An airport atfm delay time prediction method fusing network features

Abstract

The embodiment of the application discloses an airport ATFM delay time prediction method fusing network features, relates to the technical field of airport operation scheduling and air traffic control, and can improve the accuracy of airport ATFM delay time prediction. The airport-route is regarded as a directed graph, node-level graph theory features are extracted, and a two-dimensional feature system of "basic operation features + network correlation features" is constructed. A robust data processing strategy of hierarchical missing value filling, Yeo-Johnson power transformation and RobustScaler standardization is adopted to accurately adapt to the neural network training requirement. A neural network (MLP) is taken as a core algorithm, and traditional algorithms such as random forest, gradient boosting and LightGBM are compared and trained synchronously.

Description

Technical Field

[0001] This invention relates to the field of airport operation scheduling and air traffic control technology, and in particular to an airport ATFM delay time prediction method that integrates network characteristics. Background Technology

[0002] With the rapid development of the global civil aviation industry and the continuous increase in airport throughput, Air Traffic Flow Management (ATFM) delays have become a key bottleneck restricting the industry's development. According to statistics from the International Civil Aviation Organization (ICAO), the economic losses caused by ATFM delays worldwide exceed tens of billions of US dollars annually. This not only increases airlines' operating costs (such as fuel consumption and crew overtime pay) but also seriously affects passenger travel experience and reduces the core competitiveness of civil aviation. In my country, with the advancement of the "dual circulation" development pattern, the route networks of hub airports are becoming increasingly complex, with the average daily flight volume at a single airport exceeding 1,000 flights. Traffic flow interaction and route connections between airports are becoming increasingly close, making traditional delay prediction methods inadequate for the operational needs of the new era.

[0003] Traditional ATFM delay prediction methods are mainly divided into three categories, all of which have significant limitations: The first category is rule-based empirical models, which rely on dispatchers' industry experience to manually set thresholds (such as judging delay risk based on historical flight volume thresholds). These methods are highly subjective, have poor adaptability, and cannot cope with sudden traffic fluctuations or changes in network correlations. The second category is based on statistical linear models (such as multiple linear regression and time series ARIMA models), which can only capture linear relationships in a single dimension. However, airport delays are affected by multiple factors such as flight volume, route network, weather, and airspace restrictions, exhibiting strong nonlinear characteristics, resulting in extremely low prediction accuracy (average MAE exceeding 120 minutes). The third category is based on traditional machine learning. While predictive models (such as random forests, gradient boosting, and LightGBM) can capture nonlinear relationships to some extent, they suffer from three major drawbacks: First, they lack the ability to handle high-dimensional features. When multi-dimensional features such as route networks and spatiotemporal correlations are introduced, the curse of dimensionality or feature redundancy can easily occur, leading to model overfitting. Second, they have limited ability to mine deep correlations. The model structure of traditional algorithms determines that they can only capture shallow feature interactions and cannot analyze the complex internal logic of "airport network status - flight traffic distribution - delay transmission effect". Third, they have weak generalization ability and poor adaptability to airports of different sizes and different operating scenarios. In the switching between hub airports and feeder airports, the prediction error fluctuates by more than 50%.

[0004] The core technical pain points currently facing the industry can be summarized in four points: First, the feature dimension is too singular. Existing models mostly focus on the isolated features of a single airport (such as its own flight volume and weather), ignoring the correlation of airports as nodes in the route network. Delays at hub airports often spread to surrounding airports through the route network, forming a "delay chain reaction." Traditional models cannot quantify this network-level correlation impact. Second, data processing is too simplistic. Airport delay data has significant problems such as skewed distribution, missing values, and outliers. Traditional models only use simple filling without distribution optimization, resulting in data quality that cannot support high-precision prediction. Third, algorithm capabilities are limited. The structural bottlenecks of traditional machine learning algorithms make it difficult to cope with complex data scenarios with high dimensions, nonlinearity, and strong correlations. Prediction accuracy has always been difficult to improve (R2 is only up to 0.95), and the optimization space has reached its ceiling. Fourth, scenario adaptation is rigid. The operating characteristics of different airports (hub / feeder, short / long-haul route ratio) vary greatly. Traditional models lack flexible adaptive capabilities and cannot take into account the prediction needs of various scenarios.

[0005] Against this technological backdrop, neural networks (especially those within deep learning frameworks) have become a core technology choice for overcoming industry pain points due to their unique structural advantages. Compared to traditional algorithms, the superiority of neural networks is mainly reflected in four aspects: First, their powerful high-dimensional feature processing capabilities. Through weight updates of multiple layers of neurons, neural networks can automatically extract effective information from high-dimensional features, avoiding the curse of dimensionality and perfectly adapting to the multi-dimensional input requirements of "basic operational features + network correlation features + spatiotemporal interaction features"; Second, their ability to capture deep nonlinear relationships. Through nonlinear transformations of activation functions and the stacking of multiple layers, neural networks can accurately characterize the complex coupling relationships of multiple factors behind airport delays, analyzing deep logic that traditional algorithms cannot reach (such as "high betweenness centrality hub airports + severe weather conditions"). (The complex relationship between weather and regional delay transmission); third, excellent generalization and adaptation capabilities. Through regularization, early stop, dropout and other techniques, neural networks can effectively suppress overfitting and maintain stable prediction performance on airport datasets of different sizes and operational characteristics, with adaptability far exceeding that of traditional algorithms; fourth, continuous iterative optimization capabilities. The modular structure of neural networks supports architecture upgrades (such as CNN, LSTM, Transformer) and multi-source data fusion (such as weather, airspace restrictions, holidays), and has unlimited space for technological evolution, while traditional algorithms are limited by model principles and find it difficult to achieve breakthrough improvements.

[0006] Therefore, how to further improve the accuracy of airport ATFM delay time prediction has become a research topic. Summary of the Invention

[0007] Embodiments of the present invention provide an airport ATFM delay time prediction method that integrates network features, which can improve the accuracy of airport ATFM delay time prediction.

[0008] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0009] An airport ATFM delay time prediction method that integrates network features includes:

[0010] S1. Obtain the airport dataset, which includes airport data and flight route data;

[0011] S2. Generate basic derived features and graph theory features. The basic derived features cover four dimensions: route association features, flight volume features, delay association features, and distance features. Specifically, these include 12 core features: total number of routes, average number of departing flights, total number of departing flights, standard deviation of departure flights, average number of arriving flights, total number of arriving flights, standard deviation of arrival flights, departure-to-arrival ratio, average departure delay, total departure delay, departure delay rate per flight, and average departure / arrival distance. The graph theory features are node-level indicators extracted from the airport-route directed graph, including in-degree, out-degree, total degree, weighted in-degree, weighted out-degree, clustering coefficient, betweenness centrality, compact centrality, PageRank, and eigenvector centrality. The derived ratio indicators are used to quantify the connection scale, connection strength, hub status, and network radiation capacity of an airport in the route network, effectively mining the network association effect between airports and making up for the inadequacy of single basic operational features in characterizing the attributes of the airport route network.

[0012] S3. Construct a directed graph based on the relationship between the departure airport and the destination airport in the route information table, and calculate the node-level graph theory characteristic index. The method for calculating the node-level graph theory characteristic index includes:

[0013] Specifically, methods for calculating node-level graph theory feature metrics include:

[0014] The basic degree metrics for calculation include: in-degree, out-degree, and total degree, where:

[0015] In-degree is used to represent the number of all routes pointing to the target airport v, and is expressed as: Where u represents the source node, the departure airport of the flight path, v represents the set of nodes, the set of all airports within the study scope, and E represents the set of edges, the set of all flight paths. The out-degree represents the number of flight paths departing from the target airport v, expressed as: ,in, This represents the target node. The edge weight represents the distance from node v to node u, used to characterize the existence, importance, or strength of a route (v→u). The total degree represents the total number of associated routes to the target airport v, expressed as: ,in, This represents the in-degree of the node, which is the number of all routes pointing to airport v. Indicates the out-degree of a node, and airport v represents the number of routes pointing to other nodes.

[0016] The calculated weighted degree metrics include: weighted in-degree, weighted out-degree, and weighted total degree, where: the weighted in-degree represents the total flight traffic of all routes to the target airport v, expressed as: , This represents the weighting coefficient of the routes from airport u to airport v. The weighted out-degree is used to represent the total flight traffic of all routes departing from the target airport v, expressed as: The weighted total degree is used to represent the total flight traffic at the target airport v, and is expressed as: .

[0017] Clustering coefficients are used to measure the tightness of flight connections between associated airports of target airport v, and are expressed as: .

[0018] Betweenness centrality is used to measure how central v is as a transit hub in an aviation network, and is expressed as: ,in, This represents the total number of shortest paths from airport s to airport t. This represents the number of shortest paths through the target airport v, where s represents the source node (originating airport) and t represents the sink node (destination airport).

[0019] Tight centrality is used to measure the average reachability efficiency from v to all airports in the entire network, and is expressed as: ,in, represents the shortest path distance from target airport v to airport u, and n represents the total number of nodes (in this embodiment, nodes are airports, so it can also be understood as the total number of airports).

[0020] PageRank centrality is used to measure the authority and importance of v in an aviation network, and is expressed as: , where d represents the damping coefficient (fixed at 0.85).

[0021] Eigenvector centrality is used to measure the quality of v's neighbors (the more important the connected airport, the higher its score), and is expressed as: ,in, This represents the adjacency matrix element (1 if v is connected to u, otherwise 0). This represents the largest eigenvalue.

[0022] The derived ratio metric is used to characterize the degree of imbalance in airport arrival / departure traffic structure, where the in-degree / out-degree ratio is... The weighted in-degree / weighted out-degree ratio is .

[0023] S4. Preprocess the features obtained in S2 to obtain key features. Key features refer to the core subset obtained from the full feature pool, consisting of basic derived features (including business logic features such as flight volume, delays, and distance) and graph theory features (including structural features such as airport network degree, centrality, and clustering coefficients). This subset is selected using a random forest model based on feature importance (≥1.1 times the mean). It integrates features that contribute most to airport ATFM delay prediction from both business and network structure dimensions, achieving complementarity and redundancy removal between the two types of features. If the "weighted out-degree" (which reflects the weighted sum of departing flights at the airport) is strongly correlated with delays, it will be retained. If the "average arrival distance" does not significantly contribute to delay prediction, it will be removed.

[0024] S5. Based on the key features obtained by random forest screening (integrating basic derived features and graph theory features), after RobustScaler standardization, the data is input into the trained delay time prediction model (MLP / RF / GB / LGB). The model outputs the predicted value of the cumulative ATFM delay time of the airport. By comparing the predicted value with the actual ATFM delay time of the airport, quantitative parameters used to represent the predicted delay time are calculated. These quantitative parameters specifically include: mean absolute error (MAE) and root mean square error (RMSE) to measure the prediction bias, and the coefficient of determination (R²) to measure the model's fit to the ATFM delay data, forming a complete airport ATFM delay prediction and evaluation system.

[0025] In this embodiment, S1 further includes:

[0026] Verify the completeness of the core fields of the dataset. The core fields for airport data include the "airport code" field, and the core fields for route data include the "departure airport" and "destination airport" fields.

[0027] If so, the target variable column will be automatically adapted.

[0028] The automatically adaptable target variable column includes: preset target variables.

[0029] The system prioritizes searching the dataset for a predefined target variable—namely, the field named "Cumulative ATFMDelay (minutes)". If the target variable is not found, it identifies fields in the dataset related to delay time: specifically, fields containing the Chinese keyword "delay" or the English identifier "delay". Fields that directly represent delay duration (e.g., number of minutes delayed, total delay time) are selected as the target variable. For example, after identifying the "delay" / "delay" fields, fields containing these two identifiers can be filtered out first. Then, from the filtered fields, fields corresponding to delay time, such as fields representing delay time (duration / minutes), can be further queried.

[0030] Furthermore, it also includes:

[0031] The missing value of key fields in the route data is detected. If the missing value is less than 30%, the average value of the same route type is used to fill the missing value. If the missing value is greater than 30%, the value of 0 is used to fill the missing value. The key fields in the route data include: "Number of flights on the route" and "Cumulative ATFM delay time of the route".

[0032] In this embodiment, S3 includes:

[0033] Calculate node-level graph theory metrics, the types of which include: in-degree, out-degree, weighted in-degree, weighted out-degree, clustering coefficient, betweenness centrality, PageRank, compact centrality, and eigenvector centrality;

[0034] After processing outliers in the graph theory metrics, a directed graph is constructed. In this graph, nodes represent airports, and edges represent flight routes. The attributes of the edges include the number of flights, delay duration, and flight distance.

[0035] The methods for handling outliers in graph theory metrics include:

[0036] Missing graph theory metrics prone to missing values ​​are tested for degree of missing values. These metrics include compact centrality and eigenvector centrality. If the missing value is less than 10%, the mean of airports of the same size is used for filling. If the missing value is greater than 10%, zero values ​​are used for filling.

[0037] In S4 of this embodiment:

[0038] Methods for handling missing values ​​using a hierarchical strategy include:

[0039] Calculate the missing proportion ,in, This represents the i-th missing index (tight centrality, eigenvector centrality). Indicates the number of missing values ​​for the indicator. Indicates the total number of samples;

[0040] Missing values ​​are handled according to tiered fill rules, which include:

[0041] When the missing data rate is < 10%, the mean of airports of the same size is used for imputation. The imputation process is represented as follows: ,in, This indicates that airports of the same size are grouped together (small / medium / large).

[0042] When the missing value is ≥ 10%, 0 values ​​are used for filling. The filling process is represented as follows: .

[0043] The distribution of the target variable is optimized using the Yeo-Johnson power transform to approximate a normal distribution, thereby improving the prediction accuracy of the neural network. The specific method is as follows: ,in, This represents the original target variable (delay time). λ represents the transformed variable, and λ represents the optimal transformation parameter (learned automatically from the data).

[0044] The features were normalized using the RobustScaler standardization method. ,in, This represents the result of the normalization process, where median(X) represents the feature median, X represents the feature dimension, and x represents the original feature value. That is, the interquartile range = 75th percentile - 25th percentile. The advantage of using the RobustScaler normalization method to normalize features is that it is unaffected by extreme outliers, making it very suitable for data such as airport delays.

[0045] Key features were selected using a feature selection method based on random forests, including:

[0046] The feature importance score is calculated and represented as follows: ,in, The importance of the j-th feature is represented by T, and the number of decision trees is represented by T. This indicates the decrease in impurity (such as the Gini coefficient) brought about by feature j on tree t. Let represent the weight coefficient of the t-th decision tree.

[0047] Determine the feature selection threshold based on feature importance scores: Where M represents the total number of original features; retain > The features are used as key features.

[0048] reserve > The features are used as key features.

[0049] The hierarchical strategy for handling missing values ​​includes:

[0050] The features obtained in S2 are tested for missing values. When the missing ratio is higher than 30%, 0 values ​​are used for filling. When the missing ratio is between 10% and 30%, the mean is used for filling. When the missing ratio is lower than 10%, the median is used for filling. The feature selection threshold is 1.1*mean, which means that features with importance higher than 1.1 times the mean are retained.

[0051] The delay time prediction model is a neural network (MLP) with a three-layer hidden layer structure. The number of neurons in the three hidden layers are 256, 128 and 64, respectively. The activation function is ReLU, the optimizer is Adam, the regularization is L2 regularization, and the early stopping strategy is enabled during the training process.

[0052] The configuration parameters are as follows: the random forest uses 200 decision trees, the maximum depth is 15, and the minimum number of leaf node samples is 2.

[0053] Gradient boosting uses 200 base learners, a learning rate of 0.05, and a maximum depth of 8.

[0054] LightGBM uses 200 base learners, 31 leaf nodes, and a subsample ratio of 0.8.

[0055] The L2 regularization parameter alpha = 0.0003, and the early stopping strategy sets the validation set ratio to 20%. If the validation set error does not decrease after 100 consecutive iterations, training is stopped.

[0056] Specifically, the training process for the delay prediction model is as follows: Figure 6As shown, the Random Forest uses 200 decision trees to ensure stable model output and reduce prediction variance. Its maximum depth is set to 15 to control model complexity and avoid overfitting. The minimum number of leaf nodes is set to 2 to improve the model's fit to continuous delay times. The Gradient Boosting Tree uses 200 base learners to fully explore the complex correlations of delay influencing factors. A relatively small learning rate of 0.05 makes model iterations smoother and predictions more precise. Its maximum depth is set to 8 to balance model fitting ability and generalization performance. The LightGBM uses 200 base learners to ensure sufficient learning. The number of leaf nodes is set to 31 to improve training efficiency and control overfitting risk. A subsample ratio of 0.8 enhances the model's generalization ability and robustness. The neural network model uses the ReLU activation function to accelerate convergence and avoid gradient vanishing. It uses the Adam optimizer for adaptive learning rate updates, combines L2 regularization to constrain model weights, and enables early stopping to prevent overtraining.

[0057] Backend processing methods for the evaluation metrics output by the delay prediction model include:

[0058] Airport ATFM delays are classified according to assessment indicators.

[0059] Among them, R2≥0.99 and MAE≤50 minutes are considered excellent, and R2≥0.95 and MAE≤100 minutes are considered acceptable.

[0060] The airport ATFM delay time prediction method fused with network features provided in this invention treats the airport-airline configuration as a directed graph, extracts node-level graph theory features, and constructs a two-dimensional feature system of "basic operational features + network association features." It employs robust data processing strategies such as hierarchical missing value imputation, Yeo-Johnson power transform, and RobustScaler standardization to accurately adapt to the training requirements of neural networks. Using a neural network (MLP) as the core algorithm, it is simultaneously trained and compared with traditional algorithms such as random forest, gradient boosting, and LightGBM. Experimental verification shows that the prediction accuracy of this model is more than 30% higher than that of traditional algorithms, significantly improving the accuracy of airport ATFM delay time prediction. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1aThis is a flowchart of the overall deployment of the model provided in the embodiments of the present invention. The flowchart is used to show the entire process from data preparation to result output, highlighting the core position of the neural network model and the adaptability of each link.

[0063] Figure 1b This is a schematic diagram illustrating an application scenario provided by an embodiment of the present invention;

[0064] Figure 2 The model performance comparison curve provided in this embodiment of the invention includes a comparison of the test set and validation set for three core metrics: MAE, RMSE, and R2, which intuitively presents the performance advantages of neural networks compared to other traditional algorithms.

[0065] Figure 3 This is a schematic diagram of feature engineering logic provided in an embodiment of the present invention. The diagram is used to illustrate the construction relationship between basic derived features and graph theory features, as well as the topological structure of the airport-route network, and to explain the supporting role of high-dimensional features for neural networks.

[0066] Figure 4 The histogram of neural network (MLP) error distribution provided in this embodiment of the invention presents the absolute error distribution characteristics of the optimal model, verifying the stability and accuracy of the prediction results;

[0067] Figure 5 This diagram illustrates the core differences between neural networks and traditional algorithms. It compares the essential differences between neural networks and random forests, gradient boosting, and LightGBM from four dimensions: feature processing, relation capture, generalization ability, and optimization space.

[0068] Figure 6 This is a schematic diagram illustrating the training method of the delay time prediction model provided in an embodiment of the present invention. Detailed Implementation

[0069] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Embodiments of the present invention will be described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in the specification of the present invention means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0070] This embodiment involves the intersection of airport operation scheduling and machine learning technologies, focusing on feature engineering based on airport-route networks, multi-model comparative training with neural networks as the core, and accurate prediction of delay time. It is applicable to scenarios involving optimization of civil aviation airport operation efficiency and decision support for route scheduling. The design concept of this embodiment lies in proposing an airport ATFM delay time prediction model with neural networks at its core. By fusing network features, optimizing data processing, and conducting multi-model comparative verification, it fully leverages the superior characteristics of neural networks, overcoming the performance bottlenecks of traditional models, and achieving high-precision, high-generalization, and high-adaptability delay prediction, providing reliable technical support for airport scheduling decisions. This solution supports deployment in multiple environments including Windows and Linux, provides a parameter adjustment list and troubleshooting manual, and possesses scalability capabilities for architecture upgrades, multi-source data fusion, and lightweight model design.

[0071] The method flow provided in the embodiments of the present invention is as follows: Figure 1a , 1b As shown, it includes:

[0072] (a) Data loading and verification: Read the training / test / verification datasets of airports and routes. The datasets are divided into airport data and route data. Verify the integrity of core fields and automatically adapt the target variable columns.

[0073] The core fields for airport data include airport code, cumulative ATFM delay time, and basic airport operation attributes. The core fields for route data include departure airport, destination airport, number of flights on the route, cumulative ATFM delay time, flight distance, and flight time. Specifically, the core field integrity check includes: airport data must contain the "airport code" field, and route data must contain both the "departure airport" and "destination airport" fields. If any core field is missing, the process will terminate and a prompt to supplement the data will be displayed. The target variable adaptive matching mechanism is as follows: the preset target variable is "cumulative ATFMDelay (minutes)". If the preset target column is not found, the system will automatically scan fields containing the keyword "delay" or the English identifier "delay", and will prioritize the field corresponding to the delay time as the target variable.

[0074] (b) Enhanced Feature Engineering: Construct basic derived features and graph theory features. The basic derived features include route association features, flight volume features, delay association features, and distance features, totaling 12 core features. Among them, the feature robustness processing strategy used to enhance features includes: for the key fields of "route flight volume" and "route cumulative ATFM delay time", when the missing ratio is less than 30%, the average value of the same route type is used to fill the missing value, and when the missing ratio is greater than 30%, the value of 0 is used to fill the missing value, and the filling status is recorded.

[0075] (c) Graph Structure Construction and Indicator Extraction: A directed graph is constructed based on the relationship between the departure airport and the destination airport in the flight route data. Nine types of node-level graph theory feature indicators are calculated. The graph theory indicators include in-degree, out-degree, weighted in-degree, weighted out-degree, clustering coefficient, betweenness centrality, PageRank, compact centrality, and eigenvector centrality. In the directed graph, the nodes represent airports, and the directed edges represent flight routes. The attributes of the edges include the number of flights, delay time, and flight distance information of the route. The outlier handling strategy for graph theory indicators is as follows: for indicators that are prone to missing values ​​in compact centrality and eigenvector centrality, when the missing value is less than 10%, the mean of airports of the same size is used to fill the missing value. When the missing value is greater than 10%, 0 values ​​are used to fill the missing value. The effectiveness is screened in the subsequent feature selection stage.

[0076] (d) Data Preprocessing: A hierarchical strategy is used to handle missing values. The distribution of the target variable is optimized using Yeo-Johnson power transform, and the features are normalized using the RobustScaler standardization method. Key features are then selected using a feature selection method based on random forest. The layer missing value handling strategy is as follows: 0 values ​​are used to fill missing values ​​when the missing value ratio is higher than 30%; the mean is used to fill missing values ​​when the missing value ratio is between 10% and 30%; and the median is used to fill missing values ​​when the missing value ratio is lower than 10%. The feature selection threshold is set to "1.1 * mean", retaining features whose importance is 1.1 times higher than the mean. The L2 regularization parameter alpha of the neural network (MLP) is 0.0003, and the early stopping strategy sets the validation set ratio to 20%. Training stops if the validation set error does not decrease after 100 consecutive iterations.

[0077] (e) Multi-model training and optimization: Using neural networks (MLP) as the core model, three traditional algorithms, namely random forest, gradient boosting and LightGBM, are trained simultaneously as comparison models;

[0078] The neural network (MLP) adopts a three-layer hidden layer structure with 256, 128 and 64 neurons in the hidden layer, respectively. The activation function is ReLU, the optimizer is Adam, the regularization is L2 regularization, and the early stopping strategy is enabled during the training process.

[0079] The configuration parameters for the traditional algorithms are as follows: Random Forest uses 200 decision trees, a maximum depth of 15, and a minimum number of leaf node samples of 2; Gradient Boosting uses 200 base learners, a learning rate of 0.05, and a maximum depth of 8; LightGBM uses 200 base learners, 31 leaf nodes, and a subsample ratio of 0.8.

[0080] (f) Output and Validation: Output model evaluation metrics, detailed prediction results, and visualization results. The evaluation metrics include MAE, RMSE, and R², validating the model's prediction accuracy and engineering applicability. The model validity validation criteria are: R² ≥ 0.99 and MAE ≤ 50 minutes are considered excellent; R² ≥ 0.95 and MAE ≤ 100 minutes are considered acceptable. The visualization results include model metric comparison curves, neural network error distribution histograms, and feature importance heatmaps.

[0081] The following is combined Figure 2-5 The specific implementation and advantages of this embodiment will be further described in detail with corresponding experiments.

[0082] Data loading and verification process

[0083] The data required for this invention includes three types of datasets: training set, test set, and validation set. Each dataset is further divided into airport data and flight route data, stored in Excel format to ensure data compatibility. The core fields of the airport data include airport code (serving as the primary key for data association), cumulative ATFM delay time (the target variable for model prediction), and basic airport operational attributes. The core fields of the flight route data include departure airport, destination airport, flight volume, cumulative ATFM delay time, flight distance, and flight time. These fields constitute the basic data source for model training, ensuring the integrity of subsequent feature engineering and model training.

[0084] 1. Data loading and validation logic

[0085] The data loading process needs to automate path adaptation to ensure accurate file reading across different operating environments. After loading, the integrity of core fields must be verified: airport data must include the "Airport Code" field, and route data must include both "Departure Airport" and "Destination Airport" fields. If any core field is missing, the process should terminate and the user should be prompted to supplement the data to avoid subsequent graph structure construction failures or model training deviations due to missing data. Simultaneously, the data format must be validated to ensure that numeric fields (such as flight volume and delay duration) have no character-type outliers, and that date, encoding, and other fields have consistent formats, thus removing obstacles for subsequent data preprocessing.

[0086] 2. Adaptive matching of target variables

[0087] The model's default target variable is "cumulative ATFMDelay (minutes)". However, considering the potential differences in field naming across different data sources in practical applications, an adaptive matching mechanism is required. If the default target column is not found, the system will automatically scan airport data for fields containing the keyword "delay" or the English identifier "delay", prioritizing fields corresponding to delay times as the target variable. If no relevant field is found, an exception message will be displayed, ensuring that the model training objective is clear and preventing training failure due to a missing target variable. This adaptive mechanism improves the model's versatility, enabling it to adapt to airport operation datasets of different formats.

[0088] Enhanced feature engineering process

[0089] The basic derived features are generated based on the correlation between airport and route data, covering a total of 12 core features to comprehensively depict the operational status of the airport. See Table 1 for details.

[0090] Table 1

[0091]

[0092] These fundamental derived features describe the core attributes of airport operations from different dimensions, providing rich basic inputs for the model, especially providing diverse feature dimensions for neural networks, enabling them to capture complex relationships between features through multiple layers of neurons. Traditional algorithms are prone to the curse of dimensionality or feature redundancy when dealing with multi-dimensional features.

[0093] Considering that actual flight data may contain missing core fields (such as some routes not recording flight volume or delay duration), a robust imputation mechanism needs to be designed. For key fields such as "flight volume" and "cumulative ATFM delay duration," if the missing rate is less than 30%, the average value of the same route type is used for imputation; if the missing rate is greater than 30%, zero values ​​are used for imputation, and the imputation status is recorded in the log to ensure the continuity of feature calculation. This hierarchical processing method retains the information of valid data while avoiding the interference of a large number of missing values ​​on model training. It is especially suitable for the data integrity requirements of neural networks—compared to traditional algorithms, neural networks are more sensitive to outliers and missing values, and robust handling can significantly improve their training stability and prediction accuracy.

[0094] Graph structure construction and indicator extraction

[0095] 1. Directed Graph Construction

[0096] Based on the relationship between departure and destination airports in flight route data, a directed airport-flight graph is constructed. Each node represents an airport, and each directed edge represents a flight route. The attributes of each edge include core information such as flight volume, delay duration, and flight distance. For example, a flight route from airport A to airport B corresponds to an edge in the graph pointing from A to B, and the attribute values ​​of the edge represent the specific operational data of that route. This graph structure intuitively reflects the connectivity of airports within the flight route network, transforming isolated airport data into structured data with network relationships. This overcomes the shortcomings of traditional models that only consider the independent attributes of individual airports and ignore the influence of network interactions.

[0097] 2. Calculation of Node-Level Graph Theory Feature Indicators

[0098] Based on the constructed directed graph, nine core graph theory metrics are calculated to quantify the status and influence of each airport in the network, providing unique network characteristics for the model. Details are shown in Table 2.

[0099] Table 2

[0100]

[0101] These graph theory metrics supplement the core features of airports from a network perspective, forming a high-dimensional feature space together with the basic derived features. Compared to the limitations of traditional algorithms in handling high-dimensional features, neural networks (especially deep neural networks) possess powerful feature learning capabilities. Through multi-layered neural networks, they automatically uncover complex nonlinear relationships between features. The core principle lies in the fact that neural networks, through multi-layered linear transformations and the ReLU nonlinear activation function, achieve layer-by-layer abstraction and high-order combination of high-dimensional features. This allows them to automatically learn the implicit correlations between graph centrality metrics, flight volume features, delay features, and airport delay times. The model uses mean squared error as the optimization objective, iteratively updating network weights through the Adam optimizer and backpropagation algorithm, combined with L2 regularization and early stop strategies to avoid overfitting, thus accurately capturing nonlinear mapping relationships that traditional algorithms cannot express. Compared to the limitations of traditional machine learning, which can only capture low-order, linear, or piecewise linear relationships, neural networks, with their powerful high-dimensional feature learning and nonlinear fitting capabilities, can fully explore the intrinsic connection between graph theory features and delay times. This is the key reason why the prediction accuracy of this model is significantly better than traditional algorithms.

[0102]

[0103] Where i represents the node index of the current layer, for example, the i-th neuron in the l-th layer; j represents the node index of the previous layer, for example, the j-th neuron in the (l-1)-th layer; and l represents the layer index, for example, the l-th layer of the network. This represents the weighted input (pre-activation value), the original weighted summation result of the i-th neuron in layer l before activation; This represents the connection weight, the weight parameter connecting the j-th node in the previous layer to the i-th node in the current layer; This represents the final output of the j-th neuron in layer l after it has been activated by the function. This represents the final output of the i-th neuron in the l-th layer after passing through the activation function; The bias term represents the fixed offset added to the current neuron to fit the data translation; N represents the total number of samples, the total number of samples in the dataset (e.g., there are a total of N flight records). Represents the true label, and the true target value of the k-th sample; This represents the model's predicted value, specifically the prediction result for the k-th sample output by the model. This represents the regularization coefficient, or hyperparameter, used to balance the original loss and the regularization term. The larger the value, the heavier the penalty for excessive weights. This represents all weight parameters in the weight vector model; This represents the learning rate, which controls the step size for each weight update. q represents the first-order moment estimate, the exponential moving average of the gradient (momentum term), which helps accelerate convergence; q represents the second-order moment estimate, the exponential moving average of the squared gradient, which is used to adaptively adjust the learning rate. (Epsilon) represents the minimum value. It is used to prevent smoothing terms with a denominator of 0, and is typically taken as 10⁻⁸.

[0104] 3. Handling outliers in indicators

[0105] In the calculation of graph theory metrics, some metrics (such as tight centrality) may fail to be calculated due to disconnected graph structures (e.g., some small airports are only connected to a few airports by air routes), resulting in missing values. To address this, a differentiated outlier handling strategy is adopted: for metrics prone to missing values, such as tight centrality and eigenvector centrality, if the missing rate is less than 10%, the mean of airports of similar size (grouped by the total number of air routes) is used to fill the gaps; if the missing rate is greater than 10%, zero values ​​are used for filling, and validity screening is performed in the subsequent feature selection stage. This approach ensures the integrity of the features while avoiding interference from invalid metrics on neural network training, thus ensuring the quality of the input features.

[0106] Data preprocessing stage

[0107] 1. Stratified processing of missing values

[0108] The core objective of data preprocessing is to adapt to the training characteristics of neural networks and improve the stability and convergence speed of the model. A hierarchical processing strategy is adopted for missing values ​​in the feature matrix, as shown in Table 3.

[0109] Table 3

[0110]

[0111] This layered processing method ensures data integrity while preserving effective information to the greatest extent. Compared with the single-filling method commonly used in traditional algorithms, it is more adaptable to the sensitivity of neural networks to data distribution.

[0112] 2. Optimization of the distribution of the target variable

[0113] Airport ATFM delay time data typically exhibits a significant skewed distribution (most airports have short delay times, while a few have extremely long delay times). This distribution characteristic can lead to gradient vanishing or slow convergence during model training, particularly affecting neural networks. To address this, the Yeo-Johnson power transform is used to optimize the distribution of the target variable. This transform supports data containing zero and negative values, effectively correcting the skewed distribution and bringing the target variable closer to a normal distribution. The optimized target variable not only improves the training convergence speed of the neural network but also reduces the interference of extreme values ​​on the model's prediction results, thus improving prediction accuracy. While traditional algorithms can also benefit from distribution optimization, their optimization effect is far inferior to that of neural networks because they struggle to capture nonlinear relationships.

[0114] 3. Feature Standardization and Screening

[0115] Because the dimensions of basic derived features and graph theory features differ significantly (e.g., flight volume ranges from tens to tens of thousands, while clustering coefficients range from 0 to 1), directly inputting them into the model can lead to an imbalance in weight distribution, particularly affecting the gradient descent process of the neural network. Therefore, the RobustScaler normalization method is used to normalize the features. This method, based on the median and quartiles, is robust to outliers and can transform features with different dimensions into the same scale, ensuring balanced weight updates for each feature during neural network training.

[0116] After standardization, a feature selection method based on random forest is used to screen key features, setting the screening threshold to "1.1*mean" (i.e., retaining features whose importance is 1.1 times higher than the mean) and eliminating redundant features. This process can reduce feature dimensionality, improve model training efficiency, and retain core effective features, avoiding overfitting of the neural network due to feature redundancy. Compared with traditional algorithms, neural networks have more parameters and are more susceptible to the influence of redundant features, making reasonable feature selection particularly important.

[0117] Multi-model training and optimization

[0118] 1. Model Configuration and Training Logic

[0119] This invention constructs four types of models for comparative training: Neural Network (MLP), Random Forest (RF), Gradient Boosting (GB), and LightGBM (LGB). Among them, Neural Network is the core model, and the other three types are comparative models to highlight their advanced features.

[0120] (1) Configuration and training of neural networks (MLP)

[0121] The neural network employs a three-layer hidden layer structure with 256, 128, and 64 neurons respectively. This structure ensures the model's feature learning ability while avoiding overfitting caused by excessive complexity. The ReLU activation function is chosen, as its non-linear characteristics effectively capture complex relationships between features. Compared to the traditional Sigmoid function, ReLU alleviates the vanishing gradient problem and improves the training effect of deep networks. The Adam optimizer is selected, employing an adaptive learning rate strategy that dynamically adjusts the learning rate based on gradient changes, resulting in faster convergence and stronger stability than the traditional SGD optimizer. L2 regularization (parameter alpha = 0.0003) is used to suppress model overfitting. An early stopping strategy is implemented during training, setting the validation set ratio to 20%. Training stops if the validation set error does not decrease after 100 consecutive iterations, avoiding ineffective iterations.

[0122] The training logic of neural networks is to calculate predicted values ​​through forward propagation and update the weights of each layer through backpropagation, minimizing the mean squared error between the predicted and actual values. Due to its deep structure and nonlinear activation function, it can capture complex nonlinear relationships between high-dimensional features—a core advantage that traditional algorithms cannot match. Traditional algorithms such as random forests and gradient boosting are essentially ensemble models based on decision trees, which can only capture linear or simple nonlinear relationships between features and are difficult to handle the high-dimensional complex correlation between "network features + operational features" in airport delay prediction.

[0123] (2) Traditional algorithm configuration and training

[0124] To fully highlight the advantages of neural networks, three mainstream traditional algorithms are trained simultaneously, with specific configurations shown in Table 4.

[0125] Table 4

[0126]

[0127] All three types of traditional algorithms employ default optimization strategies to ensure fairness in the comparison.

[0128] 2. Model Prediction and Performance Comparison

[0129] After all models are trained, predictions are made on the test and validation sets. The neural network needs to perform an inverse power transform on the prediction results to restore them to the true time scale of the delay. The results are then analyzed using MAE (Mean Absolute Error), RMSE (Root Mean Square Error), and R-squared values. 2 The performance was evaluated using three indicators: (coefficient of determination) and the results are shown in Table 5.

[0130] Table 5

[0131]

[0132] like Figure 2, 4 As shown in Figure 5, the comparison results clearly demonstrate that the neural network far surpasses the traditional algorithm in all metrics: MAE is only 1 / 3 to 1 / 5 of the traditional algorithm, RMSE is only 1 / 4 to 1 / 5 of the traditional algorithm, and R... 2 The results are closer to 1, significantly improving prediction accuracy. The core reason is that neural networks can deeply explore the nonlinear relationships between high-dimensional features, while traditional algorithms, limited by model structure, struggle to capture the complex relationships between airport delay times and network and operational features. In addition, the adaptive learning rate and regularization mechanisms of neural networks make them more generalizable, with smaller performance differences on test and validation sets and better stability.

[0133] 3. The advantages and future potential of neural networks

[0134] Compared to traditional algorithms, the advantages of neural networks are mainly reflected in:

[0135] (1) Algorithm advancement

[0136] High-dimensional data processing capability: It can effectively integrate basic features and graph theory features, avoiding the curse of dimensionality, while traditional algorithms are prone to feature redundancy or information loss;

[0137] Non-linear relationship capture: accurately depicts the complex relationship between airport delay time and multiple factors, without the need to manually construct feature combinations, and its flexibility and accuracy far exceed those of traditional algorithms;

[0138] Stronger generalization ability: Through deep structure and regularization mechanism, it performs more stably on airport datasets of different sizes and operational characteristics, and has wider adaptability.

[0139] (2) Potential for future improvement

[0140] The modular structure and scalability of neural networks give them enormous potential for future optimization, which is difficult for traditional algorithms to match.

[0141] Architecture upgrade: The current MLP is the basic neural network. In the future, CNN (convolutional neural network) can be introduced to extract local correlation information of features, or LSTM (long short-term memory network) can be incorporated into time series features (such as historical delay trends) to further improve prediction accuracy.

[0142] Multi-source data fusion: External features such as weather, airspace restrictions, and holidays can be incorporated. Through the feature fusion capabilities of neural networks, more key factors affecting delays can be discovered. Traditional algorithms are prone to conflicts when fusing multi-source heterogeneous data.

[0143] Optimization strategy upgrade: Advanced techniques such as adaptive learning rate scheduling (e.g., cosine annealing strategy), regularization enhancement (e.g., Dropout+L2 combination), and attention mechanism can be adopted to improve model training efficiency and generalization ability.

[0144] Lightweight model: By using techniques such as model compression and quantization, the model size can be reduced while maintaining accuracy, making it suitable for deployment on edge devices and expanding application scenarios. Although traditional algorithms are lightweight, their accuracy improvement potential is limited, making it difficult to balance accuracy and deployment costs.

[0145] Results Output and Validation

[0146] 1. Saving multi-dimensional results

[0147] After the model is trained, it outputs multi-dimensional results to meet different application needs:

[0148] Model evaluation metrics: The test set and validation set metrics (MAE, RMSE, R) of the four types of models. 2 The results are summarized and saved to an Excel file for easy and intuitive performance comparison;

[0149] Detailed prediction results: The test set and validation set predicted values, actual values, absolute error, and relative error of the neural network (optimal model) are saved to a CSV file to support subsequent error analysis and outlier detection;

[0150] Visualization results: Plotting model performance comparison curves, neural network error distribution histograms, feature importance heatmaps, etc., to intuitively present model performance and feature contribution.

[0151] 2. Results Validation and Decision Support

[0152] In practical applications, the predictions from neural networks can be directly used for scenarios such as route scheduling optimization (e.g., adjusting flight takeoff and landing sequences based on predicted delay times) and airport resource allocation (e.g., optimizing ground staff allocation based on peak delay periods). Compared to traditional algorithms, neural network predictions are more accurate, providing more reliable support for decision-making; furthermore, their excellent scalability allows them to continuously iterate with data accumulation and technological advancements, maintaining a long-term technological lead.

[0153] The solution provided in this embodiment optimizes the entire process of data loading, feature engineering, graph structure construction, data preprocessing, multi-model training, and result verification, and uses neural network (MLP) as the core algorithm to achieve accurate prediction of delay time, thereby improving the accuracy of airport ATFM delay time prediction. Specifically, the approach treats the airport-flight route as a directed graph, extracting graph theory features such as in-degree and betweenness centrality to compensate for the shortcomings of traditional models that ignore network connections, providing richer feature inputs for the neural network. It employs hierarchical missing value imputation, Yeo-Johnson power transform, and RobustScaler normalization to adapt to the skewed distribution and outlier interference of delay data, accurately matching the training requirements of the neural network. With a neural network (MLP) at its core, it achieves an R2 of 0.9999 on the test set and a MAE of only 18.66 minutes. Compared to traditional algorithms such as random forests and gradient boosting, it has advantages in capturing nonlinear relationships and processing high-dimensional data, improving prediction accuracy by more than 30%. Furthermore, the neural network possesses strong scalability, continuously improving performance by introducing deep learning architectures, fusing multi-source data, and optimizing network structure, while traditional algorithms are limited by model principles and have a lower optimization ceiling. Finally, it boasts strong engineering practicality, supporting deployment in multiple environments such as Windows and Linux, providing parameter adjustment lists and troubleshooting manuals to adapt to the landing needs of airports of different sizes. The modular nature of the neural network also facilitates rapid iteration and upgrades.

[0154] In summary, this embodiment treats the airport-airline system as a directed graph, extracts node-level graph theory features, and constructs a two-dimensional feature system of "basic operational features + network association features." It employs robust data processing strategies such as hierarchical missing value imputation, Yeo-Johnson power transform, and RobustScaler standardization to accurately adapt to the training requirements of neural networks. Using a neural network (MLP) as the core algorithm, it is simultaneously trained and compared with traditional algorithms such as random forest, gradient boosting, and LightGBM. Experimental results show that the model's prediction accuracy is more than 30% higher than traditional algorithms, significantly improving the accuracy of airport ATFM delay time prediction. Furthermore, it possesses broad future optimization potential, including architecture upgrades, multi-source data fusion, and model lightweighting, effectively supporting airport route scheduling optimization and resource allocation decisions, and adapting to the operational needs of airports of different sizes.

[0155] This invention discloses a method for predicting airport ATFM (Airport Arrival and Flight Time) delays by integrating network features. This method innovatively abstracts the airport-route system into a directed graph structure. By extracting node-level graph theory features (such as centrality, clustering coefficient, and weighted degree) and combining them with basic airport operational features (flight volume, delay duration, route distance, etc.), a two-dimensional feature system of "basic operational features + network correlation features" is constructed. To address data quality issues, a combined data processing scheme is adopted, employing a hierarchical missing value imputation strategy (differentiated processing based on the proportion of missing values), Yeo-Johnson power transformation (optimizing the distribution of the target variable), and RobustScaler standardization (enhancing the robustness of outliers), precisely adapting to the training data requirements of neural networks. During the model training phase, a multilayer perceptron (MLP) neural network is used as the core algorithm, while classic machine learning algorithms such as random forest, gradient boosting, and LightGBM are selected for comparative training. Experimental results show that compared with traditional algorithms, the proposed method improves prediction accuracy by more than 30%, significantly enhancing the accuracy and reliability of airport ATFM delay prediction and providing more accurate data support for airport operation scheduling decisions.

[0156] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting airport ATFM delay time by incorporating network features, characterized in that, include: S1. Obtain the airport dataset, which includes airport data and flight route data; S2, generating basic derived features and graph theory features; S3. Construct a directed graph based on the relationship between the departure airport and the destination airport in the route data, and calculate the node-level graph theory characteristic index; S4. Preprocess the features obtained in S2 to obtain key features; S5. Input the key features obtained in S4 into the trained delay time prediction model and output the predicted value of the cumulative ATFM delay time of the airport. By comparing the predicted value with the actual ATFM delay time of the airport, the delay time prediction result is obtained. The quantitative parameters used to represent the predicted delay time include: mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²).

2. The method according to claim 1, characterized in that, The basic derived features cover four dimensions: route association features, flight volume features, delay association features, and distance features. Specifically, these include total number of routes, average number of departing flights, total number of departing flights, standard deviation of departure flight volume, average number of arriving flights, total number of arriving flights, standard deviation of arrival flight volume, departure-arrival ratio, average departure delay, total departure delay, departure delay rate per flight, and average departure / arrival distance. Graph theory features are node-level metrics extracted from airport-route directed graphs, including: in-degree, out-degree, weighted in-degree, weighted out-degree, clustering coefficient, betweenness centrality, compact centrality, PageRank, and eigenvector centrality. S1 also includes: Verify the completeness of the core fields of the dataset. The core fields for airport data include the "airport code" field, and the core fields for route data include the "departure airport" and "destination airport" fields. If so, the target variable column will be automatically adapted.

3. The method according to claim 2, characterized in that, The automatically adaptable target variable column includes: Retrieve a preset target variable from the dataset, the preset target variable including: the "cumulative ATFMDelay (minutes)" field; If the preset target variable is not found, the fields in the dataset related to the delay time are identified. These fields include fields with the keyword "delay" or the English word "delay". Fields corresponding to the delay time are selected as the target variable.

4. The method according to claim 1, characterized in that, Also includes: The missing value of key fields in the route data is detected. If the missing value is less than 30%, the average value of the same route type is used to fill the missing value. If the missing value is greater than 30%, the value of 0 is used to fill the missing value. The key fields in the route data include: "Number of flights on the route" and "Cumulative ATFM delay time of the route".

5. The method according to claim 1, characterized in that, S3 includes: Calculate node-level graph theory metrics, including the following types: in-degree, out-degree, weighted in-degree, weighted out-degree, clustering coefficient, betweenness centrality, PageRank, compact centrality, and eigenvector centrality. After processing outliers of the graph theory metrics, construct a directed graph, where nodes represent airports and edges represent flight routes. The attribute information of the edges includes: flight volume, delay duration, and flight distance. The methods for handling outliers in graph theory metrics include: detecting the degree of missing values ​​for graph theory metrics that are prone to missing values, including: compact centrality and eigenvector centrality; if the missing value is less than 10%, the mean of airports of the same size is used to fill the missing value, and if the missing value is greater than 10%, 0 values ​​are used to fill the missing value.

6. The method according to claim 1, characterized in that, S4 include: A hierarchical strategy is used to handle missing values; Optimize the distribution of the target variable using Yeo-Johnson power transform; The features were normalized using the RobustScaler standardization method. Then, key features are selected using a feature selection method based on random forest.

7. The method according to claim 6, characterized in that, The method of using a hierarchical strategy to handle missing values ​​includes: Calculate the missing proportion ,in, This represents the i-th missing index (tight centrality, eigenvector centrality). Indicates the number of missing values ​​for the indicator. This represents the total number of samples. Missing values ​​are then processed according to stratified imputation rules, which include: when the missing rate is < 10%, the mean of airports of the same size is used for imputation. The imputation process is represented as follows: ,in, This indicates grouping airports of similar size (small / medium / large); when the missing value is ≥ 10%, it is filled with 0 values, and the filling process is represented as follows: ; The method of optimizing the distribution of the target variable through Yeo-Johnson power transform to make the target variable closer to a normal distribution and improve the prediction accuracy of the neural network is as follows: ,in, This represents the original target variable (delay time). λ represents the transformed variable, and λ represents the optimal transformation parameter (automatically learned from the data). The RobustScaler standardization method is used to normalize the features; ,in, This represents the result of the normalization process, where median(X) represents the feature median, X represents the feature dimension, and x represents the original feature value. That is, the interquartile range = 75th percentile - 25th percentile; the advantage of using the RobustScaler standardization method to normalize features is that it is not affected by extreme outliers, making it very suitable for data such as airport delays; The selection of key features using a random forest-based feature selection method includes: The feature importance score is calculated and expressed as: ,in, The importance of the j-th feature is represented by T, where T represents the number of decision trees. This indicates the decrease in impurity (such as the Gini coefficient) brought about by feature j on tree t. Let represent the weight coefficients of the t-th decision tree; Determine the feature selection threshold based on feature importance scores: Where M represents the total number of original features; retain > The features are used as key features.

8. The method according to claim 6 or 7, characterized in that, The hierarchical strategy for handling missing values ​​includes: The features obtained in S2 are tested for missing values. When the missing ratio is higher than 30%, 0 values ​​are used for filling. When the missing ratio is between 10% and 30%, the mean is used for filling. When the missing ratio is lower than 10%, the median is used for filling. The feature selection threshold is 1.1*mean, which means that features with importance higher than 1.1 times the mean are retained.

9. The method according to claim 1, characterized in that, The delay time prediction model is a neural network (MLP) with a three-layer hidden layer structure. The number of neurons in the three hidden layers are 256, 128 and 64, respectively. The activation function is ReLU, the optimizer is Adam, the regularization is L2 regularization, and the early stopping strategy is enabled during the training process. The configuration parameters are as follows: the random forest uses 200 decision trees, the maximum depth is 15, and the minimum number of leaf node samples is 2. Gradient boosting uses 200 base learners, a learning rate of 0.05, and a maximum depth of 8. LightGBM uses 200 base learners, 31 leaf nodes, and a subsample ratio of 0.

8. The L2 regularization parameter alpha = 0.0003, and the early stopping strategy sets the validation set ratio to 20%. If the validation set error does not decrease after 100 consecutive iterations, training is stopped.

10. The method according to claim 1, characterized in that, Backend processing methods for the evaluation metrics output by the delay prediction model include: Airport ATFM delays are classified according to assessment indicators. Among them, R2≥0.99 and MAE≤50 minutes are considered excellent, and R2≥0.95 and MAE≤100 minutes are considered acceptable.

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