Fuzzy graph neural network method for large-area flight delay prediction
By using the fuzzy graph neural network method, a fuzzy adjacency matrix and sparse constraint function between flights are constructed, which solves the accuracy problem in large-scale flight delay prediction and achieves more accurate prediction and optimized flight resumption decision-making.
Patent Information
- Application Number
- CN202510950477.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-10
- Publication Date
- 2025-10-17
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Existing technologies are not accurate enough in predicting large-scale flight delays, especially in handling uncertainty and ambiguity, making it difficult to provide accurate prediction results.
The fuzzy graph neural network method is adopted to construct a fuzzy adjacency matrix and sparse constraint function between flights to characterize the correlation coefficient between flight nodes. Combined with the fuzzy graph convolution operator, a fuzzy graph neural network model is established to predict flight delays.
It improves the accuracy of flight delay prediction, better captures the complex dependencies between flights, optimizes flight resumption decisions, and reduces economic losses and social impact.
Smart Images
Figure CN120806253A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of flight delay prediction, and particularly relates to a fuzzy graph neural network method for large-area flight delay prediction. BACKGROUND
[0002] With the rapid expansion of global air transportation, large-area flight delay problems have gradually become a major challenge faced by airlines and airport managers. Large-area flight delays are usually caused by multiple factors, including weather and holiday factors. During the holiday period, due to the sharp increase in travel demand, the number of flights increases significantly, causing the airport flight arrangement to be tight, thereby causing delays. In addition, severe weather conditions such as snowstorms and heavy fog often cause flights to be unable to take off and land on time, further exacerbating the scale of the delay. Therefore, how to accurately and efficiently predict delays in the case of large-area flight delays and take timely and effective measures has become a research hotspot in the field of aviation management.
[0003] In the research of flight delay prediction, traditional prediction methods mainly rely on statistics and machine learning techniques. Statistical methods, such as regression analysis and time series analysis, analyze historical flight delay data to establish mathematical models for prediction. These methods can predict flight delays to some extent, but due to the weak ability to model complex and nonlinear relationships, they are difficult to effectively handle complex flight delay data. Machine learning methods, such as support vector machines and decision trees, learn from a large amount of historical data to mine complex relationships. However, many models ignore the complex factors behind flight delays, such as airline operating conditions and the mutual influence between flights, which limits the accuracy of the prediction results. In addition, traditional methods have shortcomings in dealing with data uncertainty, which can easily lead to deviations in prediction results.
[0004] In recent years, deep learning methods such as convolutional neural networks and long short-term memory networks have made significant progress in flight delay prediction, especially in the aspect of feature mining of time series data, which has improved the accuracy of short-term prediction. Graph neural network (GNN) is a deep learning model for processing graph-structured data, which has performed well in many fields in recent years, especially in handling complex dependency relationships. In flight delay prediction, the flight network itself has graph structure characteristics, and there are dependency relationships between flights, and GNN can effectively capture these associations to improve prediction accuracy.
[0005] By representing flight information as graph structure data, GNN can better model the complex dependency relationships between flights. Traditional models often overlook the relevance between flights, while GNN models the delay propagation mechanism through nodes and edges, providing more accurate predictions. In addition, the uncertainty and ambiguity of data in flight delay prediction, such as unexpected events, make prediction more challenging. Fuzzy theory can effectively handle these uncertain and ambiguous information, thereby improving the robustness and accuracy of the model.
[0006] In summary, graph neural networks have shown strong performance in flight delay prediction, but there are still limitations in handling uncertainty and ambiguity. Therefore, combining the advantages of fuzzy theory, a prediction method based on fuzzy graph neural networks will become an important direction for solving flight prediction under large-scale flight delays. SUMMARY
[0007] The purpose of the present application is to provide a fuzzy graph neural network method for large-area flight delay prediction, mainly solving the technical problem of low flight prediction accuracy under large-area flight delay. This method aims to improve the accuracy of flight delay prediction and provide strong support for the decision-making of resuming flights in large-scale flight delay situations.
[0008] To achieve the above invention purpose, the technical scheme adopted by the present application is as follows: a fuzzy graph neural network method for large-area flight delay prediction, comprising the following steps:
[0009] S1: Select civil aviation data as the data set, and define the flight with delay time exceeding 15 minutes as the delayed flight;
[0010] S2: Take the key information of the flight as the node identifier, label encode the categorical features: airline, departure airport, arrival airport, standardize the numerical features: flight distance, planned departure time features, and combine these features to form the node feature matrix V;
[0011] S3: Construct a directed graph, build edges through multiple relationships, capture the mutual connection between flights: establish edges between flights with similar departure times within 30 minutes at the same airport, establish edges between flights of the same airline, on the same day in the same month, establish edges between flights of the same pair of departure and arrival airports, establish edges between flights with departure or arrival delays exceeding 30 minutes, and complete the structure construction of the directed graph;
[0012] S4: Introduce a sparse constraint function to depict the connection coefficients between flight nodes, and standardize them to obtain the fuzzy similarity between flight data nodes, thereby constructing the fuzzy adjacency matrix A F to represent the fuzzy relationship between flights;
[0013] S5: Obtain the fuzzy adjacency matrix A based on step S4 F , quantify the fuzzy similarity between flight data nodes, construct a fuzzy graph convolution operator by combining node aggregation operations, and establish a fuzzy graph neural network model to ultimately realize flight delay prediction;
[0014] S6: Output the flight delay prediction result Output, and evaluate the performance of the model on the flight delay prediction task through the four indicators of Accuracy, F1-score, Recall, and Precision.
[0015] Further, the step S2 comprises the following steps:
[0016] S2.1: According to the key information of the flight, generate a unique identifier for each flight, which is composed of the airline code, flight number, year, month and date;
[0017] S2.2: Label encoding is performed on the classification features such as airlines and departure airports to obtain where v t =[v 1,t ,v 2,t ,...,v n,t ] T n is the number of flight data nodes, and t is the number of classification features;
[0018] S2.3: Numerical features such as flight distance and planned departure time are standardized, and the given numerical feature is data and the standardization is calculated as:
[0019]
[0020] where μ and σ represent the mean and standard deviation of the data feature respectively, and all numerical features after standardization are d is the dimension of the node feature.
[0021] S2.4: Combine all the features obtained in steps S2.2 and S2.3 into a complete node feature matrix V = [v 1 ,v 2 ,...,v d ] T where each row corresponds to all the features of a flight.
[0022] Further, the step S4 comprises the following steps:
[0023] S4.1: Describe the correlation coefficient between flight nodes through a sparse constraint function, where the flight data node feature matrix is represented as The correlation matrix R between nodes is obtained by minimizing the reconstruction error of flight data nodes, and a sparse constraint function is calculated:
[0024]
[0025] where ||·||F is the Frobenius norm of a matrix; F
[0026] S4.2: In order to enhance sparsity, the l1-norm is added to the sparse constraint function, where the subset of flight data nodes is R i is the correlation matrix of flight data node v i , and the sparse constraint function of node v i is defined as follows:
[0027]
[0028] where R i is the correlation matrix of flight data node v i , ||·||1 is the l1-norm regularization term, and p is the adjustment parameter;
[0029] S4.3: Based on the correlation matrix R i of flight data node v i obtained in step S4.2, the correlation coefficient between node v i and its connected nodes is calculated, where the set of nodes connected to node v i is e i , and m is the number of nodes in set e i . According to the positions of the nodes in e i , the correlation coefficient of each node in e i and node v i is calculated:
[0030] R i = [r i1 r i2 ...r ij ...r im ](14)
[0031] S4.4: Based on the correlation coefficient R i obtained in step S4.3, the fuzzy similarity of flight data node v i and its adjacent nodes is calculated. Then the fuzzy similarity u i of node v j and node v ij is defined as:
[0032]
[0033] wherein v j ∈e i ;
[0034] S4.5: Repeat steps S4.2-S4.4 to calculate the fuzzy similarity of all flight nodes, and finally obtain the fuzzy adjacency matrix A F :
[0035]
[0036] Further, the step S5 includes the following steps:
[0037] S5.1: Based on the fuzzy adjacency matrix A F obtained in step S4, the fuzzy similarity between the flight data node and its adjacent nodes is obtained, and the fuzzy standard adjacency matrix is further calculated
[0038]
[0039] wherein, is the fuzzy standard adjacency matrix, is the fuzzy degree matrix;
[0040] S5.2: Through the fuzzy membership and node aggregation operation, the characteristics of the node are aggregated to obtain the fuzzy graph convolution operator:
[0041]
[0042] wherein V l is the sample feature of the lth layer, W (l) is the weight matrix of the lth layer, and σ(·) is the activation function;
[0043] S5.3: Based on the fuzzy graph convolution operator obtained in step S5.2, a two-layer convolution structure for flight data node label prediction is designed:
[0044] Output=f(V,A F )(19)
[0045] wherein Output is the flight delay prediction result, if the output Output=0, the flight does not delay, if Output=1, the flight delays;
[0046] S5.4: Apply the two-layer convolution structure to predict whether the flight delays, and the calculation formula is as follows:
[0047]
[0048] wherein W (1) is the weight matrix of the first layer to the hidden layer of the convolution structure, and W (2)The Softmax(·) and ReLU(·) are activation functions for the weight matrix of the convolutional structure hidden layer to the last layer.
[0049] Compared with the prior art, the application has the following beneficial effects:
[0050] (1) Improve prediction accuracy: by introducing fuzzy graph neural networks, the application can effectively handle the uncertainty and fuzziness in flight delay prediction, thereby improving the accuracy of the prediction, especially in large-scale flight delay situations, it can provide more accurate prediction results.
[0051] (2) Capture complex dependencies: the application models the complex dependencies between flights through graph neural networks, so that flight delay prediction not only depends on the historical data of a single flight, but also considers the mutual influence between flights, thereby obtaining a more comprehensive prediction.
[0052] (3) Optimize flight resumption decision: by providing accurate flight delay prediction results, it can help airlines and airport managers make better flight resumption decisions, reduce economic losses and social impact caused by large-scale flight delays. BRIEF DESCRIPTION OF DRAWINGS
[0053] The accompanying drawings are used to provide a further understanding of the application, and form a part of the specification, together with the embodiments of the application, to explain the application, and do not constitute a limitation of the application.
[0054] Fig. 1 The flowchart of the fuzzy graph neural network method for large-area flight delay prediction of the application.
[0055] Fig. 2 The overall block diagram of the fuzzy graph neural network method for large-area flight delay prediction of the application.
[0056] Fig. 3 The flowchart of the fuzzy graph neural network method for large-area flight delay prediction of the application. DETAILED DESCRIPTION
[0057] In order to make the purpose, technical scheme and advantages of the application more clear, the application is further described in detail below in combination with the drawings and examples. Of course, the specific examples described here are only used to explain the application, and do not limit the application.
[0058] Example 1:
[0059] Referring to Figs. 1-3 The technical scheme of the present application is a fuzzy graph neural network for large-area flight delay prediction, which comprises the following steps:
[0060] S1: Select civil aviation data as a dataset, and define flights with delay time exceeding 15 minutes as delayed flights;
[0061] S2: Take the key information of the flight as the node identifier, label encode the categorical features: airline, departure airport, arrival airport, and standardize the numerical features: flight distance, scheduled departure time, and combine these features to form the node feature matrix V;
[0062] S3: Construct a directed graph, build edges through multiple relationships, and capture the mutual connection between flights: establish edges between flights with similar departure times within 30 minutes at the same airport, establish edges between flights of the same airline on the same day in the same month, establish edges between flights of the same airport pair, establish edges between flights with departure or arrival delays exceeding 30 minutes, and complete the structure construction of the directed graph;
[0063] S4: Introduce a sparse constraint function to depict the connection coefficient between flight nodes, and standardize it to obtain the fuzzy similarity between flight data nodes, thereby constructing the fuzzy adjacency matrix A F to represent the fuzzy relationship between flights;
[0064] S5: Based on the fuzzy adjacency matrix A F obtained in step S4, the fuzzy similarity between flight data nodes is quantified, the fuzzy graph convolution operator is constructed by combining node aggregation operations, and the fuzzy graph neural network model is established, finally realizing flight delay prediction;
[0065] S6: Output the flight delay prediction result Output, and evaluate the performance of the model on the flight delay prediction task through the four indicators of Accuracy, F1-score, Recall, and Precision.
[0066] Step S2 includes the following steps:
[0067] S2.1: According to the key information of the flight, generate a unique identifier for each flight, which consists of airline code, flight number, year, month, and date;
[0068] S2.2: Label encode the categorical features such as airline and departure airport to obtain where v t =[v 1,t ,v 2,t ,...,v n,t ] T , n is the number of flight data nodes, and t is the number of categorical features;
[0069] S2.3: Standardize the numerical features such as flight distance, scheduled departure time features, and the like, and give the numerical features as data and calculate the standardization as:
[0070]
[0071] wherein μ and σ represent the mean and standard deviation of the data feature respectively, and all numerical features are standardized as d is the node feature dimension;
[0072] S2.4: Combine all the features obtained in steps S2.2 and S2.3 into a complete node feature matrix V = [v 1 ,v 2 ,...,v d ] T , wherein each row corresponds to all features of a flight.
[0073] Step S4 includes the following steps:
[0074] S4.1: Through a sparse constraint function, the correlation between flight nodes is described, wherein the flight data node feature matrix is represented as By minimizing the reconstruction error of the flight data node, the correlation matrix R between nodes is obtained, and the sparse constraint function is calculated:
[0075]
[0076] wherein ||·||F is the Frobenius norm of the matrix; F
[0077] S4.2: In order to enhance the sparsity, the l1-norm is added to the sparse constraint function, wherein the flight data node subset is R i is the correlation matrix of the flight data node v i , and the sparse constraint function of the node v i is defined as follows:
[0078]
[0079] wherein R i is the correlation matrix of the flight data node v i , ||·||1 is the l1-norm regularization term, and ρ is the adjustment parameter;
[0080] S4.3: Based on the correlation matrix R i of the flight data node v i obtained in step S4.2, the correlation between the node v i and its connected nodes is calculated, wherein the connected nodes of the node v i The set of connected nodes is e i , m is the number of nodes in the set e i ; according to the position of each node in e i , the incidence matrix R i of each node in e i and node v i is calculated:
[0081] R i1 = [r i2 r ij ...r im ](24)
[0082] S4.4: Based on the incidence matrix R i obtained in step S4.3, the fuzzy similarity between flight data node v i and its adjacent nodes is calculated; then the fuzzy similarity u i between node v j and node v ij is defined as:
[0083]
[0084] where v j ∈ e i ;
[0085] S4.5: Repeat steps S4.2-S4.4 to calculate the fuzzy similarity of all flight nodes, and finally obtain the fuzzy adjacency matrix A F :
[0086]
[0087] Step S5 includes the following steps:
[0088] S5.1: Based on the fuzzy adjacency matrix A F obtained in step S4, the fuzzy similarity between flight data nodes and their adjacent nodes is obtained, and the fuzzy standard adjacency matrix is further calculated
[0089]
[0090] where A is the fuzzy standard adjacency matrix, is the fuzzy degree matrix;
[0091] S5.2: Through fuzzy membership and node aggregation operation, the characteristics of the nodes are aggregated to obtain the fuzzy graph convolution operator:
[0092]
[0093] where Vl W (l) is the weight matrix of the l-th layer, and σ(·) is an activation function.
[0094] S5.3: Based on the fuzzy graph convolution operator obtained in step S5.2, a two-layer convolution structure for flight data node label prediction is designed:
[0095] Output=f(V,A F )(29)
[0096] wherein Output is the flight delay prediction result, if the output Output=0, the flight does not delay, if Output=1, the flight delays;
[0097] S5.4: The two-layer convolution structure is applied to predict whether the flight delays, and the calculation formula is as follows:
[0098]
[0099] wherein W (1) is the weight matrix of the first layer to the hidden layer of the convolution structure, W (2) is the weight matrix of the hidden layer to the last layer of the convolution structure, and Softmax(·) and ReLU(·) are activation functions.
[0100] By using the fuzzy graph neural network method to accurately depict the fuzzy similarity between flights, a fuzzy adjacency matrix is constructed to realize efficient prediction of large-area flight delays. In this embodiment, 1590 flight data are selected and divided into five parts, one of which is the test set and the remaining four are the training set. If the flight delay time is more than 15 minutes, it is considered as delay. Table 1 shows the experimental results of applying fuzzy graph neural network to flight delay prediction of 1590 flight data.
[0101] Table 1 Experimental results of fuzzy graph neural network in 1590 flight data delay prediction
[0102]
[0103] This embodiment has achieved significant experimental results in large-area flight delay prediction by applying fuzzy graph neural network. On the 1590 flight data set, the Accuracy of the model is 0.925, the F1-score is 0.764, the Recall is 0.750, and the Precision is 0.780. These results prove that the fuzzy graph neural network can effectively predict large-area flight delays, thereby helping to reduce the loss caused by airport delays.
[0104] Embodiment 2:
[0105] Referring toFigs. 1-3 The embodiment provides a fuzzy graph neural network for large-area flight delay prediction, and the technical scheme comprises the following steps:
[0106] S1: selecting civil aviation data as a data set, and defining a flight with a delay time of more than 15 minutes as a delayed flight;
[0107] S2: taking the key information of the flight as a node identifier, performing label coding on the classification features: airline, departure airport, and arrival airport, performing standardization processing on the numerical features: flight distance and planned departure time features, and combining the features to form a node feature matrix V;
[0108] S3: constructing a directed graph, constructing edges through various relationships, capturing the mutual connection between flights: establishing an edge between flights with similar departure times within 30 minutes at the same airport, establishing an edge between flights of the same airline on the same day in the same month, establishing an edge between flights of the same airport pair, establishing an edge between flights with departure or arrival delays of more than 30 minutes, and completing the structure construction of the directed graph;
[0109] S4: introducing a sparse constraint function to depict the connection coefficients between flight nodes, and performing standardization processing to obtain the fuzzy similarity between flight data nodes, thereby constructing a fuzzy adjacency matrix A F to represent the fuzzy relationship between flights;
[0110] S5: obtaining the fuzzy adjacency matrix A F based on step S4, quantifying the fuzzy similarity between flight data nodes, constructing a fuzzy graph convolution operator by combining node aggregation operations, and establishing a fuzzy graph neural network model, to finally realize flight delay prediction;
[0111] S6: outputting the flight delay prediction result Output, and evaluating the performance of the model on the flight delay prediction task through the four indexes of Accuracy, F1-score, Recall, and Precision.
[0112] The fuzzy graph neural network method for large-area flight delay prediction according to claim 1, wherein step S2 comprises the following steps:
[0113] S2.1: generating a unique identifier for each flight according to the key information of the flight, the identifier comprising an airline code, a flight number, a year, a month, and a date;
[0114] S2.2: performing label coding on the classification features such as airlines and departure airports to obtain wherein v t =[v 1,t ,v 2,t..., v n,t ] T , n is the number of flight data nodes, t is the number of classification features;
[0115] S2.3: Standardize the numerical features such as flight distance, scheduled departure time, etc. The given numerical feature is data and the standardization is calculated as:
[0116]
[0117] where μ and σ represent the mean and standard deviation of the data feature respectively, and all the numerical features after standardization are d is the dimension of node features;
[0118] S2.4: Combine all the features obtained in steps S2.2 and S2.3 into a complete node feature matrix V = [v 1 ,v 2 ,..., v d ] T , where each row corresponds to all the features of a flight.
[0119] The fuzzy graph neural network method for large-area flight delay prediction according to claim 1, characterized in that step S4 comprises the following steps:
[0120] S4.1: Describe the correlation coefficient between flight nodes by a sparse constraint function, where the flight data node feature matrix is represented as By minimizing the reconstruction error of the flight data nodes, the correlation matrix R between the nodes is obtained, and the sparse constraint function is calculated:
[0121]
[0122] where ||·||F F is the Frobenius norm of the matrix;
[0123] S4.2: To enhance sparsity, add l1-norm to the sparse constraint function, where the flight data node subset is R i is the correlation matrix of flight data node v i , and the sparse constraint function of node v i is defined as:
[0124]
[0125] where R i is the correlation matrix of flight data node v i , ||·||1 is the l1-norm regularization term, and ρ is the adjustment parameter;
[0126] S4.3: Based on the flight data node v obtained in step S4.2, the correlation matrix R i is calculated i , and the correlation coefficient between node v i and its adjacent nodes is calculated, where the set of nodes connected to node v i is e i , and m is the number of nodes in set e i ; according to the positions of the nodes in e i , the correlation coefficient between each node in e i and node v i is calculated:
[0127] R i = [r i1 r i2 ...r ij ...r im ](34)
[0128] S4.4: Based on the correlation coefficient R i obtained in step S4.3, the fuzzy similarity between flight data node v i and its adjacent nodes is calculated; then the fuzzy similarity u i between node v j and node v ij is defined as:
[0129]
[0130] where v j ∈ e i ;
[0131] S4.5: Repeat steps S4.2-S4.4 to calculate the fuzzy similarity of all flight nodes, and finally obtain the fuzzy adjacency matrix A F :
[0132]
[0133] According to claim 1, a fuzzy graph neural network method for large-area flight delay prediction, characterized in that step S5 comprises the following steps:
[0134] S5.1: Based on the fuzzy adjacency matrix A F obtained in step S4, the fuzzy similarity between the flight data node and its adjacent nodes is obtained, and the fuzzy standard adjacency matrix A
[0135]
[0136] where A is the fuzzy standard adjacency matrix, is a fuzzy membership matrix, and A
[0137] S5.2: The features of the nodes are aggregated by fuzzy membership and node aggregation operation to obtain a fuzzy graph convolution operator:
[0138]
[0139] wherein V l is the sample feature of the lth layer, W (l) is the weight matrix of the lth layer, and σ(·) is an activation function.
[0140] S5.3: Based on the fuzzy graph convolution operator obtained in step S5.2, a two-layer convolution structure for flight data node label prediction is designed:
[0141] Output = f(V, A F )(39)
[0142] wherein Output is the flight delay prediction result, if the output Output = 0, the flight does not delay, if Output = 1, the flight delays.
[0143] S5.4: The two-layer convolution structure is applied to predict whether the flight delays, and the calculation formula is as follows:
[0144]
[0145] wherein W (1) is the weight matrix of the first layer to the hidden layer of the convolution structure, W (2) is the weight matrix of the hidden layer to the last layer of the convolution structure, and Softmax(·) and ReLU(·) are activation functions.
[0146] By using the fuzzy graph neural network method to accurately depict the fuzzy similarity between flights, a fuzzy adjacency matrix is constructed to realize efficient prediction of large-area flight delays. In this embodiment, 2490 flight data are selected and divided into five parts, one of which is a test set and the remaining four are training sets. If the flight delay time is more than 15 minutes, it is considered as a delay. Table 2 shows the experimental results of applying fuzzy graph neural network to flight delay prediction of 2490 flight data.
[0147] Table 2 Experimental results of fuzzy graph neural network in 2490 flight data delay prediction
[0148]
[0149] The present embodiment applies the fuzzy graph neural network to large-area flight delay prediction and achieves remarkable experimental results. On a dataset of 2490 flights, the model's Accuracy is 0.887, F1-score is 0.636, Recall is 0.750, and Precision is 0.692. These results demonstrate that the fuzzy graph neural network can effectively predict large-area flight delays, thereby helping to reduce the losses caused by airport delays.
[0150] The above merely describes preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims
1. A fuzzy graph neural network method for large-scale flight delay prediction, characterized by: The following steps are involved: S1: Select civil aviation data as the dataset and define flights with a delay of more than 15 minutes as delayed flights; S2: Using the key information of the flight as the node identifier, label the categorical features (airline, departure airport, arrival airport), standardize the numerical features (flight distance, scheduled departure time), and combine these features to form the node feature matrix V; S3: Build a directed graph, using multiple relationships to construct edges to capture the connections between flights. This includes establishing edges between flights departing from the same airport within 30 minutes, flights departing from the same airline on the same day of the same month, flights departing from the same airport pair, and flights with departure or arrival delays exceeding 30 minutes. This completes the structure of the directed graph. S4: By introducing a sparse constraint function, characterizing the correlation coefficient between flight nodes and normalizing it, the fuzzy similarity between flight data nodes is obtained, thereby constructing the fuzzy adjacency matrix A F , to represent the fuzzy relationship between flights; S5: Obtain the fuzzy adjacency matrix A based on step S4 F , quantify the fuzzy similarity between flight data nodes, construct a fuzzy graph convolution operator by combining node aggregation operations, and establish a fuzzy graph neural network model to ultimately achieve flight delay prediction; S6: Output the flight delay prediction result and evaluate the performance of the model in the flight delay prediction task using four indicators: Accuracy, F1-score, Recall, and Precision.
2. A fuzzy graph neural network method for large-scale flight delay prediction according to claim 1, characterized in that: The step S2 includes the following steps: S2.1: Generate a unique identifier for each flight based on the flight's key information. The identifier consists of the airline code, flight number, year, month, and day. S2.2: Label encoding of airline and departure airport classification features Among them, v t =[v 1,t ,v 2,t ,...,v n,t ] T , n is the number of flight data nodes, t is the number of classification features; S2.3: Normalize the numerical features of flight distance and planned departure time. Given the numerical features as data, calculate the normalization as: Among them, μ and σ represent the mean and standard deviation of data features respectively, so all numerical features are standardized as follows: d is the node feature dimension; S2.4: Combine all the features obtained in steps S2.2 and S2.3 into a complete node feature matrix V = [v 1 ,v 2 ,...,v d ] T , where each row corresponds to all the features of a flight.
3. The fuzzy graph neural network method for large-scale flight delay prediction according to claim 1, characterized in that: The step S4 includes the following steps: S4.1: Characterize the correlation coefficient between flight nodes through sparse constraint function, where the flight data node feature matrix is expressed as By minimizing the reconstruction error of the flight data nodes, the correlation matrix R between the nodes is obtained, and the sparse constraint function is calculated: Among them, ||·|| F is the Frobenius norm of the matrix; S4.2: Add the l1-normal form to the sparse constraint function, where the subset of flight data nodes is R i Flight data node v i The incidence matrix of node v i The sparse constraint function is defined as follows: Among them, R i Flight data node v i The correlation matrix, ||·||1 is the l1-norm regularization term, and ρ is the adjustment parameter; S4.3: Get flight data node v based on step S4.2 i The correlation matrix R i , computing node v i The correlation coefficient between the nodes connected to it, where i The set of connected nodes is e i , m is the set e i The number of nodes in e i The position of each node in the calculation of e i Each node and node v i Correlation coefficient: R i ＝[r i1 r i2 ...r ij ...r im ](4) S4.4: Get the correlation coefficient R based on step S4.3 i , calculate flight data node v i The fuzzy similarity of node v to its adjacent nodes; then node v i With node v j The fuzzy similarity u ij Defined as: Among them, v j ∈e i ; S4.5: Repeat steps S4.2-S4.4 to calculate the fuzzy similarity of all flight nodes, and finally obtain the fuzzy adjacency matrix A F :
4. The fuzzy graph neural network method for large-scale flight delay prediction according to claim 1, characterized in that: The step S5 comprises the following steps: S5.1: Obtain the fuzzy adjacency matrix A based on step S4 F , obtain the fuzzy similarity between the flight data node and its adjacent nodes, and further calculate the fuzzy standard adjacency matrix in, is the fuzzy standard adjacency matrix, is the fuzzy matrix; S5.2: Through fuzzy membership and node aggregation operations, the features of the nodes are aggregated to obtain the fuzzy graph convolution operator: Among them, V l is the sample feature of the lth layer, W (l) is the weight matrix of the lth layer, σ(·) is the activation function; S5.3: Based on the fuzzy graph convolution operator obtained in step S5.2, a two-layer convolution structure is designed for flight data node label prediction: Output=f(V,A F )(9) Wherein, Output is the flight delay prediction result. If Output = 0, the flight is not delayed. If Output = 1, the flight is delayed. S5.4: Apply a two-layer convolutional architecture to predict flight delays. The calculation formula is as follows: Among them, W (1) is the weight matrix from the first layer to the hidden layer of the convolution structure, W (2) is the weight matrix from the hidden layer to the last layer of the convolutional structure, and Softmax(·) and ReLU(·) are activation functions.