Pneumatic airfoil generation method based on de-noising diffusion probability model and variational auto-encoder

Abstract

The invention discloses an aerodynamic airfoil profile generation method based on a de-noising diffusion probability model and a variational auto-encoder in the technical field of deep learning and aerodynamic design, which comprises the following steps of: 1, acquiring airfoil profile set data from a public database, re-dividing airfoil profile coordinate points, and calculating a lift coefficient and a resistance coefficient of the airfoil profile set data; 2, preprocessing the airfoil profile data; 3, constructing a joint model based on a variational auto-encoder and a de-noising diffusion probability model, and generating airfoil profile potential representation meeting design conditions by learning potential space representation and combining the de-noising diffusion probability model; 4, inputting the re-divided airfoil profile coordinate point data set into the potential spatial diffusion model for training; and step 5, based on the trained potential spatial diffusion model, inputting different design conditions, and generating an airfoil profile sample conforming to specified geometric characteristics, and according to the method, a high-quality airfoil profile can be generated under different aerodynamic constraint conditions, so that the feasibility and reliability of aerodynamic configuration optimization are improved.

Description

Technical Field

[0001] The present invention relates to the technical fields of deep learning and aerodynamic design, and particularly relates to a method for generating an aerodynamic airfoil. Background Art

[0002] With the rapid development of aerospace technology, efficient and intelligent aerodynamic design has become one of the key factors for improving the performance of aircraft and reducing energy consumption. Traditional aerodynamic airfoil design mainly relies on wind tunnel tests, flight tests, and numerical simulations. Although these methods can obtain highly accurate results, the design process is often cumbersome and limited by computing resources and time costs. In complex aerodynamic optimization processes, designers usually need to iterate a large number of experiments repeatedly to obtain the optimal design scheme, which is not only time-consuming but also costly, seriously restricting the design efficiency.

[0003] In recent years, the rapid development of deep learning technology has brought new opportunities to aerodynamic design. Data-driven methods can automatically learn the complex mapping relationship between aerodynamic characteristics and airfoil design, thus providing an intelligent solution for airfoil generation and optimization. In particular, generative models, with their powerful data expression ability, can efficiently sample novel airfoil shapes in the latent space and meet specific aerodynamic constraint requirements.

[0004] As an unsupervised learning method, the variational autoencoder (VAE) realizes the efficient generation of airfoils by mapping input data to the latent space and learning the probability distribution of the data in this space. However, due to the limitation of the reconstruction error, traditional VAE often lacks in generation quality and distribution expression ability. In contrast, the denoising diffusion probabilistic model (DDPM) has made breakthrough progress in fields such as image and speech generation in recent years. It generates high-quality samples by gradually adding noise and recovering the data in the reverse process, while maintaining better mode diversity. Although DDPM has powerful generation ability, its sampling process usually requires a large number of time steps (1000+ steps), resulting in a large computational overhead.

[0005] To further improve the efficiency and quality of airfoil generation, introducing an implicit generation strategy is a feasible solution. For example, denoising implicit sampling (DDIM), as an improved version of DDPM, allows jumping multiple time steps during the sampling process through a non-Markov chain. It can achieve a generation quality similar to DDPM with only 50 - 100 steps, while significantly reducing the computational overhead. Therefore, by combining VAE, the denoising diffusion probabilistic model (DDPM), and the implicit sampling method (DDIM), the expression ability of the latent space can be fully utilized to achieve efficient and accurate airfoil generation and meet the requirements of automated design and aerodynamic optimization.

[0006] Compared to traditional explicit optimization methods, this method not only explores a wider design space in a shorter time, but also enables precise adjustment of the airfoil through latent space control. This provides an efficient, intelligent, and controllable new generative framework for aerodynamic airfoil design, facilitating the optimized design of future aircraft. Summary of the Invention

[0007] In response to the shortcomings of the existing technology, the present invention provides an aerodynamic airfoil generation method based on a denoising diffusion probability model and a variational autoencoder, which can significantly improve the sampling efficiency of aerodynamic optimization and reduce computational costs while ensuring the diversity and effectiveness of the generated samples. It can not only efficiently explore high-dimensional design spaces, but also generate high-quality airfoils under different aerodynamic constraints, thereby improving the feasibility and reliability of aerodynamic shape optimization.

[0008] The object of the present invention is achieved as follows: a method for generating an aerodynamic airfoil based on a denoising diffusion probability model and a variational autoencoder, comprising the following steps:

[0009] Step 1: Obtain airfoil data from a public database, re-divide the airfoil coordinate points, and calculate its lift coefficient and drag coefficient;

[0010] Step 2: Preprocess the airfoil data, including data normalization, aerodynamic data processing, and data structure organization;

[0011] Step 3: Build a joint model based on the denoising diffusion probability model and the variational autoencoder to generate a latent representation of the airfoil that meets the design conditions by learning the latent space representation and combining it with the diffusion model;

[0012] Step 4: Input the re-divided airfoil coordinate point dataset into the latent space diffusion model for training, use performance indicators to evaluate the generation effect of the model, and retain the model with the best generation results;

[0013] Step 5: Based on the trained latent space diffusion model, different design conditions are input to generate airfoil samples that meet the specified geometric characteristics.

[0014] Furthermore, the specific steps for data acquisition in step 1 are:

[0015] Step 1-1: Determine the acquisition channel and source of airfoil data from the UIUC airfoil library;

[0016] Step 1-2: Screen and filter the acquired airfoil data according to research needs and quality requirements, and eliminate low-quality or duplicate data.

[0017] Furthermore, the specific steps of data preprocessing in step 2 are:

[0018] Step 2-1: Read airfoil data. Each airfoil data is stored in a file with the extension.dat, and the file contains the coordinate points of the airfoil. Read the airfoils by traversing the files in the specified directory.

[0019] Step 2-2: Data normalization. Perform normalization processing on all the read airfoils. Calculate the normalization coefficient norm_coeff by finding the maximum value of the y-coordinates in all rows. The formula is as follows:

[0020] (1);

[0021] Then divide the y-coordinate of each airfoil by its normalization coefficient norm_coeff so that all y-coordinates are scaled to the range [-1, 1]. The formula is as follows:

[0022] (2);

[0023] where y is the original y-coordinate, norm_coeff is the normalization coefficient, is the normalized y-coordinate;

[0024] Step 2-3: Process aerodynamic data. Use the aerosandbox library to perform aerodynamic analysis on the airfoil and re-divide the airfoil coordinate points. Load the airfoil data. Through the get_aero_from_neuralfoil method, calculate the aerodynamic coefficients cl and cd of the airfoil based on the given angle of attack, Reynolds number, and Mach number, combined with the geometric information of the airfoil, and save them. Re-divide the airfoil coordinate points, divide them into the set number of coordinate points for the upper and lower airfoil surfaces, and generate more refined airfoil geometric data.

[0025] Furthermore, the specific steps of Step 3 model construction are as follows:

[0026] Step 3-1: Design the latent space model, which includes an encoder and a decoder. The encoder maps the input airfoil data to the latent space. Use a simple multi-layer perceptron model that accepts the features of an airfoil data and outputs the mean and log variance of the latent space. The decoder converts the representation in the latent space back to the original data, which is another multi-layer perceptron that generates the corresponding airfoil data features from the vector in the latent space.

[0027] Step 3-2: Design the denoising diffusion probabilistic model; the denoising diffusion probabilistic model includes a forward diffusion process and a reverse diffusion process; in the forward diffusion process, gradually transform the original data into noise through time steps. The formula is as follows:

[0028] (3);

[0029] where is the original data, is the noisy data at the t-th step, is Gaussian noise with the same dimension as the data, is the cumulative noise ratio. In the reverse diffusion process, the initial noise is denoised forward to gradually restore the original clean data, and its formula is as follows:

[0030] (4);

[0031] where represents the denoising prediction of the noise by the model at the current time step t, that is, the model predicts the noise in the current data sample in, is the noise intensity at each time step;

[0032] Step 3-3: Design conditional control and sampling control; introduce control conditions cl and cd as input information and pass them to the model. In the forward diffusion process, combine the conditional information cl and cd with the time step and provide it to the neural network; in the sampling process, in each reverse diffusion step, the conditional information cl and cd will be passed to the denoising model together with the current noisy data and the time step; in the sampling process, introduce implicit denoising, and its formula is as follows:

[0033] (5);

[0034] where and are factors adjusted by the time step to control the attenuation of the signal and the increase of the noise, and C is the designed condition c = [CL, CD].

[0035] Furthermore, the specific steps of model training in Step 4 are as follows:

[0036] Step 4-1: First, train the variational autoencoder model with the airfoil data with re-divided coordinate points, use the trained variational autoencoder model to reconstruct the original airfoil data, and judge the model training effect by comparison;

[0037] Step 4-2: Use the conditional control information, the airfoil data with re-divided coordinate points, the cl and cd data obtained through preprocessing, and the trained variational autoencoder model to train the latent space diffusion model.

[0038] Furthermore, the specific steps of sampling generation in Step 5 are as follows:

[0039] Step 5-1: Based on the trained latent space diffusion model, input the conditional control information to generate an airfoil that meets the requirements;

[0040] Step 5-2: Select excellent airfoils by comparing the cl and cd data of the generated data and their visualization.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] 1. Traditional sampling methods, such as Latin hypercube sampling, have limitations when sampling in high-dimensional design spaces; they usually rely on low-dimensional manual parameterization, which limits the flexibility of the design space. In addition, traditional methods are difficult to ensure the generation of realistic samples, resulting in low sampling efficiency; the method based on the latent space diffusion model proposed by the present invention is a new sampling method that relies on the denoising diffusion probability model and is carried out in the auto-learning shallow space of airfoils; it utilizes the expressive ability of the latent space, and this method can efficiently generate airfoils that meet the expected performance in a large-scale airfoil design space, improving the accuracy and efficiency of airfoil design and providing more reliable support for airfoil optimization.

[0043] 2. During the process of generating airfoils, the present invention uses a conditional diffusion model for sampling, so that the generated airfoils can meet specific control conditions (such as lift coefficient Cl and drag coefficient Cd); compared with traditional experience-based design methods, the present invention can generate airfoils with specific aerodynamic performance by guiding the latent space; traditional methods often rely on manual adjustment of parameters or rules, while the present invention directly controls the airfoil performance in the latent space through the conditional diffusion model, making the generated airfoils more accurate in performance and capable of meeting multiple design goals.

[0044] 3. The present invention uses a unified latent space diffusion model structure for airfoil generation. The model can generate airfoils that meet the performance requirements by taking aerodynamic performance (such as Cl and Cd) as conditional inputs; this structure generates airfoils by sharing the latent space and the decoding network, which can not only ensure the consistency of the generated airfoils in shape and performance, but also efficiently generate multiple qualified design samples; compared with traditional airfoil generation methods based on a single optimization goal, the present invention can consider multiple performance indicators simultaneously to ensure that the generated airfoils are optimal in multiple aerodynamic performances.

[0045] 4. The DDIM method is adopted during the sampling process, which is an efficient sampling method for diffusion models. Compared with traditional diffusion sampling methods, DDIM does not rely on the independent steps of Markov chains and predicts noise implicitly, allowing for generation with fewer time steps. It can significantly shorten the sampling time while ensuring the generation quality. By using DDIM, the present invention can generate high-quality airfoils in a short time while retaining the diversity of the latent space. This efficient sampling strategy not only improves the generation speed but also ensures the diversity and rationality of the generated samples, making the generated airfoils not only meet the predetermined aerodynamic performance but also satisfy various design constraints. Description of the Drawings

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to the provided drawings.

[0047] Figure 1 It is a flowchart of the airfoil data preprocessing of the present invention.

[0048] Figure 2 It is a comparison diagram of the original airfoil diagram and the airfoil reconstructed by the VAE model of the present invention.

[0049] Figure 3 It is an airfoil diagram generated by the VAE of the present invention.

[0050] Figure 4 It is a diagram of the model training loss of the present invention.

[0051] Figure 5 It is an airfoil diagram generated based on the trained latent diffusion model of the present invention.

[0052] Figure 6 It is an airfoil diagram generated based on the trained conditional control latent diffusion model of the present invention. Detailed Embodiments

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0054] An aerodynamic airfoil generation method based on a denoising diffusion probability model and a variational autoencoder includes the following steps:

[0055] Step 1: Data preparation: Collect airfoil data from the public database UIUC Airfoil Data Site (https: / / m-selig.ae.illinois.edu / ads / coord_database.html), screen and filter the obtained airfoil data, and remove low-quality or duplicate airfoil data.

[0056] Step 2: Read the airfoil data and preprocess it. The specific preprocessing process is as follows: Figure 1 shown.

[0057] Step 2-1: Read the coordinate information of the airfoil from the specified airfoil folder.

[0058] Step 2-2: Normalize the airfoil data. Adjust the y-coordinate of the airfoil to a uniform scale and scale it to a specific range, i.e. [-1, 1]. The formula is as follows:

[0059] (6);

[0060] Where y is the original y coordinate, norm_coeff is the normalization coefficient, is the normalized y coordinate, the normalization coefficient .

[0061] Step 2-3: Re-divide the airfoil coordinate points; To focus on studying the aerodynamic characteristics of the airfoil and improve calculation accuracy, use the repanel method of the Airfoil class in the aerosandbox library to re-divide the coordinate points of the airfoil, refine the geometric grid of each airfoil to 100 points per side, and then normalize the airfoil data of the re-divide airfoil coordinate points.

[0062] Step 2-4: Calculate the aerodynamic coefficients; by calling the get_aero_from_neuralfoil method, use the NeuralFoil model to calculate its aerodynamic conditions (including the lift coefficient Cl and the drag coefficient Cd) under the conditions of a specified angle of attack of 5 degrees, a Reynolds number of 1e6, and a Mach number of 0.2.

[0063] Step 3: Build a joint model based on the denoising diffusion probability model and the variational autoencoder to generate the airfoil latent representation that meets the design conditions by learning the latent space representation and combining it with the denoising diffusion probability model.

[0064] Step 3-1: Design a latent space model, which includes an encoder and a decoder. The encoder maps the input airfoil data to the latent space and uses a simple multi-layer perceptron model to accept the features of an airfoil data and output the latent variables. , mean and variance , the decoder transforms the representation in the latent space into the original data, using another multi-layer perceptron that generates the corresponding airfoil data from the vector in the latent space .

[0065] Step 3-2: Design a denoising diffusion probabilistic model. The denoising diffusion probabilistic model includes a forward diffusion process and a reverse diffusion process. In the forward diffusion process, the original data is gradually transformed into noise through a series of time steps t, and its formula is as follows:

[0066] (7);

[0067] where is the noisy data at the t-th step, is the standard Gaussian noise with the same dimension as the data, is the cumulative noise ratio. This process is a Gaussian Markov Process, which is used to gradually add noise to the data. In the forward diffusion process, the noise intensity at each time step t is defined by a cosine schedule, and the cosine schedule formula is as follows:

[0068] (8);

[0069] where is the noise intensity at each time step, which ranges between 0 and 1. In the reverse diffusion process, the initial noise is denoised forward to gradually restore the original clean data, and its formula is as follows:

[0070] (9);

[0071] where represents the denoising prediction of the model at the current time step t for the noise, that is, the model predicts the noise in the current data sample . However, since the sampling process of DDPM usually requires more than 1000 time steps and the computational cost is relatively high, the present invention further introduces denoising implicit sampling (DDIM) to improve the sampling efficiency.

[0072] Step 3-3: Design condition control and sampling control. In the denoising diffusion probability model, additional conditional information can be used to guide the generation process. The control conditions cl and cd are introduced as input information and passed to the model. During the forward diffusion process, the conditional information cl and cd are combined with the time step and provided to the neural network. During the sampling process, similarly, to ensure that the generated airfoil meets the design conditions in the latent space, in each reverse diffusion step, the conditional information cl and cd will be passed to the denoising model together with the current noise data and the time step. During the sampling process, implicit denoising is introduced to improve the sampling efficiency and reduce the number of steps required to generate samples. The formula is as follows:

[0073] (10);

[0074] where and are factors adjusted by the time step, controlling the attenuation of the signal and the increase of noise, and C is the design condition = [cl, cd].

[0075] Step 4: Input the re-divided airfoil coordinate point dataset into the latent space diffusion model for training, evaluate the generation effect of the model using performance metrics, and retain the model with the best generation result; specifically:

[0076] Step 4-1: Use the preprocessed airfoil data, that is, the airfoil data with re-divided airfoil coordinate points, to train the VAE (Variational Autoencoder) model, and observe the training effect through the comparison between the reconstructed airfoil and the original airfoil by the VAE model and the training loss graph.

[0077] Step 4-2: Use the conditional control information cl and cd, the airfoil data with re-divided airfoil coordinate points, the cl and cd data obtained through data preprocessing, and the trained VAE model to train the latent space diffusion model, and adjust parameters such as the number of steps and learning rate of the denoising diffusion probability model according to the training loss graph of the latent space diffusion model.

[0078] Step 5: Based on the trained latent space diffusion model, input different design conditions to generate airfoil samples that meet the specified geometric characteristics; specifically:

[0079] Step 5-1: Generate airfoils that meet the requirements based on the trained shallow latent space diffusion model or conditional control latent space diffusion model.

[0080] Step 5-2: Select excellent airfoils by comparing the cl and cd data of the generated data and its visualization.

[0081] The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for generating an airfoil based on a denoising diffusion probability model and a variational autoencoder, characterized in that The following steps are involved: Step 1: Obtain airfoil data from a public database, re-divide the airfoil coordinate points, and calculate its lift coefficient and drag coefficient; Step 2: Preprocess the airfoil data, including data normalization, aerodynamic data processing, and data structure organization; Step 3: Build a joint model based on the denoising diffusion probability model and the variational autoencoder to generate a latent representation of the airfoil that meets the design conditions by learning the latent space representation and combining it with the diffusion model; Step 4: Input the re-divided airfoil coordinate point dataset into the latent space diffusion model for training, use performance indicators to evaluate the generation effect of the model, and retain the model with the best generation results; Step 5: Based on the trained latent space diffusion model, different design conditions are input to generate airfoil samples that meet the specified geometric characteristics.

2. The aerodynamic airfoil generation method based on the denoising diffusion probability model and variational autoencoder according to claim 1, characterized in that, The specific steps for data acquisition in step 1 are: Step 1-1: Determine the acquisition channel and source of airfoil data from the UIUC airfoil library; Step 1-2: Screen and filter the acquired airfoil data according to research needs and quality requirements, and eliminate low-quality or duplicate data.

3. A method for generating an airfoil based on a denoising diffusion probabilistic model and a variational autoencoder according to claim 1 or 2, characterized in that, The specific steps of data preprocessing in step 2 are: Step 2-1: Read airfoil data. Each airfoil data is stored in a file with a .dat extension. The file contains the coordinate points of the airfoil. The airfoil is read by traversing the files in the specified directory. Step 2-2: Data normalization: normalize all airfoils read and obtain the normalization coefficient norm_coeff by calculating the maximum value of the y coordinates of all rows. The formula is as follows: (1)； Then divide the y coordinate of each airfoil by its normalization coefficient norm_coeff so that all y coordinates are scaled to the range of [-1,1], as follows: (2)； where y is the original y - coordinate and norm_coeff is the normalization coefficient, is the normalized y - coordinate; Step 2-3: Process aerodynamic data, use the aerosandbox library to perform aerodynamic analysis on the airfoil and re-divide the airfoil coordinate points, load the airfoil data, and use the get_aero_from_neuralfoil method to calculate the aerodynamic coefficients cl and cd of the airfoil based on the given angle of attack, Reynolds number and Mach number, combined with the geometric information of the airfoil, and save it. Redivide the airfoil coordinate points and divide them into a set number of coordinate points on the upper and lower wing surfaces to generate more detailed airfoil geometric data.

4. A method for generating an airfoil based on a denoising diffusion probabilistic model and a variational autoencoder according to claim 1 or 2, characterized in that The specific steps of step 3 model construction are: Step 3-1: Design a latent space model, which includes an encoder and a decoder. The encoder maps the input airfoil data to the latent space. A simple multi-layer perceptron model is used to accept the features of the airfoil data and output the mean and logarithmic variance of the latent space. The decoder converts the latent space representation into raw data. Another multi-layer perceptron generates the corresponding airfoil data features from the vectors in the latent space. Step 3-2: Design a denoising diffusion probability model; The denoising diffusion probability model includes a forward diffusion process and a reverse diffusion process. In the forward diffusion process, the original data is gradually converted into noise through time steps. The formula is as follows: (3)； where is the original data, is the noisy data at the t-th step, is Gaussian noise with the same dimension as the data, is the cumulative noise ratio. In the reverse diffusion process, the initial noise is denoised forward to gradually restore the original clean data, and its formula is as follows: (4)； wherein represents the denoising prediction of the noise by the model at the current moment t, that is, the model predicts the noise in the current data sample and is the noise intensity at each time step; Step 3-3: Design condition control and sampling control; introduce control conditions cl and cd as input information and pass them to the model. During the forward diffusion process, combine the condition information cl and cd with the time step and provide it to the neural network; during the sampling process, in each reverse diffusion step, the condition information cl and cd will be passed to the denoising model together with the current noise data and the time step; during the sampling process, introduce implicit denoising, and its formula is as follows: (5); where and are factors adjusted by time steps, controlling the attenuation of the signal and the increase of noise, and C is the design condition c = [CL, CD].

5. A method for generating an airfoil based on a denoising diffusion probability model and a variational autoencoder according to claim 1 or 2, characterized in that, The specific steps of model training in Step 4 are as follows: Step 4-1: First, train the variational autoencoder model with airfoil data with re-divided coordinate points, use the trained variational autoencoder model to reconstruct the original airfoil data, and judge the model training effect by comparison; Step 4-2: Use the conditional control information, airfoil data with re-divided coordinate points, cl and cd data obtained through preprocessing, and the trained variational autoencoder model to train the latent space diffusion model.

6. A method for generating an airfoil based on a denoising diffusion probabilistic model and a variational autoencoder according to claim 1 or 2, characterized in that, The specific steps of sampling generation in Step 5 are as follows: Step 5-1: Based on the trained latent space diffusion model, input the conditional control information to generate an airfoil that meets the requirements; Step 5-2: Select excellent airfoils by comparing the cl and cd data of the generated data and its visualization.

Images