Method for predicting aerodynamic forces on a local protuberance of an aircraft surface

Abstract

The application discloses a method for predicting aerodynamic force of local protrusion on aircraft surface, comprising: obtaining position information and aerodynamic parameters of a plurality of sampling points without protrusion on the aircraft surface; setting protrusion on the aircraft surface, obtaining aerodynamic parameters of each sampling point with protrusion, and obtaining training parameters of each sampling point; dividing the aircraft surface into a plurality of regions; for each region, based on the position information and the training parameters of each sampling point, respectively training AdaBoost regression model and RandomForest regression model to predict aerodynamic force, respectively calculating the determination coefficients of the AdaBoost regression model and the RandomForest regression model, and selecting the trained regression model with a larger determination coefficient as an aerodynamic force prediction model of the training parameters in the region. The application has small calculation amount, short calculation time, high calculation efficiency and small required calculation resource, can effectively improve model accuracy and ensure high calculation efficiency when small sample and model law are complex.

Description

Technical Field

[0001] This invention belongs to the field of aircraft data processing technology, specifically relating to a method for predicting the aerodynamic forces of local protrusions on the surface of an aircraft. Background Technology

[0002] Aircraft typically control their attitude using aerodynamic control surfaces, but these surfaces limit the improvement of aerodynamic performance. At low speeds and high angles of attack, control surface efficiency decreases; at high speeds, they increase drag and face severe aerodynamic heating. With increasing demands for stealth capabilities, and control surfaces being radar reflectors, stealth performance is constrained. Therefore, control surface-free control technology has become a hot topic in attitude control and is one of the important future development directions for attitude control.

[0003] In the future, smart materials can be used to create protrusions on the surface of aircraft through localized deformation, enabling real-time attitude control—a novel control surface-free technology. These protrusions (such as centimeter-scale hemispherical protrusions) can alter aerodynamic torque by changing the local pressure distribution, thereby controlling the aircraft's attitude. The required torque from the protrusion can be determined in real-time based on the aircraft's flight status, thus pinpointing its location. This first requires establishing an aerodynamic model of the protrusion at any location. Using CFD to calculate its aerodynamic characteristics would be computationally intensive and time-consuming, failing to meet the demands of online control.

[0004] Therefore, there is a particular need for a method for calculating the aerodynamic forces of bulges that requires less computation and takes less time. Summary of the Invention

[0005] The purpose of this invention is to propose an aerodynamic prediction method for local bulges on the surface of an aircraft, which requires less computation and has a shorter computation time.

[0006] This invention provides an aerodynamic prediction method for local protrusions on the surface of an aircraft, comprising: acquiring the position information of multiple sampling points and aerodynamic parameters of the aircraft surface without protrusions; setting protrusions on the aircraft surface and acquiring aerodynamic parameters of each sampling point with protrusions, the aerodynamic parameters including pitch moment, yaw moment, and axial force; obtaining training parameters based on the aerodynamic parameters without and with protrusions, the training parameters including pitch moment difference, yaw moment difference, and axial force with protrusions; dividing the aircraft surface into multiple regions based on the position information of the sampling points and the training parameters; and preprocessing the position information of each sampling point within each region. Each training parameter of each sampling point is preprocessed. For each preprocessed training parameter, the preprocessed position information of each sampling point in the region is used as input data, and the preprocessed training parameter is used as output data. The AdaBoost regression model and the RandomForest regression model are trained to predict aerodynamic forces, respectively, to obtain the trained AdaBoost regression model and the RandomForest regression model. The determination coefficients of the trained AdaBoost regression model and the RandomForest regression model are calculated, and the regression model with the larger determination coefficient is selected as the aerodynamic force prediction model for the training parameters in the region.

[0007] Optionally, the aircraft surface is divided into multiple regions using the following steps: drawing a plan view of the aircraft surface with the horizontal direction as the x-axis coordinate, the vertical direction as the z-axis coordinate, and the aircraft head as the origin; marking the position information of each sampling point on the plan view of the aircraft surface; and dividing the plan view of the aircraft surface into multiple regions according to the training parameters of each sampling point.

[0008] Optionally, the position information of each sampling point within the region is preprocessed using the following steps: For each region, the x-axis coordinate of the region is rotated until the x-axis coordinate coincides with the outer edge of the aircraft surface within the region, and the rotation angle is calculated; based on the rotation angle, the rotated x-axis and z-axis information of each sampling point are calculated; the rotated x-axis and z-axis information are respectively used as feature data; each feature data is normalized to obtain normalized feature data; multiple interactive feature data are generated based on the normalized feature data; the normalized feature data and the multiple interactive feature data are used as initial feature data; the initial feature data is dimensionality reduced to obtain dimensionality-reduced feature data; custom feature data is added to the dimensionality-reduced feature data to obtain preprocessed position information.

[0009] Optionally, the feature data can be normalized using the following formula:

[0010]

[0011] Where f' is the normalized data, f is the data to be normalized, and f' is the data to be normalized. max f is the maximum value in the data to be normalized. min This represents the minimum value in the data to be normalized.

[0012] Optionally, multiple interaction feature data can be generated using the following formula;

[0013] [x i z 3-i [1], i = 0, 1, 2, 3

[0014] Where x is the normalized x-axis information for each sampling point, z is the normalized z-axis information for each sampling point, and i is the exponent.

[0015] Optionally, principal component analysis can be used to reduce the dimensionality of the initial feature data, retaining 99% of the components.

[0016] Optionally, the custom feature data is the ratio of the distance from the sampling point to the edge of the aircraft to the spanwise width of the aircraft at the sampling point.

[0017] Optionally, the following steps are used to preprocess each training parameter at each sampling point: standardize the pitch moment difference, yaw moment difference, and axial force with protrusion respectively; normalize the standardized pitch moment difference, yaw moment difference, and axial force with protrusion to obtain the preprocessed pitch moment parameters, yaw moment parameters, and axial force parameters.

[0018] Optionally, the training parameters can be normalized using the following formula:

[0019]

[0020] Where x represents the training parameters that have undergone pre-normalization.

[0021] Optionally, the coefficient of determination of the trained regression model can be calculated using the following formula:

[0022]

[0023] R 2 As the coefficient of determination, y true For training parameters where the sampling points have a convex shape, y pre y represents the training parameters calculated based on the trained regression model at the sampling points. mean This is the average value of the training parameters calculated based on the trained regression model across all sampling points.

[0024] The beneficial effects of the present invention are as follows: Compared with the existing CFD numerical simulation methods, the aerodynamic prediction method for local protrusions on the surface of aircraft of the present invention has a small amount of computation, less computation time, higher computation efficiency, and requires less computational resources. When the sample size is small and the model has complex patterns, it can effectively improve the accuracy of the model and ensure high computational efficiency.

[0025] The present invention has other features and advantages that will be apparent from or will be set forth in detail in the accompanying drawings and following detailed description, which together serve to explain the particular principles of the invention. Attached Figure Description

[0026] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same components in the exemplary embodiments of the invention.

[0027] Figure 1 A flowchart of an aerodynamic prediction method for local protrusions on the surface of an aircraft, according to an embodiment of the present invention, is shown.

[0028] Figure 2 A schematic diagram of the AdaBoost regression principle for a method of predicting the aerodynamic forces of local protrusions on the surface of an aircraft according to an embodiment of the present invention.

[0029] Figure 3 A RandomForest regression diagram illustrating an aerodynamic prediction method for local protrusions on the surface of an aircraft according to an embodiment of the present invention is shown.

[0030] Figure 4 A schematic diagram of aircraft region division is shown in a method for predicting the aerodynamic forces of local protrusions on the surface of an aircraft according to an embodiment of the present invention.

[0031] Figures 5a-5i The diagram illustrates a method for predicting the aerodynamic forces of a local protrusion on the surface of an aircraft according to an embodiment of the present invention, showing a comparison between the predicted and actual aerodynamic forces of the protrusion. Detailed Implementation

[0032] Preferred embodiments of the invention will now be described in more detail. While preferred embodiments of the invention are described below, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0033] This invention provides an aerodynamic prediction method for local protrusions on the surface of an aircraft, comprising: acquiring the position information of multiple sampling points and aerodynamic parameters of the aircraft surface without protrusions; setting protrusions on the aircraft surface and acquiring aerodynamic parameters of each sampling point with protrusions, the aerodynamic parameters including pitch moment, yaw moment, and axial force; obtaining training parameters based on the aerodynamic parameters without and with protrusions, the training parameters including pitch moment difference, yaw moment difference, and axial force with protrusions; dividing the aircraft surface into multiple regions based on the position information of the sampling points and the training parameters; and for each region, preprocessing the position information of each sampling point within that region, and processing each sampling point... Each training parameter of the sample point is preprocessed. For each preprocessed training parameter, the preprocessed location information of each sampling point in the region is used as input data, and the preprocessed training parameter is used as output data. The AdaBoost regression model and the RandomForest regression model are trained to predict aerodynamic forces, respectively, to obtain the trained AdaBoost regression model and the RandomForest regression model. The determination coefficients of the trained AdaBoost regression model and the RandomForest regression model are calculated, and the regression model with the larger determination coefficient is selected as the aerodynamic force prediction model for the training parameters in the region.

[0034] Specifically, taking HTV2 as an example, a flight state point is selected to calculate the aerodynamic parameters without the bulge. Assuming the aircraft's bottom can locally deform to generate a hemispherical bulge, the position of the bulge is changed to obtain the calculation point, and its aerodynamic forces are calculated to obtain the aerodynamic parameters of the bulge, including yaw moment, pitch moment, and axial force. The changes in yaw moment and pitch moment with axial and spanwise position are observed; the changes are more drastic near the boundaries of the central axis and spanwise. Calculation points are added in these areas to obtain a dataset of training parameters. The numerical distribution of the training parameters (pitch moment difference, yaw moment difference, and axial force with the bulge) on the aircraft is observed, and the aircraft is divided into multiple training regions.

[0035] A predictive model for aerodynamic parameters is established through a process of data preprocessing, feature engineering, parameter tuning, and algorithm selection. First, the basic patterns of the input data are understood through analysis and visualization of location information data. Second, feature engineering is constructed for the input data, i.e., the location information of each sampling point, including coordinate system rotation, regional prediction, feature normalization, generation of interactive features, and PCA dimensionality reduction to obtain preprocessed input data. Then, each training parameter of the sampling point is used as output data, and each training parameter is standardized and normalized. Next, cross-validation is used for parameter tuning and optimization. For each region, based on the preprocessed input data and each preprocessed training parameter, two algorithms, AdaBoost regression and Random Forest regression, are used for training. Both algorithms are ensemble learning algorithms, which have good generalization ability compared to single machine learning algorithms. These two algorithms can effectively improve model accuracy and ensure high computational efficiency even with small amounts of aerodynamic data and complex model patterns. Finally, the determination coefficients of the two trained regression models are compared, and the regression model with the higher determination coefficient is selected as the aerodynamic force prediction model for that region's aerodynamic parameters.

[0036] According to the exemplary implementation, the aerodynamic prediction method for local protrusions on the surface of an aircraft has a smaller computational load, shorter computation time, higher computational efficiency, and requires less computational resources compared to existing CFD numerical simulation methods. It can effectively improve model accuracy and ensure high computational efficiency when dealing with small samples and complex model patterns.

[0037] As an optional approach, the aircraft surface is divided into multiple regions using the following steps: drawing a planar map of the aircraft surface with the horizontal direction as the x-axis coordinate, the vertical direction as the z-axis coordinate, and the aircraft head as the origin; marking the position information of each sampling point on the planar map of the aircraft surface; and dividing the planar map of the aircraft surface into multiple regions based on the training parameters of each sampling point.

[0038] Specifically, the location information of each sampling point is marked on the surface plan view of the aircraft. Based on the location information of the sampling points with multiple training parameters that have protrusions, the surface plan view of the aircraft is divided into multiple regions.

[0039] As an optional approach, the following steps are used to preprocess the position information of each sampling point within the region: For each region, rotate the x-axis coordinate until it coincides with the outer edge of the aircraft surface within the region, and calculate the rotation angle; based on the rotation angle, calculate the rotated x-axis and z-axis information of each sampling point; use the rotated x-axis and z-axis information as feature data respectively; normalize each feature data to obtain normalized feature data; generate multiple interactive feature data based on the normalized feature data; use the normalized feature data and multiple interactive feature data as initial feature data; perform dimensionality reduction on the initial feature data to obtain dimensionality-reduced feature data; add custom feature data to the dimensionality-reduced feature data to obtain preprocessed position information.

[0040] Observations show that aerodynamic parameters change more drastically and follow complex patterns closer to the edge, especially the yaw moment. Therefore, the z-axis obtained through coordinate rotation can intuitively represent the edge distance characteristics, improving model accuracy. Specifically, the coordinate system is rotated for each region, so that the x-axis is along the corresponding outer edge of the aircraft, and the z-axis is perpendicular to the corresponding x-axis and points outwards as the positive direction. After the coordinate system rotation, there are two features: x-axis data and z-axis data. These two feature data are normalized to obtain normalized x-axis and z-axis data. Based on the normalized x-axis and z-axis data, interactive features are generated to increase the number of features. Principal component analysis is used to reduce the dimensionality of the increased feature data, resulting in feature data with only 4 features. Then, custom features are added to obtain feature data with 5 features.

[0041] As an optional approach, the feature data can be normalized using the following formula:

[0042]

[0043] Where f' is the normalized data, f is the data to be normalized, and f' is the data to be normalized. max f is the maximum value in the data to be normalized. min This represents the minimum value in the data to be normalized.

[0044] Specifically, feature normalization involves normalizing each feature data point using its maximum and minimum values.

[0045]

[0046] As an optional approach, multiple interaction feature data can be generated using the following formula;

[0047] [x i z 3-i[1], i = 0, 1, 2, 3

[0048] Where x is the normalized x-axis information for each sampling point, z is the normalized z-axis information for each sampling point, and i is the exponent.

[0049] Specifically, the original features consist of two data points: x-axis data and z-axis data. The highest exponent of each feature is set to 3. Interactive features are generated, and a constant term of 1 is added, resulting in a total of 10 features.

[0050] [x i z 3-i ,1],i=0,1,2,3.

[0051] As an alternative, principal component analysis is used to reduce the dimensionality of the initial feature data, retaining 99% of the components.

[0052] Specifically, principal component analysis (PCA) was used for dimensionality reduction, retaining 99% of the information, resulting in four features after dimensionality reduction.

[0053] As an optional approach, the custom feature data is the ratio of the distance from the sampling point to the edge of the aircraft to the spanwise width of the aircraft at the sampling point.

[0054] Specifically, a custom feature is added as the ratio of the distance from the adoption point to the edge of the aircraft to the spanwise width of the aircraft at that adoption point. Note that defining the custom feature in the original coordinate system is more convenient. This custom feature can describe the significant impact of the distance from the feature to the edge on aerodynamic parameters, and it has the advantage of natural normalization. After adding one feature, five features are preferred.

[0055]

[0056] As an optional approach, the following steps are used to preprocess each training parameter at each sampling point: standardize the pitch moment difference, yaw moment difference, and axial force with protrusions respectively; normalize the standardized pitch moment difference, yaw moment difference, and axial force with protrusions to obtain the preprocessed pitch moment parameters, yaw moment parameters, and axial force parameters.

[0057] Specifically, the aerodynamic parameters on an aircraft have a wide range of values, and direct normalization would reduce the model's accuracy. Therefore, standardizing the output data first to narrow its value range, and then performing normalization, can ensure the model's accuracy.

[0058] As an optional approach, the training parameters can be normalized using the following formula:

[0059]

[0060] Where x represents the training parameters that have undergone pre-normalization.

[0061] Specifically, normalization uses the sigmoid equation.

[0062]

[0063] As an alternative, the determination coefficient of the trained regression model can be calculated using the following formula:

[0064]

[0065] R 2 As the coefficient of determination, y true For training parameters where the sampling points have a convex shape, y pre y represents the training parameters calculated based on the trained regression model at the sampling points. mean This is the average value of the training parameters calculated based on the trained regression model across all sampling points.

[0066] Specifically, the evaluation indicator is the coefficient of determination R. 2 The closer the coefficient of determination is to 1, the higher the accuracy of the regression model.

[0067]

[0068] Hyperparameter tuning. Based on the coefficient of determination R... 2 The number of weak learners in AdaBoost regression and RandomForest regression was iteratively adjusted, and R was selected. 2 The maximum number of weak learners corresponding to the two algorithms is taken as the optimal hyperparameter.

[0069] The optimal model is selected. The AdaBoost regression model with the best hyperparameters is compared with the RandomForest regression model, and the coefficient of determination R is chosen. 2 The larger value is taken as the optimal model, serving as the prediction model for the corresponding aerodynamic parameters in this region.

[0070] Example 1

[0071] Figure 1 A flowchart of an aerodynamic prediction method for local protrusions on the surface of an aircraft, according to an embodiment of the present invention, is shown. Figure 2 A schematic diagram of the AdaBoost regression principle for a method of predicting the aerodynamic forces of local protrusions on the surface of an aircraft according to an embodiment of the present invention. Figure 3 A RandomForest regression diagram illustrating an aerodynamic prediction method for local protrusions on the surface of an aircraft according to an embodiment of the present invention is shown. Figure 4A schematic diagram of aircraft region division is shown in a method for predicting the aerodynamic forces of local protrusions on the surface of an aircraft according to an embodiment of the present invention. Figures 5a-5i The diagram illustrates a method for predicting the aerodynamic forces of a local protrusion on the surface of an aircraft according to an embodiment of the present invention, showing a comparison between the predicted and actual aerodynamic forces of the protrusion.

[0072] Combination Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figures 5a-5i As shown, the aerodynamic prediction method for local bulges on the surface of the aircraft includes:

[0073] Step 1: Obtain the position information of multiple sampling points and the aerodynamic parameters of the aircraft surface when there are no protrusions;

[0074] Step 2: Set protrusions on the surface of the aircraft and obtain the aerodynamic parameters of each sampling point with protrusions. The aerodynamic parameters include pitching moment, yaw moment and axial force.

[0075] Step 3: Based on the aerodynamic parameters without and with the convex point, obtain the training parameters, which include the pitch moment difference, yaw moment difference, and axial force with the convex point.

[0076] Step 4: Using the location information of the sampling points and training parameters, the surface of the aircraft is divided into multiple regions;

[0077] Step 5: For each region, preprocess the location information of each sampling point within the region, preprocess each training parameter of each sampling point, and for each preprocessed training parameter, use the preprocessed location information of each sampling point within the region as input data and the preprocessed training parameter as output data to train the AdaBoost regression model and the RandomForest regression model for predicting aerodynamic forces, respectively, to obtain the trained AdaBoost regression model and the RandomForest regression model. Calculate the determination coefficients of the trained AdaBoost regression model and the RandomForest regression model, respectively, and select the regression model with the larger determination coefficient as the training force prediction model for aerodynamic parameters within the region.

[0078] The aircraft surface is divided into multiple regions using the following steps: a planar map of the aircraft surface is drawn with the horizontal direction as the x-axis coordinate, the vertical direction as the z-axis coordinate, and the aircraft head as the origin; the position information of each sampling point is marked on the planar map of the aircraft surface; and the planar map of the aircraft surface is divided into multiple regions according to the training parameters of each sampling point.

[0079] The following steps are used to preprocess the position information of each sampling point within the region: For each region, rotate the x-axis coordinate until it coincides with the outer edge of the aircraft surface within the region, and calculate the rotation angle; based on the rotation angle, calculate the rotated x-axis and z-axis information of each sampling point; use the rotated x-axis and z-axis information as feature data respectively; normalize each feature data to obtain normalized feature data; generate multiple interactive feature data based on the normalized feature data; use the normalized feature data and multiple interactive feature data as initial feature data; perform dimensionality reduction on the initial feature data to obtain dimensionality-reduced feature data; add custom feature data to the dimensionality-reduced feature data to obtain preprocessed position information.

[0080] The feature data is normalized using the following formula:

[0081]

[0082] Where f' is the normalized data, f is the data to be normalized, and f' is the data to be normalized. max f is the maximum value in the data to be normalized. min This represents the minimum value in the data to be normalized.

[0083] The following formula is used to generate multiple interactive feature data;

[0084] [x i z 3-i [1], i = 0, 1, 2, 3

[0085] Where x is the normalized x-axis information for each sampling point, z is the normalized z-axis information for each sampling point, and i is the exponent.

[0086] Principal component analysis was used to reduce the dimensionality of the initial feature data, retaining 99% of the components.

[0087] The custom feature data is the ratio of the distance from the sampling point to the edge of the aircraft to the spanwise width of the aircraft at the sampling point.

[0088] The following steps are used to preprocess each training parameter at each sampling point: standardize the pitch moment difference, yaw moment difference, and axial force with protrusion; normalize the standardized pitch moment difference, yaw moment difference, and axial force with protrusion to obtain the preprocessed pitch moment parameters, yaw moment parameters, and axial force parameters.

[0089] The training parameters are normalized using the following formula:

[0090]

[0091] Where x represents the training parameters that have undergone pre-normalization.

[0092] The determination coefficient of the trained regression model is calculated using the following formula:

[0093]

[0094] R 2 As the coefficient of determination, y true For training parameters where the sampling points have a convex shape, y pre y represents the training parameters calculated based on the trained regression model at the sampling points. mean This is the average value of the training parameters calculated based on the trained regression model across all sampling points.

[0095] The prediction method of this application will be verified using a specific aircraft.

[0096] For the yaw moment Dmyg, its values ​​range from large to small and are widely distributed. Therefore, two indices are used to verify the accuracy of the test model. For Dmyg with an absolute value greater than 10, the mean relative error is used as the test accuracy evaluation index; for Dmyg with an absolute value less than 10, the mean absolute error sum of squares is used as the test accuracy evaluation index.

[0097]

[0098]

[0099] For the pitch moment Dmzg, the values ​​are all relatively large, and the average relative error is used as the evaluation index for test accuracy.

[0100] For axial force F x Since the absolute values ​​of these values ​​are relatively large and their distributions are similar, the mean absolute error sum of squares is used as the evaluation index for test accuracy.

[0101] For the average relative error, the accuracy of yaw moment Dmyg and pitch moment Dmzg can be within 10%. For smaller absolute values ​​of yaw moment Dmyg, the average sum of squares of absolute errors is around 20. For axial force F... x With a mean absolute error sum of squares of around 400, the prediction accuracy is considered to be relatively high. A comparison of predicted and actual values ​​is provided. Figures 5a-5i As shown.

[0102] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for predicting the aerodynamic forces of localized protrusions on the surface of an aircraft, characterized in that, include: Acquire the position information of multiple sampling points and the aerodynamic parameters of the aircraft surface when there are no protrusions; Protrusions are set on the surface of the aircraft, and aerodynamic parameters of each sampling point with protrusions are obtained. The aerodynamic parameters include pitching moment, yaw moment and axial force. Training parameters are obtained based on the aerodynamic parameters without protrusions and the aerodynamic parameters with protrusions. The training parameters include pitch moment difference, yaw moment difference, and axial force with protrusions. Based on the location information of the sampling points and the training parameters, the surface of the aircraft is divided into multiple regions; For each region, the location information of each sampling point within the region is preprocessed, and each training parameter of each sampling point is preprocessed. For each preprocessed training parameter, the preprocessed location information of each sampling point within the region is used as input data, and the preprocessed training parameter is used as output data. The AdaBoost regression model and the RandomForest regression model are trained to predict aerodynamic forces, respectively, to obtain the trained AdaBoost regression model and the RandomForest regression model. The determination coefficients of the trained AdaBoost regression model and the RandomForest regression model are calculated, and the regression model with the larger determination coefficient is selected as the aerodynamic force prediction model for the training parameters within the region.

2. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 1, characterized in that, The surface of the aircraft is divided into multiple regions using the following steps: Using the horizontal direction as the x-axis coordinate and the height direction as the z-axis coordinate, with the aircraft's nose as the origin, draw a plan view of the aircraft's surface; The location information of each sampling point is marked on the plane diagram of the aircraft surface; Based on the training parameters of each sampling point, the surface plan view of the aircraft is divided into multiple regions.

3. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 2, characterized in that, The location information of each sampling point in the area is preprocessed using the following steps: For each region, rotate the x-axis coordinate of the region until the x-axis coordinate coincides with the outer edge of the aircraft surface within the region, and calculate the rotation angle; Based on the rotation angle, calculate the x-axis and z-axis information of each sampling point after rotation; The rotated x-axis and z-axis information are respectively used as feature data; Normalize each feature data to obtain normalized feature data; Based on the normalized feature data, generate multiple interactive feature data; The normalized feature data and multiple interaction feature data are used as the initial feature data: The initial feature data is dimensionality reduced to obtain the dimensionality-reduced feature data. Custom feature data is added to the dimensionality-reduced feature data to obtain preprocessed position information. The custom feature data is the ratio of the distance from the sampling point to the edge of the aircraft to the spanwise width of the aircraft at the sampling point.

4. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 3, characterized in that, The feature data are normalized using the following formula: Where f' is the normalized data, f is the data to be normalized, and f' is the data to be normalized. max f is the maximum value in the data to be normalized. min This represents the minimum value in the data to be normalized.

5. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 4, characterized in that, Multiple interaction feature data are generated using the following formula; Where x is the normalized x-axis information for each sampling point, z is the normalized z-axis information for each sampling point, and i is the exponent.

6. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 5, characterized in that, Principal component analysis was used to reduce the dimensionality of the initial feature data, retaining 99% of the components.

7. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 1, characterized in that, The following steps are used to preprocess each training parameter for each sampling point: The pitch moment difference, yaw moment difference, and axial force with protrusion were standardized respectively. The pitch moment difference, yaw moment difference, and axial force with protrusion after standardization are normalized to obtain the pre-processed pitch moment parameters, yaw moment parameters, and axial force parameters.

8. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 7, characterized in that, The training parameters are normalized using the following formula: in, x These are the training parameters that will be normalized beforehand.

9. The aerodynamic prediction method for local protrusions on the surface of an aircraft according to claim 1, characterized in that, The coefficient of determination of the trained regression model is calculated using the following formula: R 2 As the coefficient of determination, y true For training parameters where the sampling points have convexities, y pre The training parameters calculated based on the trained regression model at the sampling points. y mean This is the average value of the training parameters calculated based on the trained regression model across all sampling points.

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