Airfoil profile parameterization method based on auto-encoder model

Abstract

The invention provides an airfoil profile parameterization method based on an auto-encoder model, an airfoil profile auto-encoder model which does not depend on any artificial priori knowledge, is completely based on a Transform architecture and generates an airfoil profile x coordinate and an airfoil profile y coordinate at the same time is constructed, a group of potential representations capable of expressing an airfoil profile shape is explored completely through deep learning, and the airfoil profile parameterization method based on the auto-encoder model is established. And meanwhile, airfoil point cloud data are reconstructed based on the potential representations, so that the application range and the parameterization precision of an airfoil parameterization model are improved.

Description

Technical Field

[0001] The present invention relates to the field of airfoil design, and specifically to an airfoil parameterization method based on an autoencoder model. Background Art

[0002] Parameterization is an important method in the process of aircraft shape design. This technology is used to reduce the dimension of aircraft or wing point cloud data to a small number of variables and control these variables to achieve the control and deformation of the wing shape. The aircraft shape optimization design process is carried out for these variables. Among them, the CST parameterization method is a commonly used parameterization method at present. The basic principle of the CST parameterization method is to linearly superimpose different curve functions in the defined design space to obtain the designed airfoil shape. Due to the high-precision requirements for aircraft shape design, a key performance index of the parameterization method is the reconstruction error of the shape. However, with the development of airfoil research, the design curves of new airfoil shapes are becoming more and more complex, which has exceeded the design space of the CST parameterization method, making it difficult to parameterize using the CST parameterization method; moreover, the design space in the CST parameterization method itself still belongs to manually designed curve functions, which will introduce inductive bias, thus reducing the applicability of the parameterization method to point cloud data of different shapes.

[0003] At present, there are mainly two technical routes for airfoil parameterization methods based on deep learning technology: one is the model based on variational autoencoder (VAE), and the other is the model based on generative adversarial network (GAN).

[0004] The first technical route was practiced earliest. However, previous work only parameterized the y coordinate of the airfoil while fixing the x coordinate, that is, it was required that the x coordinates of the coordinate points in the airfoil point cloud data must be fixed to several set values, thus restricting the design space of the airfoil.

[0005] In the second technical route, current research has proposed adding a Bézier layer at the end of the parameterization model to generate smooth airfoil point cloud coordinates. Subsequently, an improved BSplineGAN for this model has emerged. Compared with the previous model, the improved model can provide better shape control with fewer control parameters. Although both of these models can reconstruct smooth airfoil data, due to the use of the Bézier layer, it essentially adds a manually designed function, which is equivalent to introducing inductive bias.

[0006] In addition, there is also research that combines these two technical routes to build a parameterization model based on VAEGAN. It does not rely on existing design formulas, but still only models the y coordinate of the airfoil and fixes the x coordinate, restricting the application range of the parameterization model. Summary of the Invention

[0007] In view of the problems existing in the prior art, the present invention proposes an airfoil parameterization method based on an autoencoder model, constructs an airfoil autoencoder model that does not rely on any artificial prior knowledge, is completely based on the Transformer architecture, and simultaneously generates the x and y coordinates of the airfoil. It fully explores a set of features that can represent the airfoil shape through deep learning itself, and can reconstruct the airfoil coordinate data based on these features, thereby improving the applicable range and parameterization accuracy of the airfoil parameterization model.

[0008] The technical solution of the present invention is as follows:

[0009] An airfoil parameterization method based on an autoencoder model, comprising the following steps:

[0010] Step 1: Adjust the data structure of the existing initial airfoil point cloud dataset to make the data structure of the initial airfoil point cloud data consistent, and perturb the initial airfoil point cloud data to obtain new airfoil point cloud data, which together with the initial airfoil point cloud data form a multi-source airfoil point cloud dataset;

[0011] Step 2: Construct an encoder, which can perform dimensionality reduction processing on the airfoil point cloud data to obtain the latent representation of the airfoil point cloud data;

[0012] The encoder includes a serialization processing module, a stacked ViT (Visual Transformer) module, and a convolutional module;

[0013] The serialization processing module performs serialization processing on the input airfoil point cloud data to obtain serialized data; using the serialized data as the input of the stacked ViT module, extracts the airfoil point cloud data features through the stacked ViT module, and inputs the airfoil point cloud data features into the convolutional module for dimensionality reduction to obtain the latent representation of the airfoil point cloud data;

[0014] Step 3: Construct a decoder, which can reconstruct the latent representation to obtain the airfoil point cloud data;

[0015] The decoder includes a transposed convolutional module, a stacked ViT module, an Unpatchify module, and a Softmax module;

[0016] The transposed convolutional module performs upsampling on the input latent representation, then extracts serialized feature data through the stacked ViT module, and uses the Unpatchify module to map the serialized feature data back to the original airfoil point cloud data structure; finally, the mapped data is reconstructed into the airfoil point cloud data through the Softmax module;

[0017] Step 4: Establish an airfoil autoencoder based on the encoder obtained in Step 2 and the decoder obtained in Step 3; the input of the airfoil autoencoder is airfoil point cloud data, and the output of the autoencoder is the reconstructed airfoil point cloud data; use the multi-source airfoil point cloud dataset to train the airfoil autoencoder to obtain a trained airfoil autoencoder;

[0018] Step 5: Parametrize the given airfoil point cloud data according to the airfoil autoencoder obtained in Step 4 to obtain the latent representation of the airfoil point cloud data.

[0019] Furthermore, based on the given latent representation, use the airfoil autoencoder obtained in Step 4 to generate the corresponding airfoil point cloud data.

[0020] Furthermore, in Step 1, the consistency of the data structure means that the total number of coordinate points used to represent the airfoil in the airfoil point cloud data is the same.

[0021] Furthermore, the specific method for adjusting the data structure in Step 1 is: set the number of coordinate points representing the airfoil after shaping to N. For the initial airfoil point cloud dataset, if the number of coordinate points of a certain airfoil point cloud data is less than N, then expand the number of coordinate points of this airfoil point cloud data to N through interpolation. If the number of coordinate points of a certain airfoil point cloud data is greater than N, then reduce the number of coordinate points of this airfoil point cloud data to N through sampling.

[0022] Furthermore, the method for perturbing the initial airfoil point cloud data in Step 1 is: for a certain initial airfoil point cloud data, use the traditional parameterization method for parameterization, and then perturb the airfoil design parameters after parameterization within the set perturbation range.

[0023] Furthermore, the traditional parameterization methods include the CST parameterization method and the B-Spline parameterization method.

[0024] Furthermore, in Step 2, the data structure of the serialized data obtained by the serialization processing module for serializing the input airfoil point cloud data is a three-dimensional array, and the three dimensions are: channel, length, and width; where the size C of the channel dimension is 1, the size H of the length dimension is the number of coordinate points after shaping in Step 1, and the size W of the width dimension is 2, indicating that each coordinate point has two coordinate values, x and y.

[0025] Furthermore, the stacked ViT module is composed of several ViT Blocks connected in sequence, and each ViT Block is composed of a multi-head attention module connected to an FFN module.

[0026] Further, the Softmax module in step 3 performs the following operations: First, separate the channel data representing the x - coordinate and the channel data representing the y - coordinate from the data output by the deserialization module; then perform a one - dimensional convolution operation on the channel data of the x - coordinate; then divide the data after the one - dimensional convolution operation into two parts with an equal number of data points along the x - coordinate dimension, and perform a Softmax operation on each part to obtain the x - coordinate spacing between adjacent data points; according to the x - coordinate spacing between adjacent data points, calculate the x - coordinate of the reconstructed data points, and combine it with the channel data representing the y - coordinate in the data output by the deserialization module to obtain the reconstructed airfoil point cloud data.

[0027] Further, the loss function when training the airfoil auto - encoder in step 4 is specifically:

[0028]

[0029] where z is the input airfoil point cloud data, is the reconstructed airfoil point cloud data, represents the mean square error between the input airfoil point cloud data and the reconstructed airfoil point cloud data; λ is a set weight, is a feature quantity characterizing the smoothness of the reconstructed airfoil point cloud data.

[0030] Advantageous Effects

[0031] The present invention proposes an airfoil parameterization method based on an auto - encoder model, constructs an airfoil auto - encoder model that does not rely on any artificial prior knowledge, is completely based on the Transformer architecture, and simultaneously generates the x - coordinate and y - coordinate of the airfoil. It fully explores a set of latent representations that can express the airfoil shape through deep learning itself, and at the same time reconstructs the airfoil point cloud data based on these latent representations, thereby improving the applicable range and parameterization accuracy of the airfoil parameterization model.

[0032] The additional aspects and advantages of the present invention will be partly given in the following description, partly will become obvious from the following description, or will be understood through the practice of the present invention. Description of the Drawings

[0033] The above - mentioned and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, where:

[0034] Figure 1 is the flowchart of the airfoil parameterization method according to the embodiment of the present invention;

[0035] Figure 2 is the detailed construction diagram of the airfoil auto - encoder dataset according to the embodiment of the present invention;

[0036] Figure 3It is the architecture diagram of the airfoil autoencoder according to the embodiment of the present invention;

[0037] Figure 4 It is the loss curve diagram of the airfoil autoencoder according to the embodiment of the present invention;

[0038] Figure 5 It is the performance diagram of the model under different compression ratios according to the embodiment of the present invention. (a) The overall average value of MAE. (b) The distribution of MAE. Detailed implementation manners

[0039] The embodiments of the present invention will be described in detail below. The embodiments are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0040] In this embodiment, an airfoil parameterization method based on an autoencoder model is used to parameterize the airfoil point cloud data of a certain airfoil database, as Figure 1 shown, and it includes the following steps:

[0041] Step 1: Adjust the data structure of the existing initial airfoil point cloud dataset to make the data structures of the initial airfoil point cloud data consistent, and perturb the initial airfoil point cloud data to obtain new airfoil point cloud data, which together with the initial airfoil point cloud data form a multi-source airfoil point cloud dataset; the multi-source airfoil point cloud dataset obtained in this way theoretically belongs to a mixed space composed of different feature spaces.

[0042] Here, the data structures being consistent means that the total number of coordinate points used to represent the airfoil in the airfoil point cloud data is the same.

[0043] The specific method for adjusting the data structure of the initial airfoil point cloud data is as follows: Set the number of coordinate points representing the airfoil after shaping to N. For the initial airfoil point cloud dataset, if the number of coordinate points of a certain airfoil point cloud data is less than N, then expand the number of coordinate points of this airfoil point cloud data to N through interpolation; if the number of coordinate points of a certain airfoil point cloud data is greater than N, then reduce the number of coordinate points of this airfoil point cloud data to N through sampling. In this embodiment, the number of coordinate points representing the airfoil after shaping is set to 256, and each coordinate point has two coordinate values x and y, so each airfoil point cloud data has 512 coordinate values.

[0044] The method for perturbing the initial airfoil point cloud data is as follows: For a certain initial airfoil point cloud data, parameterize it using a traditional parameterization method, and then perturb the airfoil design parameters after parameterization within a set perturbation range. As Figure 2As shown, in this embodiment, for a certain initial airfoil point cloud data, the CST parameterization method and the B-Spline parameterization method are respectively used for parameterization, and then the airfoil design parameters corresponding to each parameterization method are perturbed 100 times to obtain the perturbed airfoil point cloud data. To ensure that the perturbed airfoil meets the requirements, the set perturbation range is 0.005Δw0.005, where Δw is the perturbation amount; since there are 906 airfoils in the initial airfoil point cloud dataset, the initial airfoil point cloud dataset plus the airfoils obtained after perturbation, the finally obtained multi-source airfoil point cloud dataset includes 182,106 airfoils, and each airfoil in the multi-source airfoil dataset is represented by airfoil point cloud data (i.e., x, y coordinates).

[0045] Step 2: Construct an encoder that can perform dimensionality reduction processing on the airfoil point cloud data to obtain the latent representation of the airfoil point cloud data;

[0046] The encoder includes a serialization processing module, a stacked ViT (Visual Transformer) module, and a convolutional module;

[0047] The serialization processing module performs serialization processing on the input airfoil point cloud data to obtain serialized data; using the serialized data as the input of the stacked ViT module, the airfoil point cloud data features are extracted through the stacked ViT module, and the airfoil point cloud data features are input into the convolutional module for dimensionality reduction to obtain the latent representation of the airfoil point cloud data.

[0048] The serialization processing regards the airfoil point cloud data as image data. When performing serialization processing on the image data, for a multi-channel image, its storage structure in the computer is a three-dimensional array, and the three dimensions are: channel (size denoted as C), length (size denoted as H), and width (size denoted as W). The serialization processing method for the image data is to equally divide the image at the length and width dimensions. Assuming the distances at the length and width dimensions are P respectively, the original image can be divided into a total of L=(H / P)·(W / P)=HW / P 2 sub-images, and each sub-image has a dimension Subsequently, all the pixels in each sub-image are respectively expanded into a one-dimensional array, and its size is E = C·P 2 , in this way, the image has completed the following mapping:

[0049]

[0050] The finally obtained serialized data is X = [x ＜1＞T ,x ＜2＞T ,...,x ＜L＞T , its sequence length is L, and each element x ＜i＞All are one-dimensional arrays formed by unfolding sub-images.

[0051] In the present invention, the airfoil point cloud data is regarded as a single-channel three-dimensional array, and the three dimensions are: channel, length, and width; where the size C of the channel dimension is 1, the size H of the length dimension is 256, which is the number of reshaped coordinate points in step 1, and the size W of the width dimension is 2, indicating that each coordinate point has two coordinate values, x and y. The specific dimension is 1×256×2. Since the size of the width dimension is very small at this time, in this embodiment, only equidistant segmentation is performed in the length dimension, which is equivalent to dividing every P coordinate points. Therefore, the sequence length corresponding to the airfoil data is L = 256 / P, and the embedding dimension is E = 1·2P = 2P. Since this is single-channel data and the size of the width dimension is only 2, the value of the embedding dimension E is actually small. In order to use the multi-head attention mechanism in practice, in this embodiment, the embedding dimension is mapped to a higher hidden dimension D after serialization. Therefore, the airfoil point cloud data has completed the following mapping:

[0052]

[0053] The stacked ViT modules are composed of several ViT Blocks connected in sequence, and each ViT Block is composed of a multi-head attention module connected to an FFN module.

[0054] The multi-head attention module is specifically: for the input sequence X = [x ＜1＞T , x ＜2＞T ,..., x ＜L＞T , its sequence length is L, and each element x ＜i＞ is a one-dimensional array, that is, Let E be the embedding dimension of this input sequence. Therefore, an input sequence is actually a matrix of dimension L×E.

[0055] Each attention head in the multi-head attention module is a self-attention mechanism. For a specific input element x ＜i＞ , first, it needs to be converted into a query vector q ＜i＞ , a key vector k ＜i＞ and a value vector v ＜i＞ :

[0056] q ＜i＞ = x ＜i＞ W Q

[0057] k ＜i＞ = x ＜i＞ W K

[0058] v ＜i＞ = x＜i＞ W V

[0059] wherein respectively represent the mapping matrices in the self-attention mechanism. Implementing the above process for each input element, the input sequence X can be transformed into

[0060]

[0061] Subsequently, the output of each attention head is calculated as follows:

[0062]

[0063] In the formula, the calculated result is called the attention score, wherein is the scaling factor, and QK T is actually to perform the inner product operation between each query vector in matrix Q and the key vector in matrix K. Therefore, the attention score is a measure of the similarity between the query vector and the key vector.

[0064] The softmax function is a normalized exponential function that can map the values in any n-dimensional vector to the range [0, 1]. For the vector α = [α 1 , α 2 ,..., α n , define α′ = softmax(α), then the softmax function is calculated as follows:

[0065]

[0066] It can be seen that the vector after the softmax function operation satisfies

[0067]

[0068] When performing the softmax operation on the attention score matrix, it is calculated separately for each row, and the obtained result is called the attention weight. Finally, the output of self-attention is obtained through matrix multiplication

[0069] In scaled dot-product attention, matrices Q, K, and V have the same dimension T×d model , and in multi-head attention, we map them to dimensions d k , d k , d v , respectively, and repeat this operation h times. Then, the h groups of Q, K, and V matrices obtained are subjected to the scaled dot-product attention operation in parallel. Each group of attention is called a "head" or attention head, and the output of each attention head is of dimension T×dv matrix, and then concatenating the results of all attention heads obtained can yield a matrix of dimension T×hd v matrix, and finally remapping the output back to the initial dimension d through a dimensionality transformation model . The multi-head attention is expressed as follows:

[0070] MultiHead(Q, K, V) = Concat(head 1 , head 2 ,..., head h )W O

[0071] where head i = Attention(QW i Q , KW i K , VW i V )

[0072] It can be seen that the multi-head attention actually maps the original Q, K, V matrices to different subspaces through the mapping matrix, and by combining the representations learned by the attention heads in different subspaces, the multi-head attention learns to comprehensively understand the input information from different perspectives, which endows the attention mechanism with more powerful capabilities.

[0073] The FFN module is specifically composed of two fully connected layers and a non-linear activation layer. The first fully connected layer is used to map the output of the multi-head attention to dimension d ff , and the second fully connected layer is used to map the output of the non-linear activation layer back to the input dimension d model . In practice, generally take d ff = 4×d model . This embodiment selects the GELU function as the non-linear activation layer, and the GELU function is defined as follows:

[0074] GELU(x) = x·Φ(x)

[0075] where Φ(x) is the cumulative distribution function of the Gaussian distribution.

[0076] Step 3: Construct a decoder that can reconstruct the airfoil point cloud data from the latent representation;

[0077] The decoder includes a transposed convolution module, a stacked ViT module, an Unpatchify module, and a Softmax module;

[0078] The transposed convolution module upsamples the input latent representation, then extracts serialized feature data through stacked ViT modules, and uses an Unpatchify module to map the serialized feature data back to the original airfoil point cloud data structure; finally, the Softmax module reconstructs the mapped data into airfoil point cloud data.

[0079] The Softmax module performs the following operations: First, it separates the channel data representing the x - coordinate from the channel data representing the y - coordinate in the data output by the Unpatchify module; then it performs a one - dimensional convolution operation on the channel data of the x - coordinate; then it divides the data after the one - dimensional convolution operation along the x - coordinate dimension into two parts with an equal number of data points, and performs a Softmax operation on each part to obtain the x - coordinate spacing between adjacent data points; since the x - coordinate values of the data points range from 0 to 1, according to the x - coordinate spacing between adjacent data points, the x - coordinates of the reconstructed data points are calculated and combined with the channel data representing the y - coordinate in the data output by the Unpatchify module to obtain the reconstructed airfoil point cloud data.

[0080] Step 4: Establish an airfoil auto - encoder based on the encoder obtained in Step 2 and the decoder obtained in Step 3; the input of the airfoil auto - encoder is airfoil point cloud data, and the output of the auto - encoder is the reconstructed airfoil point cloud data; use a multi - source airfoil point cloud dataset to train the airfoil auto - encoder to obtain a trained airfoil auto - encoder.

[0081] The loss function during the training of the airfoil auto - encoder is specifically:

[0082]

[0083] where \(z\) is the input airfoil point cloud data, \(\hat{z}\) is the reconstructed airfoil point cloud data, and the first term of the loss function represents the mean square error between the input airfoil point cloud data and the reconstructed airfoil point cloud data; \(\lambda\) is a set weight; the second term of the loss function represents the smoothness of the reconstructed airfoil data, \(S\) is a characteristic quantity representing the smoothness of the reconstructed airfoil point cloud data. In this embodiment, the characteristic quantity is taken as the average value of the absolute value of the third - order discrete difference along the y - coordinate dimension \(\sum_{i = 1}^{n - 2}\left|\frac{\partial^{3}z_{i}}{\partial y^{3}}\right|\).

[0084]

[0085] During optimization, the AdamW optimizer is used, and the learning rate is fixed at \(1e - 5\) during the training of all models. The airfoil auto - encoder was trained for approximately 1.2 million steps with a global batch size of 1024.

[0086] Step 5: Parametrize the given airfoil point cloud data using the airfoil autoencoder obtained in Step 4 to obtain the latent representation of the airfoil point cloud data.

[0087] Case verification:

[0088] In this embodiment, we conducted a preliminary study on the impact of the latent space dimension on the performance of the airfoil autoencoder. We referred to the classical models of existing deep learning and selected f = L / l = 8 as our baseline model. We constructed three identical autoencoder models, only changing the dimension of the latent representation. For these models, we fixed c = 2 and set l to 32, 24, and 16 respectively. The loss descent curves are as Figure 4 shown. The mean absolute errors of these models on the test set are as Figure 5 shown.

[0089] As can be seen from the figure, the reconstruction loss of the model gradually decreases as l increases. The tolerance of the airfoil wind tunnel model provided in the literature is:

[0090]

[0091] When l is 24 and 16, the MAE of some samples exceeds the tolerance level. Therefore, under our model configuration, l = 32 is more reliable.

[0092] In this embodiment, we compared our results with the published results of other state-of-the-art related works, as shown in Table 1. It should be noted that other related works only implemented models for predicting the coordinate value y, so the evaluation metrics in the table are calculated based on the y coordinate values. The rMSE in the table represents the relative mean square error, through:

[0093]

[0094] Calculation, where the subscript +1 means that the values in x and x are both incremented by 1. Related Model 1 comes from the paper "Physically interpretable airfoil parameterization using variational autoencoder-based generative modeling. AIAA SCITECH 2024 Forum, 2024", which uses B-spline parameterization to generate smooth airfoil curves. Our model achieves a reconstruction loss that is only one order of magnitude different from their results without relying on any manually designed functions. Related Model 2 comes from the paper "Towards universal parameterization: Using variational autoencoders to parameterize airfoils. AIAA SCITECH 2024 Forum, 2024", which constructs a relatively simple model using fully connected layers, and our results are significantly better than theirs.

[0095] Table 1 Performance comparison of the airfoil parameterization method in this embodiment

[0096]

[0097] In summary, a method for airfoil parameterization of the present invention has high design accuracy when the airfoil autoencoder generates the x and y coordinates of the airfoil simultaneously.

[0098] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and purposes of the present invention.

Claims

1. A method for airfoil parameterization based on an autoencoder model, characterized in that: The following steps are involved: Step 1: Adjust the data structure of the existing initial airfoil point cloud data set to keep the data structure of the initial airfoil point cloud data consistent, and perturb the initial airfoil point cloud data to obtain new airfoil point cloud data, which together with the initial airfoil point cloud data form a multi-source airfoil point cloud data set; Step 2: construct an encoder, which can perform dimensionality reduction processing on the airfoil point cloud data to obtain a potential representation of the airfoil point cloud data; The encoder includes a serialization processing module, a stacked ViT module and a convolution module; The serialization processing module performs serialization processing on the input airfoil point cloud data to obtain serialized data; the serialized data is used as the input of the stacked ViT module, the airfoil point cloud data features are extracted through the stacked ViT module, the airfoil point cloud data features are input into the convolution module for dimensionality reduction, and the potential representation of the airfoil point cloud data is obtained; Step 3: construct a decoder, which can reconstruct the potential representation to obtain airfoil point cloud data; The decoder includes a transposed convolution module, a stacked ViT module, a deserialization module and a Softmax module; The transposed convolution module upsamples the input potential representation, then extracts the serialized feature data through the stacked ViT module, and uses the deserialization module to map the serialized feature data back to the original airfoil point cloud data structure; finally, the mapped data is reconstructed into airfoil point cloud data through the Softmax module; Step 4: Establish an airfoil autoencoder according to the encoder obtained in step 2 and the decoder obtained in step 3; the input of the airfoil autoencoder is the airfoil point cloud data, and the output of the autoencoder is the reconstructed airfoil point cloud data; train the airfoil autoencoder using a multi-source airfoil point cloud data set to obtain a trained airfoil autoencoder; Step 5: Parameterize the given airfoil point cloud data according to the airfoil autoencoder obtained in step 4 to obtain the potential representation of the airfoil point cloud data.

2. According to claim 1, a method for airfoil parameterization based on an autoencoder model is characterized in that: Based on the given potential representation, the airfoil autoencoder obtained in step 4 is used to generate the corresponding airfoil point cloud data.

3. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: In step 1, the data structure remains consistent, which means that the total number of coordinate points used to characterize the airfoil in the airfoil point cloud data is the same.

4. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: The specific method for adjusting the data structure in step 1 is: setting the number of coordinate points representing the airfoil after shaping to N, for the initial airfoil point cloud data set, if the number of coordinate points of a certain airfoil point cloud data is less than N, then the number of coordinate points of the airfoil point cloud data is expanded to N by interpolation; if the number of coordinate points of a certain airfoil point cloud data is greater than N, then the number of coordinate points of the airfoil point cloud data is reduced to N by sampling.

5. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: The method for perturbing the initial airfoil point cloud data in step 1 is: for a certain initial airfoil point cloud data, a traditional parameterization method is used for parameterization, and then the parameterized airfoil design parameters are perturbed within a set disturbance range.

6. The airfoil parameterization method based on the autoencoder model according to claim 5, characterized in that: The traditional parameterization methods include CST parameterization method and B-Spline parameterization method.

7. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: In step 2, the serialization processing module serializes the input airfoil point cloud data to obtain a data structure of the serialized data, which is a three-dimensional array. The three dimensions are: channel, length and width; the size of the channel dimension C = 1, the size of the length dimension H is the number of coordinate points after shaping in step 1, and the size of the width dimension W = 2, indicating that each coordinate point has two coordinate values ​​of x and y.

8. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: The stacked ViT module is composed of several ViT Blocks connected in sequence, and each ViT Block is composed of a multi-head attention module connected to a FFN module.

9. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: The Softmax module in step 3 performs the following operations: first, the channel data representing the x-coordinate and the channel data representing the y-coordinate in the data output by the deserialization module are separated; then a one-dimensional convolution operation is performed on the channel data of the x-coordinate; the data after the one-dimensional convolution operation is then divided into two parts with equal numbers of data points along the x-coordinate dimension, and a Softmax operation is performed on each part to obtain the x-coordinate spacing between adjacent data points; based on the x-coordinate spacing between adjacent data points, the x-coordinate of the reconstructed data point is calculated and combined with the channel data representing the y-coordinate in the data output by the deserialization module to obtain the reconstructed airfoil point cloud data.

10. The airfoil parameterization method based on the autoencoder model according to claim 1, characterized in that: The loss function for training the airfoil autoencoder in step 4 is: Among them, z is the input airfoil point cloud data, is the reconstructed airfoil point cloud data, represents the mean square error between the input airfoil point cloud data and the reconstructed airfoil point cloud data; λ is the set weight, It is a characteristic quantity that characterizes the smoothness of the reconstructed airfoil point cloud data.

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