Small sample aerodynamic modeling method based on multi-task learning

Abstract

The invention discloses a small sample aerodynamic modeling method based on multi-task learning. Comprising the following steps: constructing a multi-task prediction model, integrating an auxiliary task network and a target task network, and enhancing the feature extraction capability of an encoder through an SE layer and an attention layer; acquiring multi-source aerodynamic force data and carrying out standardized preprocessing on the multi-source aerodynamic force data; a dynamic weight mechanism is designed, the influence of auxiliary task prediction on target task output is adaptively adjusted according to input features, and effective fusion of low-fidelity data and high-fidelity data is achieved; two-stage training is carried out to ensure the efficiency and stability of multi-task learning; the prediction capability of the model under the limited sample condition is verified; through the synergistic effect of multi-task knowledge migration, feature enhancement and dynamic task integration, in combination with the feature optimization characteristics of an SE layer and an attention mechanism, high-precision aerodynamic prediction is realized under the condition of limited samples, and an efficient and accurate aerodynamic prediction method is provided for aircraft design.

Description

TECHNICAL FIELD The present application relates to the field of small sample aerodynamic force prediction, and in particular to a small sample aerodynamic force modeling method based on multi-task learning. BACKGROUND

[0001] The current aerodynamic force prediction field faces the following technical bottlenecks, which restrict the engineering application in the rapid prediction scenario: traditional methods rely on high-fidelity data (such as wind tunnel experiments or high-precision CFD simulation), but the acquisition cost of these data is high and time-consuming. Wind tunnel experiments are limited by equipment availability and experimental period, and cannot quickly provide data under diversified conditions; high-precision CFD simulation is difficult to meet the demand of rapid design iteration of aircraft due to high computational complexity and long time consumption of single simulation. On the other hand, low-fidelity data (such as simplified models or low-precision simulation) is easy to obtain, but the precision is insufficient, which cannot be directly used for high-precision engineering prediction, resulting in large deviation of the prediction results in actual application.

[0002] The application of data-driven model in aerodynamic force prediction has the following problems: insufficient feature extraction capability, traditional neural network is difficult to effectively capture key features under complex flow conditions when processing aerodynamic force data. Lack of flexibility in task integration, existing methods lack adaptive mechanism when fusing multi-source data, and cannot dynamically adjust the task contribution according to the input features, affecting the prediction effect. Unbalanced multi-task learning, the traditional multi-task learning framework is prone to gradient imbalance between auxiliary tasks (such as low-fidelity data prediction) and target tasks (such as high-fidelity data prediction), resulting in model bias to a certain task and decline of overall prediction accuracy. Poor training stability, gradient conflict and imbalance in multi-task learning make the model training process unstable and difficult to converge to the optimal solution. SUMMARY

[0003] The present application provides a small sample aerodynamic force modeling method based on multi-task learning, comprising the following steps: A multi-task prediction model is constructed, integrating auxiliary task network (low-fidelity data prediction) and target task network (high-fidelity data prediction), and embedding Squeeze-and-Excitation (SE) layer and attention layer in the encoder to optimize feature extraction and attention ability; Multi-source aerodynamic force data is acquired and standardized pretreated, and independent standardization is applied to features and targets respectively; A dynamic weight mechanism is designed to adaptively adjust the influence of auxiliary task prediction on target task output according to input features; A two-stage training process is adopted: the first stage is pre-training of auxiliary task, and the second stage is multi-task joint training using GradNormLoss to balance the gradient of auxiliary task and target task; The prediction accuracy of the model is verified, and the RMSE, MAE, R 2 and relative error are calculated, and the predicted and actual values are compared through visualization to verify the performance of the model.

[0004] Build a multi-task prediction model: design an architecture with separate encoder and decoder, the encoder consists of linear layers, ReLU activation functions, Squeeze-and-Excitation (SE) layers and attention layers, which are used to extract deep representations of input features (such as x coordinates); The auxiliary task decoder and the target task decoder generate low-fidelity and high-fidelity data predictions from the encoder output, respectively; Squeeze-and-Excitation (SE) layers generate channel-level scaling factors through global average pooling and sequential fully connected networks, recalibrate feature responses, and their output expression is: y = x * σ (W2 * ReLU (W1 * avg pool (x))) Where x is the input feature, avg pool is the adaptive average pooling, W and W are the weights of the fully connected layer, and ReLU and σ are the ReLU and Sigmoid activation functions, respectively; The attention layer calculates the feature weight through a small neural network, and the output expression is: a = σ (W * ReLU (W * x)) y = x * a Where W3 and W4 are the weights of the fully connected layer

[0005] Obtain multi-source aerodynamic data and preprocess: The input features (such as x coordinates) are standardized using StandardScaler, converted to zero mean and unit variance: x_scaled = (x - μ) / σ The output target (such as the pressure coefficient Cp) is also standardized: y_sca / ed = (y - μ - y) / σ - y Where μ and σ are the mean and standard deviation of the features and targets, respectively; Provide a reverse conversion method to restore the prediction results to the original scale.

[0006] Design a dynamic weight mechanism: calculate the dynamic weight according to the average absolute value of the encoded features, and use the Sigmoid function to generate the weight value: Where σ is the Sigmoid function, x i is the i-th element of the encoded feature; In forward propagation, the target task output is adjusted through the following formula: y = auxpred +(1-weight*w dynamic )*correction Wherein, aux pred is an auxiliary task prediction, correction is a target task correction term, and weight is a preset influence factor;The mechanism realizes adaptive fusion of low-fidelity and high-fidelity data.

[0007] Two-stage model training and optimization: The first stage is auxiliary task pre-training, and the auxiliary task is trained using low-fidelity data, and the loss function is mean square error (MSE): The Adam optimizer is used to update the model parameters;The second stage is multi-task joint training, and the auxiliary task and the target task are jointly trained, and Grad NormLoss is used to balance the task gradient: L total =w*L aux +w*L target Wherein, w and w2 are dynamic task weights, which are adjusted by GradNormLoss to align the task gradient norm;The target task loss function is mean square error:

[0008] Model verification and error analysis: calculate the prediction performance indicators, including root mean square error (RMSE), mean absolute error (MAE), determination coefficient (R 2 ) and relative error; The relative error is defined as: relative error =|y-y / (|y|+ε) Wherein, epsilon is a small constant to prevent division by zero;The scatter plot and trend line can be used to visualize the comparison between the predicted value and the high-fidelity data, low-fidelity data and training samples, and verify the accuracy of the model.

[0009] The beneficial effects of the present application are: by constructing a multi-task learning framework, combining Squeeze-and-Excitation (SE) layer and attention mechanism to optimize feature extraction, dynamic weight mechanism to adaptively integrate auxiliary task and target task prediction, GradNormLoss to balance task learning, significantly improve the accuracy and efficiency of aerodynamic force prediction under limited sample conditions, and provide a high-precision, high-robust aerodynamic force prediction method for aircraft design. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 The flowchart of the disclosed small sample aerodynamic force modeling method based on multi-task learning is shown.

[0011] Figure 2 is a structural diagram of the small sample aerodynamic force modeling method based on multi-task learning disclosed in the present application;

[0012] Figure 3 is a prediction result diagram of the negative pressure coefficient of the upper surface of the ONERA M6 airfoil in the embodiment;

[0013] Figure 4 is a prediction result diagram of the negative pressure coefficient of the lower surface of the ONERA M6 airfoil in the embodiment. DETAILED DESCRIPTION

[0014] The scheme of the present application will be described below in combination with the drawings and specific embodiments. Through the following, the advantages and characteristics of the present application can be more intuitively understood. It should be noted that the embodiments described in the present specification are only part of examples and do not represent all possible implementation manners.

[0015] The present embodiment provides an aerodynamic force modeling method based on multi-task learning, comprising the following steps:

[0016] Obtain a large amount of low-fidelity data

[0017] Obtain a small amount of high-fidelity data

[0018] Data standardization, input features: x coordinates are mapped to zero mean and unit variance through standardization processing: x scaled =(x-μ) / σ Wherein, μ is the mean of x, and σ is the standard deviation of x; output target: Cp (pressure coefficient) is standardized by the following formula: y scaled =(y-μ y ) / σ y Wherein, μ y is the mean of Cp, and σy is the standard deviation of Cp.

[0019] For the target task, high-fidelity data containing a small amount of samples are selected, and for the auxiliary task, low-fidelity data containing a large amount of samples are selected.

[0020] Basic network model: The network structure includes an encoder composed of a linear layer, a ReLU activation function, a Squeeze-and-Excitation (SE) layer and an attention layer, and the mathematical expression of the SE layer is: y=x*σ(W*ReLU(W*avg pool (x))) Wherein, x is the input feature, avg poolFor adaptive average pooling, W and W are the weights of the fully connected layer, ReLU and sigma are the ReLU and Sigmoid activation functions respectively, and the mathematical expression of the attention layer is: a = sigma(W*ReLU(W*x)) y = x*a Where W and W are the weights of the fully connected layer.

[0021] Dynamic weight mechanism: calculate the dynamic weight according to the encoded feature, and use the Sigmoid function: Where x i is the i-th element of the encoded feature; the final prediction of the target task is adjusted by the following formula: y = aux pred +(1-weight*w dynamic )*correction Where aux pred is the auxiliary task prediction, correction is the target task correction term, and weight is a preset influence factor.

[0022] Two-stage training process: first stage: auxiliary task pre-training, train the auxiliary task using low-fidelity data, and the loss function is: The model parameters are updated using the Adam optimizer; the second stage: multi-task joint training, jointly train the auxiliary task and the target task, and use GradNormLoss to balance the gradient: L total = w*L aux +w*L target Where w and w are dynamic task weights adjusted by GradNormLoss; the target task loss function is:

[0023] Model verification and performance evaluation; Error index: calculate the root mean square error (RMSE), mean absolute error (MAE), and determination coefficient (R 2 ), wherein epsilon is a small constant to prevent division by zero;

[0024] The present application provides two embodiments, which are ONERA M6 airfoils at Reynolds numbers of 11.72x10 6, the upper surface negative pressure coefficient and the lower surface negative pressure coefficient prediction experiment at Mach number 0.8395 and attack angle 3.06, wherein the high-fidelity data used in the experiment is derived from the wind tunnel experiment results in the literature report SCHMITT V, CHARPIN F. Pressure distributions on the ONERA-M6-wing at transonic Mach numbers[R]. AGARD-AR-138, 1979, and the low-fidelity data is calculated by the WIND CFD program developed by the NPARC Alliance. Embodiment 1: A multi-fidelity model is constructed for the aerodynamic force data of the ONERA M6 airfoil to predict the upper surface negative pressure coefficient, and the specific details are as follows: This embodiment uses the wind tunnel experiment data in the literature report of Schmitt and Charpin as high-fidelity data, and the results calculated by the WIND CFD program as low-fidelity data. This embodiment only uses a group of data with Reynolds number 11.72x10 6 , Mach number 0.8395 and attack angle 3.06 for experiment, taking x as the input of the model, and the output is the negative pressure coefficient. There are 4 high-fidelity data and 75 low-fidelity data. In order to simulate the engineering use scene, the high-fidelity data is only sampled 4, and the sampling method is random sampling, and all the low-fidelity data is used for model training, so as to prove the effectiveness and accuracy of the model. The result graph of the method of the present application for predicting the upper surface negative pressure coefficient of the ONERA M6 airfoil is shown in Figure 3 , the index of the prediction result is: RMSE: 0.110837, MAE: 0.064151, R 2 : 0.9290. Embodiment 2: A multi-fidelity model is constructed for the aerodynamic force data of the ONERA M6 airfoil to predict the lower surface negative pressure coefficient, and the specific details are as follows: The experimental data of this embodiment is the same as that of embodiment 1, except that all the high-fidelity data only has 2, the low-fidelity data has 75, and the output of the model changes to the lower surface negative pressure coefficient. The result graph of the method of the present application for predicting the lower surface negative pressure coefficient of the ONERA M6 airfoil is shown in Figure 4 , the index of the prediction result is: RMSE: 0.030052, MAE: 0.026570, R 2 : 0.9555. The above is only a preferred embodiment of the present application and is not used to limit the present application. Those skilled in the art can make various changes and modifications to the present application.

Claims

1. A small sample aerodynamic force modeling method based on multi-task learning, characterized in that, The application relates to a method for aerodynamic force prediction based on multi-task learning. The method comprises the following steps: A multi-task prediction model is constructed, which integrates an auxiliary task network and a target task network for low-fidelity data prediction and high-fidelity data prediction respectively, and a Squeeze-and-Excitation (SE) layer and an attention layer are embedded in the encoder to optimize feature extraction; Multi-source aerodynamic force data are acquired and standardized preprocessed, and independent standardization is applied to features and targets respectively; A dynamic weight mechanism is designed to adaptively adjust the influence of auxiliary task prediction on target task output according to input features; The prediction accuracy of the model is verified, and the RMSE, MAE, R 2 and relative error are calculated, and the model performance is verified by comparing the predicted value with the actual value through visualization; A two-stage training process is adopted: the first stage is pre-training of the auxiliary task, and the second stage is multi-task joint training using GradNormLoss to balance the gradients of the auxiliary task and the target task; 2. The method of claim 1, wherein, Through the synergistic effect of the multi-task learning framework, the feature enhancement module and the dynamic weight mechanism, efficient prediction of aerodynamic characteristics is realized.

3. The method of claim 1, wherein, The Squeeze-and-Excitation (SE) layer generates a channel-level scaling factor through global average pooling and a sequential fully connected network, which includes a dimension reduction layer, a ReLU activation layer, a dimension increasing layer and a Sigmoid activation layer, to recalibrate the feature response in the encoder.

4. The method of claim 1, wherein, The attention layer calculates the weight of the input features through a small neural network, which includes a linear layer reduced to half of the channel number, a ReLU activation, a linear layer outputting a single weight and a Sigmoid activation, and applies the calculated weight to the input features to dynamically emphasize key features.

5. The method of claim 1, wherein, The dynamic weight mechanism specifically comprises: calculating the dynamic weight based on the average absolute value of the encoded features, generating the weight value using the Sigmoid function, and adjusting the contribution of the auxiliary task prediction and the target task correction term in the forward propagation through the formula. The two-stage training process comprises the following steps: First stage: pre-training of the auxiliary task, initializing the model parameters using low-fidelity data, and updating the network parameters using the mean square error loss function and the Adam optimizer; The method according to claim 1, characterized in that, Second stage: multi-task joint training based on GradNormLoss, dynamically adjusting the task weight by calculating the initial loss and the gradient norm to balance the gradients of the auxiliary task and the target task, and optimizing the multi-task learning efficiency of the model. The standardized preprocessing specifically comprises: using independent StandardScaler to standardize the input features and target values respectively, and providing a reverse conversion method to restore the prediction results to the original scale. The method according to claim 1, characterized in that, The model validation specifically includes evaluating model prediction performance using root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R 2 ) and relative error, and visualizing the comparison of predicted values to high-fidelity data, low-fidelity data, and training samples through scatter plots and trend lines.

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