A method of airfoil design

Abstract

The application provides a wing profile generation design method. A VAE-GAN generation model is used for wing profile design, a design space is more compact, a wing profile generation design method of a non-parameter function is combined, a network architecture of the generation model is modified, the limitation of a pre-defined parameter function on the generation model can be avoided, the design space is wider, the design result is more diversified, and smooth and continuous wing profiles are realized. Geometric feature driven generation model training is adopted, relevant physical regularization term driven training is refined from the perspective of wing profile geometric features, a loss function of the generation model is modified, so that the probability of obtaining smooth and continuous wing profiles by the non-parameter function wing profile design method based on the generation model is improved, and the physical feasibility of the generation design result is further improved.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic shape design technology, and more particularly to the field of airfoil design technology, specifically an airfoil generation design method. Background Technology

[0002] The flight quality and performance of an aircraft are primarily determined by its aerodynamic shape. Due to the complex relationship between aerodynamic shape and performance, and the numerous constraints imposed upon them, aerodynamic shape design is the most challenging aspect of the entire aircraft design process. For a long time, limitations in design methods and computer hardware have confined aerodynamic design research to obtaining aerodynamic performance under given geometric shapes and flight conditions. Wind tunnel testing has essentially been the only method for obtaining reliable aerodynamic data, but it is not only extremely costly but also has a long design cycle.

[0003] With the rapid development of Computational Fluid Dynamics (CFD) and the significant improvement in computer performance, new numerical design methods have emerged. These methods transform the design problem into an optimization problem, with the design objective being to minimize the aerodynamic objective function and its corresponding constraint functions. Numerical optimization algorithms are used to automatically generate aerodynamic shapes that meet design requirements. As the performance requirements for aircraft continue to increase, optimization design methods are being used more and more widely in aircraft design. Traditional parametric methods, such as B-spline methods, Bezier curve methods, NURBS curve methods, Categorical Shape Function Transformation (CST) methods, and Freeform Surface Deformation (FFD) methods, often prevent designers from selecting a suitable width / depth of design space for exploration, leading to redundant design variables.

[0004] Traditional parametric methods are limited by predefined parameter functions in terms of design space and airfoil shapes they can describe. This is particularly true in aerodynamic optimization, where parametric methods influence not only the choice of optimization algorithm but also the scope of the design space, the physical validity of the airfoil geometry within that space, and whether the design space includes ideal optimization results. Consequently, the types of airfoils generated, their level of detail, and the coverage of the design space are all constrained by these predefined parameter functions, failing to fully utilize the capabilities of the generative model. Furthermore, compared to fields like images and text, engineering design possesses unique physical properties, posing significant challenges to the application of generative models. Specifically, ensuring the physical feasibility of the generated results is crucial. Existing generative model-based airfoil parametric methods often suffer from a lack of physical feasibility in the generated results. Directly adjusting the airfoil's surface coordinates using the generative model frequently results in self-intersecting or coarse airfoils, making further CFD calculations impossible and thus hindering their application in practical aerospace engineering. Summary of the Invention

[0005] The purpose of this invention is to address the limitations of parametric methods on generative models and the physical feasibility issues of generated results in engineering design. Therefore, it proposes a geometry-feature-driven, parameter-free airfoil generative design method suitable for airfoil design. Generative models based on deep neural networks have attracted widespread attention due to their ability to learn high-dimensional probability distributions of large datasets and generate results similar to training samples. By utilizing generative models to learn existing airfoil distributions, airfoils can be designed directly from random noise without introducing parametric functions. This intelligent design method overcomes the limitations of traditional parametric methods, enabling the design of more feasible, freer, and more diverse airfoils.

[0006] Specifically, this invention provides a geometry-feature-driven, parametric-function airfoil generation design method suitable for airfoil design. Employing a VAE-GAN generative model for airfoil design offers a more compact design space compared to other models. Furthermore, the parametric-function-driven method avoids the limitations imposed by predefined parameter functions on the generative model, resulting in a wider design space and more diverse design results. Moreover, this invention utilizes geometry-feature-driven generative model training, extracting relevant physical regularization terms from the perspective of airfoil geometry to drive training, thereby increasing the probability of obtaining geometrically smooth and continuous airfoils based on the parametric-function-driven generative model, and ultimately improving the physical feasibility of the generated design results.

[0007] This invention proposes an airfoil generation design method that employs a VAE-GAN generative model. By combining this method with a parameterless airfoil generation design approach, the network architecture of the generative model is modified to avoid the limitations imposed by predefined parameter functions. The VAE-GAN generative model combines the advantages of Generative Adversarial Networks (GANs), which allow generators and discriminators to compete against each other and easily obtain high-quality samples, with the variational autoencoder (VAE), which, through maximizing the log likelihood during training, forces coverage of all patterns in the training dataset and easily obtains diverse samples, thus achieving better airfoil generation results.

[0008] In the VAE-GAN generative model employing a parameterless function, the model uses an encoder to learn the latent features z of a given real sample x, and then uses a decoder to generate reconstructed samples. The formula is as follows:

[0009] ,

[0010] (1)

[0011] To normalize the encoder, VAE considers the prior distribution of the latent vector p(z). Assume... It follows an isotropic Gaussian distribution, therefore the loss function partially minimized by the VAE is... for:

[0012] (2)

[0013] in It is the relative entropy, also known as the Kullback-Leibler divergence (KL divergence), which measures the difference between the latent vector p(z) and a Gaussian distribution. It is the reconstruction loss, which measures the reconstructed sample. Mean squared error (MSE) between the original sample x and the original sample x. These represent different weighting coefficients. Then the discriminator... Will determine the reconstructed sample The GAN part uses fake samples and identifies x as a real sample; therefore, the loss function of the GAN part... for:

[0014] (3)

[0015] In addition, to stabilize the training process and sharpen the discriminator The decision boundary introduces another loss function during encoder and decoder training. See formula (4), measurement discriminator The distance between the values ​​of neurons in the target layer when tested with fake samples and the values ​​when tested with real samples. This layer consistency loss, as a complement to the reconstruction loss, drives the autoencoder to better reconstruct the realistic airfoil design. A discriminator is used. Calculate from the second to last hidden layer The calculation formula is as follows:

[0016] (4)

[0017] In the formula: Indicates the first specified in the discriminator layer; Represents the latent variables of the encoder output;

[0018] The complete loss function L of the VAE-GAN generative model is a weighted combination of all the loss terms given below. The encoder, decoder, and discriminator are jointly trained, and each term of the loss function is assigned a different weight λ when training each component.

[0019] (5)

[0020] in, , , , These represent different weighting coefficients.

[0021] By using the above-mentioned parameterless function to generate the model, we can avoid the limitations imposed by predefined parameter functions on the generated model, thus expanding the design space and diversifying the design results.

[0022] To ensure the physical validity of the airfoil designed by the parametric function generation model, the regularization term of the airfoil geometric features is extracted based on the characteristics of the airfoil obtained from the parametric function generation model.

[0023] To ensure the physical effectiveness of the airfoil and avoid generating airfoils with intersecting upper and lower surfaces, a regularization term to prevent airfoil intersection was designed:

[0024] (6)

[0025] In the formula: N is the batch sample size. It is the first on the lower surface i The y-coordinates of the points It is the first on the upper surface i The y-coordinates of the points.

[0026] To ensure the physical effectiveness of the airfoil, roughness is introduced. The roughness of the curve represents the degree of non-smoothness and continuity of the generated airfoil. The angle between the lines connecting adjacent coordinate points can be calculated. get;

[0027]

[0028] (7)

[0029] in, , Let x and y be the coordinates of the k-th point. , Let x and y be the coordinates of the (k+1)th point. v k It is represented as a vector pointing from the k-th point to the (k+1)-th point. v i,k Represented as the first during the training process i A wing-shaped v k vector, v i,k+1 Represented as the first during the training process i A wing-shaped v k+1 vector, This represents the angle between the lines connecting adjacent coordinate points. Representing the overall geometric features, The geometric feature representing the i-th local location, This represents the inverse cosine function.

[0030] To ensure the physical effectiveness of the airfoil and avoid generating airfoils with a sharp leading edge that are impossible to manufacture, a leading edge curvature regularization term was designed:

[0031] (8)

[0032] In the formula: Indicates the first step in the training process i The leading edge curvature of the airfoil Indicating the training process, the first i The leading edge vector of an airfoil, Indicates the first i The vector of an airfoil at the next sampling point adjacent to the leading edge.

[0033] We employ a geometric feature-driven generative model training method. Starting from the perspective of airfoil geometry, we extract relevant physical regularization terms to drive the training of the generative model, thereby increasing the probability of obtaining geometrically smooth and continuous airfoils using the parameterless function airfoil design method based on the generative model.

[0034] During the training of the generative model, the loss function is modified based on the extracted airfoil geometric feature regularization term. The airfoil geometric feature regularization term is introduced as a penalty term in the generator loss function. Therefore, formula (5) is rewritten as formula (9). After constraining the generative model with airfoil geometric features, the loss function of the entire model is... for:

[0035] (9)

[0036] in, These represent different weighting coefficients.

[0037] By incorporating the extracted airfoil geometric feature regularization term into the loss function, the loss function of the generative model is modified to increase the probability of obtaining geometrically smooth and continuous airfoils using the parameterless function airfoil design method based on the generative model, thereby improving the physical feasibility of the generative design results.

[0038] Feasibility verification of airfoil generation design results.

[0039] Select the hyperparameters of the airfoil geometry regularization term, select representatives from typical airfoils based on the airfoil geometry, and calculate the roughness;

[0040] To rationally select the hyperparameters for the regularization term of the airfoil geometry, a representative airfoil was chosen from each of the seven typical airfoils based on their geometric characteristics: symmetric airfoil NACA0012, supercritical airfoil RAE2822, plano-convex airfoil Clarky, biconvex airfoil e195, concave-convex airfoil n6409, thick airfoil NACA4418, and thin airfoil NACA16009. A comparison of the geometric shapes of the seven typical airfoils can be found in [link to documentation]. Figure 4 For these typical airfoils, calculate their roughness respectively.

[0041] The model is implemented using the PyTorch framework. Specifically, the encoder consists of three-layer perceptron (MLP) structures, each containing [256, 128, 32] neurons, with each layer using LeakyReLU as the activation function. The decoder also consists of three-layer MLP structures, each containing [128, 256, 200] neurons. The output layer uses the hyperbolic tangent (Tanh) function as the activation function, scaling all output values ​​to the range [-1, 1]. Similarly, the discriminator contains a three-layer MLP structure with [256, 128, 1] neurons, and outputs the probability of whether the input is real or fake using a sigmoid activation function.

[0042] Regarding hyperparameter settings, the VAE-GAN model was trained for 5,000 epochs, with each epoch iterating through all samples in the dataset. The initial learning rates for the encoder, decoder, and discriminator were all set to 0.0005, decaying to 0.00005 after 2,000 epochs. The batch size was set to 16, representing 1 / 100th of the database size.

[0043] The Adam optimizer is used to update all parameters in the model. Each term in the loss function is assigned a different coefficient, as mentioned above; similarly, the weight coefficients for different components (i.e., encoder, decoder, and discriminator) also differ. Specifically, to ensure that the reconstructed features contain sufficient airfoil geometry information, a specific weight is assigned to the reconstruction loss. A large coefficient of 10 was assigned, representing the prior loss. and They are then assigned weights of 1 and 0.1 respectively, and the loss function of the GAN model part is... They are assigned a weight of 1, and the geometric feature losses are 10, 0.1, and 5, respectively.

[0044] To strike a balance between computational efficiency and accuracy, the impact of the dimensionality of latent variables on the VAE-GAN generative model was investigated to determine the most suitable dimensionality. Maximum Mean Difference (MMD) was used to quantitatively assess the similarity between the airfoil distributions generated by training with latent variables of different dimensions and the training data distribution, thereby evaluating the model's learning ability on the data. MMD measures the similarity between two distributions; the smaller the value, the closer the two distributions are. The formula for calculating MMD is as follows:

[0045] (10)

[0046] When the latent dimension is low, increasing the noise dimension improves the quality of the generated data; however, when the latent dimension is high, increasing the noise dimension to a certain extent can actually decrease the generation quality. This is because sufficient latent and noise variables tend to saturate the ability to represent airfoils, and further increasing the design dimension will challenge the model training and reduce the generation quality. To further investigate the ability of airfoil geometry features to drive the VAE-GAN generative model to parameterize airfoils, the design space is analyzed.

[0047] This invention provides a geometry-feature-driven, parametric-function airfoil generative design method suitable for airfoil design. Employing a VAE-GAN generative model for airfoil design results in a more compact design space. By modifying the network architecture of the generative model in conjunction with the parametric-function-driven airfoil generative design method, the limitations imposed by predefined parameter functions on the generative model are avoided, leading to a wider design space, more diverse design results, and the achievement of smooth and continuous airfoils. The geometric feature-driven generative model training extracts relevant physical regularization terms from the perspective of airfoil geometry to drive training. Modifying the loss function of the generative model increases the probability of obtaining geometrically smooth and continuous airfoils based on the parametric-function-driven airfoil design method, thereby improving the physical feasibility of the generated design results. Attached Figure Description

[0048] To more clearly illustrate the technical solutions of this application, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort.

[0049] Figure 1 (a) is a schematic diagram of the network architecture of a parameterized generation model in the prior art; (b) is a schematic diagram of the network architecture of the parameterless generation model of the present invention.

[0050] Figure 2 This is a schematic diagram of a parameterless airfoil generation model based on VAE-GAN.

[0051] Figure 3 This is a schematic diagram of the geometric roughness of a smooth circle and an airfoil.

[0052] Figure 4 This is a comparative diagram of the geometric shapes of seven typical airfoils.

[0053] Figure 5 This is a schematic diagram illustrating the similarity between the airfoil distribution generated by training with latent variables of different dimensions and the distribution of the training data.

[0054] Figure 6 This is a schematic diagram comparing the distribution of randomly generated airfoil shapes.

[0055] Figure 7 This is a schematic diagram comparing randomly generated airfoil curvature distributions.

[0056] Figure 8 This is a schematic diagram comparing the effective airfoils sampled randomly. Detailed Implementation

[0057] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0058] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0059] Figure 1(a) is a schematic diagram of the network architecture of a parameterized generative model in the prior art, and (b) is a schematic diagram of the network architecture of the parameterless generative model of the present invention. In the figures, DGM (Deep Generative Model) represents a deep generative model, CST para (Class / Shape Function Transformation para) represents the parameters of the class / shape function transformation, and CST layer represents the CST layer, which implements the input CST parameters and outputs the result after the CST function transformation. The present invention avoids the limitation of the generative model on the generative model by adjusting the network architecture of the generative model.

[0060] Figure 2 This is a schematic diagram of a parametric airfoil generation model based on VAE-GAN. An airfoil generation and design method proposed in this invention is used, comprising the following steps:

[0061] Step 1: Generate the model using a VAE-GAN generative model. Combine this with a parameterless airfoil generative design method to modify the network architecture of the generative model, thereby avoiding the limitations imposed by predefined parameter functions on the generative model.

[0062] The VAE-GAN generative model combines the advantages of Generative Adversarial Networks (GANs), which allow generators and discriminators to compete against each other and easily obtain high-quality samples, with the advantages of Variational Autoencoders (VAEs), which are trained by maximizing the likelihood logarithm, thereby forcing coverage of all patterns in the training dataset and easily obtaining diverse samples, thus achieving better airfoil generation results.

[0063] In the VAE-GAN generative model employing a parameterless function, the model uses an encoder to learn the latent features z of a given real sample x, and then uses a decoder to generate reconstructed samples. The formula is as follows:

[0064] ,

[0065] (1)

[0066] To normalize the encoder, VAE considers the prior distribution of the latent vector p(z). Assume... Since it follows an isotropic Gaussian distribution, the loss function partially minimized by the VAE is... for:

[0067] (2)

[0068] in, It is the relative entropy, also known as the Kullback-Leibler divergence (KL divergence), which measures the difference between the latent vector p(z) and a Gaussian distribution. It is the reconstruction loss, which measures the reconstructed sample. The mean squared error (MSE) between the original sample x and the mean squared error (MSE). Then the discriminator. Will determine the reconstructed sample The GAN part uses fake samples and identifies x as a real sample; therefore, the loss function of the GAN part... for:

[0069] (3)

[0070] In the formula: Discriminator, For encoder, For decoders;

[0071] In addition, to stabilize the training process and sharpen the discriminator The decision boundary of the Discriminator during the training of the encoders. and decoder Another loss function was introduced at that time. See formula (4), measurement discriminator The distance between the values ​​of neurons in the target layer when tested with fake samples and the values ​​when tested with real samples. This layer consistency loss, as a complement to the reconstruction loss, drives the autoencoder to better reconstruct the realistic airfoil design. A discriminator is used. Calculate from the second to last hidden layer The calculation formula is as follows:

[0072] (4)

[0073] In the formula: Indicates the first specified in the discriminator layer; Represents the latent variables of the encoder output;

[0074] The complete loss function L of the VAE-GAN generative model is a weighted combination of all the loss terms given below. The encoder, decoder, and discriminator are jointly trained, and each term of the loss function is assigned a different weight λ when training each component.

[0075] (5)

[0076] in, , , , These are different weighting coefficients.

[0077] By using the above-mentioned parameterless function to generate the model, we can avoid the limitations imposed by predefined parameter functions on the generated model, thus expanding the design space and diversifying the design results.

[0078] Step 2: To ensure the physical validity of the airfoil designed by the parametric function generation model, extract the regularization term of the airfoil geometric features based on the characteristics of the airfoil obtained from the parametric function generation model.

[0079] In one embodiment, based on the main characteristics of invalid airfoils directly obtained from the airfoil generation model without parameter functions, typical and general airfoil geometric feature regularization terms are abstracted and extracted.

[0080] In one embodiment, to ensure the physical validity of the airfoil and avoid generating airfoils with intersecting upper and lower surfaces, a regularization term to prevent airfoil intersection was designed:

[0081] (6)

[0082] In the formula: N is the batch sample size. It is the first on the lower surface i The y-coordinates of the points It is the first on the upper surface i The y-coordinates of the points.

[0083] In one embodiment, roughness is introduced to ensure the physical effectiveness of the airfoil. The roughness of the curve represents the degree of non-smoothness and continuity of the generated airfoil. The angle between the lines connecting adjacent coordinate points can be calculated. get;

[0084] ,

[0085] (7)

[0086] in, , Let x and y be the coordinates of the k-th point. , Let x and y be the coordinates of the (k+1)th point. v k It is represented as a vector pointing from the k-th point to the (k+1)-th point. v i,k Represented as the first during the training process i A wing-shaped v k vector, v i,k+1 Represented as the first during the training processi A wing-shaped v k+1 vector, This represents the angle between the lines connecting adjacent coordinate points. Representing the overall geometric features, The geometric feature representing the i-th local location, This represents the inverse cosine function.

[0087] Figure 3 This is a schematic diagram of the geometric roughness of a smooth circle and an airfoil. Figure 3 (a) n Indicates the first n One point, v n Indicates from the first n The point points to the first n A vector with +1 point, Indicates from the first n -1 point points to the first n A vector of points, Indicates from the first n +1 point points to the first n +2 points of vector, Indicates from the first n The point points to the first n A vector with +1 point, Indicates from the first n +1 point points to the first n +2 points of vector; Figure 3 In (b), from the first n The point points to the first n +1 point vector An acute angle indicates a good airfoil, from the first... n The point points to the first n +1 point vector An obtuse angle indicates an incorrect airfoil. For example... Figure 3 The schematic diagrams of the geometric roughness of smooth circles and airfoils show that, when considering undistorted convex shapes, the degree of distortion varies for different geometric shapes. Figure 3 (a) A smooth, continuous circle with a distortion degree of And for Figure 3 For the airfoil in (b), compared to a smooth circular surface, a rougher airfoil surface results in greater [weight / weight]. value.

[0088] In one embodiment, to ensure the physical validity of the airfoil and avoid generating an airfoil with a sharp leading edge that is impossible to manufacture, a leading edge curvature regularization term was designed. :

[0089] (8)

[0090] 𝜙 LE This represents the curvature of the leading edge point. v LE This is represented as the vector between the first point on the upper surface and the leading edge point. v LE+1 The vector representing the point at the leading edge and the first point on the lower surface is given by the following formula: Indicating the training process, the first i The leading edge curvature of the airfoil Indicating the training process, the first i The leading edge vector of an airfoil, Indicates the first i The vector of an airfoil at the next sampling point adjacent to the leading edge.

[0091] We employ a geometric feature-driven generative model training method. Starting from the perspective of airfoil geometry, we extract relevant physical regularization terms to drive the training of the generative model, thereby increasing the probability of obtaining geometrically smooth and continuous airfoils using the parameterless function airfoil design method based on the generative model.

[0092] Step 3: During the training of the generative model, the loss function is modified based on the extracted airfoil geometric feature regularization term. The airfoil geometric feature regularization term is introduced as a penalty term in the generator loss function. Therefore, formula (5) is rewritten as formula (9). After constraining the generative model using airfoil geometric features, the loss function of the entire model is... for:

[0093] (9)

[0094] in, These represent different weighting coefficients.

[0095] By incorporating the extracted airfoil geometric feature regularization term into the loss function, the loss function of the generative model is modified to increase the probability of obtaining geometrically smooth and continuous airfoils using the parameterless function airfoil design method based on the generative model, thereby improving the physical feasibility of the generative design results.

[0096] Step 4: Feasibility verification of airfoil generation design results.

[0097] Select the hyperparameters of the airfoil geometry regularization term, select representatives from typical airfoils based on the airfoil geometry, and calculate the roughness;

[0098] In one embodiment, to reasonably select the hyperparameters of the airfoil geometry regularization term, a representative is chosen from each of seven typical airfoils based on their geometry: symmetrical airfoil NACA0012, supercritical airfoil RAE2822, plano-convex airfoil Clarky, biconvex airfoil e195, concave-convex airfoil n6409, thick airfoil NACA4418, and thin airfoil NACA16009. A comparison of the geometric shapes of the seven typical airfoils can be found in [link to documentation]. Figure 4 For these typical airfoils, calculate their roughness respectively.

[0099] Table 1. Roughness of typical airfoils

[0100]

[0101] The model is implemented using the PyTorch framework. Specifically, the encoder consists of three-layer perceptron (MLP) structures, each containing [256, 128, 32] neurons, with each layer using LeakyReLU as the activation function. The decoder also consists of three-layer MLP structures, each containing [128, 256, 200] neurons. The output layer uses the hyperbolic tangent (Tanh) function as the activation function, scaling all output values ​​to the range [-1, 1]. Similarly, the discriminator contains a three-layer MLP structure with [256, 128, 1] neurons, and outputs the probability of whether the input is real or fake using a sigmoid activation function.

[0102] Regarding hyperparameter settings, the VAE-GAN model was trained for 5,000 epochs, with each epoch iterating through all samples in the dataset. The initial learning rates for the encoder, decoder, and discriminator were all set to 0.0005, decaying to 0.00005 after 2,000 epochs. The batch size was set to 16, representing 1 / 100th of the database size.

[0103] The Adam optimizer is used to update all parameters in the model. Each term in the loss function is assigned a different coefficient, as mentioned above; similarly, the weight coefficients for different components (i.e., encoder, decoder, and discriminator) also differ. Specifically, to ensure that the reconstructed features contain sufficient airfoil geometry information, a specific weight is assigned to the reconstruction loss. A large coefficient of 10 was assigned, representing the prior loss. and They are then assigned weights of 1 and 0.1 respectively, and the loss function of the GAN model part is... They are assigned a weight of 1, and the geometric feature losses are 10, 0.1, and 5, respectively.

[0104] To strike a balance between computational efficiency and accuracy, the impact of the dimensionality of latent variables on the VAE-GAN generative model was investigated to determine the most suitable dimensionality. Maximum Mean Difference (MMD) was used to quantitatively assess the similarity between the airfoil distributions generated by training with latent variables of different dimensions and the training data distribution, thereby evaluating the model's learning ability on the data. MMD measures the similarity between two distributions; the smaller the value, the closer the two distributions are. The formula for calculating MMD is as follows:

[0105] (10)

[0106] in, P , Q This represents the probability distribution of two sets of data. k It is a kernel function defined on the sample space, from P Samples drawn from ,from Q Samples drawn from . In terms of random variables x and x ′ All follow a distribution P In the case of kernel function The mathematical expectation; Indicates in random variables y and y′ All follow a distribution Q In the case of kernel function The mathematical expectation; Indicates in random variables x Follows distribution P , y Follows distribution Q In the case of kernel function k ( x , y The mathematical expectation of ).

[0107] like Figure 5 As shown, the maximum mean difference (MMD) between the airfoil distributions obtained by the generative model and the UIUC library was calculated for latent variable dimensions of 4, 8, 16, 32, 64, and 128. The results indicate that the MMD is minimized at a dimension of 32. On the other hand, when the latent dimension is low, increasing the noise dimension improves the quality of the generated data; however, when the latent dimension is high, increasing the noise dimension to a certain extent can actually decrease the generation quality. This is because sufficient latent and noise variables saturate the ability to represent airfoils, and further increasing the design dimension can challenge model training and reduce generation quality. Considering all factors, a latent variable dimension of 32 is a more reasonable setting for VAE-GAN.

[0108] Figure 6 and Figure 7 The images show VAE-GAN generative models trained with and without airfoil geometry-driven training, and compare the geometric shapes and curvature distributions of airfoils generated from a random input z. The blue line (Airfoil geo) represents the airfoil shape trained with geometry-driven training, and the black line (Airfoil no_regular) represents the airfoil shape trained without geometry-driven training. Figure 6 The horizontal axis x / c represents the chord length of the airfoil from the leading edge 0 to the trailing edge 1.0 after normalization, and the vertical axis y / c represents the thickness of the airfoil after normalization. Figure 7 The horizontal axis represents the chord length of the airfoil from the leading edge (0) to the trailing edge (1.0) after normalization, while the vertical axis represents the curvature of the airfoil after normalization. As can be seen from the figure, when only the loss function of the VAE-GAN generation model is used without geometry-driven training, the generated airfoil is full of sharp, rough, and uneven surfaces. Observing its curvature, it is also very obvious that the curvature value is large and extremely unstable, indicating poor airfoil smoothness. After constraining with airfoil geometric feature regularization terms, the curvature of the airfoil is significantly improved, with the value decreasing and becoming more stable.

[0109] To further investigate the ability of airfoil geometry features to drive the VAE-GAN generative model to parameterize airfoils, the design space was analyzed. Specifically, 1000 airfoils were randomly generated using each generative model. Then, the tests were conducted in two steps: first, it was determined whether overlap occurred, and second, it was determined whether convergence could be calculated using Xfoil. The calculation results are shown in Table 2 below.

[0110] Table 2 Verification of Parametric Airfoil Capabilities

[0111]

[0112] Physical rules; however, after training the model using airfoil geometry features, the generated airfoils have almost no intersections, and the calculation of aerodynamic coefficients is also greatly improved.

[0113] Figure 8 The model showcases four random, non-intersecting airfoils within their respective design spaces. It can be observed that the airfoils in the design space of the VAE-GAN generative model, driven by airfoil geometry features, are smoother.

[0114] In summary, the results of the proposed airfoil generation and design method demonstrate that the design intent has been achieved, the generated airfoil has good physical feasibility, and it helps to improve optimization efficiency.

[0115] Generative models based on deep neural networks have attracted widespread attention due to their ability to learn high-dimensional probability distributions of large datasets and generate results similar to training samples. By using generative models to learn existing airfoil distributions, airfoils can be designed directly from random noise without introducing parametric functions. This intelligent design method breaks through the limitations of traditional parametric methods, enabling the design of more feasible, freer, and more diverse airfoils.

[0116] This invention provides a geometry-feature-driven, parametric-function airfoil generative design method suitable for airfoil design. Employing a VAE-GAN generative model for airfoil design results in a more compact design space. By modifying the network architecture of the generative model in conjunction with the parametric-function-driven airfoil generative design method, the limitations imposed by predefined parameter functions on the generative model are avoided, leading to a wider design space, more diverse design results, and the achievement of smooth and continuous airfoils. The geometric feature-driven generative model training extracts relevant physical regularization terms from the perspective of airfoil geometry to drive training. Modifying the loss function of the generative model increases the probability of obtaining geometrically smooth and continuous airfoils based on the parametric-function-driven airfoil design method, thereby improving the physical feasibility of the generated design results.

[0117] It should be noted that, for those skilled in the art, the technical features in the above embodiments can be freely combined, and the resulting technical solutions also belong to the embodiments disclosed in this invention.

[0118] Furthermore, without departing from the principles of this invention, several improvements and modifications can be made to this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. An airfoil generation and design method, characterized in that, Includes the following steps: Step 1: Generate the design using a VAE-GAN model, and modify the network architecture of the generative model by combining it with a parameterless airfoil generation design method; Step 1.1: In the VAE-GAN generative model using a parameterless function, the model uses an encoder to learn the latent features z of a real sample x, and then uses a decoder to generate reconstructed samples. , assuming Since it follows an isotropic Gaussian distribution, the loss function partially minimized by the VAE is... for: ； In the formula: It is relative entropy. It is the reconstruction loss. Indicates different weighting coefficients; Step 1.2: Discriminator Will determine the reconstructed sample The GAN part uses fake samples and identifies x as a real sample; therefore, the loss function of the GAN part... for: ； In the formula: Discriminator, For encoder, For decoders; Step 1.3: Introduce layer consistency loss during encoder and decoder training. Used for measuring discriminators The distance between the values ​​of neurons in the target layer under test when using fake samples and when using real samples; ； In the formula: Indicates the first specified in the discriminator layer; Represents the latent variables of the encoder output; The encoder, decoder, and discriminator are trained jointly. During the training of each component, each term of the loss function is assigned a different weight coefficient. Let each represent a different weight coefficient, then the complete loss function of the VAE-GAN generative model is... for: ； Step 2: Based on the airfoil characteristics obtained from the parameterless function generation model, extract the airfoil geometric feature regularization term; the airfoil geometric feature regularization term includes a regularization term to prevent airfoil intersection. Roughness Leading edge curvature regularization term ;in: ； In the formula: N It is the batch sample size. It is the y-coordinate of the i-th point on the lower surface. It is the y-coordinate of the i-th point on the upper surface; ； ； In the formula: Let x and y represent the coordinates of the k-th point, respectively. Let x and y represent the coordinates of the (k+1)th point, respectively. v k This represents the vector pointing from the k-th point to the (k+1)-th point. v i,k Indicates the first step in the training process i A wing-shaped v k vector, v i,k+1 Indicates the first step in the training process i A wing-shaped v k+1 vector, This represents the angle between the lines connecting adjacent coordinate points. Representing the overall geometric features, The geometric feature representing the i-th local location, Represents the inverse cosine function; ； In the formula: Indicates the first step in the training process i The leading edge curvature of the airfoil Indicates the first step in the training process i The leading edge vector of an airfoil, Indicates the first i The vector of an airfoil at the next sampling point adjacent to the leading edge; Step 3: During the training of the generative model, the loss function of the generative model is modified by introducing the extracted airfoil geometric feature regularization term into the loss function. This improves the probability of obtaining geometrically smooth and continuous airfoils by the parameterless function airfoil design method based on the generative model, thereby improving the physical feasibility of the generated design results.

2. The airfoil generation and design method according to claim 1, characterized in that: In step 3, the loss function is modified based on the extracted airfoil geometric feature regularization term. This airfoil geometric feature regularization term is introduced as a penalty term in the generator loss function. After constraining the generative model using airfoil geometric features, the overall model's loss function... for: ； In the formula: These represent different weighting coefficients.

3. The airfoil generation and design method according to claim 1, characterized in that: Following step 3, step 4 is included to verify the feasibility of the airfoil generation design results. This involves selecting hyperparameters for the geometric feature regularization term, choosing representative airfoils from typical airfoils based on their geometric features, calculating roughness, and implementing the model using the PyTorch framework. The encoder, decoder, and discriminator are all composed of three-layer MLPs. Regarding hyperparameter setting, the VAE-GAN generation model undergoes epoch training. The maximum mean difference (MMD) value between the airfoil distribution obtained by the generation model and the airfoil database is calculated when the latent variables are in different dimensions. This assesses the similarity between the airfoil distribution generated by training with latent variables of different dimensions and the training data distribution, thereby evaluating the model's learning degree from the data and the physical feasibility of the airfoil generation results.

4. The airfoil generation and design method according to claim 3, characterized in that: In step 4, based on the geometric characteristics of the airfoil, a representative is selected from each of the seven typical airfoils: symmetrical airfoil NACA0012, supercritical airfoil RAE2822, plano-convex airfoil Clarky, biconvex airfoil e195, concave-convex airfoil n6409, thick airfoil NACA4418, and thin airfoil NACA16009, and the roughness of the above typical airfoil is calculated respectively.

5. The airfoil generation and design method according to claim 3, characterized in that: In step 4, the VAE-GAN generative model is trained for 5000 epochs. An epoch refers to the process of the model traversing the entire training dataset once during the training process. Each epoch traverses all samples in the dataset.

6. The airfoil generation and design method according to claim 3, characterized in that: In step 4, the initial learning rate of the encoder, decoder and discriminator is set to 0.0005, and decays to 0.00005 after 2000 epochs. The batch size is set to 16, which is 1 / 100 of the database size.

7. The airfoil generation and design method according to claim 1, characterized in that: The Adam optimizer is used to update all parameters in the model, and different coefficients are assigned to each term in the loss function, with different weight coefficients for the encoder, decoder, and discriminator.

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