on relative entropy theory, comprising:

[0141] A data processing module is used to process the collected route opening conditions, flight frequency data and route passenger volume data between the airport group and its external airports to obtain processed data;

[0142] The network construction module is used to construct the airport cluster network topology model based on the processed data;

[0143] The network index calculation module is used to calculate the node degree, node flow intensity, route connection intensity, passenger demand intensity, route direct navigation rate and passenger direct navigation rate of each node in the airport cluster network topology model to obtain the network index calculation results;

[0144] A relative entropy calculation module is used to calculate the relative entropy value between the actual connectivity state of each airport in the airport network and the network connectivity state after assuming that the airport loses its function based on the relative entropy theory and the network indicator calculation results;

[0145] The connectivity analysis module is used to calculate the route direct flight connectivity impact measurement index and the passenger direct flight connectivity impact measurement index based on the relative entropy value, and at the same time calculate the airport cluster network connectivity index, so as to obtain the airport cluster network connectivity analysis results.

[0146] The above data processing module, network construction module, network indicator calculation module, relative entropy calculation module and connectivity analysis module are communicated and connected.

[0147] The airport cluster network connectivity analysis method and system based on relative entropy theory of the present invention improve the accuracy and effectiveness of the airport cluster network connectivity analysis.

[0148] It should be understood that accuracy in the present invention refers to the ability to more accurately reflect the network relationship between airport clusters when analyzing the connectivity of the airport cluster network through the relative entropy theory. As a method of measuring the difference in probability distribution, the relative entropy theory can effectively capture the subtle changes and potential structures in the airport cluster network, thereby accurately evaluating the degree of connectivity between different airport clusters. Compared with traditional connectivity analysis methods, the present invention can handle more complex network relationships by introducing the relative entropy theory, avoiding the errors caused by simple distance or direct connectivity indicators. For example, by considering changes in traffic distribution and network structure, the connectivity of different airport clusters can be evaluated more comprehensively, not only limited to physical connectivity, but also comprehensively considering factors such as the mobility and route density of the aviation network to improve the accuracy of the analysis results.

[0149] The effectiveness emphasizes the operability of the present invention in practical applications and its help in decision support. By constructing an analytical model based on relative entropy theory, the present invention can effectively identify and quantify the mutual influence and potential optimization space between airport clusters. This method is not only scientific and rigorous in theory, but also can provide effective guidance in the actual airport cluster network planning and operation management.

[0150] Specifically, connectivity analysis based on relative entropy theory can optimize the layout of airport clusters, help decision makers identify which airport clusters have cooperation potential or need to strengthen connections, and thus formulate more reasonable aviation network development strategies. In addition, the system of the present invention has strong adaptability in the process of data processing and analysis, can handle airport networks of various sizes and complexities, and has high application value.

[0151] Compared with the prior art, the present invention has the following beneficial effects:

[0152] (1) Improve the accuracy of analysis

[0153] In the present invention, relative entropy, as a method to measure the difference between two probability distributions, plays a key role in the analysis of airport cluster network connectivity. By calculating the relative entropy value between the actual connectivity state of the airport in the network and the network connectivity state after the airport is assumed to be out of function, the present invention can more accurately quantify the degree of connection between airports and the importance of each airport in the airport cluster network, reveal the bottlenecks and weak links in the airport network, and thus capture the characteristics of airport cluster connectivity that may not be obtained by traditional single airport connectivity analysis methods, further improving the accuracy and depth of analysis.

[0154] (2) Enhance the effectiveness of analysis

[0155] The application of the relative entropy theory of the present invention makes the analysis process more systematic and scientific. By constructing a connectivity analysis model based on relative entropy and combining the passenger volume data of each route, the present invention not only realizes the dynamic monitoring of the connectivity of the airport cluster network, but also can timely discover and respond to potential airport network risks. It also provides a solid scientific basis for the network optimization of the airport cluster, effectively guides resource allocation and route adjustment strategies, and thus comprehensively improves the operating efficiency and reliability of the entire network.

[0156] (3) Strong technical adaptability

[0157] The analysis method based on relative entropy of the present invention has wide applicability and can adapt to airport cluster networks of different sizes and structures. Whether it is a large airport cluster or a small and medium-sized airport cluster, effective connectivity analysis can be achieved through this method. More importantly, the method of the present invention can be flexibly adjusted to meet actual needs, such as considering changes in flight flow and route density in different time periods, ensuring that the analysis results are closer to the actual situation and enhancing the practicality and accuracy of the analysis.

[0158] (4) Easy to understand and implement

[0159] In the present invention, relative entropy is a mathematical tool with a broad application basis in the fields of statistics and information theory. Therefore, the airport cluster network connectivity analysis method based on relative entropy is easy to understand and accept in theory. In terms of implementation, the method can be implemented through existing data processing and computing tools, reducing technical barriers and costs.

[0160] As another example, the present invention also provides an electronic device, and now will describe an electronic device that can be used as a server or client of the present invention, which is an example of a hardware device that can be applied to various aspects of the present invention. Electronic devices are intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workbenches, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are only examples, and are not intended to limit the implementation of the present invention described and / or required herein.

[0161] The electronic device may include: a processor (processor), a communication interface (CommunicationsInterface), a memory (memory) and a communication bus.

[0162] The processor, the communication interface and the memory communicate with each other through the communication bus. The communication interface is used to communicate with other electronic devices or servers.

[0163] The processor is used to execute the program, and specifically can execute the relevant steps in the above method embodiment.

[0164] Specifically, the program may include program codes including computer operation instructions.

[0165] The processor may be a CPU, or an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of the present invention. The one or more processors included in the smart device may be processors of the same type, such as one or more CPUs; or processors of different types, such as one or more CPUs and one or more ASICs.

[0166] The memory is used to store programs and may include a high-speed RAM memory and may also include a non-volatile memory, such as at least one disk memory.

[0167] When the program is executed by a processor, it is used to enable the electronic device to execute the airport group network connectivity analysis method based on relative entropy theory of the present invention.

[0168] In addition, the specific implementation of each step in the program can refer to the corresponding description of the corresponding steps and units in the above method embodiment, which will not be repeated here. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the above-described devices and modules can refer to the corresponding process description in the above method embodiment, which will not be repeated here.

[0169] The exemplary embodiments of the present invention further provide a computer storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the methods of the various embodiments of the present invention. The corresponding process descriptions in the aforementioned method embodiments may be referred to and will not be repeated here.

[0170] The above-described method according to an embodiment of the present invention may be implemented in hardware, firmware, or as software or computer code that may be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded over a network and will be stored in a local recording medium, so that the method described herein may be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that a computer, processor, microprocessor controller, or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, processor, or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0171] Thus far, specific embodiments of the present invention have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired results. Additionally, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing may be advantageous.

[0172] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0173] Finally, it should be noted that the above implementation methods are only used to illustrate the embodiments of the present invention, and are not limitations of the embodiments of the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the embodiments of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the embodiments of the present invention. The patent protection scope of the embodiments of the present invention should be defined by the claims.

Claims

1. A method for analyzing the connectivity of airport cluster networks based on relative entropy theory, characterized in that: include: S1. Constructing the network topology model of the airport cluster: Based on the route opening situation, flight frequency data and route passenger volume data between the airports, the airports in the airport cluster are taken as nodes and the routes as edges to construct the airport cluster network model. The airports outside the airport cluster are taken as nodes and the routes as edges to construct the airport network model. The airport cluster network topology model is constructed based on the airport cluster network model and the airport network model. S2. Calculate node degree and node flow intensity: Based on the constructed airport cluster network topology model, calculate the node degree and node flow intensity of each node to reflect the connection relationship and intensity between airports; S3. Calculate the route connection strength and passenger demand strength between airport networks: Based on the node degree of each node, node traffic intensity, route opening status between airports, flight frequency data and route passenger volume data, calculate the route connection strength and passenger demand strength between airport networks; S4. Calculate the direct air route rate and the direct passenger air route rate: Calculate the direct air route rate and the direct passenger air route rate based on the air route connection strength between airport networks and the passenger demand strength of airport networks; S5. Calculate the relative entropy value: define probability distribution P and probability distribution Q. Probability distribution P is the complete network connectivity state distribution including the specific airport, and probability distribution Q is the network connectivity state distribution after assuming that the specific airport has lost its function. By calculating the relative entropy value between probability distribution P and probability distribution Q, quantitatively evaluate the importance and stability of the specific airport in the network. S6. Construct an airport cluster network connectivity analysis model: Based on the relative entropy value and the direct flight rate, construct the route direct connectivity impact measurement index ACI; based on the relative entropy value and the direct passenger flight rate, construct the passenger direct connectivity impact measurement index PCI; at the same time, based on the route direct connectivity impact measurement index ACI and the passenger direct flight connectivity impact measurement index PCI, construct the airport cluster network connectivity index NCI to comprehensively evaluate the network connectivity of the airport cluster.

2. The method according to claim 1, characterized in that In step S1, the airport cluster network topology model is constructed. The airport cluster network model is composed of a weighted matrix G P (V P ,E P ) indicates that It's G P A set of nodes representing the airports in the airport cluster, It's G P The edge set represents the routes connecting the airports. The number of network nodes in the airport cluster network model is N1, and the number of edges in the airport cluster network model is M1. The airport network model is represented by G W (V W ,E W ), where V W It's G W The node set of E represents the airports outside the airport cluster. W It's G W The edge set represents the routes between airports outside the airport cluster. The number of network nodes in the airport network model is N2, and the number of edges in the airport network model is M2. The airport cluster network topology model is expressed as G(V,E), where V is the node set of G, E is the edge set of G, the number of network nodes of the airport cluster network topology model is N, the number of edges is M, and the relationship between the airport cluster network model, the airport network model and the airport cluster network topology model is expressed as: G=G P +G W (1) The adjacency matrix of the airport cluster network topology model G is represented by A. When the node v i and v j When connecting, the element in the adjacency matrix A is a ij =1, otherwise, the element in the adjacency matrix A is a ij =0, airport cluster network model G P The adjacency matrix is ​​represented as A P , Airport Network Model G W The adjacency matrix is ​​represented as A W .

3. The method according to claim 2, characterized in that In step S2, node degree and node traffic intensity are calculated. i The node degree D(v i ) is the node v in the network i The number of nodes with edges, node degree D(v i ) is expressed as: Node v i The node traffic intensity S(v i ) is the total passenger volume of all direct flights connected to the node, and the node flow intensity S(v i ) is expressed as: Among them, w ij Indicates airport v i With Airport v j The number of passengers between.

4. The method according to claim 3, characterized in that Step S3 calculates the route connection strength and passenger demand strength between airport networks. For the connection strength between airport clusters, all airports in the airport cluster are regarded as a whole. The connection strength between two airport clusters is the sum of the connection strengths from each airport in one airport cluster to each airport in the other airport cluster. The route OD pair refers to the starting and ending point pair of the route, which is used to describe the route combination from a specific starting point to a specific destination. Assuming there are two airport clusters, in the OD pair, the airport network formed by the airports in one of the airport clusters is regarded as a whole and recorded as O. The network is defined as G O In the OD pair, the airport network formed by the airports of another airport group is regarded as a whole, denoted as D, and the network is defined as G D , Airport Network G O With Airport Network G D The total number of edges between them is expressed as the connection strength between OD pairs, denoted as S(G O -G D ), the formula for calculating the route connection strength between airport networks is as follows: Among them, S(G O -G D ) represents the strength of route connections between airport networks; Airport Network G O With Airport Network G D The passenger demand intensity S w (G O -G D ) is expressed as: Among them, w ij Representative Airport i With Airport v j The number of passengers between.

5. The method according to claim 4, characterized in that In step S4, the direct air traffic rate of routes and the direct air traffic rate of passengers are calculated. O With Airport Network G D The calculation formula of the direct navigation rate δ between the routes is: Among them, N O Airport Network G O The number of airports in D Indicates the airport network G D The number of airports in, at the same time, δ∈(0,1], the maximum value δ max =1; Airport Network G O With Airport Network G D The direct passenger rate between w The calculation formula is: Among them, NW O Airport Network G O Total number of passengers, NW D Airport Network G D The total number of passengers, at the same time, δ w ∈(0,1], maximum value δ wmax =1.

6. The method according to claim 5, characterized in that In step S5, in calculating the relative entropy value, the relative entropy D(P||Q) is defined as: D(P||Q)=∑P(i)log(P(i) / Q(i)) (8) Among them, i represents the value of the random variable, P and Q represent two probability distributions respectively. When P=Q, the relative entropy takes the minimum value of 0. At this time, the probability distribution P and the probability distribution Q are exactly the same. The greater the difference between P and Q, the greater the value of the relative entropy.

7. The method according to claim 6, characterized in that In the airport cluster network connectivity analysis model constructed by S6, when flights are normal, the airport network G O and Airport Network G D When the direct air traffic rate between the two airports is δ, the airport network G O and Airport Network G D The direct air traffic rate between the two routes is δ′. According to the relative entropy theory, the calculation formula of the direct air connectivity impact index ACI is as follows: Due to δ max =δ′ max =1, so the ACI of the direct flight connectivity between the final airport network can be expressed as: When flights are normal, the airport network G O and Airport Network G D The direct passenger traffic rate between them is that when an airport is disrupted and temporarily stops operating, the airport network G O and Airport Network G D The direct passenger traffic rate between w ′, according to the relative entropy theory, the calculation formula of the passenger direct flight connectivity impact measurement index PCI is as follows: The calculation formula of airport cluster network connectivity index NCI is: NCI=α1·ACI+α2·PCI (12) Among them, α1+α2=1, and the parameters α1 and α2 are determined according to the importance of the direct flight connectivity of routes and the direct flight connectivity of passengers on the connectivity of the entire airport cluster.

8. An airport cluster network connectivity analysis system based on relative entropy theory, characterized in that: include: A data processing module is used to process the collected route opening conditions, flight frequency data and route passenger volume data between the airport group and its external airports to obtain processed data; The network construction module is used to construct the airport cluster network topology model based on the processed data; The network index calculation module is used to calculate the node degree, node flow intensity, route connection intensity, passenger demand intensity, route direct navigation rate and passenger direct navigation rate of each node in the airport cluster network topology model to obtain the network index calculation results; A relative entropy calculation module is used to calculate the relative entropy value between the actual connectivity state of each airport in the airport network and the network connectivity state after assuming that the airport loses its function based on the relative entropy theory and the network indicator calculation results; The connectivity analysis module is used to calculate the route direct flight connectivity impact measurement index, the passenger direct flight connectivity impact measurement index, and the airport cluster network connectivity index based on the relative entropy value to obtain the airport cluster network connectivity analysis results.

9. An electronic device, characterized in that: include: processor; A memory for storing programs; The program includes instructions, which, when executed by the processor, cause the processor to perform the steps of the method as claimed in any one of claims 1 to 7.

10. A computer storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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