A method and system for analyzing airport cluster network connectivity based on relative entropy theory

Abstract

The present invention provides an airport cluster network connectivity analysis method and system based on relative entropy theory. The method includes constructing an airport cluster network topology model; calculating the node degree and node flow intensity of each node; calculating the route connection intensity and passenger demand intensity between airport networks based on the node degree and node flow intensity of each node, the route opening status between airports, flight frequency data, and route passenger volume data; calculating the route direct flight rate and passenger direct flight rate based on the route connection intensity and airport network passenger demand intensity; constructing the route direct flight connectivity impact measurement index (ACI) based on the relative entropy value and the route direct flight rate; constructing the passenger direct flight connectivity impact measurement index (PCI) based on the relative entropy value and the passenger direct flight rate; and constructing the airport cluster network connectivity index (NCI) based on the ACI and PCI to comprehensively evaluate the network connectivity of the airport cluster. The present invention improves the accuracy and effectiveness of airport cluster network connectivity analysis.

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 air transportation industry, airport clusters, as aviation hubs consisting of multiple airports, are increasingly becoming the core of modern aviation networks. Connectivity analysis of airport cluster networks is an important means of assessing transport efficiency, aviation resource sharing, and emergency response capabilities among airport clusters. Currently, several airport cluster connectivity analysis methods have been applied to air traffic management. These methods primarily rely on network topology analysis, graph theory, and network flow analysis. By abstracting airports and routes into nodes and edges in a network, they assess the network structure and connectivity of routes between airports.

[0003] In existing technologies, 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 of 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 via the shortest path. This indicator can reflect the overall compactness of routes within the airport cluster. 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 more dense.

[0005] (2) Complex network theory: Within the framework of complex network theory, the airport network can be viewed as a complex scale-free network in which the number of connections between different airports and other airports varies greatly. This theory argues that in a complex network, some airports will become "super nodes," that is, hubs with a high frequency of flights and connections to other airports. In this way, it is possible to identify which airports are key nodes that determine 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, which 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 a number of smaller airports that usually rely on hub airports for transfers or connect to other areas 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 connections between airports on the overall connectivity of the airport cluster.

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

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

[0010] Existing research often focuses on the connectivity of a single airport or single route, overlooking the synergistic effects of airport clusters as a whole system. The interactions between airports and their overall layout have a significant impact on connectivity, but these factors are often overlooked in existing research.

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

[0012] Traditional analysis methods rely primarily on static indicators such as flight numbers and frequencies, overlooking the impact of passenger traffic and direct routes on airport connectivity. While some airports may have fewer flight connections, their role as transit airports can actually result in significant passenger traffic. Furthermore, the presence of direct routes plays a significant role in improving connectivity.

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

[0014] Existing research typically focuses on single-dimensional network indicators, lacking comprehensive metrics that can comprehensively assess the connectivity of airport cluster networks and the importance of airport nodes within them. Furthermore, research on connectivity between airport clusters is relatively scarce, neglecting the interrelationships between different airport clusters and the impact of aviation network layout. Summary of the Invention

[0015] In view of this, embodiments of the present invention provide a method and system for analyzing airport cluster network connectivity based on relative entropy theory. This solution aims to address the problems existing in existing technologies for assessing airport cluster network connectivity, particularly the neglect of the integrity of airport clusters, passenger flow, the impact of direct air traffic between airports, the relationship between airport clusters, and the lack of comprehensive indicators for stability assessment. By introducing relative entropy theory, the present invention provides a method and system for quantitatively assessing the importance and stability of each airport node in an airport cluster network, thereby more accurately analyzing the network connectivity of an 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 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 strength 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 connection strength of the route 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, the importance and stability of the specific airport in the network are quantitatively evaluated; 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 influence measurement index ACI, based on the relative entropy value and passenger direct flight rate, construct the passenger direct flight connectivity influence measurement index PCI, and at the same time, construct the airport cluster network connectivity index NCI based on the route direct flight connectivity influence measurement index ACI and the passenger direct flight connectivity influence measurement index PCI to comprehensively evaluate the network connectivity of the airport cluster.

[0017] In one implementation, in step S1, the airport cluster network topology model is constructed, and 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 and 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 among 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] Among them, 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 connected 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 traffic 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, when 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 considered 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 origin and destination point pair of the route, which is used to describe the route combination from a specific origin to a specific destination. Assuming there are two airport clusters, in the OD pair, the airport network formed by the airports in one airport cluster is considered as a whole and is 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 ), 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 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 δ 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, when 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 The direct air traffic rate between the two routes is δ. When the airport is disturbed and temporarily stops operating, the airport network G O and Airport Network G D The direct air traffic rate between them 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 final direct flight connectivity index ACI between airport networks 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 airports is that when airports are disrupted and temporarily stop 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 direct flight connectivity and direct passenger flight connectivity to 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 collected route opening data, 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, based on the relative entropy theory and the network index calculation results, the relative entropy value between the actual connectivity state of each airport in the airport network and the network connectivity state assuming that the airport has lost its function; a connectivity analysis module for calculating, based on the relative entropy value, a route direct flight connectivity influence measurement index and a passenger direct flight connectivity influence measurement index, and calculating the airport cluster network connectivity index to obtain the airport cluster network connectivity analysis results.

[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 that, when executed by the processor, cause the processor to perform the steps of the method according to the first aspect.

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

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

[0053] (1) Improve the accuracy of analysis

[0054] The present invention uses relative entropy, a method for measuring the difference between two probability distributions, to play a key role in analyzing the connectivity of airport cluster networks. By calculating the relative entropy between an airport's actual connectivity within the network and the network's connectivity if that airport were to become inoperative, the present invention can more accurately quantify the degree of connectivity between airports and their importance within the airport cluster network. This reveals bottlenecks and weak links within the airport network, thereby capturing characteristics of airport cluster connectivity that traditional single-airport connectivity analysis methods may not capture, further enhancing the accuracy and depth of the analysis.

[0055] (2) Enhance the effectiveness of analysis

[0056] The application of relative entropy theory in this invention makes the analysis process more systematic and scientific. By constructing a connectivity analysis model based on relative entropy and combining it with passenger volume data from various routes, this invention not only enables dynamic monitoring of airport cluster network connectivity, enabling the timely identification and response to potential airport network risks, but also provides a solid scientific basis for airport cluster network optimization, effectively guiding resource allocation and route adjustment strategies, thereby comprehensively improving the operational efficiency and reliability of the entire network.

[0057] (3) Strong technical adaptability

[0058] The relative entropy-based analysis method of this invention has broad applicability and can be adapted to airport cluster networks of varying sizes and structures. Effective connectivity analysis can be achieved for both large and small airport clusters. Importantly, the method can be flexibly adjusted to meet specific needs, such as by taking into account changes in flight traffic and route density over different time periods. This ensures that the analysis results are more realistic, enhancing the practicality and accuracy of the analysis.

[0059] (4) Easy to understand and implement

[0060] The relative entropy used in this invention is a mathematical tool with extensive application in statistics and information theory. Therefore, the airport cluster network connectivity analysis method based on relative entropy is theoretically easy to understand and accept. In practice, this method can be implemented using 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 Flowchart of the steps of the airport cluster 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 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, specific implementation methods of the embodiments of the present invention are 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 interpreted 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 accompanying 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 them. All other embodiments obtained by those skilled in the art 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 with reference to 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 an airport cluster network topology model: Based on the route opening status, flight frequency data, and route passenger volume data between airports, the airports within the airport cluster are regarded as nodes and the routes as edges to construct an airport cluster network model. The airports outside the airport cluster are regarded as nodes and the routes as edges to construct an airport network model. Based on the airport cluster network model and the airport network model, the airport cluster network topology model is constructed.

[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 strength between airports;

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

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

[0075] S5. Calculate relative entropy: 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 solution of the present invention is further described according to the following examples:

[0078] The working principle of this invention is based on the theory of relative entropy. It calculates the relative entropy value by comparing the actual connectivity status of an airport in the network with the network connectivity status if the airport is inoperative. The larger the relative entropy value, the more important the airport is 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 situation, flight frequency data and route passenger volume data between airports, the airports in the airport cluster are regarded as nodes and the routes as edges to construct the airport cluster network model G. P (V P ,E P ); take the external airports of the airport cluster as nodes and the routes as edges to construct the airport network model G 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 intensity between airport networks: Based on the node degree and node flow intensity of each node, combined with the route opening situation, 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 direct air route rate and direct passenger air route rate: Based on the air route connection strength between airport networks and the passenger demand strength of airport networks, the direct air route rate δ and the direct passenger air route rate δ are calculated. w ;

[0083] (5) Calculate the relative entropy: 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 if the airport is no longer functional. 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 assessed.

[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 flight 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 an airport cluster network topology model

[0086] With the rapid development of the air transport industry, the aviation network between airport clusters has become increasingly complex. Measuring the connectivity of aviation networks has become a key research topic in the field of air transport. From the perspective of network topology, the structural characteristics of aviation networks between airport clusters can be effectively analyzed, thereby assessing their connectivity level. Network topology principles are fundamental to studying the relationships between nodes and edges in a network and their spatial distribution patterns. When analyzing airport aviation networks, airports or airport clusters as a whole are considered nodes, and routes are considered the edges connecting these nodes. By analyzing topological metrics such as node degree, node flow intensity, and edge connection strength, characteristics such as the connectivity of aviation networks 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 within 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 represented by G W (V W ,E W ), where V W It's G W The node set (airports outside the airport cluster), E W It's G W The network consists of only airports outside the cluster and the routes between them, and is called an airport network. The entire airport network, including all airports within the cluster and all external airports, is represented by the airport cluster network topology model G(V,E), where V is the node set of G and E is the edge set of G. The network has N nodes and M edges. 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 as 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, the 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 total passenger volume 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 strength of route connections and passenger demand 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 each airport in one airport cluster to each airport 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 are 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, and 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 DAirport 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 ), reflecting the passenger flow between two airport clusters. Unlike the strength of route connections between airport networks, here we consider 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 and passenger direct air traffic rate

[0107] (1) Direct air traffic rate

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

[0109]

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

[0111] (2) Direct passenger flight rate

[0112] Airport Network G O With Airport Network G D The direct passenger traffic rate between w , which is 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 fundamental 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] Here, 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, describing how effectively one distribution describes the other. When P = Q, the relative entropy reaches its minimum value of 0, indicating that the two distributions are identical. The greater the difference between P and Q, the greater the relative entropy.

[0120] Relative entropy, a method in information theory that measures the difference between two probability distributions, can be effectively applied to assessing the connectivity of airport route networks. In an airport network, each airport can be considered a node, and routes form the edges between nodes. When applied to this scenario, relative entropy theory can be used to measure the impact of an airport on the overall network connectivity by comparing its actual connectivity with the network connectivity assumed to be inoperative.

[0121] Specifically, two probability distributions can be defined: one for the connectivity state of the complete airport network, including a specific airport, and the other for the network connectivity state if that airport were to be inoperative. By calculating the relative entropy between these two distributions, we can quantify the importance of that airport to maintaining overall network connectivity. A higher relative entropy value indicates a more critical role for the airport in the network, and its inoperativeness would lead to a significant decrease in network connectivity.

[0122] Therefore, the relative entropy-based metric not only reflects the level of airport connectivity within the aviation network but also reveals the importance of different airports within the network and their mutual influence. This metric helps to more accurately assess the connectivity of airport cluster aviation networks, providing strong support for route planning, network optimization, and risk control. Therefore, relative entropy theory has important application value in assessing airport route network connectivity. Next, we will develop an airport cluster network connectivity analysis model based on relative entropy theory.

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

[0124] (1) Direct flight connectivity impact measurement index

[0125] When flights are normal, the airport network G O and Airport Network G D The direct air connectivity rate between airports is δ. However, when airports are disrupted and temporarily cease operations, the integrity of the airport network is also affected. In this case, the direct air connectivity rate between airports is δ′. Based on the relative entropy theory, the direct air connectivity impact index (expressed as ACI) is calculated as follows:

[0126]

[0127] Due to δ max =δ′ max =1, so the impact measurement 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 cease operations, the integrity of the airport network is also affected, and the direct passenger traffic rate between airport networks is δ w According to the relative entropy theory, the passenger direct flight connectivity impact measurement index (expressed as PCI) is calculated as follows:

[0131]

[0132] (3) Airport cluster network connectivity index

[0133] The relative entropy-based direct flight connectivity impact metric, characterized by entropy variations, effectively reflects the fluctuations in air traffic flow rates across airport networks. As a measure of the difference between two probability distributions, relative entropy possesses desirable properties such as non-negativity, symmetry, and additivity. Within an airport network, the application of relative entropy can effectively and accurately measure the fluctuations in air traffic flow rates across airports.

[0134] Specifically, the relative entropy-based direct flight connectivity impact metric reflects the fluctuations in flights between airports within an airport network. When the number of flights between two airports changes, the relative entropy also changes accordingly. A large value for this metric indicates a significant change in the flight rate between the two airport networks, significantly impacting airport route connectivity. Conversely, a small value for this metric indicates a small change in the flight rate between the two airport networks, with a relatively small impact on airport route connectivity.

[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 operations management. By using this index, the impact of different flight changes on route connectivity can be better assessed, leading to the development of more reasonable and efficient flight plans.

[0136] Therefore, the calculation formula for 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, the parameters α1 and α2 need to be determined based on the importance of the direct flight connectivity and direct passenger flight connectivity to the connectivity of the entire airport cluster. For example, if the direct flight connectivity and direct passenger flight connectivity are considered to be equally important to the connectivity of the entire airport cluster, then the values ​​of α1 and α2 are 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 information, flight frequency data and route passenger volume data between the airport cluster 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 has lost its function based on the relative entropy theory and the calculation results of the network indicators;

[0145] The connectivity analysis module is used to calculate the 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, thereby obtaining 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 with each other.

[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 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 airport cluster networks 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] Effectiveness emphasizes the practical operability of this invention and its usefulness in decision support. By constructing an analytical model based on relative entropy theory, this invention effectively identifies and quantifies the mutual influences between airport clusters and the potential for optimization. This approach is not only scientific and rigorous in theory, but also provides effective guidance in the actual planning and operational management of airport cluster networks.

[0150] Specifically, connectivity analysis based on relative entropy theory can optimize the layout of airport clusters, helping decision-makers identify areas with potential for collaboration or areas requiring strengthened connectivity, thereby formulating more rational aviation network development strategies. Furthermore, the system presented in this paper possesses strong adaptability during data processing and analysis, capable of handling airport networks of various sizes and complexities, and possesses 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] The present invention uses relative entropy, a method for measuring the difference between two probability distributions, to play a key role in analyzing the connectivity of airport cluster networks. By calculating the relative entropy between an airport's actual connectivity within the network and the network's connectivity if that airport were to become inoperative, the present invention can more accurately quantify the degree of connectivity between airports and their importance within the airport cluster network. This reveals bottlenecks and weak links within the airport network, thereby capturing characteristics of airport cluster connectivity that traditional single-airport connectivity analysis methods may not capture, further enhancing the accuracy and depth of the analysis.

[0154] (2) Enhance the effectiveness of analysis

[0155] The application of relative entropy theory in this invention makes the analysis process more systematic and scientific. By constructing a connectivity analysis model based on relative entropy and combining it with passenger volume data from various routes, this invention not only enables dynamic monitoring of airport cluster network connectivity, enabling the timely identification and response to potential airport network risks, but also provides a solid scientific basis for airport cluster network optimization, effectively guiding resource allocation and route adjustment strategies, thereby comprehensively improving the operational efficiency and reliability of the entire network.

[0156] (3) Strong technical adaptability

[0157] The relative entropy-based analysis method of this invention has broad applicability and can be adapted to airport cluster networks of varying sizes and structures. Effective connectivity analysis can be achieved for both large and small airport clusters. Importantly, the method can be flexibly adjusted to meet specific needs, such as by taking into account changes in flight traffic and route density over different time periods. This ensures that the analysis results are more realistic, enhancing the practicality and accuracy of the analysis.

[0158] (4) Easy to understand and implement

[0159] The relative entropy used in this invention is a mathematical tool with extensive application in statistics and information theory. Therefore, the airport cluster network connectivity analysis method based on relative entropy is theoretically easy to understand and accept. In practice, this method can be implemented using existing data processing and computing tools, reducing technical barriers and costs.

[0160] As another example, the present invention also provides an electronic device, which will now be described as an electronic device that can serve 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. The electronic device is intended to represent various forms of digital electronic computer equipment, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device 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 merely 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, a communication interface, a memory, and a communication bus.

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

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

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

[0165] The processor may be a CPU, 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 high-speed RAM memory or non-volatile memory, such as at least one disk storage.

[0167] When the program is executed by the 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 embodiments, and will not be repeated here. Those skilled in the art will clearly understand that for the convenience and brevity of description, the specific working process of the above-described devices and modules can refer to the corresponding process description in the above method embodiments, and will not be repeated here.

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

[0170] The method according to the embodiment of the present invention described above can be implemented in hardware, firmware, or as software or computer code that can 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 via a network and will be stored in a local recording medium, so that the method described herein can 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 can be understood that a computer, a processor, a 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, a processor or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown here, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown here.

[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 can be performed in a different order and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or sequential order to achieve the desired results. In certain 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 can 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 on 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 fall within the scope of the embodiments of the present invention, and the scope of patent protection of the embodiments of the present invention should be defined by the claims.

Claims

1. A method for analyzing airport cluster network connectivity based on relative entropy theory, characterized in that: include: S1. 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 within the airport cluster are regarded as nodes and the routes as edges to construct an airport cluster network model. The airports outside the airport cluster are regarded as nodes and the routes as edges to construct an airport network model. Based on the airport cluster network model and the airport network model, the airport cluster network topology model is constructed. 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 strength between airports; S3. Calculate the strength of route connections and passenger demand between airport networks: Based on the node degree, node traffic intensity, route opening status between airports, flight frequency data, and route passenger volume data of each node, calculate the strength of route connections and passenger demand between airport networks; S4. Calculate the direct air route rate and direct passenger air route rate: Calculate the direct air route rate and direct passenger air route rate based on the strength of air route connections between airport networks and the strength of passenger demand within 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 assuming that the specific airport is no longer functional. 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 the 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, 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: G=G P +G W (1) Among them, 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 connected 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 traffic 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 In step S3, the route connection strength and passenger demand strength between airport networks are calculated. For the connection strength between airport clusters, all airports in the airport cluster are considered 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 origin and destination point pair of the route, which is used to describe the route combination from a specific origin to a specific destination. Assuming there are two airport clusters, in the OD pair, the airport network formed by the airports in one airport cluster is considered as a whole and is recorded as O. This 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 ), 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 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 route rate and the direct passenger air passenger rate 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 δ 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, the relative entropy value is calculated, and 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 The direct air traffic rate between the two routes is δ. When the airport is disturbed and temporarily stops operating, the airport network G O and Airport Network G D The direct air traffic rate between them 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 final direct flight connectivity index ACI between airport networks can be expressed as: When flights are normal, the airport network G O and Airport Network G D The direct passenger traffic rate between airports is that when airports are disrupted and temporarily stop 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 direct flight connectivity and direct passenger flight connectivity to the connectivity of the entire airport cluster.

8. An airport cluster network connectivity analysis system based on relative entropy theory, characterized by: include: A data processing module is used to process the collected route opening information, flight frequency data and route passenger volume data between the airport cluster 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 has lost its function based on the relative entropy theory and the calculation results of the network indicators; The connectivity analysis module is used to calculate the direct flight connectivity impact measurement index and the passenger direct flight connectivity impact measurement index based on the relative entropy value, and calculate the airport cluster network connectivity index to obtain the airport cluster network connectivity analysis results.

9. An electronic device, characterized in that: include: processor; Memory for storing programs; The program includes instructions, which, when executed by the processor, cause the processor to perform the steps of the method according to 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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