A method for processing aircraft aerodynamic parameters based on GNN-LSTM network

Abstract

This invention discloses a method for processing aircraft aerodynamic parameters based on a GNN-LSTM network, comprising: acquiring aircraft surface grid data; constructing a graph structure by treating grid points as nodes and based on adjacency relationships; constructing an input feature vector for each node; inputting the graph structure and feature vectors into a graph neural network and extracting node spatial features through graph convolution; arranging the spatial features of the same node under different operating conditions in the order of operating conditions to form an operating condition sequence, and inputting it into a bidirectional long short-term memory network to extract temporal features; finally, obtaining the predicted pressure coefficient of each node under each operating condition through an output regression layer. This invention also introduces a joint loss function including data loss and multiple physical constraints for model training. The method, through collaborative modeling of the graph neural network and the bidirectional long short-term memory network, takes into account both the local spatial details of pressure distribution and the evolution law across operating conditions, significantly improving the accuracy, physical consistency, and generalization ability of aerodynamic parameter prediction.

Description

Technical Field

[0001] This invention relates to the field of aircraft aerodynamics analysis technology, and in particular to a method for processing aircraft aerodynamic parameters based on GNN-LSTM networks. Background Technology

[0002] Aircraft performing high-speed maneuvers and long-range missions in complex aerodynamic environments have aerodynamic characteristics that directly affect lift generation, drag levels, and attitude stability, serving as the foundation for flight performance evaluation and flight control law design. For aircraft adopting new layouts and aerodynamic shapes, accurately obtaining the wing surface pressure distribution and key aerodynamic coefficients not only determines the upper limit of aerodynamic shape optimization but also relates to subsequent handling and stability analysis and flight safety margins. Therefore, aerodynamic parameter modeling and estimation for actual operating conditions has significant engineering value.

[0003] Currently, aerodynamic modeling methods can be divided into two categories. The first category relies on wind tunnel tests and high-fidelity numerical simulations, constructing an aerodynamic database through offline interpolation or simplified mechanistic models, and obtaining aerodynamic forces and moments by looking up tables at a given angle of attack and Mach number. This type of method has high accuracy but is costly, inconvenient to update, and exhibits significant errors when extrapolating operating conditions. The second category is based on data-driven methods, utilizing multilayer perceptrons, convolutional neural networks, or recurrent neural networks to map operating parameters and geometric information to lift coefficients, drag coefficients, or pressure distributions. This type of method reduces modeling costs to some extent, but it is often difficult for a single structure to simultaneously account for local spatial details and overall distribution consistency, and fitting errors and local oscillations still exist.

[0004] Existing research has shown that aerodynamic surrogate models constructed based on response surface methodology, polynomial fitting, and Kriging techniques can be used to quickly estimate lift, drag, and pitching moment for typical configurations. Other works have combined simplified mechanical models with interpolation methods to calibrate and extrapolate polar curves at different angles of attack and Mach numbers. These methods perform well in low-dimensional aerodynamic coefficient spaces, but most only address a small number of scalar coefficients, limiting their ability to describe high-dimensional airfoil pressure distribution and local flow details. Summary of the Invention

[0005] The purpose of this invention is to provide a method for processing aircraft aerodynamic parameters based on GNN-LSTM networks. GNN-LSTM networks can take into account both spatial details and the evolution of operating conditions, while also providing high-precision prediction of aerodynamic parameters with physical consistency, thereby improving the accuracy, physical consistency, and generalization ability of aerodynamic parameter prediction.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for processing aircraft aerodynamic parameters based on GNN-LSTM networks includes the following steps: Obtain grid data of the aircraft surface, take each grid point in the grid data as a node, construct edges according to the adjacency relationship between grid points, and form a graph structure; An input feature vector is constructed for each node, which includes the node's geometric location information, current operating parameters, and area markers; The graph structure and the input feature vector of each node are input into the graph neural network. The neighborhood information of each node is aggregated through graph convolution operation, and the spatial features of each node under the current working condition are extracted to obtain the node spatial feature vector. The node spatial feature vectors corresponding to the same node under multiple different working conditions are arranged in the order of working conditions to form working condition sequence features; The working condition sequence features are input into a bidirectional long short-term memory network, and temporal features are extracted along the positive and negative directions of the working condition sequence to obtain a node temporal feature vector that integrates spatial and working condition information. The node time-series feature vectors are input into the output regression layer to obtain the predicted pressure coefficient of each node under various working conditions.

[0007] Furthermore, the geometric position information is the three-dimensional coordinate data of the node; the current operating parameters include angle of attack, Mach number, and control surface deflection angle; the area markings include upper wing surface markings, lower wing surface markings, and segment numbers in the wingspan direction.

[0008] Furthermore, the update formula for node features in the graph convolution operation is as follows: , In the formula, , Indicates the first Layer and first The features of the i-th node of the layer, This represents the number of neighbors of the i-th node. It is a non-linear activation function. Indicates the first Features of the j-th node in the layer; , Let represent the learnable weight matrix of the l-th layer, which is used to perform linear transformations on the node's own features and the features of its neighboring nodes, respectively.

[0009] Furthermore, the bidirectional long short-term memory network includes a forward long short-term memory network and a backward long short-term memory network, and the node temporal feature vector is obtained by concatenating the forward hidden state output by the forward long short-term memory network and the backward hidden state output by the backward long short-term memory network.

[0010] Furthermore, this is achieved by minimizing the joint loss function when training the graph neural network and the bidirectional long short-term memory network;

[0011] Joint loss function: ; in, For the data loss term, mean squared error (MSE) is used to measure the difference between the predicted and actual values. As the global aerodynamic consistency loss term, the lift, drag and pitching moment coefficients are obtained by integrating the predicted pressure coefficient and then calculated with the actual values; The gradient consistency loss term constrains the pressure difference between adjacent nodes to remain consistent with the actual pressure difference. This is a tangential gradient constraint term to ensure that the change in pressure along the tangential direction of the object surface conforms to geometric relationships; The Laplace smoothing term constrains the spatial smoothness of the predicted pressure. As a symmetry constraint term, the pressure coefficients on geometrically symmetric nodes are kept consistent. This is a range constraint term, where the constraint pressure coefficient is within the range of physical extreme values. ~ These are the weighting coefficients for each constraint term.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) By constructing the aircraft surface mesh as a graph structure and using graph neural networks to perform graph convolution operations, the local features of pressure distribution (such as peaks and valleys, gradients) can be accurately captured by explicitly utilizing the mesh topology relationship, which significantly improves the ability to describe the pressure distribution and local flow details of high-dimensional airfoils.

[0013] (2) By modeling different working conditions as a sequence, it is possible to effectively learn the dynamic trend and dependency of pressure distribution with working conditions (such as angle of attack), ensure the continuity and consistency of prediction results in the working condition dimension, and improve the generalization ability of the model when extrapolating working conditions.

[0014] (3) Introduce multi-level physical constraints (including global aerodynamic consistency constraints, local physical consistency constraints, symmetry constraints and range constraints, etc.) into the loss function so that the model not only fits the data during the training process, but also learns solutions that conform to the basic laws of aerodynamics, effectively avoiding the non-physical oscillation and local error accumulation problems common in pure data-driven models.

[0015] (4) Experimental verification on the CHN-F1 aerodynamic dataset shows that the GNN-BiLSTM network model outperforms the baseline models such as MLP, GNN-only, and BiLSTM-only in key indicators such as mean square error and mean absolute error. Moreover, the predicted pressure coefficient curve is highly consistent with the actual results in terms of shape, demonstrating excellent fitting accuracy and stability. Attached Figure Description

[0016] Figure 1 The test set overall error index and scatter plot provided by this invention.

[0017] Figure 2 This is a comparison chart of the actual pressure coefficient and the predicted pressure coefficient under a single operating condition provided by the present invention.

[0018] Figure 3 This is a detailed comparison diagram of the actual pressure coefficient and the predicted pressure coefficient in a local area provided by the present invention. Detailed Implementation

[0019] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0020] This embodiment discloses a method for processing aircraft aerodynamic parameters based on GNN-LSTM networks, including the following steps: Step 1: Data preprocessing and graph construction; The process involves acquiring grid data of the aircraft surface and designating each grid point as a node V. Edges E are constructed based on the adjacency relationships between grid points, forming a graph structure G=(V,E). Simultaneously, an input feature vector h is constructed for each node. This input feature vector includes the node's geometric position information, current operating parameters, and region markers. The geometric position information consists of the node's three-dimensional coordinates (x, y, z). The region markers are the upper and lower wing surfaces, and the segment numbers along the wingspan. The current operating parameters are the power angle α, Mach number M, and control surface deflection angle β under the current operating conditions.

[0021] All input features are linearly normalized according to sample statistics to make features of different dimensions fall within a similar numerical range.

[0022] Step 2: Construct the GNN-LSTM network model; The GNN-LSTM network model includes a spatial feature extraction module, a temporal feature extraction module, and an output module.

[0023] The spatial feature extraction module is implemented using a graph neural network (GNN). The graph structure and the input feature vector of each node are input into the graph neural network. The neighborhood information of each node is aggregated through graph convolution operations to extract the spatial features of each node under the current working condition, thus obtaining the node spatial feature vector. The node spatial feature vectors corresponding to the same node under multiple different working conditions are arranged in the order of working conditions to form the working condition sequence feature.

[0024] The update of the graph neural network is as follows: , In the formula, , Indicates the first Layer and first The features of the i-th node of the layer, This represents the number of neighbors of the i-th node. It is a non-linear activation function. Indicates the first Features of the j-th node in the layer; , Let represent the learnable weight matrix of the l-th layer, which is used to perform linear transformations on the node's own features and the features of its neighboring nodes, respectively.

[0025] By stacking multiple layers of graph convolutions, the features of each node can aggregate information from a larger neighborhood, thereby capturing patterns in the local stress distribution. For each operating condition, the graph neural network outputs a node spatial feature vector for that condition.

[0026] The temporal feature extraction module is implemented using a bidirectional long short-term memory network (BiLSTM). The working condition sequence features are input into the BiLSTM network, and temporal features are extracted along the positive and negative directions of the working condition sequence to obtain a node temporal feature vector that integrates spatial and working condition information. Let the input at time step (operating condition number) t be... (Node features output by the graph neural network), hidden state is The memory unit is The update for the Bidirectional Long Short-Term Memory (BiLSTM) network is as follows: Input gate , Forgotten Gate , Output gate , Candidate cell status , memory unit , Hidden state , in, It is the Sigmoid activation function. , , , This is the scaling factor parameter matrix; , , The hidden state of the previous time step is represented by the cyclic weight matrix of each gate unit. for, , , , For the corresponding bias vector, For element-wise multiplication, It is the hyperbolic tangent function.

[0027] To fully utilize the information at both ends of the sequence, a bidirectional long short-term memory network with a bidirectional structure is adopted. The long short-term memory network is run once from front to back and once from back to front along the operational dimension to obtain the forward hidden state. and backward hidden state And concatenate them to obtain the node temporal feature vector. This representation includes information on changes in both directions: from low angle of attack to high angle of attack and from high angle of attack to low angle of attack.

[0028] The output module is implemented using a multi-layer fully connected layer. The temporal feature vector of the node is input to the output regression layer to obtain the predicted pressure coefficient of each node under various working conditions.

[0029] For each operating condition and node, the corresponding bidirectional time-series features are input to and output to the regression layer to obtain the predicted pressure coefficient value: , This represents the pressure coefficient of the i-th node under operating condition t. It is a regression mapping consisting of fully connected layers and nonlinear activations.

[0030] Step 3: Optimize all trainable parameters of the GNN-LSTM network model by minimizing the joint loss function to obtain the final GNN-LSTM network model, and use the predicted pressure coefficient of each node of the GNN-LSTM network model under each working condition.

[0031] Joint loss function: ; in, For the data loss term, mean squared error (MSE) is used to measure the difference between the predicted and actual values. As the global aerodynamic consistency loss term, the lift, drag and pitching moment coefficients are obtained by integrating the predicted pressure coefficient and then calculated with the actual values; The gradient consistency loss term constrains the pressure difference between adjacent nodes to remain consistent with the actual pressure difference. This is a tangential gradient constraint term to ensure that the change in pressure along the tangential direction of the object surface conforms to geometric relationships; The Laplace smoothing term constrains the spatial smoothness of the predicted pressure. As a symmetry constraint term, the pressure coefficients on geometrically symmetric nodes are kept consistent. This is a range constraint term, where the constraint pressure coefficient is within the range of physical extreme values. ~ These are the weighting coefficients for each constraint term.

[0032] Global aerodynamic consistency loss term , This is the lift coefficient loss term. This is the drag coefficient loss term. This is the pitch moment coefficient loss term. This constraint controls the pressure distribution at the overall force and moment level, effectively avoiding global deviations caused by the accumulation of local errors.

[0033] Gradient consistency loss term , , This represents the pressure coefficients of the i-th node and the j-th node. This represents the pressure difference between nodes in the reference data. This constraint suppresses non-physical high-frequency oscillations, making the prediction results smoother and consistent with flow continuity.

[0034] Tangential gradient constraint term , Here, is the surface tangential gradient operator, representing the gradient along the direction of the tangential plane on the object's surface. Let Cp be the spatial full gradient of the pressure coefficient Cp at node i. This is the projection matrix of the tangent plane. This constraint ensures that the direction of pressure change is consistent with the surface geometry, thereby improving the physical plausibility of the boundary layer region.

[0035] Trulaplatz smoothing term L is the graph Laplace matrix, which can be regarded as a discrete diffusion process and helps to improve the stability of the predicted distribution.

[0036] Symmetry constraint terms , Let be the spatial coordinates of surface node i. For nodes Regarding the mirror coordinates of the model's symmetry plane, this constraint significantly reduces the model's prediction bias in symmetric regions and improves its generalization ability.

[0037] Range constraint terms , , The maximum and minimum pressure coefficients are respectively used as soft constraints, which help stabilize the training process.

[0038] This embodiment was validated on the CHN-F1 aerodynamic dataset. Under the same data partitioning and training configuration, the proposed GNN-BiLSTM network model was compared with baseline models such as MLP, GNN-only, BiLSTM-only, 1D-CNN, and the simplified GraphSAGE.

[0039] Figure 1 The overall error metrics and scatter plot relationships obtained from the test set are shown. The top left subplot presents a scatter plot of the actual Cp values ​​versus the predicted values, along with the main evaluation metrics. It can be seen that most sample points are closely distributed along the ideal diagonal. According to the statistical data in the figure: the mean absolute error (MAE) is 0.1159, the root mean square error (RMSE) is 0.1475, the coefficient of determination (R²) is 0.9887, and the sample size is 1080, indicating that the model can generally reconstruct the pressure coefficient relatively accurately. Figure 2 The top right subplot shows the histogram distribution of the prediction error. The average error is approximately 0.003, and the data distribution is concentrated around zero with no obvious long-tail characteristics, indicating that the model does not have a systematic overestimation or underestimation bias. Figure 2 The box plot at the bottom shows the statistical results divided according to the actual Cp value intervals. It can be seen that the median error within each interval remains close to zero, the box heights do not differ significantly, and only a few intervals have a small number of outliers. This indicates that the model maintains relatively consistent fitting accuracy across different pressure coefficient ranges.

[0040] Under a single operating condition, 13 representative cases were selected from the test set. Figure 2 The comparison between the actual pressure coefficient and the predicted pressure coefficient along the discrete point index direction is shown under this working condition. Figure 2 The upper part presents a multi-cycle comparison curve of the actual CP value and the predicted CP value. The prediction results in each cycle closely match the shape and amplitude of the actual curve. Figure 2 The lower half shows the corresponding pointwise error curves. It can be seen that the error range is small for most points, and the positive and negative errors are roughly symmetrically distributed, with no sustained positive or negative biases. Overall, under typical operating conditions, the model maintains consistency in its periodic structure and provides a relatively detailed fit in local regions.

[0041] Figure 3 The upper right subplot magnifies the sample index range [250, 400], clearly showing that the true curve and the predicted curve almost perfectly match in this transition range, with an extremely narrow error range. This indicates that even in regions of drastic local change, the model can still maintain a smooth fit. Figure 3 The box plot at the bottom statistically analyzes the absolute error across different sample index intervals (e.g., 0-135, 135-270, 270-405). The median and box height for each interval do not differ significantly, with only a few intervals showing a small number of outliers. No obvious concentration of "high error segments" was observed. This indicates that the model's error level remains generally balanced across different sample ranges.

[0042] Under the same data partitioning and training configuration, the proposed GNN-BiLSTM collaborative framework was compared with several representative deep learning baseline models, including MLP using only fully connected networks, GNN-only using only graph convolutions, BiLSTM-only relying only on bidirectional long short-term memory networks, one-dimensional convolutional neural networks (CNN1D), and a simplified version of GraphSAGE. The results show that the proposed GNN+BiLSTM model achieved the lowest mean squared error and mean absolute error (MSE=0.005451, MAE=0.0467) on the test set, outperforming other baseline models overall. In summary, GNN+BiLSTM exhibits stronger generalization ability and stability in the pressure coefficient fitting task, validating the necessity and effectiveness of combining graph structure modeling with sequence modeling. As shown in Table 1, it achieved the lowest mean squared error (MSE=0.005451) and mean absolute error (MAE=0.0467) on the test set, and the coefficient of determination R0 was also the lowest. 2 The score reached 0.9887, with the scatter points closely distributed along the ideal diagonal, and its overall performance was better than other baseline models.

[0043] Table 1 Error Analysis Comparison GNN+BiLSTM (This invention) 0.005451 0.0738 0.0467 1D CNN 0.005806 0.0762 0.0506 MLP 0.006057 0.0778 0.0508 GraphSAGE (simplified) 0.006228 0.0789 0.0535 GNN-only 0.006471 0.0804 0.0509 BiLSTM-only 0.008172 0.0904 0.0695 In summary, the CHN-F1 flying wing discrete mesh is formalized as a graph structure, with measurement points as nodes and mesh connections as edges. A graph neural network aggregates information in local neighborhoods and extracts pressure field features using topological relationships, demonstrating stronger spatial representation capabilities compared to vectorized input MLPs. Different angles of attack and other operating conditions are treated as "operating condition sequences." A bidirectional long short-term memory network is introduced after graph encoding to model the trend and dependence of Cp (pressure field value) across operating conditions, rather than training or simply concatenating parameters for each condition, thus improving cross-condition consistency. A "spatial graph encoding + operating condition sequence modeling" framework is proposed: a GNN extracts local Cp, and a BiLSTM learns cross-condition associations and outputs the Cp of each node. Compared to GNN-only and LSTM-only approaches, this framework is superior in terms of error and robustness, exhibiting better fitting accuracy and stability on the CHN-F1 wind tunnel multi-condition dataset.

[0044] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for processing aircraft aerodynamic parameters based on GNN-LSTM networks, characterized in that, Includes the following steps: Obtain grid data of the aircraft surface, take each grid point in the grid data as a node, construct edges according to the adjacency relationship between grid points, and form a graph structure; An input feature vector is constructed for each node, which includes the node's geometric location information, current operating parameters, and area markers; The graph structure and the input feature vector of each node are input into the graph neural network. The neighborhood information of each node is aggregated through graph convolution operation, and the spatial features of each node under the current working condition are extracted to obtain the node spatial feature vector. The node spatial feature vectors corresponding to the same node under multiple different working conditions are arranged in the order of working conditions to form working condition sequence features; The working condition sequence features are input into a bidirectional long short-term memory network, and temporal features are extracted along the positive and negative directions of the working condition sequence to obtain a node temporal feature vector that integrates spatial and working condition information. The node time-series feature vectors are input into the output regression layer to obtain the predicted pressure coefficient of each node under various working conditions.

2. The method for processing aircraft aerodynamic parameters based on GNN-LSTM network according to claim 1, characterized in that, The geometric position information is the three-dimensional coordinate data of the node; the current operating parameters include angle of attack, Mach number and control surface deflection angle; the area markings include upper wing surface markings, lower wing surface markings and segment numbers in the wingspan direction.

3. The method for processing aircraft aerodynamic parameters based on GNN-LSTM network according to claim 1, characterized in that, The formula for updating node features in the graph convolution operation is as follows: ， In the formula, , Indicates the first Layer and first The features of the i-th node of the layer, This represents the number of neighbors of the i-th node. It is a non-linear activation function. Indicates the first Features of the j-th node in the layer; , Let represent the learnable weight matrix of the l-th layer, which is used to perform linear transformations on the node's own features and the features of its neighboring nodes, respectively.

4. The method for processing aircraft aerodynamic parameters based on GNN-LSTM network according to claim 1, characterized in that, The bidirectional long short-term memory network includes a forward long short-term memory network and a backward long short-term memory network. The node temporal feature vector is obtained by concatenating the forward hidden state output by the forward long short-term memory network and the backward hidden state output by the backward long short-term memory network.

5. The method for processing aircraft aerodynamic parameters based on GNN-LSTM network according to claim 1, characterized in that, This is achieved by minimizing the joint loss function when training the graph neural network and the bidirectional long short-term memory network; Joint loss function: ； in, For the data loss term, mean squared error (MSE) is used to measure the difference between the predicted and actual values. As the global aerodynamic consistency loss term, the lift, drag and pitching moment coefficients are obtained by integrating the predicted pressure coefficient and then calculated with the actual values; The gradient consistency loss term constrains the pressure difference between adjacent nodes to remain consistent with the actual pressure difference. This is a tangential gradient constraint term to ensure that the change in pressure along the tangential direction of the object surface conforms to geometric relationships; The Laplace smoothing term constrains the spatial smoothness of the predicted pressure. As a symmetry constraint term, the pressure coefficients on geometrically symmetric nodes are kept consistent. This is a range constraint term, where the constraint pressure coefficient is within the range of physical extreme values. ~ These are the weighting coefficients for each constraint term.

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