An aircraft wake vortex prediction method based on multi-model fusion

Abstract

This invention relates to the field of air traffic management technology and discloses a multi-model fusion-based method for predicting aircraft wake vortices. It constructs a high-confidence, dimensionless evolutionary dataset by weighted fusing multiple wake vortex physical models with a small amount of radar data. A CNN-BiLSTM deeply coupled network model is built, and Bayesian optimization algorithms are used for global automatic hyperparameter optimization and model training. Real-time flight and meteorological features are input for a single forward propagation to output a deterministic evolutionary trajectory. During the inference phase, Monte Carlo dropout techniques are incorporated to generate dynamic probability confidence intervals. This invention significantly improves long-term prediction accuracy and real-time inference efficiency, providing a quantifiable scientific safety margin for the safe reduction and risk assessment of dynamic wake vortex intervals at airports.

Description

Technical Field

[0001] This invention relates to the field of air traffic management technology, and in particular to a method for predicting aircraft wake vortices based on multi-model fusion. Background Technology

[0002] An aircraft wake vortex is a pair of counter-rotating vortices formed at the wingtip due to the pressure difference between the upper and lower surfaces of the wing as the wing generates lift. When a following aircraft encounters the wake vortex flow field generated by the preceding aircraft, it is prone to tumbling, instability, or even crashing.

[0003] Aircraft wake vortices have become a significant factor affecting aircraft safety. To ensure aircraft operations are unaffected by wake vortexes, organizations such as the International Civil Aviation Organization (ICAO) have developed wake vortex classification standards (RECAT standards) for different aircraft types based on parameters such as maximum takeoff weight and wingspan. These standards specify the static longitudinal separation that aircraft should maintain under different wake vortex categories to avoid wake vortex-related risks. While current static wake separation standards are effective in ensuring aircraft safety, in large, busy airports with numerous takeoffs and landings, they result in lower aircraft operational efficiency and airport capacity. Therefore, the development of dynamic wake separation technology is urgently needed to improve aircraft operational efficiency and airport runway capacity.

[0004] Accurately predicting the evolution of wake vortex height and circulation over time is crucial for achieving dynamic wake intervals. Currently, most wake vortex prediction methods rely on traditional physical models, computational simulations, and data-driven machine learning. Wake vortex evolution is influenced by various factors, including the atmospheric environment, exhibiting complex nonlinear characteristics. Traditional physical models, limited by fixed parameters, have limited accuracy in predicting wake vortexes and struggle to accurately invert their evolution. Wake vortex computational simulations, such as CFD technology, offer high accuracy and can fully reproduce the entire lifecycle evolution of wake vortices; however, their computational efficiency is low, making them unsuitable for large-scale, automated, and rapid wake vortex prediction scenarios due to the large number of airport flights. With the continuous development of big data, machine learning methods are increasingly being integrated with wake vortex inversion and prediction. Utilizing the nonlinearity and multivariate functional relationships of neural networks can improve the accuracy of wake vortex evolution prediction. However, most current methods rely on single machine learning approaches for wake vortex evolution prediction, which struggle to fully identify the long-term and short-term characteristics of wake vortex circulation and height evolution, resulting in limited recognition of wake vortex evolution features.

[0005] To address the issues of low accuracy in predicting wake vortices using traditional physical models and single machine learning methods, as well as the slow efficiency of computational simulation methods, this invention proposes a multi-model fusion method for predicting aircraft wake vortices. First, initial wake vortex parameters and atmospheric environmental parameters are acquired through detection methods such as lidar. Then, Convolutional Neural Networks (CNNs) are used to identify short-term wake vortex evolution features, and Bidirectional Long Short-Term Memory (BiLSTM) neural networks are used to identify long-term wake vortex evolution features. Finally, Bayesian optimization of model hyperparameters and Monte Carlo Dropout (MC Dropout) are combined to improve the model's ability to identify wake vortex features, thereby enhancing the accuracy of wake vortex prediction and providing technical support for achieving dynamic wake intervals. Summary of the Invention

[0006] This invention aims to at least solve one of the technical problems existing in related technologies. To this end, this invention provides a method for predicting aircraft wake vortices based on multi-model fusion.

[0007] A method for predicting aircraft wake vortices based on multi-model fusion, comprising the following steps: S1. Obtain the initial parameters of the wake vortex and atmospheric environment parameters, perform dimensionless processing, and combine them into a multi-dimensional feature vector; S2. Based on the measured data of lidar, determine the fusion weights of multiple traditional inversion prediction models of wake vortex; input the multidimensional feature vectors from step S1 into each traditional inversion prediction model, and perform weighted fusion according to the fusion weights to construct a model training dataset. S3. Construct a CNN-BiLSTM deeply coupled neural network model with a Dropout layer; train the model using the training dataset from step S2, and use the Bayesian optimization algorithm to perform global hyperparameter optimization to obtain the optimal model. S4. Obtain the initial parameters of the wake vortex and atmospheric environment parameters in real time, and construct a real-time feature vector; input the real-time feature vector into the optimal model for a single forward propagation, output the dimensionless wake vortex prediction value, de-dimensionize the dimensionless wake vortex prediction value, generate the physical space evolution trajectory, so as to achieve deterministic prediction of the wake vortex. S5. During the inference phase, the Dropout layer of the optimal model is forcibly kept on, and the optimal model is controlled to perform multiple forward propagations of the real-time feature vectors to generate a set of prediction samples. Based on the set of prediction samples, the probability interval of the wake vortex evolution is statistically calculated to achieve the prediction of the wake vortex evolution probability.

[0008] Furthermore, the initial parameters of the wake vortex mentioned in S1 and the initial parameters of the real-time wake vortex mentioned in S4 both include at least: the initial circulation of the wake vortex and the initial height of the wake vortex; The atmospheric environmental parameters mentioned in S1 and the real-time atmospheric environmental parameters mentioned in step S4 both include at least: vortex dissipation rate and buoyancy frequency.

[0009] Furthermore, the dimensionless processing specifically includes: calculating the initial vortex core spacing and the initial descent velocity of the wake vortex; Using the initial vortex core spacing and the initial descent velocity of the wake vortex, the dimensionless time series, dimensionless vortex dissipation rate, dimensionless buoyancy frequency, dimensionless initial circulation of the wake vortex, and dimensionless initial height of the wake vortex are calculated respectively.

[0010] Furthermore, the multiple conventional inversion prediction models for wake vortices mentioned in S2 include at least one of the P2P model, TDAWP model, Eddy-Dissipation model, and APA model.

[0011] Furthermore, the determination of the fusion weights of multiple traditional wake vortex inversion prediction models described in S2 specifically includes: calculating the root mean square error of each traditional wake vortex inversion prediction model; The reciprocal score of the error of each traditional inversion prediction model for the wake vortex is calculated based on the root mean square error. The normalized weights are calculated based on the inverse error score, and these normalized weights are used as the global fusion weights.

[0012] Furthermore, the construction of the CNN-BiLSTM deeply coupled neural network model including the Dropout layer described in S3 includes: The convolutional neural network module is used to extract local correlation features within a short time step as short-term local features by calculating and extracting them through a sliding window. The short-term local features are input into the bidirectional long short-term memory neural network module, and forward features are extracted by forward LSTM and backward features are extracted by backward LSTM. The information flow is regulated by gating mechanisms such as forget gate, input gate, and output gate, and the state vectors corresponding to the forward features and the backward features are concatenated. After passing through the Dropout layer, the predicted value is mapped out through a fully connected layer; The Dropout layer sets the dropout ratio.

[0013] Furthermore, the global hyperparameter optimization using the Bayesian optimization algorithm described in S3 specifically includes: Construct a hyperparameter search space that includes kernel size, number of kernels, number of BiLSTM neurons, Dropout ratio, learning rate, and batch size; The posterior probability distribution between the hyperparameters and the root mean square error loss function is fitted using a Gaussian process. The next hyperparameter combination is selected using the expected improvement strategy, and the iteration continues until the convergence condition is met.

[0014] Furthermore, after generating the physical space evolution trajectory as described in S4, it also includes: Based on the physical space evolution trajectory, the time required for the predicted circulation to decay to a level that poses no harm to the following aircraft is calculated and used as the wake dissipation time. Calculate the time required for the predicted wake height to drop below the preset safe height, and use this as the safe vertical interval.

[0015] Furthermore, after generating the prediction sample set as described in S5, the process also includes: Calculate the prediction mean and prediction variance at each dimensionless time step; Based on the predicted mean and the predicted variance, the upper and lower confidence limits are calculated, and the prediction interval at the specified confidence level is constructed as the wake vortex evolution probability interval.

[0016] Furthermore, the deterministic prediction results output by S4 and the probabilistic prediction results output by S5 are used as the decision basis for dynamic wake interval reduction. When the width of the wake evolution probability interval exceeds a preset threshold, switch to a conservative strategy or extend the flight wake interval.

[0017] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: By generating training data through weighted fusion of multiple traditional physical models, the problem of the extreme scarcity of large-scale measured full-lifetime wake vortex data is effectively overcome. A high-confidence dataset is constructed in the absence of measured data, thereby improving the model training efficiency and generalization ability.

[0018] A deep coupled network architecture of CNN and BiLSTM is adopted, with CNN responsible for short-term local features and BiLSTM responsible for long-term bidirectional dependencies. Compared with a single neural network, this architecture can jointly identify evolutionary features, significantly improve prediction accuracy and reduce error accumulation caused by long-term prediction.

[0019] By introducing a Bayesian optimization algorithm to automatically optimize core hyperparameters globally, training efficiency is improved while reducing the risk of performance instability and overfitting caused by manual parameter tuning based on experience.

[0020] By using Monte Carlo Dropout (MC Dropout) to output confidence intervals, the original "black box" prediction is transformed into a probabilistic estimate, providing an interpretable safety margin for the implementation of dynamic wake intervals and significantly improving the reliability of the model's decision-making.

[0021] Deterministic predictions during the deployment phase require only one forward pass, meeting the airport's extremely high real-time requirements; while probabilistic predictions can be obtained with a limited number of forward passes, achieving a balance between prediction accuracy and reliability under the premise of controllable computational overhead.

[0022] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 This is a flowchart of the multi-model fusion method for predicting aircraft wake vortices in this invention.

[0025] Figure 2 This is a structural diagram of the multi-model fusion method for predicting aircraft wake vortices in this invention.

[0026] Figure 3 This is a diagram of the LSTM network structure in this invention.

[0027] Figure 4 This is a diagram of the BiLSTM network structure in this invention.

[0028] Figure 5 This is a comparison chart of the predicted wake vortex circulation in the large eddy simulation of this invention.

[0029] Figure 6 This is a comparison chart of the predicted wake vortex height in the large eddy simulation of this invention.

[0030] Figure 7 This is a prediction diagram of the evolution probability of the vortex circulation in the CNN-BiLSTM model in this invention.

[0031] Figure 8 This is a probability prediction diagram of the wake height evolution of the CNN-BiLSTM model in this invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but cannot be used to limit the scope of this invention.

[0033] This invention proposes a method for predicting aircraft wake vortices based on multi-model fusion, the overall process of which is as follows: Figure 1 As shown, the model structure is as follows Figure 2 As shown, this method first obtains initial parameters of the wake vortex and atmospheric environmental parameters from multi-source data and performs dimensionless processing. A large-scale, high-confidence dataset for training the deep learning model is constructed by weighted fusion of LiDAR measured data using multiple traditional physical models. A CNN-BiLSTM deeply coupled neural network model is constructed and trained, and its hyperparameters are globally optimized using Bayesian optimization. In the prediction stage, the model can perform deterministic prediction of the wake vortex and further predict the wake vortex evolution probability using Monte Carlo Dropout technology, outputting the prediction mean and confidence interval, providing a quantifiable range of uncertainty for the dynamic wake interval.

[0034] To address the problems of low prediction accuracy of existing traditional wake vortex inversion models under complex atmospheric conditions, low practical efficiency of computational simulation methods (such as CFD), and insufficient identification of long-term and short-term time series characteristics of wake vortices by single machine learning methods, this invention proposes an aircraft wake vortex prediction method based on "multi-model data fusion + CNN-BiLSTM deep learning model + Bayesian optimization model hyperparameters + MC Dropout uncertainty quantization". This method uses dimensionless time series data of wake vortices (… Key environmental parameters (dimensionless vortex dissipation rate) With dimensionless buoyancy frequency ), dimensionless initial circulation of the wake vortex ( ), dimensionless initial height of the vortex tail ( Using these data as model inputs, multiple traditional wake vortex inversion prediction models (P2P, TDAWP, APA, Eddy-Dissipation) are matched and analyzed with lidar-measured wake vortex lifetime evolution data. Weighted fusion of wake vortex evolution data from multiple models is then performed to establish a dataset closely resembling the real-world wake vortex evolution scenario for deep learning model training. Regarding wake vortex evolution feature identification, CNN and BiLSTM are used to extract short-term evolution features of wake vortex circulation and height, as well as the forward and backward long-term dependencies of wake vortex time-series evolution. Bayesian optimization is employed to automate the global search of hyperparameters. In the wake vortex prediction stage, MC Dropout is used to obtain the mean and confidence interval of wake vortex evolution predictions, enabling probabilistic prediction of the evolution of wake vortex circulation and height over time. This provides a quantifiable range of uncertain wake vortex evolution for determining dynamic wake intervals.

[0035] The implementation steps of this method are as follows: Step 1: Acquisition of initial data and feature construction for wake vortex evolution: This step aims to acquire the raw data required for aircraft wake vortex prediction and to standardize it to fit the model input.

[0036] The initial parameters of the wake vortex and atmospheric environmental parameters of the target flight are obtained through detection devices or stations such as lidar, wind radar or airport weather stations, including at least the initial circulation of the wake vortex Г0, the initial height of the wake vortex Z0, the vortex dissipation rate ε, and the buoyancy frequency N.

[0037] Initial circulation Γ0 of the wake: reflects the initial intensity of the wake.

[0038] Initial height Z0 of the wake: reflects the initial spatial position of the wake.

[0039] Vortex dissipation rate ε: reflects the effect of atmospheric turbulence on the decay of wake vortices.

[0040] Buoyancy frequency N: reflects the influence of atmospheric stability on the evolution of the wake vortex.

[0041] Furthermore, due to significant differences in parameters between different aircraft models, directly using actual physical quantities to construct data can lead to overfitting of the model to a specific aircraft model. Therefore, it is necessary to perform dimensionless processing on the observed data according to a unified time base to obtain dimensionless time. Dimensionless vortex dissipation rate Dimensionless buoyancy frequency Dimensionless initial circulation of the wake Initial height of the dimensionless wake These parameters serve as input features for the model, thus ensuring the model's effectiveness in practical applications. The specific method for making these parameters dimensionless is as follows: (1) (2) (3) (4) (5) Where t represents the actual time in seconds, t0 represents the initial time, and b0 represents the initial vortex core spacing, which is usually taken as... w0 represents the initial descent velocity of the wake vortex, calculated as follows: Г0 represents the initial circulation of the wake vortex, calculated as follows: Г(t) represents the actual circulation evolution value, Z(t) represents the actual vortex height evolution value, Z0 represents the initial vortex height, ε represents the actual vortex dissipation rate value, and N represents the actual buoyancy frequency value.

[0042] Step 2: Multi-model fusion to generate deep learning model training data: To address the scarcity of large-scale datasets on the life-cycle evolution of wake vortices in actual measurements, this step obtains high-quality training data by fusing multiple traditional physical models and LiDAR measured data.

[0043] Due to the lack of large-scale datasets of the entire lifecycle evolution of wake vortices in actual measurements, it is difficult to meet the large-scale dataset requirements of data-driven deep learning models. Therefore, this invention studies the matching degree between lidar-measured wake vortex lifecycle evolution data and wake vortex physical evolution models. The traditional wake vortex models used include the P2P (Probabilistic Two-Phase Wake Vortex Decay and Transport Model), TDAWP (TASS Driven Algorithms for Wake Prediction), Eddy-Dissipation, and APA (NWRA AVOSS Prediction Algorithm). The weight of each model is determined by the matching degree between lidar-measured wake vortex lifecycle evolution data and the wake vortex evolution data of the above models. The wake vortex circulation and wake vortex height predicted by each traditional wake vortex model at each time step are weighted and fused to obtain wake vortex circulation and wake vortex height data that closely approximate the actual wake vortex lifecycle evolution. Table 1 shows the weight of each model in the lidar and wake vortex physical model matching study in this invention.

[0044] Table 1. Weighting of the Dataset Wake Vortex Evolution Model

[0045] The weights of each wake vortex physical model shown in Table 1 are from an embodiment of this invention, and their determination method is as follows: A verification sample set D={(x...} is constructed based on lidar-measured wake vortex lifetime evolution data. n ,y n ),n=1,2,…,N}, where N represents the samples in the validation set, x n The input features for the nth sample (e.g., meteorological parameters, aircraft type, weight, speed, time series window, etc., specifically defined by the system input) y n The true or reference value (e.g., measured value or high-fidelity simulation value) corresponding to the nth sample is used as the benchmark for error calculation. Under the same initial conditions and environmental parameters, the i-th wake vortex model is obtained for sample x. n Predicted value .

[0046] The specific steps for calculating the weights are as follows: (1) Calculate the root mean square error (RMSE): (6) Where M represents the number of physical models of the wake vortex.

[0047] (2) Score based on the reciprocal of the error: (7) Among them, s i δ represents the reciprocal score of the error of the i-th model, and δ represents the zero-prevention term, which can be 1e-5, to avoid the reciprocal being too large and the weights being extremely biased when RMSE(i) is extremely small.

[0048] (3) Normalized weights: (8) in, This represents the global fusion weight of the i-th model.

[0049] (4) Weighted fusion output: For any input x, the output of the i-th model is Then the fusion prediction ( )for: (9) When local measurement data for the target airport is unavailable, a set of general initial weights can be used based on publicly available lidar data or typical meteorological conditions. During engineering deployment, these weights can be updated by incorporating historical statistics or online calibration of the target airport.

[0050] Step 3: Dataset Construction and Preprocessing: This step uses the data generated in Step 2 to construct a dataset for training, validating, and testing deep learning models.

[0051] Randomly generate dimensionless vortex dissipation rates within a given parameter range. Dimensionless buoyancy frequency The initial wake vortex height Z0 and initial wake vortex circulation Γ0 are obtained by dimensionless processing of the initial wake vortex height and circulation, vortex dissipation rate, and buoyancy frequency according to the method in step one. These are then input into the various traditional wake vortex evolution models in step two as initial conditions for the evolution of wake vortex height and circulation. The wake vortex circulation evolution and wake vortex height evolution data obtained from each wake vortex evolution model are weighted and fused to construct the model training dataset. The dataset is divided into training, validation, and test sets according to a ratio of 70%, 20%, and 10%, respectively, as shown in Table 2. Furthermore, the dataset size and parameter range can be adjusted according to airport operational needs.

[0052] Table 2 Basic Information of the Dataset

[0053] The parameter ranges listed in Table 2 are used to construct the value range of the training dataset to cover typical airport approach or takeoff phase wake vortex evolution scenarios. The dimensionless vortex dissipation rate is included. With dimensionless buoyancy frequency The ε and N values ​​obtained from meteorological observations are calculated using dimensionless methods in step one. Their ranges can be set based on typical values ​​from historical meteorological statistics or literature. The dimensionless vortex dissipation rate and buoyancy frequency ranges set in this example cover most wake vortex evolution environmental conditions and have broad applicability. The initial wake vortex height Z0 is related to the aircraft type and approach or climb profile; this embodiment provides 100m-350m to cover common operating altitudes. The wake vortex evolution time is set to 180s, which can cover the entire lifecycle evolution of wake vortices for most aircraft types under various environments. The above ranges are not fixed constants and can be expanded or reduced according to the operational and meteorological characteristics of the target airport.

[0054] Step 4: Construct a deeply coupled CNN-BiLSTM neural network model: This step constructs a deep learning model capable of effectively capturing short-term local features and long-term dependencies in the wake vortex evolution. A schematic diagram of the LSTM network structure is shown below. Figure 3 As shown in the diagram, the BiLSTM network structure is as follows: Figure 4 As shown.

[0055] During the model training phase, the dimensionless time series ( ), dimensionless vortex dissipation rate ( ), dimensionless buoyancy frequency ( ) and the initial state parameters of the wake vortex (dimensionless circulation) With dimensionless height Combined into a multidimensional feature vector [ , , , , ] as input features for the model.

[0056] Leveraging the powerful feature extraction capabilities of Convolutional Neural Networks (CNNs), convolution operations are first performed on the wake vortex circulation and height evolution data. The CNN module then performs sliding window calculations on the time axis using convolution kernels to capture local correlations and abrupt changes in wake vortex evolution data within short time steps, thereby identifying short-term local features of wake vortex evolution. This process effectively extracts the nonlinear mapping relationship between input parameters and the current state of the wake vortex, providing feature-enhanced local feature representations for subsequent time-series predictions.

[0057] The local features identified by the CNN module are input into a bidirectional long short-term memory neural network (BiLSTM). Since the evolution of the wake vortex is not only related to the current state, but also strongly correlated with the historical process and future evolution trend, a single LSTM cannot utilize future information. BiLSTM is composed of forward LSTM and backward LSTM, which can more deeply identify the evolution features of the wake vortex.

[0058] Among them, forward LSTM: processes the input sequence in chronological order to extract historical time-series information (forward features) of the wake vortex evolution. Backward LSTM: Processes the input sequence in reverse time order to capture the reverse dependency of the wake evolution (backward feature). Gating mechanism: BiLSTM internally utilizes a forget gate (f t ), input gate (i t ) and output gate (o t The system uses a gating mechanism to regulate information flow. The forget gate discards redundant historical information about the wake vortex, while the input gate updates the environmental parameters to the storage unit (C). t In ), the output gate controls the final hidden state (h) t This mechanism effectively alleviates the gradient vanishing problem in long-sequence training and enables the full extraction of long-term characteristics of vortex evolution.

[0059] Finally, the forward and backward output state vectors of BiLSTM are concatenated to form a complete feature vector containing the bidirectional spatiotemporal characteristics of the wake vortex evolution.

[0060] To prevent overfitting during training, a Dropout layer is introduced to randomly discard neurons at a predetermined ratio. Then, a fully connected layer maps the high-dimensional features to the output space, outputting the future dimensionless time series. The predicted dimensionless wake circulation ( ) and dimensionless wake height ( ).

[0061] Step 5: To address the problem that traditional manual experience or grid search for determining hyperparameters is inefficient and prone to getting trapped in local optima, this step uses the Bayesian optimization algorithm to globally optimize the key hyperparameters of the CNN-BiLSTM model.

[0062] This method constructs a probabilistic model (surrogate model) of the objective function, utilizing prior knowledge to approximate the complex mapping relationship between hyperparameters and model prediction performance. The specific implementation process is as follows: (1) Constructing the hyperparameter search space: Determine the key hyperparameters to be optimized and their value ranges. Based on the characteristics of the wake prediction model, the following hyperparameter search space is set in this example.

[0063] Kernel size: The search range is [3,7], which is used to adjust the receptive field of the CNN for extracting local features; Number of convolution kernels: The search range is [16, 128], which determines the richness of feature extraction; Number of BiLSTM neurons: The search range is [32, 256], which affects the model's memory capacity for long-term dependencies; Dropout ratio: The search range is [0.1, 0.5], used to control the regularization strength to prevent overfitting; Learning rate: Search range is

[10] -4 10 -2 [Controls the step size for updating model parameters; batch size:] The search range is [32, 128], balancing training speed and gradient stability.

[0064] (2) Initialization and Gaussian process regression: Randomly sample a small number of initial points in the hyperparameter space and run the CNN-BiLSTM model to calculate the root mean square error (RMSE) on the validation set as the initial observations. Using a Gaussian process as a surrogate model, fit the posterior probability distribution between the hyperparameters and the RMSE loss function based on the existing observations. This not only predicts the function value (mean) of unknown points, but also provides the uncertainty (variance) of the prediction.

[0065] (3) Acquisition Function-Guided Search: Using the acquisition function, the expected improvement (EI) strategy is adopted to find the next evaluation point in the hyperparameter space. The acquisition function takes into account both "exploration" (i.e., searching near the current optimal value) and "exploration" (i.e., searching in regions with high uncertainty), and selects the hyperparameter combination with the largest acquisition function value as the parameters for the next round of model training.

[0066] (4) Model Training and Iterative Update: Substitute the hyperparameter combination selected in step (3) into the CNN-BiLSTM model, train it using the Adam optimizer, and calculate its RMSE on the validation set. Add the new hyperparameters and their corresponding RMSE values ​​to the observation set and update the posterior distribution of the Gaussian process surrogate model. Repeat the steps of "finding the maximum acquisition function point, training and evaluating, and updating the surrogate model" until the preset number of iterations or performance convergence conditions are met, and finally output the globally optimal hyperparameter combination.

[0067] Table 3 shows the hyperparameter search range settings and Bayesian optimization results as an implementation example of this invention.

[0068] Table 3. Hyperparameter results of the Bayesian optimization model

[0069] Step Six: Deterministic Wake Vortex Prediction: In actual aviation operation scenarios, the pre-trained CNN-BiLSTM optimal model is deployed for online prediction. This step not only includes forward inference of the model but also transforms the dimensionless output of the neural network into a practical physical quantity that can be used for air traffic control through a rigorous physical parameter restoration mechanism. The specific process is as follows: (1) Real-time feature vector construction: Receive real-time data transmitted from lidar, airborne data link, or weather station, including the target aircraft's flight parameters (wingspan B, initial circulation of the wake vortex Γ0, initial wake vortex height Z0) and current atmospheric environmental parameters (vortex dissipation rate ε, buoyancy frequency N). Calculate the dimensionless feature vector according to the preprocessing standards in step one. , , , , [Use as model input]

[0070] (2) Model Inference and Prediction: The constructed feature vectors are input into the optimal CNN-BiLSTM model determined in step five. The model performs a single forward propagation on the time axis and outputs the dimensionless wake circulation prediction value for a future time series. ( and dimensionless wake height value ( ).

[0071] (3) Dedimensionalization of physical parameters: In order to convert the wake vortex circulation and altitude output by the model into flight parameters with actual physical meaning, it is necessary to dedimensionalize them. The specific method for dedimensionalizing wake vortex circulation and wake vortex altitude is as follows: (10) (11) (12) Where t represents the actual time, and b0 represents the initial vortex core spacing, which is usually taken as... , The time interval is dimensionless, and w0 represents the initial descent velocity of the wake vortex, calculated as follows: , Indicates dimensionless The dimensionless wake circulation at time t, where Γ0 represents the initial wake circulation, is calculated as follows: Г(t) represents the actual circulation value at time t, Z(t) represents the actual height of the wake at time t, and Z0 represents the initial height of the wake. Indicates dimensionless The dimensionless wake height corresponding to the given moment.

[0072] (4) Trajectory Generation and Index Output: Through the above calculations, the complete evolution trajectory of the wake vortex in real physical space [Г(t), Z(t)] is generated. Based on the wake vortex intensity safety threshold and height safety envelope specified by the International Civil Aviation Organization (ICAO), this invention will automatically calculate two key operational indicators: ① Wake vortex dissipation time: the time required for the predicted circulation Г(t) to decay to a level that poses no harm to following aircraft; ② Safe vertical separation: the time required for the predicted wake vortex height Z(t) to descend below the preset safe height. These indicators will serve as the decision-making basis for dynamic wake separation reduction.

[0073] Step 7: Wake Vortex Evolution Probability Prediction: To quantify the impact of atmospheric uncertainties (such as wind shear and turbulence) on wake vortex evolution, this step constructs a probabilistic prediction model based on the CNN-BiLSTM model using Monte Carlo Dropout (MC Dropout) technology. This method does not require changes to the network structure; it approximates the posterior probability distribution of the Bayesian neural network simply through random sampling in the inference phase, thus providing a reliable range for wake vortex evolution for the dynamic interval standard. The specific implementation process is as follows: (1) Enable random dropout during the inference phase: Unlike traditional neural networks that disable Dropout during the testing phase, this method forces the Dropout layer to remain enabled during the actual application (inference) phase of the model. Based on the Bayesian optimization results in step five, the Dropout probability is set (in this invention, it is set to p=0.1), so that neurons in the network are randomly dropped with probability p during each forward propagation.

[0074] (2) Monte Carlo sampling: For the same set of real-time input feature vectors, the control model performs forward propagation predictions T times (e.g., T=100). Due to the randomness introduced by Dropout, the wake vortex circulation and height trajectories obtained in each prediction are slightly different. The resulting wake vortex circulation prediction sample set and wake vortex height prediction sample set are represented as follows: (13) (14) in, This indicates that the i-th forward propagation occurs at a dimensionless time. Predicted values ​​for dimensionless wake vortex annulus. This indicates that the i-th forward propagation occurs at a dimensionless time. Predicted values ​​for the dimensionless wake height, i=1,2,…,T.

[0075] (3) Statistical analysis and distribution fitting: Statistical analysis is performed on the T groups of predicted sequences obtained from sampling, and the results at each time step are calculated. The predicted mean and variance of the wake circulation and wake height are used. The predicted mean represents the most probable trajectory of the wake evolution, while the predicted variance quantifies the uncertainty of the current prediction results. The calculation method is as follows: (15) (16) (17) (18) in, , They are respectively The predicted mean and predicted variance of the wake vortex circulation. , They are respectively The predicted mean and variance of the wake height, where T represents the number of Monte Carlo simulations. It represents dimensionless time.

[0076] (4) Constructing the probability prediction interval: Based on the prediction mean and variance, a prediction interval at a specified confidence level (e.g., 95%) can be constructed. The upper confidence limit for the wake circulation is specified in the figure. With confidence lower limit The calculation method is as follows: (19) Similarly, the upper confidence limit for wake vortex height. With confidence lower limit The calculation method is as follows: (20) This range visually illustrates the potential range of wake vortex evolution; a wider range indicates higher prediction uncertainty (e.g., in the later stages of evolution or under extreme weather conditions). In practical applications, the wake vortex evolution prediction range can be used for conservative control. For example, when the probability range is too wide, it can trigger a switch to a more conservative strategy or extend the flight wake vortex interval, thereby explicitly incorporating model uncertainty into the safety management closed loop.

[0077] Figure 5 , Figure 6 This paper demonstrates the technical effectiveness of the present invention in predicting the accuracy of wake vortex circulation and height evolution. Using the results of large eddy simulation as the reference ground truth, the prediction curves are compared with those of single deep learning models (CNN, BiLSTM), traditional physical models (P2P, Eddy-Dissipation, TDAWP, APA), and the CNN-BiLSTM fusion model of the present invention. Figure 5 and Figure 6 As can be seen intuitively, the prediction curve of this invention is more consistent with the reference true curve throughout the entire time period. Especially in the rapid decay stage of circulation and the middle and late stages of high sedimentation, it can maintain both the ability to track local changes and the stability of long-term trends, demonstrating the coupling advantage of "CNN extracting short-term local features combined with BiLSTM extracting bidirectional long dependencies".

[0078] Figure 7 , Figure 8 This demonstrates the uncertainty quantification effect of the present invention. During the inference phase, Dropout is kept on and multiple Monte Carlo samplings are performed to obtain the predicted mean and a 95% confidence interval. The degree to which the confidence interval covers the reference true curve reflects the prediction reliability, and the change in interval width over time reflects the accumulation of uncertainty in the wake evolution. This interval can quantify the uncertainty of the model at different evolution stages. A narrower interval indicates stable prediction, while a wider interval suggests that a more conservative dynamic interval strategy should be adopted in the later stages of the wake or when there is greater uncertainty in the recorded meteorological data.

[0079] Figure 7 As can be seen, the prediction interval basically maintains its width. Figure 8 Because the initial time period prediction was relatively accurate and the interval was narrow, although it gradually widened in the later period, the overall width was still relatively narrow, which fully demonstrates that the uncertainty quantification effect of this prediction method is good.

[0080] In summary, this invention constructs a high-confidence dataset through weighted fusion of multiple wake vortex physical models, effectively overcoming the challenge of scarce measured full-lifetime wake vortex data. Utilizing a deeply coupled architecture of CNN and BiLSTM, it accurately captures local abrupt changes and long-term dependent features in wake vortex evolution. Simultaneously, it combines Bayesian optimization to achieve global automatic optimization of hyperparameters and introduces MC Dropout technology to output probability predictions with a 95% confidence interval. This ensures real-time performance while providing a quantifiable range of wake vortex evolution uncertainty for the implementation of dynamic wake intervals.

[0081] The beneficial effects of this invention include: (1) By constructing training data labels through weighted fusion of multiple traditional models, a more stable and reliable dataset can be generated in the absence of large-scale measured life-cycle wake vortex data, thereby improving model training efficiency and generalization ability. (2) The deep coupling of CNN and BiLSTM enables the joint identification of short-term and long-term features of the wake vortex, which can significantly improve the prediction accuracy and reduce the accumulation of long-term prediction errors compared with a single CNN or a single BiLSTM. (3) Bayesian optimization enables automatic hyperparameter search, improves training efficiency and reduces the risk of performance instability and overfitting caused by manual experience-based parameter tuning; (4) MC Dropout outputs confidence intervals, providing an interpretable safety margin range for dynamic wake intervals and improving the reliability of model decisions; (5) The method of the present invention only requires one forward propagation during the deployment phase to obtain a deterministic prediction result, which meets the real-time requirements of airport operations. When risk assessment is required, the probability interval can be obtained through a limited number of MC Dropout forward propagations (e.g., 50-100 times), achieving a balance between prediction accuracy and reliability under the premise of controllable computational overhead.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting aircraft wake vortices based on multi-model fusion, characterized by the following steps: include: S1. Obtain the initial parameters of the wake vortex and atmospheric environment parameters, perform dimensionless processing, and combine them into a multi-dimensional feature vector; S2. Based on the measured data of lidar, determine the fusion weights of multiple traditional inversion prediction models of wake vortex; input the multidimensional feature vectors from step S1 into each traditional inversion prediction model, and perform weighted fusion according to the fusion weights to construct a model training dataset. S3. Construct a CNN-BiLSTM deeply coupled neural network model with a Dropout layer; train the model using the training dataset from step S2, and use the Bayesian optimization algorithm to perform global hyperparameter optimization to obtain the optimal model. S4. Obtain the real-time initial parameters of the wake vortex and atmospheric environment parameters, and construct the real-time feature vector; The real-time feature vector is input into the optimal model for a single forward propagation, and a dimensionless wake prediction value is output. The dimensionless wake prediction value is then dediminished to generate a physical space evolution trajectory, thereby achieving deterministic prediction of the wake. S5. During the inference phase, the Dropout layer of the optimal model is forcibly kept on, and the optimal model is controlled to perform multiple forward propagations of the real-time feature vectors to generate a set of prediction samples. Based on the set of prediction samples, the probability interval of the wake vortex evolution is statistically calculated to achieve the prediction of the wake vortex evolution probability.

2. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, The initial parameters of the wake vortex described in S1 and the initial parameters of the real-time wake vortex described in S4 both include at least: the initial circulation of the wake vortex and the initial height of the wake vortex; The atmospheric environmental parameters mentioned in S1 and the real-time atmospheric environmental parameters mentioned in step S4 both include at least: vortex dissipation rate and buoyancy frequency.

3. The aircraft wake vortex prediction method based on multi-model fusion according to claim 2, characterized in that, The dimensionless processing specifically includes: calculating the initial vortex core spacing and the initial descent velocity of the wake vortex; Using the initial vortex core spacing and the initial descent velocity of the wake vortex, the dimensionless time series, dimensionless vortex dissipation rate, dimensionless buoyancy frequency, dimensionless initial circulation of the wake vortex, and dimensionless initial height of the wake vortex are calculated respectively.

4. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, The multiple conventional inversion prediction models for wake vortices mentioned in S2 include at least one of the P2P model, TDAWP model, Eddy-Dissipation model, and APA model.

5. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, The determination of the fusion weights of multiple traditional wake vortex inversion prediction models described in S2 specifically includes: calculating the root mean square error of each traditional wake vortex inversion prediction model; The reciprocal score of the error of each traditional inversion prediction model for the wake vortex is calculated based on the root mean square error. The normalized weights are calculated based on the inverse error score, and these normalized weights are used as the global fusion weights.

6. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, The construction of the CNN-BiLSTM deep coupled neural network model with Dropout layers described in S3 includes: The convolutional neural network module is used to extract local correlation features within a short time step as short-term local features by calculating and extracting them through a sliding window. The short-term local features are input into the bidirectional long short-term memory neural network module, and forward features are extracted by forward LSTM and backward features are extracted by backward LSTM. The information flow is regulated by gating mechanisms such as forget gate, input gate, and output gate, and the state vectors corresponding to the forward features and the backward features are concatenated. After passing through the Dropout layer, the predicted value is mapped out through a fully connected layer; The Dropout layer sets the dropout ratio.

7. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, The use of Bayesian optimization algorithm for global hyperparameter optimization described in S3 specifically includes: Construct a hyperparameter search space that includes kernel size, number of kernels, number of BiLSTM neurons, Dropout ratio, learning rate, and batch size; The posterior probability distribution between the hyperparameters and the root mean square error loss function is fitted using a Gaussian process. The next hyperparameter combination is selected using the expected improvement strategy, and the iteration continues until the convergence condition is met.

8. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, After generating the physical space evolution trajectory as described in S4, it also includes: Based on the physical space evolution trajectory, the time required for the predicted circulation to decay to a level that poses no harm to the following aircraft is calculated and used as the wake dissipation time. Calculate the time required for the predicted wake height to drop below the preset safe height, and use this as the safe vertical interval.

9. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, After generating the prediction sample set as described in S5, the following is also included: Calculate the prediction mean and prediction variance at each dimensionless time step; Based on the predicted mean and the predicted variance, the upper and lower confidence limits are calculated, and the prediction interval at the specified confidence level is constructed as the wake vortex evolution probability interval.

10. The aircraft wake vortex prediction method based on multi-model fusion according to claim 1, characterized in that, The deterministic prediction results output by S4 and the probabilistic prediction results output by S5 are used as the decision basis for dynamic wake interval reduction. When the width of the wake evolution probability interval exceeds a preset threshold, switch to a conservative strategy or extend the flight wake interval.

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