An airport capacity prediction method based on a causal diagram neural network
By using the causal graph neural network method, the causal relationships and spatial features between airports are extracted, and airport capacity is predicted by combining time series information. This solves the problem that the mutual influence between airports is not considered in the existing technology, and achieves higher prediction accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2023-04-11
- Publication Date
- 2026-05-29
AI Technical Summary
Existing airport capacity forecasting methods fail to effectively consider the mutual influence between airports, resulting in insufficient forecast accuracy.
A causal graph neural network-based approach is adopted to extract the causal relationship matrix between airports by calculating the transfer entropy and performing significance tests. The adaptive flow map and causal graph are generated by combining the flight flow matrix and the trainable parameter matrix. Spatial information is extracted by using a graph convolutional network and temporal information is extracted by using a gated recurrent unit. Finally, the spatiotemporal information is fused for prediction.
It significantly improves the accuracy of airport capacity forecasting, makes up for the shortcomings of existing technologies that ignore the mutual influence between airports, and provides a data foundation for efficient flight control.
Smart Images
Figure CN117371568B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of airport capacity prediction, specifically to an airport capacity prediction method based on causal graph neural networks. Background Technology
[0002] Airports are critical infrastructure in the air transport system, undertaking numerous important functions such as aircraft takeoffs and landings, ground handling services, air traffic control, and crew linkage. Their capacity is a bottleneck determining air operations. Airport capacity is typically defined as the maximum number of flights that can take off and land per hour, representing the airport's operational capacity at any given time and serving as the primary basis for air traffic management personnel to control and regulate air operations. Underestimating or overestimating airport capacity can both have significant negative impacts on air operations. Overestimating airport capacity often leads to flights being unable to take off or land as scheduled, resulting in widespread delays, flight cancellations, and other risky events.
[0003] Domestic and foreign researchers have conducted systematic studies on the problem of airport capacity prediction, which can be roughly divided into two categories: clustering methods and regression methods.
[0004] Clustering methods first cluster historical conditions to generate conditional probability distributions for capacity scenarios. Then, they obtain new predictions by matching current features to appropriate clusters; therefore, historical airport capacity is a crucial factor in clustering. However, regression methods are typically more popular in capacity prediction problems. These methods use regression models to fit the complex relationship between airport features and capacity, thereby predicting airport capacity. Compared to clustering methods, regression methods offer more accurate predictions, but at the cost of higher model complexity and more difficult-to-interpret parameters.
[0005] While research on airport capacity forecasting has made some progress, it still has shortcomings. Current methods predict airport capacity by fitting the relationship between factors such as meteorological conditions, airport operational status, and airport capacity. However, existing technologies do not consider the mutual influence of capacity among airports. Due to the interconnectedness of airports, the capacity change of one airport can be affected by the status of other airports. Therefore, current airport forecasting research neglects the mutual influence between airports, and there is still considerable room for improvement in forecast accuracy. Summary of the Invention
[0006] This application proposes an airport capacity prediction method based on causal graph neural networks to address the above-mentioned shortcomings of existing technologies. This method accurately represents the relationships between airports using an adaptive causal graph and extracts effective spatial features from the graph using feature masks combined with graph convolutional neural networks (GCNs). Finally, by fusing spatial and temporal information, the accuracy of airport capacity prediction is significantly improved.
[0007] To achieve the above objectives, this application discloses an airport capacity prediction method based on causal graph neural networks, the method comprising the following steps:
[0008] Step S1: Calculate the transfer entropy of the time series representing the capacity of each airport, perform a significance test, and extract the causal relationship matrix A between airports. C ;
[0009] Step S2, generate a trainable parameter matrix M, and combine the flight flow matrix A between airports. F and the causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph
[0010] Step S3, design the mask matrix W mask Using the mask matrix W mask From the original feature vector X t Mining mask features with spatial correlation
[0011] Step S4: Design a spatial information extraction module based on a graph convolutional network (GCN), utilizing the adaptive flow graph. Adaptive Cause-Effect Graph and mask features Obtain spatial information
[0012] Step S5: Design a time-series dependency extraction module based on a gated recurrent unit (GRU), utilizing the masked features. Obtain timing information
[0013] Step S6: Transfer the spatial information and timing information The final airport capacity prediction is obtained through fusion and a fully connected layer (FC()).
[0014] Optionally, in step S1, the transfer entropy of the time series representing the capacity of each airport is calculated, and a significance test is performed to extract the causal relationship matrix A between airports. C ,include:
[0015] Capacity data for each airport is extracted and discretized at 1-hour intervals to obtain time series representing capacity changes at each airport. The length of the time series is denoted as r, and the time series for airport i is denoted as C. i (t), calculate the transfer entropy between the time series of each airport using the following formula:
[0016] TE j→i =H(C i (t)|C i p (t-Δt))-H(C i (t)|C j q (t-Δt),C i p (t-Δt)),
[0017] Where t = Tr, ..., T, T is the current time; Δt represents the time step, which is taken as 1 in this formula; C i p (t-Δt)={C i (t-Δt),…,C i (t-pΔt)} represents C i (t) The value of the past p time steps; C j q (t-Δt)={C i (t-Δt),…,C i (t-qΔt)} represents C i (t) represents the value of the past q time steps; in this formula, both p and q are taken as 2; H(·|·) represents the conditional entropy, which is calculated as follows:
[0018]
[0019] Where p(x,y) is the joint probability distribution of X and Y, and p(y|x) is the conditional probability distribution;
[0020] The calculated transfer entropy is subjected to a significance test. The transfer entropy between airports that does not meet the given significance level is set to 0. Finally, the causal relationship matrix A is constructed. C Causal relationship matrix A C Element A in C [ij] represents the transfer entropy between airport i and airport j.
[0021] Optionally, in step S2, a trainable parameter matrix M is generated, and the flight flow matrix A between airports is used. F and the causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph include:
[0022] Generate a trainable parameter matrix M, where the trainable parameters are on the diagonal and all other positions are 0. Then, generate the inter-airport flight flow matrix A. F Causal relationship matrix A between airportsC Combined with the trainable parameter matrix M, an adaptive flow graph is obtained. and adaptive cause-effect graph as follows:
[0023]
[0024]
[0025] Optionally, in step S3, the mask matrix W is designed. mask Using the mask matrix W mask From the original feature vector X t Mining mask features with spatial correlation include:
[0026] Design the mask matrix W mask ={w1,w2,…,w k}∈R K Where K is the number of features, w k These are trainable parameters, representing the original feature vector X. t and mask matrix W mask Features obtained after performing Hadamard product and mask
[0027]
[0028] Where σ() represents the activation function;
[0029] The masked features After normalization, the mask features are obtained.
[0030] Correspondingly, the masked features for: This is subsequently used to predict changes in the airport's own capacity, where J∈R K This represents a matrix whose elements are all 1s.
[0031] Optionally, the masked features Normalization includes:
[0032] The normalization function is designed as follows:
[0033]
[0034] Where e is a mathematical constant;
[0035] Features after masking The mask features are obtained after inputting the normalization function.
[0036]
[0037] Optionally, the design is based on the spatial information extraction module of a graph convolutional network (GCN), utilizing the adaptive flow graph. Adaptive Cause-Effect Graph and mask features Obtain spatial information include:
[0038] Based on the adaptive flow graph respectively and the adaptive causal graph mask features Input the graph convolutional network (GCN) module and the ELU activation function, and obtain the outputs respectively. and Output and This is used to characterize the potential information about how airport capacity changes due to the influence of other airports, and outputs these two parts. and With concealed features The data is stitched together and then processed through a fully connected layer to obtain the final spatial information. The calculation is as follows:
[0039]
[0040] Where FC() represents a fully connected layer, and Contact() represents a feature concatenation operation.
[0041] Optionally, the design is based on the time dependency extraction module of a gated recurrent unit (GRU), utilizing masked features. Obtain timing information include:
[0042] Timing information is extracted by stacking gated recurrent unit (GRU) modules. The calculation method for each stack is as follows:
[0043]
[0044]
[0045] Among them, h t h represents the output result after t stacking operations. t-1 W represents the output result after t-1 stacking operations. h U h and b h It is a trainable parameter or parameter matrix, z t Indicates the update gate, r t This indicates that the door is being reset. Indicates the features that have been masked;
[0046] The output of the stacked gated recurrent units (GRUs) is then passed through a fully connected layer to obtain the final timing information.
[0047]
[0048] Optionally, in step S6, the spatial information and timing information The final airport capacity prediction is obtained through fusion and a fully connected layer (FC()). include:
[0049] The spatial information is processed according to the following formula. and timing information Integration to gain airport capacity
[0050] Predicted value:
[0051]
[0052] The above-described technical solutions adopted in the embodiments of this application can achieve the following beneficial effects:
[0053] This application addresses the airport capacity prediction problem by designing a deep learning model that efficiently captures and utilizes the relationships between airports and organically integrates them with temporal information. The method accurately represents the relationships between airports through an adaptive causal graph and extracts effective spatial features from the adaptive causal graph using feature masks combined with Geometric Networks (GCN). Finally, by fusing with temporal information, the accuracy of airport capacity prediction is significantly improved, overcoming the deficiency of existing technologies in lacking information on the mutual influence factors between airports. This application focuses on the accurate prediction of airport capacity, starting from the accurate representation of relationships between airports, and conducts research on deep learning methods for airport capacity prediction. This method has significant practical implications for improving the accuracy of airport capacity prediction and lays a data foundation for efficient flight control schemes. Attached Figure Description
[0054] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:
[0055] Figure 1 A diagram illustrating an adaptive cause-effect graph and flow graph generation method according to an embodiment of this application is shown.
[0056] Figure 2 This diagram illustrates a feature masking flowchart according to one embodiment of the present application;
[0057] Figure 3A schematic diagram of a timing information extraction module according to an embodiment of this application is shown;
[0058] Figure 4 The diagram shows an overall flowchart of an airport capacity prediction method based on a causal graph neural network according to an embodiment of this application.
[0059] Figure 5 A graph showing an airport capacity prediction result according to an embodiment of this application is compared with that of existing methods. Detailed Implementation
[0060] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0061] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.
[0062] Unlike existing technologies that only consider factors affecting airport capacity such as weather, this application considers the following problem in its prediction: for an airport, taking into account the various factors affecting its capacity and the mutual influence between airports, the mapping relationship between features and capacity is fitted based on historical samples, and the future airport capacity is predicted through features.
[0063] Through research, the inventors discovered that the connections between airports are mainly reflected in three aspects. First, there is the connection of flight traffic: airports with close traffic flow have similar flight takeoffs and landings, thus their capacities are somewhat similar. Second, there is the connection of geographical distance: airports geographically close face similar control measures and weather conditions, thus their capacity changes are also synchronous. Third, there is the more difficult-to-characterize resource linkage connection: because the aircraft, crew, passengers, and other elements of preceding and subsequent flights may be identical or related, there is resource sharing between airports, leading to connections in their operational status. Therefore, this application comprehensively considers both the airports themselves and the connections between airports, specifically involving the connections in terms of traffic, space, and time.
[0064] The technical concept of this application is as follows: First, by calculating the transfer entropy and performing significance tests on the time series of airport capacity, causal relationships between airports are extracted. Then, the flow relationships and causal relationships between airports are combined with a trainable parameter matrix to generate adaptive flow graphs and adaptive causal graphs describing the mutual influence between airports. Next, feature masks are designed to mine features with spatial correlation. Then, spatial information of features is extracted using a Graph Convolutional Network (GCN). Temporal dependencies of features are extracted using a gated recurrent unit (GRU). Finally, a spatiotemporal information fusion module is designed to achieve accurate prediction of airport capacity by efficiently combining the extracted spatiotemporal information.
[0065] refer to Figures 1 to 5 As shown, this application discloses an airport capacity prediction method based on causal graph neural networks, the method including the following steps:
[0066] Step S1: Calculate the transfer entropy of the time series representing the capacity of each airport, perform a significance test, and extract the causal relationship matrix A between airports. C Among them, transfer entropy is a method based on probability distribution and statistics to derive causality in time series data, which can be used to mine the correlation between changes in traffic flow between airports.
[0067] Step S2, generate a trainable parameter matrix M, and combine the flight flow matrix A between airports. F and causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph This describes the mutual influence between airports and is used for airport traffic forecasting.
[0068] Step S3, design the mask matrix W mask Using the mask matrix W mask From the original feature vector X t Mining mask features with spatial correlation Mask matrix W mask The purpose is to correct the weights of different influencing factors. Considering that even if an airport can influence other airports, not all of its features affect other airports; each feature has a different range of influence. For example, temperature has a larger range of influence, while heavy rain has a smaller range. Therefore, we propose a mask matrix to adjust the weights of different influencing factors from the original feature vectors. Features that can influence other airports and have spatial correlations were discovered. Where N is the number of airports.
[0069] Step S4: Design a spatial information extraction module based on Graph Convolutional Network (GCN) and utilize adaptive flow graph. Adaptive Cause-Effect Graph and mask features Obtain spatial information
[0070] Step S5: Design a time-series dependency extraction module based on a gated recurrent unit (GRU), utilizing the masked features. Obtain timing information That is, by stacking gated recurrent unit (GRU) modules, the temporal dependence of capacity and characteristic changes of each airport is captured, thereby extracting temporal information.
[0071] Step S6: Transfer spatial information and timing information The final airport capacity prediction is obtained through fusion and a fully connected layer (FC()).
[0072] As can be seen from the above, the method of this application accurately represents the relationship between airports through adaptive causal graphs, and uses feature masks combined with graph convolutional networks (GCN) to extract effective spatial features from the adaptive causal graphs. Finally, by fusing with temporal information, the accuracy of airport capacity prediction is greatly improved, making up for the deficiency of existing technologies in lacking mutual influence factors between airports. This has important practical significance for improving the accuracy of airport capacity prediction.
[0073] In one embodiment of this application, in step S1, the transfer entropy of the time series representing the capacity of each airport is calculated, and a significance test is performed to extract the causal relationship matrix A between airports. C Specifically, it includes:
[0074] Capacity data for each airport is extracted and discretized at 1-hour intervals to obtain time series representing capacity changes at each airport. The length of this time series is denoted as r, and the time series for airport i is denoted as C. i (t). Reference Figure 1 As shown in (a), r time steps are taken to form the time series of each airport's capacity. The airport capacity data can be provided by the Civil Aviation Administration. This application extracts the time series at 1-hour intervals according to actual needs.
[0075] Based on the extracted time series data for each airport, the transfer entropy between the time series data for each airport is calculated using the following formula:
[0076] TE j→i =H(C i (t)|C i p (t-Δt))-H(Ci (t)|C j q (t-Δt),C i p (t-Δt)),
[0077] Where t = Tr, ..., T, T is the current time; Δt represents the time step, which is taken as 1 in this formula; C i p (t-Δt)={C i (t-Δt),…,C i (t-pΔt)} represents C i (t) The value of the past p time steps; C j q (t-Δt)={C i (t-Δt),…,C i (t-qΔt)} represents C i (t) represents the value of the past q time steps; in this formula, both p and q are taken as 2, based on the fact that the average stay time of an aircraft at the airport is about 2 hours, which is sufficient to meet the requirements of traffic flow monitoring; H(·|·) represents the conditional entropy, which is calculated as follows:
[0078]
[0079] Where p(x,y) is the joint probability distribution of X and Y, and p(y|x) is the conditional probability distribution.
[0080] Considering that the transfer entropy between time series may be affected by factors such as the distribution and periodicity of the series themselves, the calculation may not be accurate. Therefore, it is necessary to perform a significance test on the calculated transfer entropy, and only those that meet a given significance level should be accepted. The transfer entropy (typically 5%) is calculated accurately. Transfer entropy between airports that do not meet a given significance level is set to 0. Finally, a causal relationship matrix A is constructed. C Causal relationship matrix A C Element A in C [ij] represents the transfer entropy between airport i and airport j. The causal inference process for transfer entropy can be found in [reference needed]. Figure 1 As shown in (b).
[0081] In one embodiment of this application, such as Figure 1 As shown in (c), in step S2, a trainable parameter matrix M is generated, and the flight flow matrix A between airports is... F and causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph include:
[0082] Generate a trainable parameter matrix M (i.e. Figure 1 (c) The adaptive parameter matrix), the trainable parameter matrix M has trainable parameters on the diagonal, and the other positions are 0, and the inter-airport flight flow matrix A F Causal relationship matrix A between airports C Combined with the trainable parameter matrix M, an adaptive flow graph is obtained. and adaptive cause-effect graph as follows:
[0083]
[0084]
[0085] In one embodiment of this application, reference is made to Figure 2 As shown, in step S3, the mask matrix W is designed. mask Using the mask matrix W mask From the original feature vector X t Mining mask features with spatial correlation include:
[0086] Design the mask matrix W mask ={w1,w2,…,w k}∈R K Where K is the number of features, w k These are trainable parameters, representing the original feature vector X. t and mask matrix W mask Features obtained after performing Hadamard product and mask
[0087]
[0088] Where σ() represents the activation function.
[0089] Then mask the features After normalization, the mask features are obtained.
[0090] At the same time, the features that are concealed This data is also stored and will be used later to predict changes in the airport's own capacity, where J∈R K This represents a matrix whose elements are all 1s.
[0091] In one embodiment of this application, when normalizing the mask features to [0,1], considering that setting a hard threshold would cause the gradient of the model training to decrease and prevent it from passing through the module, the inventors designed a normalization function that is extremely steep near 0, thus simulating the effect of a mask while ensuring the differentiability of the function. Specifically, the normalization function is designed as follows:
[0092]
[0093] Where e is a mathematical constant. The masked features After inputting the above normalization function, the mask features are obtained.
[0094]
[0095] In one embodiment of this application, a spatial information extraction module based on a graph convolutional network (GCN) is designed, utilizing an adaptive flow graph. Adaptive Cause-Effect Graph and mask features Obtain spatial information include:
[0096] Based on adaptive flow graphs and adaptive cause-effect graph mask features Input the graph convolutional network (GCN) module and the ELU activation function, and obtain the outputs respectively. and (refer to Figure 4 (As shown). Output and This is used to characterize the potential information about how airport capacity changes due to the influence of other airports, and outputs these two parts. and With concealed features The data is stitched together and then processed through a fully connected layer to obtain the final spatial information. The calculation is as follows:
[0097]
[0098] Where FC() represents a fully connected layer, and Contact() represents a feature concatenation operation.
[0099] In one embodiment of this application, a time-dependent extraction module based on a gated recurrent unit (GRU) is designed, utilizing masked features. Obtain timing information include:
[0100] Timing information is extracted by stacking gated recurrent unit (GRU) modules. The calculation method for each stack is as follows:
[0101]
[0102]
[0103] Among them, h th represents the output result after t stacking operations. t-1 W represents the output result after t-1 stacking operations. h U h and b h It is a trainable parameter or parameter matrix, z t Indicates the update gate, r t This indicates that the door is being reset. This indicates the masked features. See the appendix for details. Figure 3 .
[0104] The output of the stacked gated recurrent units (GRUs) is then passed through a fully connected layer to obtain the final timing information.
[0105]
[0106] In one embodiment of this application, in step S6, spatial information is... and timing information The final airport capacity prediction is obtained through fusion and a fully connected layer (FC()). include:
[0107] Spatial information is processed according to the following formula. and timing information By integrating the data, we can obtain predicted airport capacity values.
[0108]
[0109] Figure 4 This paper presents an overall flowchart of an airport capacity prediction method based on causal graph neural networks, according to an embodiment of this application. Figure 4 The following explanation is provided: This embodiment first calculates the transfer entropy and performs significance tests based on the time series data of each airport's capacity to extract the causal relationships between airports and obtain the flight traffic relationship matrix A. F and causal relationship matrix A C ; and then the flight flow matrix A F and causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph Next, a mask matrix and a normalization function are designed and used to extract the original feature vector X. t Mining mask features with spatial correlation Then, spatial information is extracted using a graph convolutional neural network (GCN). Timing information is extracted using a gated recurrent unit (GRU). Finally, a spatiotemporal information fusion module was designed to achieve accurate prediction of airport capacity by efficiently combining the extracted spatiotemporal information.
[0110] Therefore, the method in this embodiment accurately represents the relationship between airports through adaptive causal graphs, and extracts effective spatial features from the adaptive causal graphs by using feature masks combined with GCN. Finally, by fusing with time series information, the accuracy of airport capacity prediction is greatly improved, making up for the deficiency of existing technologies in lacking mutual influence factors between airports, and laying a data foundation for efficient flight control schemes.
[0111] Figure 5 This figure shows a comparison between airport capacity prediction results of an embodiment of this application and existing methods. For each method, the mean squared error between the predicted capacity and the actual capacity is used to measure the prediction performance. The figure shows the percentage reduction in mean squared error of the proposed method compared to existing methods. It can be seen that the prediction bias of the proposed method is significantly smaller than that of commonly used airport capacity prediction methods such as Bayesian Regression (BR), Random Forest (RF), Long Short-Term Memory Recurrent Neural Network (LSTM), GCN, GCGRU, and Diffused Convolutional Recurrent Neural Network (DCRNN). It comprehensively considers the correlation between airports and effectively improves the accuracy of airport capacity prediction.
[0112] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.
Claims
1. An airport capacity prediction method based on causal graph neural networks, characterized in that, The method includes the following steps: Step S1: Calculate the transfer entropy of the time series representing the capacity of each airport, perform a significance test, and extract the causal relationship matrix A between airports. C ; Step S2, generate a trainable parameter matrix M, and combine the flight flow matrix A between airports. F and the causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph Step S3, design the mask matrix W mask Using the mask matrix W mask From the original feature vector X t Mining mask features with spatial correlation Step S4: Design a spatial information extraction module based on a graph convolutional network (GCN), utilizing the adaptive flow graph. Adaptive Cause-Effect Graph and mask features Obtain spatial information Step S5: Design a time-series dependency extraction module based on a gated recurrent unit (GRU), utilizing the masked features. Obtain timing information Step S6: Transfer the spatial information and timing information The final airport capacity prediction is obtained through fusion and a fully connected layer (FC()).
2. The method according to claim 1, characterized in that, In step S1, the transfer entropy of the time series representing the capacity of each airport is calculated and a significance test is performed to extract the causal relationship matrix A between airports. C ,include: Capacity data for each airport is extracted and discretized at 1-hour intervals to obtain time series representing capacity changes at each airport. The length of the time series is denoted as r, and the time series for airport i is denoted as C. i (t), calculate the transfer entropy between the time series of each airport using the following formula: TE j→i =H(C i (t)|C i p (t-Δt))-H(C i (t)|C j q (t-Δt),C i p (t-Δt)), Where t = Tr, ..., T, T is the current time; Δt represents the time step, which is taken as 1 in this formula; C i p (t-Δt)={C i (t-Δt), ..., C i (t-pΔt)} represents C i (t) The value of the past p time steps; C j q (t-Δt)={C i (t-Δt), ..., C i (t-qΔt)} represents C i (t) represents the value of the past q time steps; in this formula, both p and q are taken as 2; H(·|·) represents the conditional entropy, which is calculated as follows: Where p(x, y) is the joint probability distribution of X and Y, and p(y|x) is the conditional probability distribution; The calculated transfer entropy is subjected to a significance test. The transfer entropy between airports that does not meet the given significance level is set to 0. Finally, the causal relationship matrix A is constructed. C Causal relationship matrix A c Element A in C [ij] represents the transfer entropy between airport i and airport j.
3. The method according to claim 1, characterized in that, In step S2, a trainable parameter matrix M is generated, and the inter-airport flight flow matrix A is used. F and the causal relationship matrix A C Combined with the trainable parameter matrix M, an adaptive flow map describing the interactions between airports is generated. and adaptive cause-effect graph include: Generate a trainable parameter matrix M, where the trainable parameters are on the diagonal and all other positions are 0. Then, generate the inter-airport flight flow matrix A. F Causal relationship matrix A between airports C Combined with the trainable parameter matrix M, an adaptive flow graph is obtained. and adaptive cause-effect graph as follows:
4. The method according to claim 1, characterized in that, In step S3, the mask matrix W is designed. mask Using the mask matrix W mask From the original feature vector X t Mining mask features with spatial correlation include: Design the mask matrix W mask ={w1, w2, ..., w k }∈R K Where K is the number of features, w k These are trainable parameters, representing the original feature vector X. t and mask matrix W mask Features obtained after performing Hadamard product and mask Where σ() represents the activation function; The masked features After normalization, the mask features are obtained. Correspondingly, the masked features for: This is subsequently used to predict changes in the airport's own capacity, where J∈R K This represents a matrix whose elements are all 1s.
5. The method according to claim 4, characterized in that, The masked features Normalization includes: The normalization function is designed as follows: Where e is a mathematical constant; Features after masking The mask features are obtained after inputting the normalization function.
6. The method according to claim 1, characterized in that, The design is based on the spatial information extraction module of the Graph Convolutional Network (GCN), utilizing the adaptive flow graph. Adaptive Cause-Effect Graph and mask features Obtain spatial information include: Based on the adaptive flow graph respectively and the adaptive causal graph mask features Input the graph convolutional network (GCN) module and the ELU activation function, and obtain the outputs respectively. and Output and This is used to characterize the potential information about how airport capacity changes due to the influence of other airports, and outputs these two parts. and With concealed features The data is stitched together and then processed through a fully connected layer to obtain the final spatial information. The calculation is as follows: Where FC() represents a fully connected layer, and Contact() represents a feature concatenation operation.
7. The method according to claim 1, characterized in that, The design is based on a time dependency extraction module of a gated recurrent unit (GRU), utilizing masked features. Obtain timing information include: Timing information is extracted by stacking gated recurrent unit (GRU) modules. The calculation method for each stack is as follows: Among them, h t h represents the output result after t stacking operations. t-1 W represents the output result after t-1 stacking operations. h U h and b h It is a trainable parameter or parameter matrix, z t Indicates the update gate, r t This indicates that the door is being reset. Indicates the features that have been masked; The output of the stacked gated recurrent units (GRUs) is then passed through a fully connected layer to obtain the final timing information.
8. The method according to claim 1, characterized in that, In step S6, the spatial information and timing information The final airport capacity prediction is obtained through fusion and a fully connected layer (FC()). include: The spatial information is processed according to the following formula. and timing information By integrating the data, we can obtain predicted airport capacity values.