Method for predicting wing aerodynamic shape and pressure distribution based on beta-VAE

Abstract

The application discloses a wing aerodynamic shape and pressure distribution prediction method based on beta-VAE, relates to the technical field of computers, and comprises the following steps: extracting parameterized design variables based on a wing aerodynamic shape, and constructing a sample data set based on obtained target variables and corresponding pressure distributions; constructing an initial beta-VAE model based on a variational autoencoder to which preset adjustment parameters are introduced, determining a training set and a test set based on the sample data set, training the initial beta-VAE model by using the training set, determining a target pressure distribution based on the test set and by using the trained deep generative latent space model, and judging whether an error between the target pressure distribution and an actual pressure distribution is within a preset error range; if the error is within the preset error range, the trained deep generative latent space model is determined as a target deep generative latent space model, and a wing aerodynamic shape and pressure distribution prediction operation is performed. The method takes into account the geometric shape feature expression capability and the pressure distribution physical consistency.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a method for predicting wing aerodynamic shape and pressure distribution based on β-VAE. Background Technology

[0002] With the increasing demands for accuracy and efficiency in aerodynamic performance analysis and design in the aerospace field, the efficient representation and modeling of the three-dimensional aerodynamic shape and flow field physical characteristics of airfoils has gradually become a research hotspot. The airfoil shape determines the flow field structure and surface pressure distribution characteristics, while the pressure distribution directly reflects the flow state and aerodynamic properties; a complex nonlinear coupling relationship exists between the two. Achieving a unified low-dimensional representation of the airfoil's three-dimensional shape and flow field pressure distribution is of great significance for aerodynamic physical law analysis, rapid flow field reconstruction, and data-driven aerodynamic modeling.

[0003] With the development of deep learning technology, latent space modeling methods are increasingly being applied to the study of low-dimensional representations of complex physical fields. Models such as autoencoders and variational autoencoders (VAEs) can map high-dimensional data into a low-dimensional latent space, enabling compressed representation and feature extraction of complex data. Current research utilizes latent space models for low-dimensional modeling of two-dimensional airfoils or local flow fields, improving data representation efficiency to some extent. However, most existing methods only model single objects in geometry or flow pressure, lacking a unified ability to represent the coupling relationship between the wing's three-dimensional shape and pressure distribution. Furthermore, data distribution varies significantly across different wing configurations and flight conditions. Traditional deep learning models typically require a large number of samples for training, and under small sample conditions, they are prone to insufficient generalization ability and decreased reconstruction accuracy. In research on a unified latent space representation of the wing's three-dimensional shape and flow pressure distribution, deep generative modeling methods are still lacking.

[0004] As can be seen from the above, how to balance the ability to express geometric shape features and the physical consistency of pressure distribution is an urgent problem to be solved. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for predicting wing aerodynamic shape and pressure distribution based on β-VAE, which can balance the ability to represent geometric shape features and the physical consistency of pressure distribution. The specific solution is as follows: In a first aspect, this application provides a method for predicting wing aerodynamic shape and pressure distribution based on β-VAE, including: The parameterized design variables based on the aerodynamic shape of the wing are extracted using the Latin hypercube sampling method to obtain the corresponding target variables. A sample dataset is then constructed based on the target variables and the corresponding pressure distribution. An initial β-VAE model is constructed based on a variational autoencoder with pre-defined adjustment parameters. A corresponding training set and test set are determined based on the sample dataset. The initial β-VAE model is trained using the training set to obtain a trained deep generative latent space model. The encoder and decoder in the initial β-VAE model have a symmetrical structure. Based on the test set and using the trained deep generation latent space model, the target pressure distribution is determined, and it is determined whether the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within a preset error range. If the target depth generation latent space model is within the preset error range, the trained depth generation latent space model is determined as the target depth generation latent space model, so as to use the target depth generation latent space model to predict the aerodynamic shape and pressure distribution of the wing.

[0006] Optionally, the parameterized design variables based on the wing's aerodynamic shape, extracted using the Latin hypercube sampling method to obtain the corresponding target variables, include: The parametric design variables of the wing's aerodynamic shape are determined using free deformation technology. Based on these parametric design variables, the corresponding target variables are obtained by sampling using the Latin hypercube sampling method.

[0007] Optionally, constructing the sample dataset based on the target variable and the corresponding stress distribution includes: The pressure distribution of the target airfoil profile corresponding to each of the target variables is determined using a CFD solver, and a sample dataset is constructed based on the target variables and the corresponding pressure distribution.

[0008] Optionally, the construction of the initial β-VAE model based on the variational autoencoder with preset adjustment parameters includes: An initial β-VAE model is constructed based on a variational autoencoder with pre-defined adjustment parameters, combined with an encoder and a decoder; the pre-defined adjustment parameters are determined experimentally based on the requirements of the target task.

[0009] Optionally, the encoder includes a first fully connected neural network with a target number of layers; The number of neurons in the first fully connected neural network is negatively correlated with the number of layers.

[0010] Optionally, the decoder includes a second fully connected neural network with the target number of layers; The number of neurons in the second fully connected neural network is positively correlated with the number of layers.

[0011] Optionally, determining the corresponding training and test sets based on the sample dataset, and training the initial β-VAE model using the training set to obtain a trained deep generative latent space model, includes: The sample dataset is divided according to a preset division ratio to obtain corresponding training and test sets; The training set is input into the initial β-VAE model based on preset training parameters, so as to compress the training set into target low-dimensional latent variables using the initial β-VAE model, and then use the decoder to restore the target low-dimensional latent variables into target high-dimensional data to obtain a trained deep generative latent space model.

[0012] Optionally, the step of determining the target pressure distribution based on the test set and using the trained deep latent space model, and determining whether the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within a preset error range, includes: The pressure distribution of the test set is reconstructed using the trained deep generative latent space model to obtain the target pressure distribution; The CFD solver is used to determine the true pressure distribution corresponding to the test set, and it is determined whether the error between the target pressure distribution and the true pressure distribution is within a preset error range.

[0013] Optionally, after determining whether the error between the target pressure distribution and the actual pressure distribution corresponding to the test set is within a preset error range, the method further includes: If the error is not within the preset error range, the process jumps to the step of determining the corresponding training set and test set based on the sample dataset, until the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within the preset error range, so as to obtain the target depth generation latent space model.

[0014] Optionally, the step of using the target depth to generate a latent space model for predicting wing aerodynamic shape and pressure distribution includes: Latent variables are extracted from the latent space of the target dimension, and the target depth is used to generate a latent space model to generate wing design variables and pressure distribution data corresponding to the latent variables, so as to complete the prediction operation of wing aerodynamic shape and pressure distribution.

[0015] This application uses parameterized design variables of wing aerodynamic shape and extracts them using the Latin hypercube sampling method to obtain corresponding target variables. A sample dataset is constructed based on the target variables and the corresponding pressure distribution. An initial β-VAE model is constructed based on a variational autoencoder with preset adjustment parameters. Based on the sample dataset, corresponding training and test sets are determined. The initial β-VAE model is trained using the training set to obtain a trained deep generation latent space model. The encoder and decoder in the initial β-VAE model have a symmetrical structure. A target pressure distribution is determined based on the test set and the trained deep generation latent space model. The error between the target pressure distribution and the actual pressure distribution corresponding to the test set is judged to be within a preset error range. If it is within the preset error range, the trained deep generation latent space model is determined as the target deep generation latent space model, and the target deep generation latent space model is used to predict wing aerodynamic shape and pressure distribution.

[0016] As can be seen from the above, this application uses parametric design variables and Latin hypercube sampling to ensure that the target variables uniformly cover the wing aerodynamic design space and are bound to the corresponding pressure distribution to construct a sample dataset. A β-VAE model with preset adjustment parameters and a symmetrical encoder-decoder structure is employed to accurately learn the nonlinear coupling law between shape and pressure. The sample dataset is divided into training and testing sets. The training set is used to train the model. Based on the trained model, the error between the target pressure distribution generated on the testing set and the corresponding real pressure distribution on the testing set is compared to quantitatively determine the model's accuracy and generalization ability, thus obtaining a qualified target model. In this way, a latent space model generated using the target depth can be used to predict wing aerodynamic shape and pressure distribution, enabling rapid aerodynamic design and analysis. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present 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 only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a flowchart of a wing aerodynamic shape and pressure distribution prediction method based on β-VAE disclosed in this application; Figure 2 This is a schematic diagram of an aircraft wing disclosed in this application. Figure 2 Image (a) is a three-dimensional axonometric view. Figure 2 (b) is a top-down projection view; Figure 3This is a schematic cross-sectional view of an M6 wing design disclosed in this application; Figure 4 This is a schematic diagram of an initial depth generation latent space model structure disclosed in this application; Figure 5 This is a schematic diagram of the total loss variation curve of the training and testing sets of a model disclosed in this application; Figure 6 This is a schematic diagram showing the reconstruction and comparison of sample pressure distribution of a test set sample disclosed in this application. Figure 6 (a) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 2 at spanwise section 1. Figure 6 (b) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 2 at spanwise section 2. Figure 6 Image (c) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 2 at spanwise section 3. Figure 6 (d) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 2 at spanwise section 4; Figure 7 This is a comparative schematic diagram showing the reconstruction of sample pressure distribution for another test set sample disclosed in this application. Figure 7 (a) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 98 at spanwise section 1. Figure 7 (b) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 98 at spanwise section 2. Figure 7 (c) is a schematic diagram showing the reconstruction and comparison of the sample pressure distribution of test set sample 98 at spanwise section 3. Figure 7 The diagram in (d) shows a reconstruction and comparison of the sample pressure distribution at spanwise section 4 for test set sample 98. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Currently, existing research utilizes latent space models for low-dimensional modeling of two-dimensional airfoils or local flow fields, improving data representation efficiency to some extent. However, most existing methods only model single objects in the geometry or flow pressure, lacking a unified ability to represent the coupling relationship between the wing's three-dimensional shape and pressure distribution. Furthermore, data distribution varies significantly across different wing configurations and flight conditions, requiring traditional deep learning models typically for training with large numbers of samples, leading to insufficient generalization ability and decreased reconstruction accuracy under small sample conditions. Therefore, this application provides a β-VAE-based method for predicting wing aerodynamic shape and pressure distribution. See Figure 1 As shown in the figure, this invention discloses a method for predicting wing aerodynamic shape and pressure distribution based on β-VAE, including: Step S11: Based on the parameterized design variables of the wing aerodynamic shape, extract them using the Latin hypercube sampling method to obtain the corresponding target variables, and construct a sample dataset based on the target variables and the corresponding pressure distribution.

[0021] In this embodiment, a fixed M6 wing can be selected, and the aerodynamic shape of the wing can be parameterized using an aerodynamic shape parameterization method to describe the changes in the wing's aerodynamic shape and obtain parameterized design variables. The aerodynamic shape parameterization method includes a free-form deformation method; the aerodynamic shape changes within a control frame are controlled by varying the position of the controlled apex, thus defining the aerodynamic shape design variables. If there are n parameterized design variables, m design variables are extracted from them using the Latin hypercube sampling method. The process involves obtaining the corresponding target variables. Specifically, the parametric design variables based on the wing's aerodynamic shape are extracted using the Latin hypercube sampling method to obtain the corresponding target variables. This includes: determining the parametric design variables of the wing's aerodynamic shape using free deformation technology, and then extracting the corresponding target variables based on these parametric design variables using the Latin hypercube sampling method.

[0022] It is understandable that CFD numerical analysis is performed on the target variable to obtain the corresponding pressure distribution data. . Figure 2 This is a schematic diagram of an aircraft wing. Figure 2 Image (a) is a three-dimensional axonometric view. Figure 2 (b) is a top-view projection, with the z-axis representing the span, the x-axis the chord direction, and the y-axis the normal direction. Figure 2 The gray dashed line in (a) marks the position of z=n, indicating the airfoil section obtained by taking a plane perpendicular to the z-axis at the spanwise position z=n and intersecting with the wing. In this embodiment, pressure distribution data of the section at n is extracted by selecting multiple different n. Figure 2 In (b) The angle between the leading edge line and the straight line perpendicular to the wing's plane of symmetry (z=0) is a key parameter affecting the wing's aerodynamic characteristics; the orange solid line is the projection line of the wing's leading edge, which is an important boundary for wing aerodynamic analysis; the 1 / 4 chord line is the line connecting the 1 / 4 positions of the airfoil chord length of each section. Figure 3 The first example is a schematic cross-sectional view of an M6 wing design, with 20%, 55%, 80%, and 90% spanwise sections selected as exemplary cross-sectional locations. This proposed solution, based on CFD numerical results, selects sections at 25%, 50%, 75%, and 95% spanwise to obtain the corresponding pressure distribution data. Figure 3 This diagram illustrates a cross-sectional view of an M6 airfoil. A set of sample data is constructed by combining the target variables of each airfoil with the pressure distribution data at four cross-sections. Specifically, constructing the sample dataset based on the target variables and their corresponding pressure distributions includes: using a CFD solver to determine the pressure distribution of the target airfoil cross-section corresponding to each target variable, and constructing the sample dataset based on the target variables and their corresponding pressure distributions.

[0023] Step S12: Construct an initial β-VAE model based on a variational autoencoder with preset adjustment parameters, determine the corresponding training set and test set based on the sample dataset, and train the initial β-VAE model using the training set to obtain a trained deep generation latent space model; the encoder and decoder in the initial β-VAE model are symmetric structures.

[0024] In this embodiment, VAE (Variational Autoencoder) is a nonlinear dimensionality reduction method based on probabilistic generative models. It learns low-dimensional representations of high-dimensional data by introducing latent variables to model the data. However, standard VAEs, when learning latent space representations, often tend to capture the overall statistical characteristics of the data, lacking the ability to explicitly separate the data-generating factors. This leads to strong coupling between latent variables, limiting their application in interpretable modeling and reconstruction tasks. To address this issue, based on the traditional VAE model, an adjustment parameter β is introduced into the objective function to constrain the information capacity of the latent space, thereby prompting the model to learn more independent and meaningful latent representations. From the perspective of probabilistic generative models, VAEs assume that high-dimensional observation data x is generated by latent variables z, and the joint distribution of all samples can be expressed as: ; in, The joint distribution of the sample dataset; These are the parameters of the VAE model; The prior probability distribution of the latent variable z is usually set to a standard normal distribution to ensure the continuity and sampleability of the latent space; Let x be the conditional probability distribution of a sample x given a latent variable z; since the true posterior distribution... Difficult to solve directly, VAE introduces a parameterized variational distribution. We approximate it and train the model by maximizing the variational lower bound of the marginal likelihood.

[0025] It is understandable that the variational lower bound can be expressed as: ; in, This is the marginal likelihood term, which is the log probability of the model generating sample x; It is a variational approximation of the posterior distribution; The joint distribution of the sample dataset; It is the prior distribution; This is the KL divergence term; The objective function described above contains two mutually constraining parts: on the one hand, the reconstruction term requires the model to reconstruct the input data as accurately as possible; on the other hand, the KL divergence term constrains the latent distribution to approximate the prior distribution, thereby avoiding overfitting the training data. In standard VAEs, the weights of these two parts are fixed, which to some extent limits the model's ability to manipulate the latent space structure. β-VAEs explicitly adjust this constraint by introducing a weight coefficient β before the KL divergence term, and their objective function can be written as: ; in, This is the marginal likelihood term, which is the log probability of the model generating sample x; It is a variational approximation of the posterior distribution; The joint distribution of the sample dataset; It is the prior distribution; This is the KL divergence term; For expectations; To adjust the hyperparameters for latent space constraints, a weighting coefficient β is introduced into the objective function of the variational autoencoder, establishing an adjustable trade-off between the model's data reconstruction capability and latent representation. When β=1, the model degenerates into a standard variational autoencoder; when β>1, the weights of the KL divergence term are enhanced, thereby imposing stronger distribution constraints on the latent variables, making their dimensions tend to be independent, thus improving the decoupling of the latent space. When β<1, the KL divergence constraint weakens, the model focuses more on minimizing reconstruction error, and the latent variables can encode more detailed information, but it is also easier to introduce redundant information and inter-dimensional correlations.

[0026] Furthermore, Figure 4 This is a schematic diagram of an initial depth generation latent space model structure, namely, an initial β-VAE model. For the input sample dataset, and These are the mean vector and standard deviation vector of the latent variable distribution, respectively; Represents the standard normal distribution. Let z be a noise vector sampled from a standard normal distribution; z is a latent variable. The output consists of wing aerodynamic shape design variables and corresponding pressure distribution data. In one specific implementation, the β-VAE model encoder consists of a six-layer fully connected neural network with 1024, 512, 256, 128, 64, and 16 neurons, respectively. The activation function is ReLU, and the latent space dimension can be set to 5, parameterized to a Gaussian distribution through mean and variance parameters. The decoder adopts a symmetrical structure to the encoder, i.e., 16, 64, 128, 256, 512, and 1024 neurons, used to reconstruct high-dimensional data from latent variables. A β value of 2.0 is preferred. The value of β is selected based on specific task requirements and through experiments. Multiple tests show that when β=2.0, the model achieves a reasonable balance between reconstruction accuracy and latent space constraints. During training, a fixed batch size of 64 is used, with 1000 iterations. The input sample set is normalized. The Adam optimizer is used, with a learning rate set to 0.0001.

[0027] Specifically, the construction of the initial β-VAE model based on the variational autoencoder with preset adjustment parameters includes: constructing the initial β-VAE model based on the variational autoencoder with preset adjustment parameters, combined with an encoder and a decoder; the preset adjustment parameters are adjustment parameters determined experimentally based on the target task requirements. The encoder includes a first fully connected neural network with the target number of layers; wherein the number of neurons in the first fully connected neural network is negatively correlated with the corresponding number of layers. The decoder includes a second fully connected neural network with the target number of layers; wherein the number of neurons in the second fully connected neural network is positively correlated with the corresponding number of layers.

[0028] In this embodiment, a training set and a test set are determined based on the sample dataset. The training set is input into the initial β-VAE model. The encoder can obtain the low-dimensional latent variables corresponding to the sample dataset composed of design variables and pressure distribution. The decoder can obtain the high-dimensional data sample set corresponding to the low-dimensional latent variables. The model training ends to obtain the trained deep generation latent space model.

[0029] Specifically, the step of determining the corresponding training set and test set based on the sample dataset, and training the initial β-VAE model using the training set to obtain a trained deep generative latent space model includes: dividing the sample dataset according to a preset partitioning ratio to obtain corresponding training set and test set; inputting the training set into the initial β-VAE model based on preset training parameters, so as to compress the training set into target low-dimensional latent variables using the initial β-VAE model, and using the decoder to restore the target low-dimensional latent variables into target high-dimensional data to obtain a trained deep generative latent space model.

[0030] Step S13: Based on the test set and using the trained deep latent space model, determine the target pressure distribution, and determine whether the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within a preset error range.

[0031] In this embodiment, it is determined whether the error between the predicted pressure distribution output by the trained deep generative latent space model and the actual pressure distribution output by the CFD solver is within a preset error range. Specifically, the step of determining the target pressure distribution based on the test set and using the trained deep generative latent space model, and determining whether the error between the target pressure distribution and the actual pressure distribution corresponding to the test set is within a preset error range, includes: reconstructing the pressure distribution of the test set using the trained deep generative latent space model to obtain the target pressure distribution; determining the actual pressure distribution corresponding to the test set using the CFD solver; and determining whether the error between the target pressure distribution and the actual pressure distribution is within a preset error range.

[0032] Understandably, if the error is not within the preset error range, the model is retrained or the model parameters are reset until the error is within the preset error range, thereby obtaining the target depth generation latent space model. The preset error range can be determined according to the actual situation. Specifically, after determining whether the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within the preset error range, the method further includes: if it is not within the preset error range, proceeding to the step of determining the corresponding training set and test set based on the sample dataset, until the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within the preset error range, to obtain the target depth generation latent space model.

[0033] Step S14: If the preset error range is met, the trained depth generation latent space model is determined as the target depth generation latent space model, so as to use the target depth generation latent space model to perform the prediction operation of wing aerodynamic shape and pressure distribution.

[0034] In this embodiment, latent variables are randomly extracted from the latent space, and the target depth latent space generation model is used to generate wing design variables and pressure distribution data corresponding to the latent variables. Specifically, the operation of predicting wing aerodynamic shape and pressure distribution using the target depth latent space generation model includes: extracting latent variables from the latent space in the target dimension, and using the target depth latent space generation model to generate wing design variables and pressure distribution data corresponding to the latent variables, thereby completing the prediction operation of wing aerodynamic shape and pressure distribution.

[0035] Understandably, model training and testing can be done using PyTorch and Python 3.10. Figure 5 This is a schematic diagram of the total loss curve of a model during training and testing. The horizontal axis represents the number of training iterations, and the vertical axis represents the total loss value of the model. The training set loss and the test set loss are always close and there is no obvious separation, which proves that the model has no overfitting and has excellent generalization ability.

[0036] Furthermore, Figure 6 This is a schematic diagram showing the reconstruction and comparison of sample pressure distribution for a test set. Figure 7 This diagram illustrates the reconstruction of pressure distribution from a different test set. The horizontal axis represents the chordal position, ranging from 0 to 1, and the vertical axis represents the dimensionless pressure coefficient. Two samples were randomly selected from the latent space variables of the test set for pressure distribution reconstruction. The diagram shows that the β-VAE curves of all cross-sections highly overlap with the CFD curves, indicating that the model trained using this method achieves a reasonable balance between reconstruction accuracy and latent space constraints. On the one hand, the reconstruction results effectively preserve the overall shape and key local features of the pressure distribution; on the other hand, the latent space still possesses certain structural constraints, thus avoiding overfitting. A β=2 setting is beneficial for balancing prediction accuracy and generalization performance in modeling high-dimensional pressure distribution data.

[0037] As can be seen from the above, this application uses parametric design variables and Latin hypercube sampling to ensure that the target variables uniformly cover the wing aerodynamic design space and are bound to the corresponding pressure distribution to construct a sample dataset. A β-VAE model with preset adjustment parameters and a symmetrical encoder-decoder structure is employed to accurately learn the nonlinear coupling law between shape and pressure. The sample dataset is divided into training and testing sets. The training set is used to train the model. Based on the trained model, the error between the target pressure distribution generated on the testing set and the corresponding real pressure distribution on the testing set is compared, allowing for quantifiable assessment of the model's accuracy and generalization ability to obtain a qualified target model. In this way, a latent space model generated using the target depth can be used to predict wing aerodynamic shape and pressure distribution, enabling rapid aerodynamic design and analysis.

Claims

1. A method for predicting wing aerodynamic shape and pressure distribution based on β-VAE, characterized in that, include: The parameterized design variables based on the aerodynamic shape of the wing are extracted using the Latin hypercube sampling method to obtain the corresponding target variables. A sample dataset is then constructed based on the target variables and the corresponding pressure distribution. An initial β-VAE model is constructed based on a variational autoencoder with pre-defined adjustment parameters. A corresponding training set and test set are determined based on the sample dataset. The initial β-VAE model is trained using the training set to obtain a trained deep generative latent space model. The encoder and decoder in the initial β-VAE model have a symmetrical structure. Based on the test set and using the trained deep generation latent space model, the target pressure distribution is determined, and it is determined whether the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within a preset error range. If the target depth generation latent space model is within the preset error range, the trained depth generation latent space model is determined as the target depth generation latent space model, so as to use the target depth generation latent space model to predict the aerodynamic shape and pressure distribution of the wing.

2. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The parameterized design variables based on the wing's aerodynamic shape are extracted using the Latin hypercube sampling method to obtain the corresponding target variables, including: The parametric design variables of the wing's aerodynamic shape are determined using free deformation technology. Based on these parametric design variables, the corresponding target variables are obtained by sampling using the Latin hypercube sampling method.

3. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The construction of the sample dataset based on the target variable and the corresponding stress distribution includes: The pressure distribution of the target airfoil profile corresponding to each of the target variables is determined using a CFD solver, and a sample dataset is constructed based on the target variables and the corresponding pressure distribution.

4. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The construction of the initial β-VAE model based on the variational autoencoder with pre-defined adjustment parameters includes: An initial β-VAE model is constructed based on a variational autoencoder with pre-defined adjustment parameters, combined with an encoder and a decoder; the pre-defined adjustment parameters are determined experimentally based on the requirements of the target task.

5. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The encoder comprises a first fully connected neural network with a target number of layers; The number of neurons in the first fully connected neural network is negatively correlated with the number of layers.

6. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 5, characterized in that, The decoder includes a second fully connected neural network with the target number of layers; The number of neurons in the second fully connected neural network is positively correlated with the number of layers.

7. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The step of determining the corresponding training and test sets based on the sample dataset, and training the initial β-VAE model using the training set to obtain a trained deep generative latent space model includes: The sample dataset is divided according to a preset division ratio to obtain corresponding training and test sets; The training set is input into the initial β-VAE model based on preset training parameters, so as to compress the training set into target low-dimensional latent variables using the initial β-VAE model, and then use the decoder to restore the target low-dimensional latent variables into target high-dimensional data to obtain a trained deep generative latent space model.

8. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The step of determining the target pressure distribution based on the test set and using the trained deep latent space model, and determining whether the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within a preset error range, includes: The pressure distribution of the test set is reconstructed using the trained deep generative latent space model to obtain the target pressure distribution; The CFD solver is used to determine the true pressure distribution corresponding to the test set, and it is determined whether the error between the target pressure distribution and the true pressure distribution is within a preset error range.

9. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, After determining whether the error between the target pressure distribution and the actual pressure distribution corresponding to the test set is within a preset error range, the method further includes: If the error is not within the preset error range, the process jumps to the step of determining the corresponding training set and test set based on the sample dataset, until the error between the target pressure distribution and the real pressure distribution corresponding to the test set is within the preset error range, so as to obtain the target depth generation latent space model.

10. The method for predicting wing aerodynamic shape and pressure distribution based on β-VAE according to claim 1, characterized in that, The operation of generating a latent space model using the target depth to predict wing aerodynamic shape and pressure distribution includes: Latent variables are extracted from the latent space of the target dimension, and the target depth is used to generate a latent space model to generate wing design variables and pressure distribution data corresponding to the latent variables, so as to complete the prediction operation of wing aerodynamic shape and pressure distribution.

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