Wing automatic generation and performance evaluation method based on structured point cloud and variational auto-encoder
By combining structured point cloud and variational autoencoder, an end-to-end automatic design system for automatic wing generation and performance evaluation was constructed, which solved the problems of design space uncertainty and low optimization efficiency in traditional methods and achieved efficient wing shape generation and optimization.
Patent Information
- Application Number
- CN202511624202.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-07
- Publication Date
- 2026-02-10
AI Technical Summary
Traditional wing aerodynamic design methods suffer from problems such as large design space uncertainty, high dimensionality, and low optimization efficiency, making it difficult to achieve efficient wing shape generation and optimization.
We employ a method based on structured point cloud and variational autoencoder to reconstruct the wing surface through generative modeling and combine it with aerodynamic optimization to build an end-to-end automatic design system. We utilize encoder-decoder structure and gradient optimization algorithm for efficient feature extraction and aerodynamic performance evaluation.
The entire process of wing shape design has been automated, which has improved design efficiency, geometric modeling accuracy and engineering applicability, and generated a smooth wing shape with a high lift-to-drag ratio.
Smart Images
Figure CN121502910A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of aircraft design, specifically a method for automatic wing generation and performance evaluation based on structured point clouds and variational autoencoders. Background Technology
[0002] Rapid wing generation and aerodynamic optimization are important research directions in aircraft design.
[0003] Aerodynamic design, as a crucial link in the aircraft development process, plays a vital role in translating target requirements into specific manufacturing solutions, directly impacting the achievement of core indicators such as range, aerodynamic performance, and payload. The wing, as the primary lifting surface of an aircraft, has its shape design as a core element of aerodynamic design, decisively influencing the overall performance of the aircraft.
[0004] In aerodynamic shape design optimization, traditional methods typically employ parametric modeling techniques, such as the PARSEC method, freeform surface deformation method, B-spline method, or Bézier curve method, to mathematically describe the geometry of airfoils and wings.
[0005] These methods characterize geometry using a limited set of design variables (such as control points and shape parameters), thereby significantly compressing the dimensionality of the shape representation. Compared to directly processing hundreds of discrete value points, this greatly improves the compactness of the modeling. This dimensionality reduction is particularly important for optimization efficiency, especially when using population optimization strategies such as evolutionary algorithms, as it can effectively reduce computational complexity.
[0006] However, geometric parameterization methods also face two main challenges:
[0007] First, the range of values for each parameter is often difficult to define precisely, and the setting of the design space relies heavily on engineering experience, which involves strong subjectivity and uncertainty.
[0008] Secondly, in order to fully capture the details of shape changes, the dimension of the design space constructed by the parametric system is often much higher than the basic dimension required by actual physics, which leads to problems such as too many design variables, too large search space, and complex objectives and constraints when characterizing the aerodynamic layout of aircraft.
[0009] In addition, the limitations of optimization algorithms in handling high-dimensional problems contribute to the dilemma of long aerodynamic optimization design cycles and low efficiency for aircraft.
[0010] To address these challenges, some research focuses on reducing the complexity of aerodynamic configuration characterization and exploring novel representation methods that can extract geometric features or dominant variables that have a key impact on aerodynamic performance.
[0011] In recent years, generative model-based 3D shape design has provided a new approach to this problem. Summary of the Invention
[0012] This invention proposes an automatic wing generation and performance evaluation method based on structured point cloud and variational autoencoder. It combines a generative model of point cloud representation with automatic wing shape design based on aerodynamic optimization, aiming to achieve more efficient wing aerodynamic shape design and optimization.
[0013] The specific steps of the automatic wing generation and performance evaluation method based on structured point cloud and variational autoencoder are as follows:
[0014] Step 1: For a certain baseline wing shape, construct an initial wing surface dataset and represent it with a structured point cloud to generate a structured point cloud dataset.
[0015] The specific steps are as follows:
[0016] First, Latin hypercube sampling is performed on the design parameters of the baseline wing shape;
[0017] Design parameters include: aspect ratio, tip-to-root ratio, sweep angle, dihedral angle, twist angle, and airfoil shape.
[0018] Then, using parametric modeling methods, corresponding wing surfaces are generated in batches based on design parameters, constructing a sample size of [number missing]. The initial wing surface dataset.
[0019] Next, each wing surface is uniformly cut along its span to form Each section is analyzed, and the contour curve of each section is extracted. These points form a unified, structured point cloud representation.
[0020] In the structured point cloud, individual sample data are organized into a A three-dimensional data structure, where 3 represents Three coordinate axis channels; index for any given span section All of the sections The spanwise coordinates of each point cloud were all assigned the same value. .
[0021] Finally, the point cloud data of all samples are integrated to construct a structured point cloud dataset for training the generative model. The shape of this dataset is... .
[0022] Step 2: Construct a generative model based on variational autoencoder and input a structured point cloud dataset to reconstruct a smooth wing surface.
[0023] The generative model adopts an encoder-decoder structure, in which:
[0024] First, shape is The structured point cloud data of the wing surface is input into the encoder, where... This indicates the training batch size. The encoder maps high-dimensional point cloud data to a low-dimensional latent space and outputs the mean of the probability distribution. and variance All shapes ,in The dimension of the latent space is given, and then a low-dimensional latent vector is obtained through reparameterized sampling. :
[0025]
[0026] It is random noise obtained by resampling from a standard normal distribution; This represents element-wise multiplication.
[0027] Then, the decoder consists of two parallel sub-decoders, responsible for processing the low-dimensional latent vector. Reconstruct the point cloud data into a structured form consistent with the original point cloud shape;
[0028] Specifically as follows:
[0029] The two parallel sub-decoders are a folded sub-decoder and a multilayer perceptron sub-decoder. Wherein:
[0030] Folded sub-decoder will latent variables As input, generate shape as It generates a 3D point cloud, but its output does not have an explicit cross-sectional structure, i.e., an unstructured point cloud.
[0031] The multilayer perceptron decoder also uses latent variables. As input, the output spanwise coordinate sequence , shape The two-dimensional tensor. The spanwise coordinate sequence corresponding to each sample in the training batch is:
[0032]
[0033] coordinate sequence Perform vector expansion, transforming each spanning coordinate... repeat This (corresponding to the number of points on each section) forms a complete spanwise coordinate vector. :
[0034]
[0035] coordinate vector Replace the corresponding point cloud in the output point cloud of the folded sub-decoder The coordinates of the channel, thus constraining each consecutive... Each point has the same spanwise coordinate and lies on the same spanwise section. Ultimately, this results in structured point cloud data with the same shape as the original structured point cloud.
[0036] Finally, using the structured point cloud data output by the decoder, the airfoil curves of each section are reconstructed sequentially; and by adding guide lines, all sections are connected using the multi-section surface method, thereby constructing a complete and smooth airfoil surface.
[0037] The loss function used in the generative model is:
[0038]
[0039] In the formula To reconstruct the loss, For KL divergence loss; The weights for the KL divergence loss;
[0040] Step 3: Extract features from the initial structured point cloud dataset and the structured point cloud of the reconstructed smooth wing surface using the encoder of the generative model to obtain the latent variable set. and latent variable set This forms a set of potential variables for the wing sample.
[0041] Step 4: Perform batch mesh generation on the initial wing surface and the reconstructed wing surface, and use computational fluid dynamics (CFD) method to perform numerical simulation to obtain aerodynamic performance data for each wing surface, forming a high-fidelity aerodynamic dataset.
[0042] Aerodynamic performance datasets include: at a given Mach number With Reynolds number Below, the steady-state flow field at different angles of attack; and the aerodynamic coefficients under various operating conditions, including the lift coefficient. With drag coefficient ;
[0043] Step 5: Train the aerodynamic performance surrogate model using the outputs of the high-fidelity aerodynamic dataset and the latent variable set of the wing samples;
[0044] The aerodynamic performance surrogate model employs Gaussian process regression, trained through supervised learning, and is established under given Mach and Reynolds numbers, based on latent variables. The mapping relationship between angle of attack and aerodynamic coefficient is expressed as:
[0045]
[0046] Let be any one of the latent variables in the set of latent variables for the wing sample.
[0047] The proxy model uses latent variables and angle of attack As input, the lift coefficient and drag coefficient As the expected output.
[0048] Step 6: Based on gradient optimization and potential space regularization of the aerodynamic performance proxy model, a performance-driven design with a high lift-to-drag ratio is obtained.
[0049] First, the latent variable set of the wing sample is input into the variational autoencoder to form the prior distribution of the latent variables, and then the trained aerodynamic performance surrogate model is loaded.
[0050] Subsequently, gradient descent algorithms (such as Adam) are used for iterative optimization to obtain the optimal latent variables. ;
[0051] Perform the following operations in each iteration:
[0052] The gradient of the lift-to-drag ratio with respect to the latent variables is calculated using automatic differentiation. Simultaneously, the KL divergence between the latent variables and the prior distribution is calculated as a regularization term. The gradient is then weighted and backpropagated to the latent variables to update them. This optimization process ultimately converges to the latent variables corresponding to the optimal lift-to-drag ratio aerodynamic shape. .
[0053] During the optimization process, the optimization formula for the latent variables is as follows:
[0054]
[0055] in Indicates the current number Potential variables of step iteration The potential variables for the initial iteration step are set manually based on experience. For learning rate, The objective function consists of aerodynamic performance indicators, represented by the lift-to-drag ratio, and a regularization term. Specifically, the gradient of the objective function... It can be decomposed into:
[0056]
[0057] In the formula Indicates the aerodynamic performance target (lift-to-drag ratio). Distribution of latent variables With prior distribution KL divergence between them This is the regularization coefficient.
[0058] Finally, the optimal latent variables In the decoder of the input generative model, the output structural point cloud is then reconstructed into a smooth wing surface, resulting in a high lift-to-drag ratio wing shape.
[0059] The advantages of this invention are:
[0060] 1) This invention integrates geometry generation and aerodynamic optimization to achieve end-to-end automated design. Specifically, it combines structured point cloud representation with a variational autoencoder (VAE) to construct a complete closed-loop system from geometry generation to aerodynamic performance optimization, realizing full-process automation of wing shape design and significantly improving design efficiency;
[0061] 2) Introducing structured point cloud representation improves geometric modeling accuracy and engineering applicability; by discretizing the wing surface into structured point cloud, complete geometric details are preserved, and subsequent surface reconstruction and integration with CAD software are facilitated, ensuring the engineering usability of the generated shape.
[0062] 3) Efficient feature extraction and shape reconstruction are achieved by using variational autoencoders; the generative model based on VAE can compress high-dimensional point cloud data into a low-dimensional latent space, extract key shape features, and quickly reconstruct the wing shape with rich details and reasonable geometry after optimization, while supporting the generation of diverse shapes.
[0063] 4) Combining gradient optimization and regularization strategies to balance performance and geometric rationality; in the latent space, the gradient descent algorithm is used to optimize aerodynamic indicators such as lift-to-drag ratio, while KL divergence is introduced as a regularization term to prevent latent variables from deviating from a reasonable distribution, ensuring the physical feasibility and diversity of the generated shape. Attached Figure Description
[0064] Figure 1 This is a framework diagram of the automatic wing generation and performance evaluation method based on structured point cloud and variational autoencoder of the present invention.
[0065] Figure 2 This is a flowchart of the automatic wing generation and performance evaluation method based on structured point cloud and variational autoencoder of the present invention;
[0066] Figure 3 This is a detailed structural diagram of the wing shape generative model based on variational autoencoder (VAE) in this invention. Detailed Implementation
[0067] To make the technical solution of the present invention clearer and easier to understand, the present invention will be further described in detail below with reference to the accompanying drawings.
[0068] To address the problems of wing generation and aerodynamic optimization, this invention proposes an automatic wing generation and performance evaluation method based on structured point clouds and variational autoencoders. A three-dimensional point cloud serves as a unified representation of the wing's geometry. A core generator, composed of a variational autoencoder (VAE) and a parallel decoder, is constructed by learning from a large amount of wing shape data to build a low-dimensional continuous latent design space. Based on this, a differentiable surrogate model is established, from latent variables to key aerodynamic coefficients (such as lift and drag coefficients). Gradient-based optimization algorithms are used for efficient search and inverse design within the latent space, achieving comprehensive optimization of aerodynamic performance under given Mach and Reynolds numbers and angle-of-attack combinations. Ultimately, a high-performance wing shape that meets the target requirements is automatically generated.
[0069] The structured point cloud generated by this invention has a clear cross-sectional topology and supports direct smooth surface reconstruction. It forms a complete technical link from dataset construction, intelligent generation, aerodynamic optimization to high-quality smooth surface output, which significantly improves the automation level and engineering applicability of wing design.
[0070] like Figure 1 and Figure 2 As shown, the specific steps are as follows:
[0071] Step 1: For a certain baseline wing shape, construct an initial wing surface dataset and represent it with a structured point cloud to generate a structured point cloud dataset.
[0072] The specific steps are as follows:
[0073] First, Latin hypercube sampling is performed on the design parameters of the baseline wing shape;
[0074] Design parameters include: aspect ratio, tip-to-root ratio, sweep angle, dihedral angle, twist angle, and airfoil shape.
[0075] Then, using parametric modeling methods, corresponding wing surfaces are generated in batches based on the design parameters of the samples, with the number of generated samples being [number missing]. The initial wing surface dataset.
[0076] Next, each wing surface is uniformly cut along its span to form Each section is analyzed, and the contour curve of each section is extracted. These points form a unified, structured point cloud representation.
[0077] In the structured point cloud, individual sample data are organized into a A three-dimensional data structure, in which, The number of cross sections on the wing surface. The number of points on each cross section, 3 represents Three coordinate axis channels; index for any given span section All of the sections The spanwise coordinates of each point cloud are all assigned the same value. .
[0078] Finally, the point cloud data of all samples are integrated to construct a structured point cloud dataset for training the generative model. The shape of this dataset is... .
[0079] Step 2: Construct a generative model based on variational autoencoder and input a structured point cloud dataset to reconstruct a smooth wing surface.
[0080] The generative model adopts an encoder-decoder structure, in which:
[0081] First, shape is The structured point cloud data of the wing surface is input into the encoder, where... This indicates the training batch size. The encoder maps high-dimensional point cloud data to a low-dimensional latent space and outputs the mean of the probability distribution. and variance All shapes are ,in The dimension of the latent space is given, and then a low-dimensional latent vector is obtained through reparameterized sampling. ;
[0082] The formula for reparameterized sampling is expressed as:
[0083]
[0084] It is random noise obtained by resampling from a standard normal distribution; This represents element-wise multiplication.
[0085] Then, the decoder consists of two parallel sub-decoders, responsible for processing the denoised low-dimensional latent vector. Reconstruct the point cloud data into a structured form consistent with the original point cloud shape;
[0086] Specifically as follows:
[0087] The two parallel sub-decoders are a folded sub-decoder and a multilayer perceptron sub-decoder. Wherein:
[0088] Folded sub-decoder will latent variables As input, generate shape as It generates a 3D point cloud, but its output does not have an explicit cross-sectional structure, i.e., an unstructured point cloud.
[0089] The multilayer perceptron decoder also uses latent variables. As input, the output spanwise coordinate sequence , shape A two-dimensional tensor. In this training batch, the first... Taking one sample as an example ( ), thus obtaining the spanwise coordinate sequence of the corresponding section for this sample:
[0090]
[0091] Will Perform vector expansion, transforming each spanning coordinate... repeat This (corresponding to the number of points on each section) forms a complete spanwise coordinate vector. :
[0092]
[0093] vector Replace the corresponding point cloud in the output point cloud of the folded sub-decoder The coordinates of the channel, thus constraining each consecutive... Each point has the same spanwise coordinate and lies on the same spanwise section. Ultimately, this results in structured point cloud data with the same shape as the original structured point cloud.
[0094] Finally, using the structured point cloud data output by the decoder, the airfoil curves of each section are reconstructed sequentially; and by adding guide lines, the multi-section surface method is used to connect all sections, thereby constructing a complete and smooth airfoil surface, ultimately achieving a parameter-free transformation from implicit features to explicit geometry.
[0095] Meanwhile, to achieve effective exploration in the latent space, a Latin hypercube sampling method is used to generate new latent vectors. By inputting these latent variables into the trained decoder and repeating the surface reconstruction process described above, a new set of wing surface samples can be generated.
[0096] The loss function used in the generative model is:
[0097]
[0098] In the formula To reconstruct the loss, For KL divergence loss; The weights for the KL divergence loss;
[0099] Step 3: Construct the latent variable set for the wing samples. This is done by using the encoder trained in Step 2 to process the variables obtained in Step 1. Feature extraction was performed on individual wing surface samples to obtain the latent variable set for each wing sample. Furthermore, the latent variable set of the newly generated wing samples in step two is merged. This ultimately forms the wing sample latent variable set used for training the aerodynamic agent model in subsequent steps.
[0100] Step 4: Construct a high-fidelity aerodynamic performance dataset. Batch meshing is performed on the initial wing surface sample set and the newly generated wing surface set. Computational fluid dynamics (CFD) methods are then used for numerical simulation to obtain the aerodynamic performance data for each wing surface, forming a high-fidelity aerodynamic dataset.
[0101] Aerodynamic performance datasets include: at a given Mach number With Reynolds number Below, the steady-state flow field at different angles of attack; and the aerodynamic coefficients under various operating conditions, including the lift coefficient. With drag coefficient ;
[0102] Step 5: Train the aerodynamic performance surrogate model using the output of the high-fidelity aerodynamic dataset and the latent variable set;
[0103] The aerodynamic performance surrogate model employs Gaussian process regression, trained through supervised learning, and is established under given Mach and Reynolds numbers, based on latent variables. The mapping relationship between angle of attack and aerodynamic coefficient is expressed as:
[0104]
[0105] Let be any one of the latent variables in the latent variable set of the wing sample in step three.
[0106] The proxy model uses latent variables and angle of attack As input, the lift coefficient and drag coefficient As the desired output, a mean squared error loss function is used during training to minimize the error between the predicted value and the actual CFD numerical calculation result.
[0107] Step 6: Based on gradient optimization and potential space regularization of the aerodynamic performance proxy model, a performance-driven design with a high lift-to-drag ratio is obtained.
[0108] First, the structured point cloud data of the initial wing surface dataset and the reconstructed wing surface are input into the variational autoencoder to form the prior distribution of the initialized latent variables, and the trained aerodynamic performance surrogate model is loaded.
[0109] Subsequently, gradient descent algorithms (such as Adam) are used for iterative optimization to obtain the optimal latent variables. ;
[0110] Perform the following operations in each iteration:
[0111] The gradient of the lift-to-drag ratio with respect to the latent variables is calculated using automatic differentiation. Simultaneously, the KL divergence between the latent variables and the prior distribution is calculated as a regularization term. The gradient is then weighted and backpropagated to the latent variables to update them. This optimization process ultimately converges to the latent variables corresponding to the optimal lift-to-drag ratio aerodynamic shape. .
[0112] During the optimization process, the optimization formula for the latent variables is as follows:
[0113]
[0114] in Indicates the current number Potential variables of step iteration The potential variables for the initial iteration step are set manually based on experience. For learning rate, The objective function consists of aerodynamic performance indicators, represented by the lift-to-drag ratio, and a regularization term. Specifically, the gradient of the objective function... It can be decomposed into:
[0115]
[0116] In the formula Indicates the aerodynamic performance target (lift-to-drag ratio). Distribution of latent variables With prior distribution KL divergence between them This is the regularization coefficient.
[0117] Finally, the optimal latent variables In the decoder of the input generative model, the output structural point cloud is then reconstructed into a smooth wing surface, resulting in a high lift-to-drag ratio wing shape for engineering design.
[0118] Example
[0119] Step 1: Using the CRM wing as the initial configuration of the reference shape, perform Latin hypercube sampling within the range of 0.8 to 1.2 times its design parameter reference value to generate a sample set with a sample size of 2500.
[0120] The corresponding wing surfaces are generated in batches using parametric modeling methods to construct the initial geometric dataset.
[0121] Each wing surface is evenly divided into 80 sections along the span, and 80 points are extracted from the profile curve of each section to form a unified structured point cloud representation.
[0122] Finally, the point cloud data of all samples are integrated to construct a point cloud dataset suitable for training generative models. In this example, the number of samples is... , number of cross sections and the number of points per cross section We take 2500, 80 and 80 respectively, so the final point cloud dataset size is 2500×6400×3;
[0123] Step 2: Construct and train a generative model based on a variational autoencoder (VAE). This model employs a "dimensionality reduction-reconstruction" encoder-decoder structure, transforming the data into a generative model with the shape of... The structured point cloud dataset is used as the training input.
[0124] In this structure:
[0125] Encoder: Transforms high-dimensional point cloud samples (of shape...) into... The tensor is mapped to the probability distribution parameters in the latent space—the mean. and variance And low-dimensional latent vectors are obtained by sampling through reparameterization techniques. ,in This represents the batch size of the training samples.
[0126] The formula for the reparameter repetition technique is expressed as:
[0127]
[0128] in:
[0129] Represents the latent variables obtained from the calculation;
[0130] The mean of the potential spatial probability distribution;
[0131] The standard deviation represents the probability distribution of the potential space.
[0132] It is random noise obtained by resampling from a standard normal distribution;
[0133] This represents element-wise multiplication.
[0134] The decoder employs a hybrid decoding strategy, consisting of two parallel sub-decoders responsible for processing the denoised latent variables. Reconstructed point cloud data with the same shape as the original sample (shape is ).
[0135] Specifically, it includes:
[0136] • Folding decoder: Generates a shape as It generates a 3D point cloud, but its output does not have an explicit cross-sectional structure;
[0137] • Multilayer perceptron decoder: from the same latent variable Predicted cross section span coordinates The output shape is A two-dimensional tensor representing the positions at 80 cross-sections. Coordinates, based on the first position in this training batch Taking one sample as an example ( ), thus obtaining the spanwise coordinate sequence of the corresponding section for this sample:
[0138]
[0139]
[0140] To apply cross-sectional structured constraints, the output of the MLP is... Vector expanded into shape Two-dimensional tensor This replaces the corresponding point cloud in the output point cloud of the folded decoder. The coordinate values are used to rigidly constrain every 80 consecutive points to be in the same radial section.
[0141] When jointly optimizing the encoder and decoder, the point cloud dataset is first normalized using the Min-Max Normalization method to adjust the range of values for each coordinate axis. The range. The encoder-decoder structure is as follows: Figure 3 As shown. The optimizer used is AdamW, the learning rate scheduling uses a cosine annealing strategy, and the initial learning rate is... The minimum learning rate is set to The loss function consists of two parts: reconstruction loss and KL divergence.
[0142] • Reconstruction Loss: Measured by the difference between the point cloud reconstructed by the decoder and the original point cloud, calculated using the Chamfer Distance (CD). The Chamfer Distance is defined as follows:
[0143]
[0144] In the formula: It is the original point cloud. To reconstruct the point cloud, For points in the original point cloud, To reconstruct the points in the point cloud;
[0145] • KL divergence loss: Used to constrain the difference between the latent variable distribution output by the encoder and the standard normal distribution.
[0146]
[0147] In the formula: As latent variables, For approximate posterior distribution, and denoted as the mean and variance of each dimension of the latent space. Let be the dimension of the latent space, which is 64 in this example;
[0148] The final loss function is:
[0149]
[0150] In the formula The weights for the KL divergence loss are taken as follows in this example. ;
[0151] After training, the encoder-decoder architecture enables efficient compression and reconstruction of wing point cloud data. The encoder extracts the essential features of the point cloud and embeds them into a low-dimensional latent space; the decoder then reconstructs the latent vector into structured point cloud data.
[0152] Smooth Surface Reconstruction for Airfoil Design. The structured point cloud data output from the decoder is imported into professional modeling software to reconstruct the airfoil curves of each section in sequence. Then, by adding guide lines and using a multi-section surface method to connect all sections, a complete and smooth airfoil surface is constructed.
[0153] Meanwhile, to achieve effective exploration in the latent space, a Latin hypercube sampling method is used to generate new latent vectors. By inputting these latent variables into the trained decoder and repeating the surface reconstruction process described above, a new set of wing surface samples can be generated.
[0154] Step 3: Construct the latent variable set for the wing samples. This is done by using the encoder trained in Step 2 to process the variables obtained in Step 1. Feature extraction was performed on individual wing surface samples to obtain the latent variable set for each wing sample. Furthermore, the latent variable set of the newly generated wing samples in step two is merged. This ultimately forms the wing sample latent variable set used for training the aerodynamic agent model in subsequent steps.
[0155] Step 4: Construct a high-fidelity aerodynamic performance dataset.
[0156] Each wing sample was batch-meshed, and computational fluid dynamics (CFD) methods were used for numerical simulation to solve for the wing at a given Mach number. With Reynolds number The steady-state flow field was analyzed at angles of attack ranging from -4° to 4°. Aerodynamic coefficients (including lift coefficient) were extracted for each operating condition. With drag coefficient This ultimately forms an aerodynamic performance dataset corresponding to the geometric samples;
[0157] Step 5: Construct a surrogate model for aerodynamic performance.
[0158] This surrogate model employs Gaussian Process Regression (GPR) and is trained using samples obtained through CFD calculations. During the modeling process, latent variables... Angle of attack Common inputs:
[0159]
[0160] in, The dimension of the potential vector is 64 in this example. The output target is the aerodynamic coefficients, i.e., the lift coefficients, obtained from the CFD calculation. With drag coefficient Within the GPR framework, for a given input The predicted aerodynamic coefficients can be expressed as:
[0161]
[0162] in: For the predicted aerodynamic coefficients, The mean of the training samples. The actual aerodynamic coefficients obtained from CFD calculations in the training set. It is a unit vector of the same length as the sample. The correlation matrix has elements defined by the kernel function:
[0163]
[0164] In the formula This is a hyperparameter that controls the correlation scale of different input dimensions. Input quantity The correlation vector between the training samples and the training samples.
[0165] In addition, GPR can also provide the forecast uncertainty, and its variance estimation formula is as follows:
[0166]
[0167] in This represents the process variance. This uncertainty measure can be used to guide subsequent sampling strategies. By actively sampling in regions of high prediction uncertainty (low confidence regions), the exploration and exploitation can be effectively balanced, thereby efficiently improving the global fitting accuracy of the surrogate model and ultimately establishing the latent variables. and angle of attack A surrogate model for rapid prediction of aerodynamic coefficients:
[0168]
[0169] Training aerodynamic performance surrogate model: Establishing a mapping relationship from latent variables and angle of attack to aerodynamic coefficients at given Mach and Reynolds numbers. This surrogate model uses the latent variables obtained in the previous step. and angle of attack As input, the lift coefficient obtained by CFD calculation and drag coefficient As the expected output, the surrogate model can be trained using Gaussian Process Regression (GPR) through supervised learning, and its mapping relationship can be expressed as:
[0170]
[0171] The mean squared error loss function is used during training to minimize the error between the predicted value and the actual CFD numerical calculation result;
[0172] Step 6: Performance-driven design based on surrogate model gradient optimization and latent space regularization.
[0173] This step aims to directly optimize latent variables using gradient information obtained from the surrogate model to achieve efficient wing shape design. To avoid the latent variables deviating from their prior distribution during the optimization process, resulting in unreasonable generated geometry, KL divergence is introduced as a regularization constraint to ensure that the optimization results meet both aerodynamic performance requirements and maintain geometric rationality.
[0174] First, latent variables are initialized from the prior distribution using a pre-trained variational autoencoder, and a pre-trained aerodynamic performance surrogate model is loaded. Then, an iterative optimization is performed using a gradient descent algorithm (such as Adam). In each iteration, the following operations are performed: the gradient of the lift-to-drag ratio with respect to the latent variables is calculated via automatic differentiation; simultaneously, the KL divergence between the latent variables and the prior distribution is calculated as a regularization term; and the weighted gradient is backpropagated to the latent variables to update them. This optimization process ultimately converges to the latent variables corresponding to the optimal lift-to-drag ratio aerodynamic shape.
[0175] Specifically, the aerodynamic performance-based design is transformed into a constrained optimization problem. The objective function is to maximize the weighted average aerodynamic performance index at each design angle of attack. Taking the weighted average lift-to-drag ratio as an example, the KL divergence between the latent variables and the prior distribution is constrained, and key design points within the angle of attack range are selected. Construct a weighted comprehensive objective function:
[0176]
[0177] Weights in the formula The weighting should be allocated according to design requirements; for example, the cruise condition should be assigned a higher weight. The constrained optimization problem can then be transformed into an unconstrained optimization problem:
[0178]
[0179] in To control the hyperparameters of regularization strength, a gradient descent-based optimization algorithm is then used to iteratively update the latent variables:
[0180]
[0181] The gradient term can be decomposed into:
[0182]
[0183] Performance gradient in the formula By using backpropagation calculations through the surrogate model, latent variables are guided to move towards the high-performance region, and the KL divergence gradient is calculated. Ensure that latent variables do not deviate too far from the prior distribution, and maintain the rationality of the decoder's reconstruction geometry.
[0184] Based on this, the decoder and corresponding geometric reconstruction method trained in step two are called to generate the final smooth wing surface, realizing the generation of high lift-to-drag ratio wing shape for engineering design.
[0185] The overall architecture of this invention includes the following two core parts:
[0186] The first part is based on variational autoencoder to realize dimensionality reduction and reconstruction of 3D point cloud data. This part first uses the encoder to map the high-dimensional wing point cloud to a low-dimensional latent space and extracts representative shape features; then the decoder reconstructs the wing point cloud with complete details and reasonable geometry from the latent variables, realizing high-quality recovery from latent variables to a smooth 3D surface, while providing the ability to generate surface geometry of new samples for subsequent optimization;
[0187] The second part constructs an aerodynamic performance proxy model and conducts shape optimization with lift-to-drag ratio as the objective. This part establishes a mapping relationship from latent variables to aerodynamic coefficients (such as lift coefficient and drag coefficient) in the latent space, forming an efficient and differentiable performance evaluation model. Based on this, with the goal of maximizing lift-to-drag ratio, it automatically searches for wing shapes with better aerodynamic performance in the latent space by combining gradient optimization algorithms and distributed constraint strategies.
[0188] Through the deep integration of the above two parts, this invention realizes an end-to-end automated design process from geometry generation to aerodynamic optimization, which significantly improves the efficiency and performance of wing aerodynamic shape design.
Claims
1. A method for automatic wing generation and performance evaluation based on structured point cloud and variational autoencoder, characterized in that, The specific steps are as follows: Step 1: For a certain reference wing shape, construct an initial wing surface dataset and represent it with structured point cloud to generate a structured point cloud dataset; The initial number of samples for the wing surface is Individual sample data are organized into a Three-dimensional data structure, The number of cross sections on a single wing surface. The number of points on each cross section, 3 represents Three coordinate axis channels; Step 2: Construct a generative model based on variational autoencoder and input a structured point cloud dataset to reconstruct a smooth wing surface; The generative model employs an encoder-decoder structure, in which: First, shape is The structured point cloud data of the wing surface is input into the encoder, whereby... Indicates the training batch size; The encoder maps high-dimensional point cloud data to a low-dimensional latent space and outputs the mean of the probability distribution. and variance All shapes ,in The dimension of the latent space is given, and then a low-dimensional latent vector is obtained through reparameterized sampling. : It is random noise obtained by resampling from a standard normal distribution; This represents element-wise multiplication; Then, the decoder consists of two parallel sub-decoders, responsible for processing the low-dimensional latent vector. Reconstruct the point cloud data into a structured form consistent with the original point cloud shape; Specifically as follows: The two parallel sub-decoders are a folded sub-decoder and a multilayer perceptron sub-decoder; where: Folded sub-decoder will latent variables As input, generate shape as It generates a 3D point cloud, but its output does not have an explicit cross-sectional structure, i.e., an unstructured point cloud. The multilayer perceptron decoder also uses latent variables. As input, the output spanwise coordinate sequence , shape The two-dimensional tensor; the cross-sectional spanning coordinate sequence corresponding to each sample in the training batch is: coordinate sequence Perform vector expansion, transforming each spanning coordinate... repeat This, along with the number of points on each cross section, forms a complete spanwise coordinate vector. : coordinate vector Replace the corresponding point cloud in the output point cloud of the folded sub-decoder The coordinates of the channel, thus constraining each consecutive... Each point has the same spanwise coordinate and lies in the same spanwise section; ultimately, structured point cloud data with the same shape as the original structured point cloud is formed. Finally, using the structured point cloud data output by the decoder, the airfoil curves of each section are reconstructed sequentially; and by adding guide lines, all sections are connected using the multi-section surface method, thereby constructing a complete and smooth airfoil surface. Step 3: Use the encoder of the generative model to extract features from the initial structured point cloud dataset and the structured point cloud of the reconstructed smooth wing surface to obtain the latent variable set of the wing samples. Step 4: Perform batch mesh generation on the initial wing surface and the reconstructed wing surface, and use computational fluid dynamics to perform numerical simulation to obtain the aerodynamic performance data of each wing surface, forming a high-fidelity aerodynamic dataset. Step 5: Train the aerodynamic performance surrogate model using the outputs of the high-fidelity aerodynamic dataset and the latent variable set of the wing samples; Step 6: Based on gradient optimization and potential space regularization of the aerodynamic performance surrogate model, a performance-driven design with a high lift-to-drag ratio is obtained. First, the latent variable set of the wing sample is input into the variational autoencoder to form the prior distribution of the latent variables, and then the trained aerodynamic performance surrogate model is loaded. Subsequently, gradient descent algorithm was used for iterative optimization to obtain the optimal latent variables. ; Perform the following operations in each iteration: The gradient of lift-to-drag ratio with respect to latent variables is calculated by automatic differentiation; simultaneously, the KL divergence between the latent variables and the prior distribution is calculated as a regularization term; the gradient is then weighted and backpropagated to the latent variables to update them; this optimization process ultimately converges to the latent variables corresponding to the optimal lift-to-drag ratio aerodynamic shape. ; Finally, the optimal latent variables In the decoder of the input generative model, the output structural point cloud is then reconstructed into a smooth wing surface, resulting in a high lift-to-drag ratio wing shape.
2. The method as described in claim 1, characterized in that, Step one specifically includes: First, Latin hypercube sampling is performed on the design parameters of the baseline wing shape; Design parameters include: aspect ratio, tip-to-root ratio, sweep angle, dihedral angle, twist angle, and airfoil shape; Then, using parametric modeling methods, corresponding wing surfaces are generated in batches based on design parameters, constructing a sample size of [number missing]. The initial wing surface dataset; Next, each wing surface is uniformly cut along its span to form Each section is analyzed, and the contour curve of each section is extracted. These points form a unified, structured point cloud representation. In the structured point cloud, for any specific spanwise section index All of the sections The spanwise coordinates of each point cloud were all assigned the same value. ; Finally, the point cloud data of all samples are integrated to construct a structured point cloud dataset for training the generative model. The shape of this dataset is... .
3. The method as described in claim 1, characterized in that, In step two, the loss function used by the generative model is: In the formula To reconstruct the loss, For KL divergence loss; The weights are the KL divergence loss values.
4. The method as described in claim 1, characterized in that, In step four, the aerodynamic performance dataset includes: at a given Mach number With Reynolds number Below, the steady-state flow field at different angles of attack; and the aerodynamic coefficients under various operating conditions, including the lift coefficient. With drag coefficient .
5. The method as described in claim 1, characterized in that, In step five, the aerodynamic performance surrogate model employs Gaussian process regression, trained through supervised learning, and is established under given Mach and Reynolds numbers, based on latent variables. The mapping relationship between angle of attack and aerodynamic coefficient is expressed as: Let be any one of the latent variables in the latent variable set of the wing sample; The proxy model uses latent variables and angle of attack As input, the lift coefficient and drag coefficient As the expected output.
6. The method as described in claim 1, characterized in that, In step six, during the optimization process, the optimization formula for the latent variables is as follows: in Indicates the current number Potential variables of step iteration The potential variables for the initial iteration step are set manually based on experience; For learning rate, The objective function consists of aerodynamic performance indices, represented by the lift-to-drag ratio, and a regularization term; specifically, the gradient of the objective function... It can be decomposed into: In the formula This represents the aerodynamic performance target, namely the lift-to-drag ratio. Distribution of latent variables With prior distribution KL divergence between them This is the regularization coefficient.