Airport network multi-step delay prediction method based on space-time diagram convolution

Abstract

The invention discloses an airport network multi-step delay prediction method based on space-time diagram convolution, and belongs to the technical field of flight delay prediction, and the method comprises the following steps: S1, collecting historical flight data and airport weather data, and obtaining airport delay data, airport weather data and an inter-airport adjacency matrix relation through data preprocessing; s2, converting the airport delay data and the airport weather data into high-dimensional representations, and performing fusion processing to obtain fused data; s3, inputting the fusion data and the inter-airport adjacency matrix relationship into a space-time learning module to obtain space-time representation; and S4, obtaining a final prediction result by using the gating linear unit and the full connection layer. According to the method, the dynamic interaction relationship between the airport network time and space can be effectively extracted, and airport network multi-step delay prediction is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of flight delay prediction, and particularly relates to a multi-step delay prediction method for airport networks based on spatio-temporal graph convolution. Background Art

[0002] The rapid growth of air traffic travel demand and the complexity of the air transportation network have led to air network congestion and exacerbated flight delays. In recent decades, flight delays have risen to a key issue in airport management and flight scheduling. A study by the Federal Aviation Administration of the United States shows that flight delays cost the US economy $32.9 billion in 2019. A report released by the European Commission in 2020 shows that flight delays increased from 61,000 in 2011 to 109,000 in 2018. Given the complex spatio-temporal dependence of the air traffic network, flight delays always spread throughout the entire air network, causing a series of delays and even disruptions. Therefore, it is crucial to reveal the complexity of delay propagation in the air network and improve the accuracy of airport delay prediction.

[0003] Predicting delay propagation in airport networks is not a simple time series problem, but a problem affected by complex spatio-temporal correlations and numerous external factors. The propagation of airport delays is affected by various factors, including geographical proximity, weather conditions, flight schedules, and flight traffic. For example, due to geographical proximity, bad weather conditions in the Pearl River Delta of China have caused flight takeoff delays at CAN and SZX airports. Over time, these takeoff delays have led to an increase in arrival delays at CKG and CTU airports in the central region. This cascading effect gradually spreads across the country and ultimately affects airports in the west.

[0004] In the past two decades, research efforts on modeling airport network delay propagation have surged. These efforts have evolved from traditional mathematical methods to machine learning methods and more recently to deep learning methods that specifically address spatio-temporal dependencies. Traditional methods aim to analyze the underlying mechanisms of delay propagation and use mathematical models to identify key factors affecting delays. These include probability models, regression models, and queuing theory. Although these methods generally provide principle-based explanations, they may face challenges in dealing with high-dimensional, large-scale delay propagation data due to the inherent constraints of handling complex datasets. Machine learning methods mainly perform classification and prediction through data learning, such as using random forests to predict airport network delays. Although effective, the shallow structure of traditional machine learning methods cannot effectively handle the spatial dependencies in big data. In recent years, deep learning techniques have been widely adopted in modeling airport network delay propagation and can better capture complex non-linear relationships. Given the complex spatio-temporal dependencies of air traffic networks, the spatio-temporal graph neural network (ST-GNN) framework has become the general framework for predicting air network delay propagation. Among them, GNN-based models are usually used to extract spatial relationships between nodes, while recurrent neural networks (RNNs), temporal convolutional networks (TCNs), and self-attention mechanisms (ATTs) are usually used to extract temporal dependencies in time series data.

[0005] However, these methods are far from fully solving the complex challenges faced in delay propagation modeling. One major problem is the failure to consider the impact of spatio-temporal dynamic interactions. Summary of the Invention

[0006] To solve the above problems, the present invention proposes a multi-step delay prediction method for airport networks based on spatio-temporal graph convolution.

[0007] The technical solution of the present invention is: A multi-step delay prediction method for airport networks based on spatio-temporal graph convolution includes the following steps:

[0008] S1. Collect historical flight data and airport weather data, and obtain airport delay data, airport weather data, and the adjacency matrix relationship between airports through data preprocessing;

[0009] S2. Convert the airport delay data and airport weather data into high-dimensional representations and perform fusion processing to obtain fusion data;

[0010] S3. Construct a spatio-temporal learning module, input the fusion data and the adjacency matrix relationship between airports into the spatio-temporal learning module to obtain spatio-temporal representations; among them, the spatio-temporal learning module includes a time sub-module, a space sub-module, and a spatio-temporal interaction sub-module;

[0011] S4. Based on the spatio-temporal representations, use gated linear units and fully connected layers to obtain the final prediction result.

[0012] Furthermore, in S1, the airport delay data includes the departure delay value and the arrival delay value;

[0013] Departure delay value The calculation formula is:

[0014] ;

[0015] In the formula, represents the set of flights departing from the airport, represents the set of flights departing during the time stamp period, represents the departure delay of the flight departing from the airport at time , represents the minimum value operation;

[0016] Arrival delay value The calculation formula is:

[0017] ;

[0018] In the formula, represents the set of flights arriving at the airport, represents the set of flights arriving during the time stamp period, represents the arrival delay of the flight from the airport at time .

[0019] Furthermore, in S1, the adjacency matrix relationship between airports includes the global distance adjacency matrix and the traffic adjacency matrix;

[0020] The normalization calculation formula of the global distance adjacency matrix is:

[0021] ;

[0022] In the formula, represents the normalization result of the global distance adjacency matrix, represents the exponential function, represents airport and airport distance between, represents the bandwidth parameter of the Gaussian kernel;

[0023] The normalization calculation formula of the traffic adjacency matrix is:

[0024] ;

[0025] In the formula, represents the normalization result of the traffic adjacency matrix, represents the total number of flights from the airport to the airport in the training dataset, and represents the maximum value of the OD pair flight volume in the training dataset.

[0026] Furthermore, in S2, the fully connected layer is used to expand the dimensions of the airport delay data and the airport weather data, and the expanded airport delay data and airport weather data are fused to obtain the fused data;

[0027] The fused data is calculated as follows:

[0028] ;

[0029] In the formula, represents the airport delay data after dimension expansion, represents the airport weather data after dimension expansion.

[0030] Furthermore, in S3, the MLP module is used as the time sub-module;

[0031] The MLP module is expressed as:

[0032] ;

[0033] In the formula, represents the hidden representation of the MLP module, represents the fully connected layer, represents the activation function.

[0034] Furthermore, in S3, the diffusion graph convolution module is used as the time sub-module;

[0035] The diffusion graph convolution module is expressed as:

[0036] ;

[0037] In the formula, represents the sigmoid function, represents the number of diffusion steps, represents the number of matrix categories, represents the power series of the transition matrix, represents the learnable weight, represents the input data, represents the matrix category number, represents the diffusion step number.

[0038] Furthermore, in S3, the expression of the spatio-temporal interaction sub-module is:

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] In the formula, represents the first subsequence of the input of the spatio-temporal interaction module obtained by using interval division, represents the second subsequence of the input of the spatio-temporal interaction module obtained by using interval division, represents interval division based on odd and even indices, represents the input of the spatio-temporal interaction module, represents the first output after the first round of interactive learning, represents the second output after the first round of interactive learning, represents the first output after the second round of interactive learning, represents the second output after the second round of interactive learning, represents the activation function, represents the diffusion graph convolutional neural network, represents the first MLP unit, represents the second MLP unit, represents the third MLP unit, represents the fourth MLP unit, represents the Hadamard product.

[0045] Furthermore, in S4, the final prediction result has the following expression:

[0046] ;

[0047] In the formula, represents the fully connected layer, represents the activation function, represents the sigmoid function, represents the Hadamard product, represents the output of the encoder.

[0048] The beneficial effects of the present invention are as follows:

[0049] (1) The present invention represents the multi-airport network in a graph structure, and uses the distance between airports and the total traffic as the weight expression in the adjacency matrix of the airport network;

[0050] (2) Based on the DGCN neural network model, the present invention captures the correlation of the airport network space; based on the MLP linear model, it captures the time correlation of the airport network; based on the spatio-temporal interaction model, spatio-temporal interaction is carried out; it can effectively extract the dynamic interaction relationship between the time and space of the airport network and realize the multi-step delay prediction of the airport network.

[0051] (3) The present invention can accurately predict the future multi-step delay values of the airport network. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flowchart of a multi-step delay prediction method for an airport network based on spatio-temporal graph convolution;

[0053] Figure 2 It is a schematic structural diagram of a multi-airport flight delay prediction model. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0055] As Figure 1 shown, the present invention provides a multi-step delay prediction method for an airport network based on spatio-temporal graph convolution, including the following steps:

[0056] S1. Collect historical flight data and airport weather data, and obtain airport delay data, airport weather data, and the adjacency matrix relationship between airports through data preprocessing;

[0057] S2. Convert the airport delay data and airport weather data into high-dimensional representations and perform fusion processing to obtain fusion data;

[0058] S3. Construct a spatio-temporal learning module, input the fusion data and the adjacency matrix relationship between airports into the spatio-temporal learning module to obtain spatio-temporal representations; wherein, the spatio-temporal learning module includes a time sub-module, a space sub-module, and a spatio-temporal interaction sub-module;

[0059] S4. Based on the spatio-temporal representations, use gated linear units and fully connected layers to obtain the final prediction results.

[0060] In S1, for the historical airport flight data, the flight delay information and weather information of Chinese airports from April 30, 2015 to May 1, 2017 were selected. Fifty airports with relatively large traffic volumes were screened to minimize abnormal data from remote areas. There is a strong correlation between weather and airport delays, and weather data is crucial for airport delay prediction. Seven weather types were selected: normal weather 0, rain 1, cloud 2, thunderstorm 3, heavy fog 4, storm 5, and snowfall 6. To more closely combine the data with peak flight times, the present invention excluded flight records between 12:00 am and 6:00 am from the dataset.

[0061] In the embodiment of the present invention, in S1, the airport delay data includes a departure delay value and an arrival delay value;

[0062] Departure delay value The calculation formula is:

[0063] ;

[0064] In the formula, represents the set of flights departing from the airport, represents the set of flights departing during the time stamp , represents the departure delay of the flight departing from the airport at time from the airport , represents the minimum value operation;

[0065] Arrival delay value The calculation formula is:

[0066] ;

[0067] In the formula, represents the set of flights arriving at the airport, represents the set of flights arriving during the time stamp , represents the arrival delay of the flight from the airport at time .

[0068] In the embodiment of the present invention, in S1, the adjacency matrix relationship between airports includes a global distance adjacency matrix and a traffic adjacency matrix;

[0069] The normalization calculation formula of the global distance adjacency matrix is:

[0070] ;

[0071] In the formula, represents the normalization result of the global distance adjacency matrix, represents the exponential function, represents airport and airport the distance between, represents the bandwidth parameter of the Gaussian kernel;

[0072] The normalization calculation formula of the traffic adjacency matrix is:

[0073] ;

[0074] In the formula, represents the normalization result of the traffic adjacency matrix, Denote the total number of flights from the airport to the airport in the training dataset, and denote the maximum value of the OD pair flight volume in the training dataset.

[0075] In the embodiment of the present invention, in S2, as Figure 2 shown, convert the original airport delay data and the airport weather data into and respectively through the fully connected layer, where denotes the number of nodes ( airports), 2 denotes the feature dimension (departure delay and arrival delay values), denotes the feature dimension (different weather categories), denotes the extended feature channel number. Subsequently, fuse the dimension-expanded delay data with the weather data to incorporate the prior weather information into the delay data and obtain the fused data Use the fully connected layer to expand the dimensions of the airport delay data and the airport weather data, and fuse the dimension-expanded airport delay data and airport weather data to obtain the fused data.

[0076] Fused data The calculation formula is:

[0077] ;

[0078] In the formula, denotes the dimension-expanded airport delay data, denotes the dimension-expanded airport weather data.

[0079] In the embodiment of the present invention, in S3, use the MLP module as the time sub-module;

[0080] MLP module The expression is:

[0081] ;

[0082] In the formula, denotes the hidden representation of the MLP module, denotes the fully connected layer, denotes the activation function.

[0083] In the embodiment of the present invention, in S3, use the diffusion graph convolutional module as the time sub-module;

[0084] Diffusion graph convolutional module The expression is:

[0085] ;

[0086] In the formula, represents the sigmoid function, represents the number of diffusion steps, represents the number of matrix classes, represents the power series of the transition matrix, represents the learnable weight, represents the input data, represents the matrix class number, represents the diffusion step number.

[0087] In the embodiment of the present invention, in S3, the expression of the spatio-temporal interaction sub-module is:

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] In the formula, represents the first subsequence of the input of the spatio-temporal interaction module obtained by interval division, represents the second subsequence of the input of the spatio-temporal interaction module obtained by interval division, represents interval division based on odd and even indices, represents the input of the spatio-temporal interaction module, represents the first output after the first round of interactive learning, represents the second output after the first round of interactive learning, represents the first output after the second round of interactive learning, represents the second output after the second round of interactive learning, represents the activation function, represents the diffusion graph convolutional neural network, represents the first MLP unit, represents the second MLP unit, represents the third MLP unit, represents the fourth MLP unit, represents the Hadamard product.

[0094] In the embodiment of the present invention, in S4, the final prediction result has the following expression:

[0095] ;

[0096] In the formula, represents a fully connected layer, represents an activation function, represents the sigmoid function, represents the Hadamard product, represents the output of the encoder.

[0097] In the embodiments of the present invention, the evaluation indexes are:

[0098] ;

[0099] ;

[0100] In the formula, represents the mean absolute error, represents the root mean square error, represents predicting the network-wide airport delay value within a period of time, represents the original observed value, represents the number of nodes ( airports), represents the future time series, represents the delay type (departure delay and arrival delay), represents at time airport the actual arrival delay or departure delay value, represents at time airport the predicted arrival delay or departure delay value.

[0101] The present invention will be described below with reference to specific embodiments.

[0102] Select the historical flight data and meteorological data of Chinese airports from April 30, 2015 to May 1, 2017. According to the data processing flow in the present invention, a multi-airport delay prediction data set is established. Based on this data set, the STDIGNN model, historical average (HA) method, vector autoregression (VAR) model, GRU neural network model, ASTGCN model, STPN model, and FAST-CA model proposed by the present invention are respectively applied to predict the airport network delay value. The input length of each model is set to 36 time steps, with an interval of 30 minutes for each time step, and the model output length is 12 time steps. The model training processes are as follows:

[0103] Construct Input: The dataset is divided into a training set, a validation set, and a test set in a ratio of 7:1:2, divided in units of 18 hours, and input into each model. According to the training feedback results, the parameters such as the learning rate, the number of iterations, and BatchSize are continuously adjusted and optimized.

[0104] Output: The model outputs a length of 12 time steps, and the prediction time span is 6 hours.

[0105] The summary of the prediction results is shown in Table 1.

[0106] Table 1

[0107]

[0108] Judging from the various indicators in Table 1, models using spatio-temporal methods, including ASTGCN, STPN, FAST-CA, and STDIGNN, have significant advantages in performance over traditional statistical and machine learning models (HA, VAR, GRU). These spatio-temporal models are good at capturing the inherent spatio-temporal dynamics existing in the delay data. STDIGNN is the most effective among the spatio-temporal models, superior to the current optimal benchmark model FAST-CA, and FAST-CA itself is also superior to STPN and STGCN.

[0109] In terms of short-term prediction, compared with the current optimal benchmark model FAST-CA, STDIGNN shows significant improvement in the Chinese dataset. The present invention realizes a 34.3% reduction in the MAE of the 1.5h arrival delay prediction and a 39.3% reduction in the MAE of the 1.5h departure delay prediction. This performance highlights the superior prediction performance of STDIGNN, making it a valuable tool for airport network prediction scenarios.

[0110] In practical applications, the excellent performance of the STDIGNN model provides strong support for air traffic flow management. Its ability to accurately predict arrival and departure delays hours in advance is particularly beneficial for managing complex situations and incomplete datasets. This overall effectiveness makes STDIGNN an important model for dealing with real challenges such as airport delay prediction.

[0111] Those of ordinary skill in the art will realize that the embodiments described herein are for helping readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A multi-step delay prediction method for airport network based on spatiotemporal graph convolution, characterized in that: The following steps are involved: S1, collect historical flight data and airport weather data, and obtain airport delay data, airport weather data and the adjacency matrix relationship between airports through data preprocessing; S2, converting the airport delay data and the airport weather data into high-dimensional representations, and fusing them to obtain fused data; S3, constructing a spatiotemporal learning module, inputting the fused data and the adjacency matrix relationship between airports into the spatiotemporal learning module to obtain a spatiotemporal representation; wherein the spatiotemporal learning module includes a time submodule, a space submodule and a spatiotemporal interaction submodule; S4. Based on spatiotemporal representation, the final prediction result is obtained using gated linear units and fully connected layers.

2. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In said S1, the airport delay data includes a departure delay value and an arrival delay value; Departure delay value The calculation formula is: ； In the formula, represents the set of flights departing from an airport, Indicates the timestamp A collection of flights departing during the period, Indicates the flight time From the Airport Departure delays, Indicates minimum operation; The arrival delay value The calculation formula is: ； In the formula, represents the set of flights arriving from an airport, Indicates the timestamp The collection of flights arriving during the period, Indicates the flight from the airport In time arrival delay.

3. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In S1, the adjacency matrix relationship between airports includes a global distance adjacency matrix and a traffic adjacency matrix; The normalized calculation formula of the global distance adjacency matrix is: ； In the formula, represents the normalized result of the global distance adjacency matrix, represents the exponential function, Indicates the airport and Airport The distance between represents the bandwidth parameter of the Gaussian kernel; The normalized calculation formula of the traffic adjacency matrix is: ； In the formula, represents the normalized result of the traffic adjacency matrix, Indicates that the training data set is from the airport To the Airport Total flights, It represents the maximum value of OD to flight quantity in the training data set.

4. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In S2, the airport delay data and the airport weather data are dimensionally expanded using a fully connected layer, and the dimensionally expanded airport delay data and the airport weather data are fused to obtain fused data; The fused data The calculation formula is: ； In the formula, Represents the airport delay data after dimension expansion, Represents the airport weather data after dimension expansion.

5. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In S3, the MLP module is used as a time submodule; The MLP module The expression is: ； In the formula, represents the hidden representation of the MLP module, represents the fully connected layer, Represents the activation function.

6. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In S3, the diffusion graph convolution module is used as a time submodule; The diffusion graph convolution module The expression is: ； In the formula, represents the sigmoid function, represents the number of diffusion steps, represents the number of matrix categories, represents the power series of the transfer matrix, represents the learnable weights, Represents input data, represents the matrix category number, Indicates the diffusion step number.

7. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In S3, the expression of the spatiotemporal interaction submodule is: ； ； ； ； ； In the formula, represents the first subsequence of the input of the spatiotemporal interaction module obtained by interval division, represents the second subsequence of the input of the spatiotemporal interaction module obtained by interval division, represents interval division based on odd and even indexes, represents the input of the spatiotemporal interaction module, represents the first output after the first round of interactive learning, represents the second output after the first round of interactive learning, represents the first output after the second round of interactive learning, represents the second output after the second round of interactive learning, represents the activation function, represents the diffusion graph convolutional neural network, represents the first MLP unit, represents the second MLP unit, represents the third MLP unit, represents the fourth MLP unit, Represents the Hadamard product.

8. The airport network multi-step delay prediction method based on spatiotemporal graph convolution according to claim 1 is characterized in that: In S4, the final prediction result The expression is: ； In the formula, represents the fully connected layer, represents the activation function, represents the sigmoid function, represents the Hadamard product, Represents the output of the encoder.

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