A method and system for aviation flow prediction and uncertainty quantification based on MSGF-Net

Abstract

This invention relates to the field of air traffic forecasting technology, and in particular to an air traffic forecasting and uncertainty quantification method and system based on MSGF-Net. The method includes: preprocessing air trajectory data and extracting traffic data; constructing and normalizing input features based on the preprocessed air trajectory data and extracted traffic data; constructing an MSGF-Net-based traffic forecasting model; optimizing and training the constructed traffic forecasting model based on a loss function; predicting the input features based on the trained traffic forecasting model; and outputting the prediction result. This invention, through a parallel multi-scale encoder and gating fusion mechanism of TCN and GRU, solves for the first time the aforementioned deficiency of standard models in capturing multi-scale temporal patterns, greatly improving the model's generalization ability.

Description

Technical Field

[0001] This invention relates to the field of air traffic forecasting technology, and in particular to an air traffic forecasting and uncertainty quantification method and system based on MSGF-Net. Background Technology

[0002] With the rapid development of the air transport industry, air traffic flow has continued to grow, making accurate forecasting of air traffic flow a crucial link in ensuring flight safety, improving airspace utilization, and optimizing air traffic control resource allocation. Existing air traffic flow forecasting methods mainly include traditional methods based on statistical analysis and modern methods based on machine learning. Traditional methods, such as time series analysis (ARIMA, etc.), have limitations in handling complex spatiotemporal characteristics and nonlinear relationships, making them difficult to adapt to the suddenness and variability of air traffic flow. While some machine learning-based models have improved forecast accuracy, they still have shortcomings in feature fusion, model generalization ability, and adaptability to zero-inflation and long-tail distributions of traffic data. Furthermore, existing methods often rely on single indicators for model evaluation, lacking quantitative analysis of the reliability of forecast results, resulting in limited interpretability and practicality of the models in actual air traffic control decision-making.

[0003] Traditional DeepAR models, designed specifically for time-series data, possess the core advantage of autonomously learning long-term dependencies in time-series data through a recurrent neural network (RNN) structure. However, this standard RNN architecture suffers from limited receptive field and vanishing gradients when processing air traffic data with multiple seasonalities and cross-scale dependencies (e.g., a mixture of short-term fluctuations at the minute level and long-term trends at the daily / weekly level). This makes it difficult to efficiently capture multi-scale patterns simultaneously, thus limiting the model's generalization ability. DeepAR models, on the other hand, output confidence intervals for predictions based on probability distribution models, a characteristic highly compatible with the "strong temporal correlation, high dynamic fluctuations, and need for risk quantification" of air traffic prediction. However, the application of traditional DeepAR models in air traffic prediction scenarios still suffers from insufficient adaptability: First, they fail to preprocess outliers in air traffic data, making the model susceptible to interference from abnormal data during training and reducing generalization ability. Second, they do not fully utilize their probabilistic prediction capabilities to provide uncertainty quantification and risk assessment support for air traffic control decisions.

[0004] Furthermore, existing methods primarily rely on single-point predictions in their model evaluation systems, lacking quantitative analysis of the uncertainty of prediction results. They fail to provide prediction confidence intervals, risk probabilities, and reliability assessments, making it difficult for air traffic controllers to make differentiated decisions based on prediction credibility. Consequently, the models have limited guiding value in actual air traffic control risk management. Therefore, there is an urgent need for an air traffic flow prediction method based on a multi-scale gating fusion framework that integrates spatiotemporal correlation features, optimizes abnormal data processing mechanisms, strengthens uncertainty quantification functions, and constructs a multi-dimensional error assessment system. This method would meet the multiple requirements of actual air traffic control decision-making regarding prediction accuracy, reliability, and risk perception. Summary of the Invention

[0005] This invention proposes an autoregressive probabilistic prediction architecture that integrates multi-scale temporal data and gating mechanisms, named Multi-Scale Gated Fusion Network (MSGF-Net).

[0006] To address the limitations of existing air traffic forecasting methods, such as insufficient model generalization ability and lack of quantitative analysis of forecast uncertainty, which leads to limited risk management capabilities, this invention provides an air traffic forecasting and uncertainty quantification method and system based on MSGF-Net. By constructing a spatiotemporal fusion dataset and employing an MSGF-Net model with a log-likelihood loss function based on Poisson distribution for probabilistic prediction, accurate prediction of future air traffic flow and comprehensive quantification of uncertainty are achieved, providing risk perception capabilities for air traffic control decision-making.

[0007] Firstly, the present invention provides an air traffic forecasting and uncertainty quantification method based on MSGF-Net, which adopts the following technical solution:

[0008] A method for air traffic forecasting and uncertainty quantification based on MSGF-Net, comprising:

[0009] Flight trajectory data preprocessing and traffic flow data extraction;

[0010] Input features are constructed and normalized based on preprocessed flight trajectory data and extracted traffic data;

[0011] Construct a traffic prediction model based on MSGF-Net;

[0012] The traffic prediction model is optimized and trained based on the loss function;

[0013] Predict input features based on the trained traffic prediction model;

[0014] Output the prediction results.

[0015] Furthermore, the aviation trajectory data preprocessing and traffic flow data extraction include processing the acquired raw radar trajectory dataset. ,in It is a set of flight identifiers, and each flight's trajectory ,in This indicates that the trajectory contains One sampling point, For timestamps, Let be the three-dimensional spatial coordinates, denoted as . The original trajectory data is downsampled over time, and then a two-stage filtering strategy is adopted to improve matching efficiency through spatial domain partitioning and association. First, coarse-grained filtering is performed based on all predefined spatial domain regions. The minimum bounding box is calculated to quickly coarsely filter the downsampled trajectory data. Then, spatial indexing and shapely polygon matching algorithms are used on the coarsely filtered data to accurately match each trajectory point to its corresponding spatial region. Within this area, region labels are added to the trajectory points; finally, traffic statistics are performed in fixed time slices. Divide the day into time slices to obtain a set of time slices. In each time slice Within, through statistical airspace The number of flights within a time slice represents the airspace traffic within that time slice. Within, through statistical airspace The number of unique aircraft identification codes within a given time slice is used to calculate airspace traffic during that time slice. After the statistics are completed, a continuous-time index covering the entire period is generated, and this index is used to analyze the traffic sequence. Resampling is performed to obtain the spatial flow sequence within the time slice. The statistical methods for airspace traffic include defining airspace traffic as:

[0016] ,

[0017] in The indicator function is defined as follows:

[0018] .

[0019] Furthermore, the input feature construction and normalization based on preprocessed flight trajectory data and extracted traffic data includes decomposing and normalizing timestamps using periodic encoding, including minute encoding, hour encoding, weekday encoding, and date encoding. By mapping individual time features onto a two-dimensional ring, the model can unambiguously understand the continuity and periodicity of time. Then, for historical traffic features, past... Flow sequence of time slices For traffic statistics characteristics, based on past time windows The mean and variance are calculated and expressed as follows:

[0020] ,

[0021] ,

[0022] For traffic trend characteristics, the slope of the historical traffic series is calculated and expressed as: .

[0023] Furthermore, the construction of the traffic prediction model based on MSGF-Net includes constructing an autoregressive probabilistic prediction architecture MSGF-Net that integrates multi-scale temporal series and gating mechanisms as the traffic prediction model. This involves optimizing the single RNN structure in the standard DeepAR model, preprocessing the input dynamic covariates and historical targets in the feature embedding; then replacing the single RNN with a multi-scale temporal encoder, employing a parallel dual-branch architecture to simultaneously capture short-term fluctuations and long-term trends in traffic. Branch A is a short-term dependent RNN, which... and The data is fed into the GRU (Government Regulator) layer to capture high-frequency, localized timing dependencies and output the data. Branch B is a long-term dependency on TCN, which will... and The data is fed into the Temporal Convolutional Network (TCN) layer for causal convolution and dilated convolution to efficiently capture long-term traffic patterns and output the results. Next, a gating fusion mechanism is used to replace feature splicing to fuse the above multi-scale temporal information. First, short-term features are... and long-term characteristics To splice: ; calculate the fusion gate through the gate control unit : , Weights between 0 and 1, representing the final fused features. Obtained through gating weighting: Finally, a probability output layer is constructed to integrate the fused multi-scale temporal features. Feed to the output MLP.

[0024] Furthermore, the construction of the MSGF-Net-based traffic prediction model also includes, to address the gradient degradation problem in deep network training, introducing residual connections and layer normalization mechanisms in the construction of branches A and B of the multi-scale temporal encoder. Specifically, at the outputs of the TCN and GRU layers, the input signal is added to the processed output signal, as shown in the following formula: This is used to ensure the integrity of information during the transmission of multi-scale features, so that the model can maintain convergence stability when stacking more layers.

[0025] Furthermore, the optimization training of the constructed traffic prediction model based on the loss function includes maximizing the log-likelihood of the observed historical traffic data under the conditional probability distribution given by the prediction model, and modeling the data using a Poisson distribution. First, the probability mass function (PMF) of the Poisson distribution is defined as:

[0026] ,in It is the observed actual flow rate; The mean of the distribution is given, and then the negative log-likelihood loss function is calculated, expressed as:

[0027] ,

[0028] in For the first Each sample in time slice Real traffic, This represents the conditional probability distribution output by the MSGF-Net model. This is a historical flow sequence over the past 15 time slices. , , , These are the normalized time features for hours, days of the week, dates, and minutes, respectively. The model parameters are then used; subsequently, the probability distribution is output and uncertainty is quantified, resulting in the conditional probability distribution for the MSGF-Net model. N prediction samples are generated through Monte Carlo sampling. Based on the sample, the predicted mean, predicted standard deviation, confidence interval, and predicted quantile are calculated, where the predicted mean is expressed as: The predictive standard deviation is expressed as: The confidence interval is expressed as: ,in At the significance level, the predicted quantile is , ∈[0,1] represents the quantile probability.

[0029] Furthermore, the optimization training of the constructed traffic prediction model based on the loss function also includes using a rolling origin prediction strategy for model evaluation to prevent the model from seeing future data during training and to accurately simulate the rolling prediction scenario in actual applications. First, an initial training set and a continuous test set are set. The model is trained and predictions are made using the initial training set. Based on the window sliding mechanism, the window is slid forward by one unit. The model is retrained and predictions are made using the new training set. The training is repeated iteratively until all available test data is traversed. The final evaluation metric is calculated by summarizing the prediction results of all test sets.

[0030] Furthermore, the prediction of input features based on the trained traffic prediction model includes prediction of spatial features. Based on real-time radar trajectory data and a trained MSGF-Net model, for future... Probabilistic prediction of spatial traffic within a time slice is performed, and a conditional probability distribution is output:

[0031] ,

[0032] The final traffic prediction is a statistic extracted from the distribution. During the training phase, different training subsets are validated using different random seed sliding windows, and training is performed independently. One MSGF-Net model, in the application phase. Each model simultaneously predicts the future. Predictions are made for each time slice, and each slice generates its own prediction. Based on a Monte Carlo sample, the final prediction result is for all The results were obtained by summarizing and statistically analyzing a sample. When dividing a spatial domain into sub-spatial domains, each sub-spatial domain... Based on real-time radar trajectory data and a trained MSGF-Net model, predict future... Probabilistic prediction of airspace traffic within a time slice is performed, and a conditional probability distribution is output.

[0033] Furthermore, the prediction of input features based on the trained traffic prediction model also includes employing a Monte Carlo sampling ensemble strategy when generating prediction results. Specifically, for the probability distribution parameters output by the model at each time step, the system extracts data from the distribution... Generated after random sampling One possible future traffic value, for For each flow value, quantile statistics are calculated at each time step. First, the 50% quantile is extracted as the final flow prediction value to obtain a more robust prediction result than the mean. Then, the 10% and 90% quantiles are extracted to construct confidence intervals, which visually demonstrate the range of uncertainty in the prediction.

[0034] Secondly, an air traffic forecasting and uncertainty quantification system based on MSGF-Net includes:

[0035] The data acquisition module is configured to perform preprocessing of aviation trajectory data and extraction of traffic data.

[0036] The feature construction module is configured to construct and normalize input features based on preprocessed aviation trajectory data and extracted traffic data;

[0037] The model building module is configured to build a traffic prediction model based on MSGF-Net;

[0038] The training module is configured to optimize and train the constructed traffic prediction model based on the loss function.

[0039] The prediction module is configured to predict input features based on the trained traffic prediction model and output the prediction results.

[0040] Thirdly, the present invention provides a computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the aforementioned MSGF-Net-based air traffic forecasting and uncertainty quantification method.

[0041] Fourthly, the present invention provides a terminal device, including a processor and a computer-readable storage medium, wherein the processor is used to implement various instructions; the computer-readable storage medium is used to store multiple instructions, the instructions being adapted to be loaded and executed by the processor to provide the described method for predicting air traffic flow and quantifying uncertainty based on MSGF-Net.

[0042] In summary, the present invention has the following beneficial technical effects:

[0043] This invention abandons the single RNN architecture in standard DeepAR and innovatively proposes the MSGF-Net architecture. Through the parallel multi-scale encoder and gating fusion mechanism of TCN and GRU, it solves for the first time the aforementioned deficiency of the standard model in capturing multi-scale temporal patterns, greatly improving the model's generalization ability.

[0044] To address the common issues of zero inflation (i.e., zero traffic for a large number of periods) and long-tailed distribution in air traffic data, this invention cleverly introduces the Poisson distribution as the output layer of the model and selects the negative log-likelihood based on the Poisson distribution as the loss function. This design enables the model to effectively handle such non-Gaussian distributed data characteristics, greatly improving the accuracy and robustness of the prediction results.

[0045] This invention achieves comprehensive quantification of prediction uncertainty, filling the gaps in traditional point prediction methods. Addressing the shortcomings of existing prediction methods, which are mostly point predictions and lack quantitative analysis of result reliability, this invention provides complete probabilistic prediction capabilities. The model output is not a single predicted value, but a complete probability distribution. Based on the quantified probability distribution of uncertainty, a wealth of prediction indicators are calculated, including the prediction mean (as a reference for point prediction), prediction confidence interval, prediction standard deviation (or variance), and even the probability of extreme events where future traffic exceeds key thresholds.

[0046] This in-depth quantification of uncertainty provides unprecedented risk assessment basis for air traffic control decision-making. The results of the implementation example show that the model achieved an actual coverage rate of 99.44% at a 90% confidence level, strongly demonstrating the high reliability of its uncertainty quantification results and significantly enhancing the model's guiding value in actual air traffic control risk management. Attached Figure Description

[0047] Figure 1 This is the overall flowchart of the present invention as described in Embodiment 1 of the present invention.

[0048] Figure 2 This is a model architecture diagram of Embodiment 1 of the present invention.

[0049] Figure 3 This is a visualization diagram of the 15-minute airspace traffic prediction results of Embodiment 1 of the present invention.

[0050] Figure 4 This is a schematic diagram of confidence interval coverage analysis in Embodiment 1 of the present invention.

[0051] Figure 5 This is a schematic diagram of the uncertainty analysis of the prediction error distribution in Embodiment 1 of the present invention.

[0052] Figure 6 This is a schematic diagram of MAE uncertainty analysis at different time periods in Embodiment 1 of the present invention.

[0053] Figure 7 This is a schematic diagram illustrating the analysis of the change in prediction uncertainty over time in Embodiment 1 of the present invention. Detailed Implementation

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

[0055] Example 1

[0056] Reference Figure 1 This embodiment of an air traffic forecasting and uncertainty quantification method based on MSGF-Net includes:

[0057] (1) Preprocessing of flight trajectory data and extraction of traffic flow data:

[0058] a) Data cleaning and anomaly handling

[0059] 1) Data cleaning and downsampling: The radar trajectory reports sent by the aircraft during flight were used as the original radar trajectory dataset. ,in It is a set of flight identifiers, and each flight's trajectory ,in This indicates that the trajectory contains One sampling point, For timestamps, For three-dimensional spatial coordinates, abbreviated as The original trajectory data is downsampled over time to reduce data density; for example, trajectory points within a specific time window are filtered and retained for each time unit (e.g., per minute).

[0060] 2) Abnormal traffic data identification and smoothing:

[0061] After step c) traffic statistics and before step (2) feature construction, this invention also includes an anomaly data processing step to address the outlier interference problem mentioned in the background art. This step specifically includes:

[0062] (1) Anomaly identification: The statistical 3-Sigma principle (or Z-score) is used to analyze the flow sequence. Perform rolling calculations (e.g., based on the mean and standard deviation of the past 24 hours) to identify those exceeding... Extreme anomalies within a range (e.g., instantaneous traffic spikes caused by data errors or extreme weather).

[0063] (2) Data smoothing: To preserve the temporal sequence without directly deleting data, this invention preferably employs the median smoothing method. For identified outliers... This replaces the value with the median within its nearest time window (e.g., 5 minutes before and after), thus eliminating extreme interference while preserving local traffic trends.

[0064] b) Spatial domain partitioning and association: A two-stage filtering strategy is employed to improve matching efficiency.

[0065] 1) Coarse-grained filtering: First, based on all predefined spatial regions ( Calculate a minimum bounding box and perform a quick coarse screening on the downsampled trajectory data, removing all data points outside the bounding box.

[0066] 2) Then, for the coarsely filtered data, spatial indexing (R-tree) and shapely polygon matching algorithms are used to precisely match each trajectory point to its corresponding spatial region. Within the area, region labels are added to the trajectory points;

[0067] During the polygon matching process, vertical height constraint verification is performed simultaneously. For each spatial region... Set its corresponding vertical control height range , In determining the trajectory points Does it belong to the airspace? In addition to verifying whether its latitude and longitude projections are within the polygon, it is also necessary to determine its height value. Does it meet the requirements? Only when both the horizontal position and vertical height conditions are met will an airspace be marked as valid traffic, thereby eliminating interference from overflying flights that are within the horizontal projection but actually at different altitude levels.

[0068] c) Traffic statistics: based on fixed time slices Divide the day into time slices to obtain a set of time slices. In each time slice Within, through statistical airspace The number of flights within a time slice represents the airspace traffic within that time slice. Inside (e.g.) = 1 minute), through statistical airspace The number of unique aircraft identification codes within a given time slice is used to calculate airspace traffic during that time slice. After the statistics are completed, to ensure the continuity of the time series, this method will generate a continuous time index covering the entire period (e.g., the whole day), and use this index to analyze the flow series. Resampling is performed, and for any minute with no traffic record (i.e., a missing time slice), the traffic value is filled with 0. This ensures the integrity of the dataset and correctly reflects the zero-inflation characteristic of traffic. The spatial traffic sequence within that time slice is then obtained. The airspace traffic is statistically analyzed as follows, and airspace traffic is defined as:

[0069] ,

[0070] in The indicator function is defined as follows:

[0071] ,

[0072] (2) Construction and normalization of input features:

[0073] a) Normalized temporal dynamics:

[0074] To enable the model to accurately understand the periodicity of time (e.g., 11 PM and midnight are adjacent), this invention preferably employs periodic encoding to decompose and normalize the timestamp, specifically including:

[0075] Minute Code (The cycle is 24):

[0076] ,

[0077] ,

[0078] Hour code (The cycle is 24):

[0079] ,

[0080] ,

[0081] Weekday Code (Period is 7):

[0082] ,

[0083] ,

[0084] Date Code (Period is 31):

[0085] ,

[0086] ,

[0087] This encoding method maps individual time features (such as hours) onto a two-dimensional ring, enabling the model to unambiguously understand the continuity and periodicity of time.

[0088] b) Historical flow characteristics: past Flow sequence of time slices

[0089] c) Traffic statistics characteristics: based on past time windows Calculate the mean and variance.

[0090] ,

[0091] ,

[0092] d) Flow trend characteristics: the slope of the historical flow series,

[0093] ,

[0094] To mitigate the impact of long-tail distribution in air traffic data on model training stability, the target air traffic values ​​are adjusted before inputting the data into the model. Logarithmic transformation is used for processing:

[0095] ,

[0096] in To input the network's traffic characteristics, It is the natural logarithm. This is used to prevent calculation errors when there is zero flow. After the model outputs the prediction results, an exponential transformation is used to restore the predicted values ​​to their original dimensions. This process can significantly improve the model's ability to fit flow peaks and abrupt changes.

[0097] (3) Construction of a traffic prediction model based on MSGF-Net:

[0098] a) Construction of supervised learning dataset:

[0099] Using the features extracted in step (2) as input and spatial traffic as labels, a time series prediction dataset is constructed; the MSGF-Net framework is used for model training and validation, and the model input is the data from step (2) c). The traffic sequence of each time slice is the main feature. Only the normalized time dynamic features (such as hour, day of the week, date, and minute encoding) from step (2) a) are used as auxiliary features input to the model. This embodiment has been verified to achieve the 99.44% coverage described in the beneficial effects. As an optional enhancement, the traffic statistics features ( , The flow trend characteristics of step d) and step d) It can also be calculated and fed into the model as an additional real covariate for accuracy enhancement in specific scenarios.

[0100] b) MSGF-Net: An autoregressive probabilistic prediction architecture that integrates multi-scale temporal data and gating mechanisms.

[0101] To address the problem that standard RNN models are insufficient in capturing complex temporal patterns (such as short-term fluctuations and long-term trends), this invention proposes an autoregressive probabilistic prediction architecture (MSGF-Net) that integrates multi-scale temporal data and gating mechanisms.

[0102] This architecture replaces the single RNN structure in the standard DeepAR model, and it consists of the following four core hierarchical modules:

[0103] 1. Feature embedding layer:

[0104] Hierarchical implementation: This layer preprocesses the input.

[0105] Dynamic covariates: for example, the time characteristics of step (2)-a). (like , (etc.), are input into a multilayer perceptron block to generate .

[0106] Historical target: i.e., the historical flow of step (2)-b). It is input into another MLP block to generate .

[0107] 2. Multi-scale timing encoder:

[0108] This module replaces the original single RNN and adopts a parallel dual-branch architecture to simultaneously capture short-term fluctuations and long-term trends in traffic.

[0109] Branch A: Short-term dependencies (RNN): and It is fed into a gated recurrent unit (GRU) layer to capture high-frequency, local timing dependencies, and outputs... .

[0110] Branch B: Long-term dependency (TCN): and The data is fed into a Temporal Convolutional Network (TCN) layer. This layer uses causal convolution (ensuring no leakage of future information) and dilated convolution (exponentially expanding the receptive field) to efficiently capture long-term (e.g., daily, weekly) traffic patterns and output... .

[0111] To address the gradient degradation problem in deep network training, residual connections and layer normalization mechanisms are introduced in the construction of the multi-scale temporal encoder (branch A and branch B).

[0112] In practice, at the outputs of the TCN and GRU layers, the input signal is added to the output signal processed by the network, using the following formula: This ensures the integrity of information during the transmission of multi-scale features, enabling the model to maintain convergence stability even when stacking more layers.

[0113] 3. Gating fusion mechanism:

[0114] This layer replaces simple feature splicing and is used to intelligently fuse the aforementioned multi-scale temporal information.

[0115] Hierarchical implementation:

[0116] First, short-term characteristics and long-term characteristics To splice: .

[0117] Secondly, a fusion gate is calculated using a gated unit (an MLP layer with a Sigmoid activation function). :

[0118] ,

[0119] It is a weight between 0 and 1 that dynamically determines whether short-term information or long-term information is more important at the current point in time.

[0120] Final fusion features Obtained through gating weighting:

[0121] ,

[0122] 4. Probability Output Layer:

[0123] Hierarchical implementation:

[0124] The fused multi-scale temporal features Feed to an output MLP.

[0125] The output of this MLP is not the flow rate value, but rather the parameters of the probability distribution (such as Poisson, negative binomial, or zero-inflated (ZIP) distribution) described in step (3)-c). ).

[0126] c) The loss function chosen is the log-likelihood loss based on the Poisson distribution:

[0127] The training objective of the model is to maximize the log-likelihood of observed historical air traffic data under the conditional probability distribution given by the prediction model. Considering the non-negative integer counting characteristic of air traffic data, the model employs a Poisson distribution to model the data. The probability mass function (PMF) of the Poisson distribution is defined as:

[0128] ,

[0129] It is the observed actual flow rate (a non-negative integer);

[0130] It is the mean of the distribution, and this parameter is dynamically output by the neural network of the MSGF-Net model based on historical inputs;

[0131] The model's loss function is based on the probability distribution output, using the negative log-likelihood loss function, defined as:

[0132] ,

[0133] in For the first Each sample in time slice Real traffic, This represents the conditional probability distribution output by the MSGF-Net model. For the past Historical flow sequences of time slices (of which) The value is large enough to cover the receptive field required for TCN to capture long-term data. , , , These are the normalized time features for hours, days of the week, dates, and minutes, respectively. As model parameters, this loss function can effectively handle the zero-inflation and long-tailed distribution characteristics of air traffic data and provide quantification of prediction uncertainty.

[0134] As an optional implementation of the present invention, considering that the variance of air traffic data may be much greater than the mean during certain periods (such as peak periods), the probability distribution model in step (3)-c) can also be replaced with a negative binomial distribution. At this time, the loss function is replaced with the negative log-likelihood loss of the negative binomial distribution.

[0135] d) Probability distribution output and uncertainty quantification:

[0136] MSGF-Net model output conditional probability distribution N prediction samples are generated through Monte Carlo sampling. Based on these samples, the following calculations were performed:

[0137] Predicted mean: ,

[0138] Predictive standard deviation: ,

[0139] Confidence interval: ,

[0140] in significance level

[0141] Predicted quantiles: , ∈[0,1] represents the quantile probability.

[0142] e) Employ a sliding window validation strategy:

[0143] To prevent the model from seeing future data during training and to accurately simulate the rolling prediction scenario in real-world applications, this invention employs a sliding window (or rolling origin prediction) strategy for model evaluation.

[0144] The specific implementation method of this strategy is as follows:

[0145] 1. Initialization: Set an initial training set (e.g., data from day 1 to day 30) and a continuous test set (e.g., data from day 31).

[0146] 2. Training and Prediction - 1: Train the model using the initial training set and make a prediction for day 31.

[0147] 3. Window sliding: Slide the window forward by one unit (e.g., 1 day), and the training set becomes (data from day 2 to day 31), and the test set becomes (data from day 32).

[0148] 4. Training and Prediction - 2: Retrain or update the training model using a new training set and make a prediction for day 32.

[0149] 5. Iteration: Repeat steps 3 and 4 until all available test data has been traversed.

[0150] The final evaluation metrics (such as MAE, coverage) are calculated by summing the prediction results across all test sets (day 31, day 32, etc.). This strategy ensures the unbiasedness of the evaluation results and effectively tests the model's generalization ability and robustness over dynamic time.

[0151] ( The number of hidden units is 128. )

[0152] f) Hyperparameter optimization based on Bayesian optimization:

[0153] To determine the RNN architecture parameters in steps (3)-b)-4) (e.g. , ), the length of the historical context in step (3)-a) In addition to key hyperparameters such as the learning rate during the training process, this invention also includes an automatic hyperparameter optimization step before model training.

[0154] This step preferably employs a Bayesian optimization algorithm (rather than the traditional Grid Search). Bayesian optimization, by constructing a probabilistic surrogate model between hyperparameters and model performance (e.g., negative log-likelihood loss or MAE on the validation set), can intelligently search the hyperparameter space with fewer iterations, efficiently finding globally optimal or near-optimal parameter combinations.

[0155] In this invention , These parameters represent the optimal configuration determined through this Bayesian optimization mechanism on the sliding window validation set in step (3)-e).

[0156] (4) Establishment of a multi-dimensional evaluation system:

[0157] a) This invention establishes a comprehensive set of model evaluation criteria. In addition to using traditional indicators such as mean absolute error (MAE) and root mean square error (RMSE), it places greater emphasis on evaluating the model's ability to quantify uncertainty. (See attached...) Figures 3 to 7 As shown in the detailed analysis, the present invention performs excellently in terms of prediction accuracy, confidence interval coverage, error distribution, and risk perception, fully verifying the effectiveness of the method.

[0158] b) Analyze the predicted confidence interval coverage, calculate the actual coverage of the 90% confidence interval, and verify the reliability of uncertainty quantification. For example... Figure 4 As shown, the model's 90% confidence interval coverage reaches 99.44%, indicating that the model's uncertainty quantification is reliable, and the vast majority of true values ​​fall within the prediction interval. This is very important for air traffic control decision-making scenarios that require risk assessment.

[0159] c) Uncertainty analysis of prediction error distribution, using histogram analysis to analyze the frequency distribution characteristics of prediction errors. For example... Figure 5 As shown, the prediction errors are mainly concentrated between -2.5 and 0, and the error distribution is approximately symmetrical with the center close to zero, indicating that the model has no systematic bias. The error distribution exhibits a left-skewed characteristic, with most prediction errors concentrated near the zero error line, verifying the stability and reliability of the model.

[0160] d) Prediction error analysis for different time periods: Calculate the MAE and its confidence interval for each time period to ensure the reliability of the model's predictions during critical periods. For example... Figure 6 As shown, the model has the highest prediction accuracy (MAE of about 0.9) and the narrowest confidence interval during the 4-5 AM period, indicating that the prediction is most stable during this period. However, the MAE is higher (about 4.2-4.5) and the confidence interval is wider during the 0-1 AM, 8-9 AM, and 4-5 PM periods, indicating that the prediction is more uncertain during these periods, which is consistent with the actual variation of air traffic.

[0161] e) Analysis of the changes in forecast uncertainty over time, using time series plots to illustrate the dynamic characteristics of forecast uncertainty. For example... Figure 7As shown, the forecast uncertainty is low in the initial stage (approximately 0-5), followed by a period of high volatility. For most of the time, the uncertainty value fluctuates between 15 and 55, with several peaks exceeding 50. This pattern of uncertainty variation reflects the complexity of air traffic forecasting: uncertainty is low during periods of relatively stable traffic, while it increases significantly during periods of drastic traffic changes, providing air traffic controllers with crucial risk warning information.

[0162] f) The above multi-dimensional evaluation criteria not only comprehensively reflect the overall performance of the model, but also reveal the reliability level of the prediction through uncertainty quantification. This facilitates differentiated decision-making by air traffic controllers based on prediction credibility, significantly improving the model's interpretability and practical value. Visualization results of the evaluation indicators can be found in [link to visualization]. Figures 3-7 .

[0163] Comparison of predicted and actual values ​​( Figure 3 From the perspective of prediction error distribution, most points are distributed near the fitted line, indicating that the overall prediction effect of the model is good and can accurately reflect the actual flow trend; Figure 5 From the perspective of [missing information], the error distribution is approximately symmetrical, with the center close to zero, indicating that the model as a whole does not have systematic bias, and the prediction errors are mainly concentrated in a small range with few extreme errors, further verifying the stability and reliability of the model; from the confidence interval coverage analysis ( Figure 4 As can be seen, the actual coverage of the 90% confidence interval is approximately 99.44%, indicating that the uncertainty quantification of the model is reliable; from the analysis of the change in prediction uncertainty over time ( Figure 7 It can be seen that the forecast uncertainty is relatively high during peak periods, which is consistent with actual experience; finally, based on the MAE analysis of different time periods ( Figure 6 As can be seen, the model has the highest and most stable prediction accuracy in the early morning period, while the prediction error is larger and the uncertainty is higher in the night, morning and evening periods.

[0164] During the evaluation phase, we adopted a more rigorous evaluation strategy, focusing on the model's performance during actual operating hours. Analysis of the prediction results across different time periods revealed that the model exhibited extremely high prediction accuracy during low-traffic periods (e.g., 4-5 AM), with a MAE value approaching 0.9. This is primarily due to the relatively stable and minimally fluctuating traffic flow during these times. However, during peak air traffic periods (e.g., 8-9 AM and 4-5 PM), the model's prediction error increased significantly, with MAE values ​​reaching 4.2-4.5, reflecting the complexity of traffic variations during peak hours.

[0165] Confidence interval analysis revealed that the model exhibits lower prediction uncertainty and narrower confidence intervals during low-flow periods, while uncertainty increases significantly and confidence intervals widen during peak periods. This pattern of uncertainty variation closely aligns with actual air traffic control experience: predictions are relatively reliable during periods of relatively stable flow, while uncertainty naturally increases during periods of drastic flow changes.

[0166] The model performs relatively poorly during the typical peak periods of 10:00-11:00 and 18:00-19:00, which is consistent with the actual variation of air traffic. These periods are usually peak times for flight takeoffs and landings, with complex traffic variations and numerous influencing factors, making prediction more difficult.

[0167] Comparative analysis revealed that focusing solely on the overall MAE index might obscure the model's true performance across different time periods. Therefore, we adopted a time-segmented evaluation method, ensuring both comprehensiveness and highlighting the model's key performance indicators in practical applications, thus providing a more reliable reference for air traffic control decision-making.

[0168] The experimental results fully verify the effectiveness and practicality of the method of this invention in real-time traffic flow prediction of air routes. The model not only has high overall prediction accuracy and a reasonable error distribution, but also can identify key features and adapt to traffic flow changes in different time periods, demonstrating promising prospects for practical application.

[0169] (5) Real-time airspace traffic prediction during the application phase:

[0170] airspace Based on real-time radar trajectory data and a trained MSGF-Net model, for future... Probabilistic prediction of spatial traffic within a time slice is performed, and a conditional probability distribution is output:

[0171] ,

[0172] The final traffic forecast is a statistic extracted from this distribution.

[0173] In this embodiment, a Monte Carlo sampling ensemble strategy is used when generating prediction results.

[0174] Since the model outputs probability distribution parameters at each time step, the system does not directly output deterministic values, but rather derives them from this distribution. random sampling (e.g.) ),generate One possible future traffic value.

[0175] In response to this For each flow value, calculate its quantile statistics for each time step:

[0176] Extract the 50th percentile (median) as the final traffic forecast value to obtain a more robust forecast result than the mean;

[0177] Confidence intervals are constructed by extracting the 10% and 90% quantiles, which visually demonstrate the range of uncertainty in the prediction.

[0178] This sampling-based reasoning method effectively preserves the correlation between time series sequences and avoids the neglect of cumulative error in traditional point prediction methods.

[0179] In a preferred embodiment of the present invention, to further improve the robustness and reliability of the prediction, the present invention employs a model ensemble strategy:

[0180] 1. Multi-model training: In the training phase of step (3), independent training is performed by using different random seeds or by utilizing different training subsets from the sliding window validation in step (3)-e). One (e.g.) =5 or 10) MSGF-Net model.

[0181] 2. Integrated prediction: In the application phase of step (4), Each model simultaneously predicts the future. Predictions are made for each time slice, and each slice generates its own prediction. A Monte Carlo sample.

[0182] 3. Result Fusion: The final prediction result is for all The result is derived by summarizing and statistically analyzing a sample. For example, the final "predicted mean" is the sum of all samples. The mean of the samples; the final "90% confidence interval" is for all... Each sample was taken at the 5th and 95th percentiles.

[0183] This integrated strategy effectively smooths out the prediction bias of a single model, making the final uncertainty quantification result (such as the 99.44% coverage mentioned above) more stable and reliable.

[0184] When dividing a spatial domain into sub-spatial domains, for each sub-spatial domain Based on real-time radar trajectory data and a trained MSGF-Net model, predict future... Probabilistic prediction of spatial traffic within a time slice is performed, and a conditional probability distribution is output:

[0185] ,

[0186] in For the past continuous Time slices; conditional inputs in the formula and They respectively represent: corresponding to the subspace From the past The historical flow sequence from one time slice to the previous time slice, and the time covariates covering past and future time ranges extracted through step (2).

[0187] One of the core advantages of step (4) of this invention is that it also includes uncertainty quantification output. (For the spatial domain) (or any subspace) Based on the conditional probability distribution output by the model, not only can the mean of the traffic forecast be extracted. It can also output a series of quantitative indicators to assess the reliability and risk of the prediction, specifically including:

[0188] Traffic prediction distribution: The model directly outputs a complete conditional probability distribution. ,in These are the parameters of the pre-trained model. This is the foundation for all uncertainty quantification.

[0189] Confidence interval: Based on the probability distribution, the confidence interval is calculated at a preset significance level using Monte Carlo sampling or a quantile function. (For example =0.1 (corresponding to a 90% confidence level) confidence interval: in For quantile functions, this interval gives the range into which the future true value may fall.

[0190] Prediction uncertainty: Based on the probability distribution, calculate the standard deviation of the predicted flow. As a direct measure of prediction uncertainty, the larger the standard deviation, the more uncertain the model's prediction for that point. ,

[0191] Extreme traffic risk: Based on the probability distribution, it is possible to calculate whether future traffic will exceed a preset critical business threshold. The probability of (e.g., sector capacity) provides decision support for risk management: ,

[0192] This method has real-time probabilistic prediction capabilities. After receiving the latest radar trajectory data, it can quickly complete multi-dimensional feature extraction and traffic prediction. It not only provides point prediction values, but also outputs prediction confidence intervals and risk assessment indicators, meeting the timeliness requirements of dynamic airspace traffic control and risk perception, and significantly improving the scientific nature, response speed and risk control capabilities of air traffic control decisions.

[0193] A technical solution refers to the technical measures (i.e., technical concept, technical solution) taken to achieve the aforementioned inventive objectives. The invention's structure, organization, shape, functional relationships, principles, etc., should be clearly and completely described, disclosed to the extent that a person skilled in the art can implement the invention.

[0194] Example 2

[0195] This embodiment provides an air traffic forecasting and uncertainty quantification system based on MSGF-Net, including:

[0196] The data acquisition module is configured as follows:

[0197] A computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the aforementioned MSGF-Net-based air traffic forecasting and uncertainty quantification method.

[0198] A terminal device includes a processor and a computer-readable storage medium, the processor being configured to implement various instructions; the computer-readable storage medium being configured to store multiple instructions adapted for loading and execution by the processor of the aforementioned MSGF-Net-based air traffic forecasting and uncertainty quantification method.

[0199] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for air traffic forecasting and uncertainty quantification based on MSGF-Net, characterized in that, include: Flight trajectory data preprocessing and traffic flow data extraction; Input features are constructed and normalized based on preprocessed flight trajectory data and extracted traffic data; Construct a traffic prediction model based on MSGF-Net; The traffic prediction model is optimized and trained based on the loss function; Predict input features based on the trained traffic prediction model; Output the prediction results; The construction of the traffic prediction model based on MSGF-Net includes building an autoregressive probabilistic prediction architecture MSGF-Net that integrates multi-scale temporal series and gating mechanisms as the traffic prediction model. Specifically, it optimizes the single RNN structure in the standard DeepAR model by preprocessing the input dynamic covariates and historical targets at the feature embedding layer; then, it replaces the single RNN with a multi-scale temporal encoder, employing a parallel dual-branch architecture to simultaneously capture short-term fluctuations and long-term trends in traffic. Branch A is a short-term dependent RNN, which... and The data is fed into the GRU (Government Regulator) layer to capture high-frequency, localized timing dependencies and output the data. Branch B is a long-term dependency on TCN, which will... and The data is fed into the Temporal Convolutional Network (TCN) layer for causal convolution and dilated convolution to efficiently capture long-term traffic patterns and output the results. Next, a gating fusion mechanism is used to replace feature splicing to fuse the above multi-scale temporal information. First, short-term features are... and long-term characteristics To splice: ; calculate the fusion gate through the gate control unit : , Weights between 0 and 1, representing the final fused features. Obtained through gating weighting: Finally, a probability output layer is constructed to integrate the fused multi-scale temporal features. Feed to the output MLP.

2. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 1, characterized in that, The flight trajectory data preprocessing and traffic data extraction include processing the acquired raw radar trajectory dataset. ,in It is a set of flight identifiers, and each flight's trajectory ,in This indicates that the trajectory contains One sampling point, For timestamps, Let be the three-dimensional spatial coordinates, denoted as . The original trajectory data is downsampled over time, and then a two-stage filtering strategy is adopted to improve matching efficiency through spatial domain partitioning and association. First, coarse-grained filtering is performed based on all predefined spatial domain regions. The minimum bounding box is calculated to quickly coarsely filter the downsampled trajectory data. Then, spatial indexing and shapely polygon matching algorithms are used on the coarsely filtered data to precisely match each trajectory point to its corresponding spatial region. Within this area, region labels are added to the trajectory points; finally, traffic statistics are performed in fixed time slices. Divide the day into time slices to obtain a set of time slices. In each time slice Within, through statistical airspace The number of flights within a time slice represents the airspace traffic within that time slice. Within, through statistical airspace The number of unique aircraft identification codes within a given time slice is used to calculate airspace traffic during that time slice. After the statistics are completed, a continuous-time index covering the entire period is generated, and this index is used to analyze the traffic sequence. Resampling is performed to obtain the spatial flow sequence within the time slice. The statistical methods for airspace traffic include defining airspace traffic as: ， in The indicator function is defined as follows: 。 3. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 2, characterized in that, The input feature construction and normalization based on preprocessed flight trajectory data and extracted traffic data includes decomposing and normalizing timestamps using periodic encoding, including minute, hour, weekday, and date encoding. By mapping individual time features onto a two-dimensional ring, the model unambiguously understands the continuity and periodicity of time. Then, for historical traffic features, past... Flow sequence of time slices For traffic statistics characteristics, based on past time windows The mean and variance are calculated and expressed as follows: ， ， For traffic trend characteristics, the slope of the historical traffic series is calculated and expressed as: .

4. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 3, characterized in that, The construction of the traffic prediction model based on MSGF-Net also includes, to address the gradient degradation problem in deep network training, the introduction of residual connections and layer normalization mechanisms in the construction of branches A and B of the multi-scale temporal encoder. Specifically, at the outputs of the TCN and GRU layers, the input signal is added to the processed output signal, as shown in the following formula: This is used to ensure the integrity of information during the transmission of multi-scale features, so that the model can maintain convergence stability when stacking more layers.

5. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 4, characterized in that, The optimization training of the traffic prediction model based on the loss function includes maximizing the log-likelihood of the observed historical traffic data under the conditional probability distribution given by the prediction model, and modeling the data using a Poisson distribution. First, the probability mass function (PMF) of the Poisson distribution is defined as follows: ,in It is the observed actual flow rate; The mean of the distribution is given, and then the negative log-likelihood loss function is calculated, expressed as: ， in For the first Each sample in time slice The real traffic, This represents the conditional probability distribution output by the MSGF-Net model. For the past Historical traffic sequence of a time slice For the length of the history context window, , , , These are the normalized time features for hours, days of the week, dates, and minutes, respectively. The model parameters are then used; subsequently, the probability distribution is output and uncertainty is quantified, resulting in the conditional probability distribution for the MSGF-Net model. N prediction samples are generated through Monte Carlo sampling. Based on the sample, the predicted mean, predicted standard deviation, confidence interval, and predicted quantile are calculated, where the predicted mean is expressed as: The predictive standard deviation is expressed as: ， The confidence interval is expressed as: ,in At the significance level, the predicted quantile is , ∈[0,1] represents the quantile probability.

6. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 5, characterized in that, The optimization training of the traffic prediction model based on the loss function also includes using a rolling origin prediction strategy for model evaluation to prevent the model from seeing future data during training and to accurately simulate the rolling prediction scenario in actual applications. First, an initial training set and a continuous test set are set. The model is trained and predictions are made using the initial training set. Based on the window sliding mechanism, the window is slid forward one unit. The model is retrained and predictions are made using the new training set. The training is repeated iteratively until all available test data is traversed. The final evaluation metric is calculated by summarizing the prediction results of all test sets.

7. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 6, characterized in that, The traffic prediction model based on the trained data predicts input features, including spatial features. Based on real-time radar trajectory data and a trained MSGF-Net model, for future... Probabilistic prediction of spatial traffic within a time slice is performed, and a conditional probability distribution is output: ， in Indicates the future Spatial flow sequence of a time slice ,…., ; This represents the corresponding spatiotemporal covariate sequence; The final traffic prediction is a statistic extracted from the distribution. During the training phase, different training subsets are validated using different random seed sliding windows, and training is performed independently. One MSGF-Net model, in the application phase. Each model simultaneously predicts the future. Predictions are made for each time slice, and each slice generates its own prediction. Based on a Monte Carlo sample, the final prediction result is for all The results were obtained by summarizing and statistically analyzing a sample. When dividing a spatial domain into sub-spatial domains, each sub-spatial domain... Based on real-time radar trajectory data and a trained MSGF-Net model, predict future... Probabilistic prediction of airspace traffic within a time slice is performed, and a conditional probability distribution is output.

8. The method for air traffic forecasting and uncertainty quantification based on MSGF-Net according to claim 7, characterized in that, The prediction of input features based on the trained traffic prediction model also includes employing a Monte Carlo sampling ensemble strategy when generating prediction results. Specifically, for the probability distribution parameters output by the model at each time step, the system extracts data from the distribution... Generated after random sampling One possible future traffic value, for For each flow value, quantile statistics are calculated at each time step. First, the 50% quantile is extracted as the final flow prediction value to obtain a more robust prediction result than the mean. Then, the 10% and 90% quantiles are extracted to construct confidence intervals, which visually demonstrate the range of uncertainty in the prediction.

9. An air traffic forecasting and uncertainty quantification system based on MSGF-Net, executing the air traffic forecasting and uncertainty quantification method based on MSGF-Net as described in claim 1, characterized in that, include: The data acquisition module is configured to perform preprocessing of aviation trajectory data and extraction of traffic data. The feature construction module is configured to construct and normalize input features based on preprocessed aviation trajectory data and extracted traffic data; The model building module is configured to build a traffic prediction model based on MSGF-Net; The training module is configured to optimize and train the constructed traffic prediction model based on the loss function. The prediction module is configured to predict input features based on the trained traffic prediction model and output the prediction results.

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