Airfoil flow field prediction method and system based on spectral domain residual error perception neural network

Abstract

The invention provides an airfoil flow field prediction method and system based on a spectral domain residual error perception neural network, and belongs to the technical field of aircraft design. Comprising the following steps: constructing an airfoil profile geometric database containing multiple pieces of standard airfoil profile coordinate information; constructing an airfoil flow field database, carrying out steady compressible flow field simulation under the condition of high Reynolds number based on a Fluent solver of a finite volume method, and generating airfoil flow field data; an autoencoder model with a residual connection mechanism is adopted to extract geometric features of the airfoil; constructing a spectral domain residual error perception neural network, and introducing Fourier transform and a conditional position coding mechanism; and utilizing the trained spectral domain residual error perception neural network to carry out airfoil flow field prediction. According to the method, geometric feature extraction and the flow field prediction process are decoupled through a sectional modeling framework, efficient modeling can be achieved under different types of grid and data distribution, and accurate prediction of the airfoil flow field is achieved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of aircraft design, and particularly relates to a wing profile flow field prediction method and system based on a spectral domain residual perception neural network. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] In the field of aircraft design, the wing profile is a key component that determines the generation of lift and the regulation of aerodynamic characteristics, and its performance directly affects the flight efficiency and stability of the whole machine. The traditional method of evaluating the aerodynamic performance of the wing profile mainly includes wind tunnel experiments and numerical simulations. Although wind tunnel experiments can obtain relatively accurate experimental results, the equipment is complex, the test period is long, and the cost is high, which is not suitable for rapid iterative design under multiple parameter conditions. The Computational Fluid Dynamics (CFD) method obtains the flow field distribution and aerodynamic parameters by solving the fluid control equation, and has high calculation accuracy, but the calculation cost is extremely high under high Reynolds number and complex boundary conditions, which is difficult to meet the real-time and rapid optimization requirements in aircraft design.

[0004] In order to overcome the above problems, in recent years, data-driven aerodynamic surrogate models based on deep learning have emerged. This kind of method learns the mapping relationship between the geometric characteristics of the wing profile, the incoming flow parameters and the aerodynamic response, and can quickly predict the aerodynamic characteristics after training, significantly reducing the dependence on CFD solvers. Therefore, it is of great engineering application value to carry out efficient aerodynamic characteristic prediction research for different wing profile forms and multiple working conditions. Although data-driven methods have made positive progress in wing profile flow field prediction, there are still many bottlenecks in their development, and some key problems include: (1) The existing data-driven surrogate relies heavily on the number of high-fidelity samples and data preprocessing, resulting in high modeling cost and low data utilization.

[0005] (2) Current researches mainly focus on low Reynolds number (laminar flow) flow fields, and have poor adaptability to high Reynolds number conditions, with significantly reduced prediction accuracy, and some models may even fail, which cannot meet the engineering requirements.

[0006] (3) The field-to-field surrogate model based on convolution in existing technologies is difficult to directly process non-uniform data such as wing profile flow field, and usually needs to use flow field projection and other preprocessing techniques, which may lead to loss of information near the wall region and may cause non-physical solutions in the wing profile. SUMMARY

[0007] In order to overcome the above-mentioned deficiencies of the prior art, the present application provides a wing profile flow field prediction method and system based on a spectral domain residual perception neural network, which decouples the geometric feature extraction and flow field prediction process through a segmented modeling framework, can realize efficient modeling under different types of grids and data distribution, and realizes accurate prediction of the wing profile flow field.

[0008] In order to achieve the above-mentioned purpose, one or more embodiments of the present application provide the following technical solutions: The present application provides a wing profile flow field prediction method based on a spectral domain residual perception neural network in the first aspect.

[0009] The wing profile flow field prediction method based on a spectral domain residual perception neural network comprises: A wing profile geometry database containing a plurality of standard wing profile coordinate information is constructed, and the contour of each standard wing profile is pixelized to generate a corresponding black and white binary image; A wing profile flow field database is constructed, and a steady compressible flow field simulation under high Reynolds number conditions is carried out based on a Fluent solver of finite volume method to generate wing profile flow field data under a plurality of geometric and incoming flow conditions; A self-encoder model with residual connection mechanism is used to extract wing profile geometric features: the black and white binary image is compressed into a low-dimensional geometric feature vector through the encoding module of the self-encoder model; the decoding module of the self-encoder model is used to reconstruct the wing profile and verify the extraction effect; A spectral domain residual perception neural network is constructed, Fourier transform and conditional position encoding mechanism are introduced into the spectral domain residual perception neural network and trained; the spatial coordinates are mapped to different scale domains through multi-scale projection, so that the spatial coordinates of the near-wall region and the far-field region are projected to different frequency bands; finally, the trained spectral domain residual perception neural network is used for wing profile flow field prediction.

[0010] Further, the control equation set of the Fluent solver is based on the Reynolds averaged RANS equation system, specifically including the continuity equation, the momentum equation and the energy equation.

[0011] Further, an ideal gas state equation is used to represent the corresponding relationship between pressure, density and temperature to realize the thermodynamic closure relationship of the Reynolds averaged RANS equation system.

[0012] Further, the Transition SST model is used to realize the balance between the transition of the boundary layer flow and the simulation accuracy of the high Reynolds number turbulent region, and the steady equation set in the Transition SST model includes the turbulent kinetic energy equation, the specific dissipation rate equation, the intermittency factor equation and the momentum thickness Reynolds number equation.

[0013] Further, the self-encoder model adopts a ReLU activation function, and takes a mean square error as a loss function.

[0014] Further, the spectral domain residual perception neural network takes the geometric features extracted by the self-encoder model, the inflow condition, the grid node coordinates and the unsigned distance function as inputs, and outputs the velocity component and the pressure coefficient of the corresponding node.

[0015] Further, the Fourier transform is subjected to amplitude and bias modulation by using conditional position coding, including: first, obtaining adjustment parameters based on the inflow condition, and then generating the modulated position coding by channel-by-channel modulation.

[0016] The second aspect of the present application provides an airfoil flow field prediction system based on a spectral domain residual perception neural network.

[0017] The airfoil flow field prediction system based on the spectral domain residual perception neural network comprises: The airfoil geometry database construction module is configured to: construct an airfoil geometry database containing coordinate information of a plurality of standard airfoils, and perform pixelization processing on the profile of each standard airfoil to generate a corresponding black-and-white binary image. The airfoil flow field database construction module is configured to: construct an airfoil flow field database, and based on a Fluent solver of the finite volume method, carry out steady compressible flow field simulation under high Reynolds number conditions to generate airfoil flow field data under a plurality of geometric and inflow conditions. The airfoil geometry feature extraction module is configured to: extract airfoil geometry features by using a self-encoder model with a residual connection mechanism; compress the black-and-white binary image into a low-dimensional geometry feature vector through the encoding module of the self-encoder model; and reconstruct the airfoil profile through the decoding module of the self-encoder model and verify the extraction effect. The airfoil flow field prediction module is configured to: construct a spectral domain residual perception neural network, introduce Fourier transform and conditional position coding mechanism into the spectral domain residual perception neural network and perform training; map the spatial coordinates into different scale domains through multi-scale projection, so that the spatial coordinates of the near-wall region and the far-field region are projected into different frequency bands; and finally use the trained spectral domain residual perception neural network to predict the airfoil flow field. The third aspect of the present application provides a computer readable storage medium having a program stored thereon, wherein the program is executed by a processor to implement the steps of the airfoil flow field prediction method based on the spectral domain residual perception neural network according to the first aspect of the present application.

[0018] The fourth aspect of the present application provides an electronic device, comprising a memory, a processor and a program stored in the memory and executable on the processor, wherein the processor implements the steps in the airfoil flow field prediction method based on the spectral domain residual perception neural network according to the first aspect of the present application when executing the program.

[0019] The above one or more technical solutions have the following beneficial effects: (1) The present application first extracts airfoil geometric features using an autoencoder model with a residual connection mechanism, and then uses a spectral domain residual perception neural network with Fourier transform and conditional position encoding mechanism to predict the airfoil flow field, decoupling the airfoil geometric feature extraction and flow field prediction process. First, the autoencoder extracts a low-dimensional, dense geometric feature vector from the airfoil binary image, achieving efficient compression and representation of the original geometric data. Then, the spectral domain residual perception neural network uses the feature vector, combined with a small amount of input such as flow conditions and spatial coordinates, to directly predict the point-to-point flow field physical quantities. This framework significantly reduces the dependence on massive high-fidelity CFD samples, and still enables high-precision modeling under sparse sample conditions, greatly improving data utilization efficiency and effectively reducing computational and time costs for model construction.

[0020] (2) After constructing the spectral domain residual perception neural network, the present application introduces a multi-scale Fourier transform and a conditional position encoding mechanism, which significantly enhances the model's ability to capture complex flow characteristics. The multi-scale Fourier transform maps the spatial coordinates to different frequency bands, enabling the model to analyze both high-frequency variations such as boundary layer in the near-wall region and leading edge shock, and low-frequency flow characteristics in the far-field region. The conditional position encoding allows the model to adaptively modulate the frequency feature response based on the flow conditions. This design enables the proxy model constructed by the present application to effectively adapt to the simulation requirements of high Reynolds number turbulent flow, maintaining good prediction accuracy and stability in subsonic and even transonic ranges, meeting the prediction requirements of complex working conditions in engineering practical applications.

[0021] (3) The spectral domain residual perception neural network of the present application directly uses the flow field grid node coordinates and their corresponding geometric features, flow conditions, etc. as input, and outputs the flow field physical quantities of the node, thus naturally adapting to non-uniform data distribution such as non-structured grids. This method avoids information distortion that may be introduced by pre-processing such as flow field projection, and accurately preserves flow details in key areas such as the near-wall region. At the same time, since the model learns the continuous function mapping in physical space, the prediction results are more physically consistent, effectively avoiding non-physical numerical solutions inside the airfoil, and ensuring the physical reasonableness and reliability of the prediction results.

[0022] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a structured flowchart of the airfoil flow field prediction method based on spectral domain residual sensing neural network in Embodiment 1 of the present invention.

[0025] Figure 2 This is a schematic diagram of the black-and-white binary image of the airfoil in Embodiment 1 of the present invention; wherein, Figure 2 (a) in the image represents the binary image of the airfoil for NACA0021. Figure 2 (b) in the image represents the binary image of the A18 airfoil. Figure 2 (c) in the figure represents the black-and-white binary image of the airfoil of 2032C.

[0026] Figure 3 This is a structural diagram of the autoencoder model in Embodiment 1 of the present invention.

[0027] Figure 4 This is a structural diagram of the spectral domain residual sensing neural network in Embodiment 1 of the present invention.

[0028] Figure 5 This is a comparative schematic diagram showing the distribution characteristics of the x-direction velocity of the airfoil flow field under specific operating conditions in Embodiment 1 of the present invention; wherein, Figure 5 In the diagram, (a) represents the velocity distribution characteristics in the x-direction of the CFD flow field within the airfoil. Figure 5 In the diagram, (b) represents the distribution characteristics of the velocity in the x-direction of the spectral domain residual sensing neural network in the airfoil flow field. Figure 5 In the figure, (c) represents the absolute error distribution of the velocity in the x-direction of the CFD and the spectral domain residual sensing neural network in the airfoil flow field.

[0029] Figure 6 This is a comparative schematic diagram showing the distribution characteristics of the y-direction velocity of the airfoil flow field under specific operating conditions in Embodiment 1 of the present invention; wherein, Figure 6 In the diagram, (a) represents the velocity distribution characteristics in the y-direction of the CFD flow field in the airfoil. Figure 6 In the diagram, (b) represents the distribution characteristics of the velocity in the y-direction of the spectral domain residual sensing neural network in the airfoil flow field. Figure 6 In the figure, (c) represents the absolute error distribution of the velocity in the y-direction of the CFD and the spectral domain residual sensing neural network in the airfoil flow field.

[0030] Figure 7This is a comparative schematic diagram showing the distribution characteristics of the pressure coefficient of the airfoil flow field under specific operating conditions in Embodiment 1 of the present invention; wherein, Figure 7 In the diagram, (a) represents the distribution characteristics of the pressure coefficient in the CFD flow field of the airfoil. Figure 7 In the diagram, (b) represents the distribution characteristics of the pressure coefficient in the airfoil flow field by the spectral domain residual sensing neural network. Figure 7 In the figure, (c) represents the absolute error distribution of the pressure coefficient in the airfoil flow field by CFD and spectral domain residual sensing neural network. Detailed Implementation

[0031] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0032] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0033] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0034] Example 1 This embodiment discloses a method for predicting airfoil flow fields based on spectral domain residual sensing neural networks.

[0035] Airfoil flow field prediction methods based on spectral domain residual sensing neural networks include: Step S1: Construct an airfoil geometry database containing coordinate information of multiple standard airfoils, and pixelate the outline of each standard airfoil to generate the corresponding black and white binary image. Step S2: Construct an airfoil flow field database. Based on the Fluent solver of the finite volume method, conduct steady compressible flow field simulation under high Reynolds number conditions to generate airfoil flow field data under various geometric and incoming flow conditions. Step S3: Extract airfoil geometric features using an autoencoder model with residual connection mechanism: compress the black and white binary image into a low-dimensional geometric feature vector through the encoding module of the autoencoder model; reconstruct the airfoil profile and verify the extraction effect through the decoding module of the autoencoder model; Step S4: Construct a spectral domain residual sensing neural network, introduce Fourier transform and conditional position coding mechanism into the spectral domain residual sensing neural network and train it; map spatial coordinates to different scale domains through multi-scale projection, so that the spatial coordinates of the near-wall region and the far-field region are projected to different frequency bands respectively; finally, use the trained spectral domain residual sensing neural network to predict the airfoil flow field.

[0036] Based on the above process, the present application can realize efficient modeling under different types of grids and data distribution by decoupling the geometric feature extraction and flow field prediction process through a segmented modeling framework, and realize accurate prediction of airfoil flow field. For a single airfoil working condition, the present application can complete the reconstruction of velocity and pressure field within milliseconds, and the calculation speed is nearly 1000 times higher than that of the existing CFD solver. In addition, the architecture has good generalization ability in the training parameter space, which can effectively meet the current engineering demand of aerodynamic performance prediction. In order to facilitate the understanding of the technical scheme of the present application, the specific implementation method in the technical scheme of the present application will be further explained and described below.

[0037] As shown in Figure 1 When predicting the airfoil flow field based on the spectral domain residual perception neural network, first, high-precision flow field data is generated by a traditional CFD method, including creating an airfoil model, dividing the calculation grid, performing flow field numerical simulation and completing post-processing, and arranging the obtained velocity field, pressure field and other physical quantities into samples that can be used for training; these data are collected to form a "flow field data set" as the basis for training a deep learning model; further, a "autoencoder + flow field proxy network" structure is used in the deep learning part; among them, the encoder is used to compress the airfoil geometric representation into a low-dimensional latent space feature, which is then input into the flow field proxy model together with the incoming flow conditions to realize fast prediction of the target two-dimensional flow field; the overall process embodies the use of CFD high-fidelity data to drive the deep learning model, which greatly improves the flow field prediction efficiency while maintaining accuracy.

[0038] In step S1, an airfoil geometry database containing coordinate information of a plurality of standard airfoils is constructed, and the contours of each standard airfoil are pixelated to generate corresponding black and white binary images.

[0039] A large amount of standard airfoil data is selected from the published dynamic database, and a wing coordinate database is constructed accordingly. On this basis, the geometric contours of each airfoil are pixelated. The specific method is to generate a uniform pixel grid with a size of 216x216 in a smaller circumscribed rectangle that can completely contain the airfoil contour; then, according to the airfoil geometric shape, it is judged whether each pixel center point is located on the airfoil contour or its adjacent area. If the pixel center point falls within the airfoil contour range, the gray value of the pixel is set to 1; if it is not within the range, the gray value is set to 0. Through this method, black and white binary images for training and performance verification can be obtained. Figure 2 Three typical airfoils in the airfoil database are shown, wherein, Figure 2 (a) in FIG. 1 shows the black and white binary image of the NACA0021 airfoil, Figure 2 (b) in FIG. 1 shows the black and white binary image of the A18 airfoil, Figure 2(c) in the above-mentioned method represents a black-and-white binary image of the airfoil profile. The 216x216 binary image formed under the above-mentioned method, wherein the white pixels correspond to the airfoil profile region, and the black pixels correspond to the background region. Such a binary image can accurately reflect the geometric characteristics of different airfoils in terms of leading edge shape, thickness distribution, camber variation and trailing edge shape, etc., providing a reliable data basis for subsequent geometric feature extraction of the autoencoder model.

[0040] In step S2, the airfoil flow field database is constructed, and the steady compressible flow field simulation is carried out under high Reynolds number conditions based on the Fluent solver of the finite volume method, to generate airfoil flow field data under various geometric and incoming flow conditions.

[0041] The present application utilizes the Fluent solver based on the finite volume method to carry out steady compressible flow field simulation under high Reynolds number conditions, to generate high-fidelity airfoil flow field data under different geometric and incoming flow conditions. The control equation system solved by Fluent is based on the Reynolds-averaged Navier-Stokes (RANS) equation system, which specifically includes the continuity equation, the momentum equation and the energy equation, i.e. ; ; ; wherein, represents the average density; and represent the mass-weighted average velocity components, and the subscript , can be 1, 2, 3, respectively representing x axis, y axis and z axis; and represent the spatial coordinate components; represents the average static pressure; and represent the velocity fluctuation components; represents the density-weighted velocity fluctuation correlation term; represents the total energy per unit mass; represents the effective thermal conductivity; represents the mass-weighted average value of temperature. represents the effective stress tensor, which is defined as follows: ; wherein, represents the molecular dynamic viscosity of air; represents the turbulent eddy viscosity; represents the mass-weighted average velocity component, and the subscript can be 1, 2, 3, respectively representingx Axis, y Axis and z Axis direction; denotes the Kronecker symbol, which is 1 when , otherwise 0.

[0042] Unit mass total energy , defined as: ; where, denotes the specific internal energy. Effective thermal conductivity , defined as: ; where, denotes the molecular thermal conductivity; denotes the turbulent thermal conductivity; denotes the specific heat capacity at constant pressure, denotes the effective Prandtl number.

[0043] To achieve the thermodynamic closure of the equation system, the present application adopts the ideal gas state equation to represent the corresponding relationship between pressure, density and temperature, which is specifically shown as follows: ; where, R denotes the gas constant, and the air takes 287.0 J / (kg·K). The molecular dynamic viscosity of air is described by Sutherland law, which is mathematically defined as follows: ; where, denotes the reference viscosity; denotes the reference temperature; denotes the Sutherland constant. The Reynolds stress term in the RANS equation should be closed by the turbulent viscosity hypothesis: ; where, denotes the turbulent kinetic energy; S ij denotes the average strain rate tensor, which can be specifically defined as: .

[0044] To simultaneously consider the transition of the boundary layer flow and the simulation accuracy of the high Reynolds number turbulent flow region, the present application selects the Transition SST model based on the k - ω SST improved Transition SST model, which is a model that is improved on the basis of the traditional k - ωBased on the SST turbulence model, additional control variables related to transition are introduced, enabling it to simultaneously describe the transition process from laminar to turbulent flow and the flow characteristics of the mature turbulent region. Among these, turbulent kinetic energy... k The governing equations are used to characterize the kinetic energy of turbulent fluctuations and reflect the evolution of turbulence intensity; specific dissipation rate ω The governing equations describe the rate at which turbulent kinetic energy is dissipated to smaller scales, thus determining the turbulent viscosity and energy dissipation characteristics. Combining these equations allows for the calculation of effective eddy viscosity, thereby enabling accurate prediction of turbulent shear stress. The steady governing equations of this model include the turbulent kinetic energy equation, the specific dissipation rate equation, the intermittent factor equation, and the momentum-thickness Reynolds number equation, the specific forms of which are shown below: ; ; ; ; in, Indicates density; k It is turbulent kinetic energy; Specific dissipation rate; and These are the empirical constants of the SST model; , and Here, is the diffusion coefficient constant, used respectively for k , Equations and Cross-diffusion term; F 1 is the SST mixing function, used to adjust the weights of the near-wall and free flow regions; This is an intermittent factor, where "0" represents laminar flow and "1" represents fully turbulent flow; and They are respectively k The generating and dissipating terms of the equation; and They represent The source and dissipation terms of the equation; Indicates the thickness Reynolds number of the transition momentum; express The source term of the equation; and They are respectively and The diffusion coefficient constant of the equation.

[0045] In step S3, an autoencoder model with a residual connection mechanism is used to extract airfoil geometric features: the black and white binary image is compressed into a low-dimensional geometric feature vector through the encoding module of the autoencoder model; the airfoil profile is reconstructed and the extraction effect is verified through the decoding module of the autoencoder model.

[0046] The present application designs an autoencoder model with a residual connection mechanism for extracting airfoil geometric features. As shown in the figure, the model is composed of an encoding module and a decoding module; wherein the encoding module combines a residual convolutional neural network (Convolutional Neural Network, CNN) and a multi-layer perceptron (Multi-Layer Perceptron, MLP) to compress a two-dimensional black and white airfoil image into a low-dimensional geometric feature vector; the decoding module is composed of an MLP, which is used to reconstruct the airfoil profile to verify the learning and extraction effect of the core geometric features of the autoencoder. Figure 3

[0047] The autoencoder constructed in the present application uses a ReLU activation function, and the loss function is mean square error, which is defined as follows: ; Wherein, N represents the number of samples in a training batch, and the subscript , , respectively represent the values of the pixels in the height and width directions; represents the pixel value, and the superscript , respectively represent the true value and the predicted value.

[0048] In step S4, a spectral domain residual perception neural network is constructed, and Fourier transform and conditional position encoding mechanism are introduced into the spectral domain residual perception neural network and trained.

[0049] The present application designs a spectral domain residual perception neural network for airfoil flow field proxy modeling, and the model architecture is shown in the figure. Figure 4 As shown in the figure, specifically, the network input includes incoming Mach number Ma , angle of attack AOA, spatial coordinates x , y ), geometric code G and wall distance d . First, the spatial coordinates x , y ) are mapped to the frequency domain through the Fourier transform module to enhance the network's perception of high-frequency changes in the flow field. At the same time, the geometric code G and the incoming flow parameters L (including Ma , AOA,​d ) are fed into the conditional encoding module to generate the conditional modulation information that matches the network deep residual blocks. The Fourier transformed features and the conditional encoding outputs are jointly fed into the feature concatenation layer of the backbone network, and then fed into multiple serially arranged residual blocks to realize the step-by-step feature extraction and cross-layer information transmission through the residual structure. Finally, the network outputs the velocity components U 、 V and the pressure coefficient C p of the airfoil flow field. Through the synergistic effect of Fourier mapping and conditional encoding, the spectral domain residual perception network of the present application effectively improves the learning ability and generalization performance of the surrogate model. The network can be formally expressed as the following function: ; To further alleviate the "spectral bias" (difficulty in fitting high frequency and sharp changes) of the classic MLP, the spectral domain residual perception neural network projects the flow field coordinates x , y onto a multi-scale triangular basis. For the th scale, its random projection matrix is represented as: ; wherein represents the number of random basis vectors sampled at the th scale, the subscript represents the row index of the projection matrix (representing a certain random frequency), the subscript represents the column index of the random matrix (consistent with the coordinate dimension), and represents the variance corresponding to the th scale (controlling the frequency range). Then, the coordinates are projected into the frequency space using the projection matrix , and the corresponding sine and cosine features are constructed: ; wherein represents the th random basis vector at the th scale; represents the transpose. For each projection result , the sine and cosine are calculated, generating two features at each frequency: ; Finally, all the frequency and scale features are spliced to obtain the final representation: ; This invention maps spatial coordinates to different scale domains, projecting the coordinates of the near-wall and far-field regions onto different frequency bands. Through this multi-scale Fourier expansion, the model can better characterize flows with high-frequency or locally abrupt changes, such as rapid leading-edge transitions, trailing-edge recirculation, and thin boundary layer structures.

[0050] To enable the model to adapt to the incoming flow conditions, conditional position coding is used to perform amplitude / bias modulation on the aforementioned Fourier transform. Firstly, based on the incoming flow conditions... L = [ Ma Obtain the adjustment parameters using [OA]. ; The adjustment parameters are obtained through a two-layer feedforward neural network. W 1 and W 2 are the weight matrices for the two layers respectively; b 1 and b 2 represents the corresponding bias vector. These parameters are continuously updated during training. It is important to note that... F =2 K r That is, each Fourier code corresponds to two adjustment parameters. γ and β Subsequently, regarding Channel-by-channel modulation, thus obtaining the first l Position encoding after layer modulation: ; Conditional location encoding enables the model to operate under different conditions ( Ma By adaptively amplifying or suppressing the corresponding spatial frequency bands under each channel (AoA), multiple flow patterns can be covered in the same network, avoiding reliance on "condition-specific networks" and further improving the model's generalization ability to incoming flow conditions.

[0051] To further illustrate the significant advancements of this invention, this embodiment simultaneously trains and tests high Reynolds number flows for multiple airfoils within a defined range of incoming flow parameters. The training and validation of the spectral domain residual sensing neural network considers seven airfoils: NACA0006, NACA1410, NACA2410, NACA4421, NACA6412, RAE5213, and S4083. Ma The range is set to 0.2 to 0.6 (intervals of 0.1), and the range of AOA is... to (interval This parameter setting not only covers the typical Mach number range for subsonic flows but also encompasses the angle of attack range commonly used in engineering applications. Specifically, it is applicable to the NACA0006, NACA1410, and RAE5213 airfoils.Ma With AOA taking even values in its range, each airfoil contains 15 working conditions, totaling 45 working conditions; the remaining four airfoils take odd values in the range, each airfoil contains 12 working conditions, totaling 48 working conditions. Therefore, there are 93 working conditions in total for training and testing, of which 80% are used for training, 10% are used for cross-validation during training, and the remaining 10% are used for generalization testing after training is completed.

[0052] As shown in Figure 5 is a comparison diagram of the distribution characteristics of the x-direction velocity of the airfoil flow field under a specific working condition, and the selected test working condition is the test working condition of the NACA4421 airfoil under Ma=0.5, AOA=0° and the ambient condition. Among them, (a) of Figure 5 indicates the distribution characteristics of the x-direction velocity of the CFD in the airfoil flow field, Figure 5 (b) of indicates the distribution characteristics of the x-direction velocity Figure 5 of the spectral domain residual perception neural network in the airfoil flow field, (c) of indicates the absolute error distribution of the x-direction velocity

[0053] of the CFD and the spectral domain residual perception neural network in the airfoil flow field. Figure 6 is a comparison diagram of the distribution characteristics of the y-direction velocity of the airfoil flow field under a specific working condition, and the selected test working condition is the test working condition of the NACA4421 airfoil under Ma=0.5, AOA=0° and the ambient condition. Among them, (a) of Figure 6 indicates the distribution characteristics of the y-direction velocity of the CFD in the airfoil flow field, Figure 6 (b) of indicates the distribution characteristics of the y-direction velocity Figure 6 of the spectral domain residual perception neural network in the airfoil flow field, (c) of indicates the absolute error distribution of the y-direction velocity

[0054] of the CFD and the spectral domain residual perception neural network in the airfoil flow field. Figure 7 is a comparison diagram of the distribution characteristics of the pressure coefficient of the airfoil flow field under a specific working condition in the embodiment one of the application, and the selected test working condition is the test working condition of the NACA4421 airfoil under Ma=0.5, AOA=0° and the ambient condition. Among them, (a) of Figure 7 indicates the distribution characteristics of the pressure coefficient of the CFD in the airfoil flow field, Figure 7 (b) of distribution characteristics of the absolute error of the pressure coefficient (p) in the flow field of the airfoil, Figure 7 (c) represents the absolute error distribution of the pressure coefficient (p) in the flow field of the airfoil. ) of the CFD and the spectral domain residual aware neural network.

[0055] Figure 5 , Figure 6 , Figure 7 are all in the form of two-dimensional cloud maps, and the abscissa and the ordinate of the two-dimensional cloud map correspond to the x coordinate and the y coordinate of the discrete points of the airfoil flow field respectively; the discrete flow field value of each point in the two-dimensional cloud map can be judged in the specific value range through the color gradient according to the color scale on the right side of the corresponding image. Meanwhile, the x coordinate and the y coordinate in Figure 5 , Figure 6 , Figure 7 are all dimensionless, that is, they are normalized to [-1, 1] by being compared with the maximum absolute value.

[0056] According to Figure 5 , the model of the application can accurately reproduce the typical suction peak structure near the leading edge of the airfoil, and successfully predict the velocity recovery process in the trailing edge region; the overall streamline shape is highly consistent with the CFD result, and the error is mainly located in the far field region and has a small amplitude. According to Figure 6 , the prediction field can effectively capture the velocity gradient change characteristics on the upper and lower surfaces of the airfoil, and the overall distribution trend is highly consistent with the CFD; the error only increases slightly in the local flow turning and small range shear region, but the overall amplitude is low. According to Figure 7 , the model of the application not only accurately reproduces the leading edge low pressure area and the pressure gradient change on the upper surface, but also correctly captures the pressure recovery trend in the trailing edge; the error is mainly concentrated in the high gradient region where the pressure suddenly changes, and the overall deviation is still maintained in a small range.

[0057] According to the results of Figures 5-7 , it can be known that the modeling framework proposed in the application still exhibits stable and reliable prediction ability under the combination of geometry shape and incoming flow parameter that does not appear in the training set, which fully verifies the generalization performance of the network structure. In addition, in the prediction of the working condition of a single airfoil, the model of the application can complete the reconstruction of the velocity field and the pressure field in milliseconds, and the calculation efficiency is improved by about three orders of magnitude compared with the traditional CFD solution, which greatly meets the timeliness requirement of rapid evaluation of aerodynamic performance in engineering.

[0058] Embodiment Two The embodiment discloses an airfoil flow field prediction system based on a spectral domain residual aware neural network.

[0059] The airfoil flow field prediction system based on the spectral domain residual aware neural network comprises: The airfoil geometry database construction module is configured to: construct an airfoil geometry database containing a plurality of standard airfoil coordinate information, and perform pixelization processing on the profile of each standard airfoil to generate a corresponding black-and-white binary image. The airfoil flow field database construction module is configured to: construct an airfoil flow field database, and based on a Fluent solver of the finite volume method, perform steady compressible flow field simulation under high Reynolds number conditions to generate airfoil flow field data under a plurality of geometric and incoming flow conditions. The airfoil geometry feature extraction module is configured to: extract airfoil geometry features by using a self-encoder model with a residual connection mechanism; compress the black-and-white binary image into a low-dimensional geometry feature vector through the encoding module of the self-encoder model; and reconstruct the airfoil profile through the decoding module of the self-encoder model and verify the extraction effect. The airfoil flow field prediction module is configured to: construct a spectral domain residual perception neural network, introduce Fourier transform and conditional position encoding mechanism into the spectral domain residual perception neural network and perform training; map spatial coordinates into different scale domains through multi-scale projection, so that the spatial coordinates of the near-wall region and the far-field region are projected into different frequency bands; and finally use the trained spectral domain residual perception neural network to predict the airfoil flow field. Embodiment three The purpose of this embodiment is to provide a computer-readable storage medium.

[0060] The computer-readable storage medium has a computer program stored thereon, and the program, when executed by a processor, implements the steps in the airfoil flow field prediction method based on the spectral domain residual perception neural network according to Embodiment One of the present disclosure.

[0061] Embodiment four The purpose of this embodiment is to provide an electronic device.

[0062] The electronic device includes a memory, a processor, and a program stored on the memory and executable on the processor, and the processor implements the steps in the airfoil flow field prediction method based on the spectral domain residual perception neural network according to Embodiment One of the present disclosure when executing the program.

[0063] The steps and methods involved in the above embodiments two, three and four correspond to Embodiment One, and the specific implementation can be referred to the relevant description part of Embodiment One. The term "computer-readable storage medium" should be understood to include a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium that can store, encode or carry instruction sets for execution by a processor and cause the processor to perform any method in the present disclosure.

[0064] Those skilled in the art should understand that the modules or steps of the present application described above can be realized by general computer devices, or alternatively, they can be realized by program codes executable by the computer devices, so that they can be stored in the storage devices and executed by the computer devices, or they can be respectively manufactured into individual integrated circuit modules, or a plurality of modules or steps among them can be manufactured into a single integrated circuit module. The present application is not limited to any specific combination of hardware and software.

[0065] The specific embodiments of the present application described above in conjunction with the accompanying drawings are not intended to limit the protection scope of the present application. Those skilled in the art should understand that various modifications or changes made on the basis of the technical solutions of the present application without creative labor are still within the protection scope of the present application.

Claims

1. A method for airfoil flow field prediction based on spectral domain residual perception neural network, characterized in that, The method comprises the following steps: a wing profile geometry database is constructed, and the profile of each standard airfoil is pixelated to generate a corresponding black-and-white binary image; a wing profile flow field database is constructed, and a steady compressible flow field is simulated under high Reynolds number conditions based on a Fluent solver of finite volume method to generate wing profile flow field data under various geometric and incoming flow conditions; an autoencoder model with a residual connection mechanism is used to extract wing profile geometric features: the black-and-white binary image is compressed into a low-dimensional geometric feature vector through the encoding module of the autoencoder model; the wing profile is reconstructed and the extraction effect is verified through the decoding module of the autoencoder model; a spectral domain residual perception neural network is constructed, Fourier transform and conditional position encoding mechanism are introduced into the spectral domain residual perception neural network and trained; the spatial coordinates are mapped into different scale domains through multi-scale projection, so that the spatial coordinates of the near-wall region and the far-field region are projected into different frequency bands; finally, the trained spectral domain residual perception neural network is used to predict the wing profile flow field.

2. The spectral-domain residual perception neural network based airfoil flow field prediction method of claim 1, wherein, The control equation set of the Fluent solver is based on the Reynolds averaged RANS equation system, which specifically includes the continuity equation, the momentum equation and the energy equation.

3. The spectral-domain residual perception neural network based airfoil flow field prediction method of claim 2, wherein, An ideal gas state equation is used to represent the corresponding relationship between pressure, density and temperature to achieve the thermodynamic closure relationship of the Reynolds averaged RANS equation system.

4. The spectral-domain residual perception neural network based airfoil flow field prediction method of claim 1, wherein, The Transition SST model is used to balance the transition of boundary layer flow and the simulation accuracy of high Reynolds number turbulent flow region, and the steady equation set in the Transition SST model includes the turbulent kinetic energy equation, the specific dissipation rate equation, the intermittency factor equation and the momentum thickness Reynolds number equation.

5. The spectral-domain residual perception neural network based airfoil flow field prediction method of claim 1, wherein, The autoencoder model uses the ReLU activation function, and the mean square error is used as the loss function.

6. The spectral-domain residual perception neural network based airfoil flow field prediction method of claim 1, wherein, The spectral domain residual perception neural network takes the geometric features extracted by the autoencoder model, the incoming flow conditions, the grid node coordinates and the unsigned distance function as inputs, and outputs the velocity components and pressure coefficients of the corresponding nodes; wherein the incoming flow conditions include the Mach number and the angle of attack.

7. The spectral-domain residual perception neural network based airfoil flow field prediction method of claim 1, wherein, The conditional position encoding is used to modulate the amplitude and bias of the Fourier transform, including: first, adjusting parameters based on the incoming flow conditions, and then generating the modulated position encoding through channel-by-channel modulation.

8. A system for airfoil flow field prediction based on spectral domain residual aware neural networks, characterized in that, The method comprises the following steps: a wing profile geometry database is constructed, and the profile of each standard airfoil is pixelated to generate a corresponding black-and-white binary image; a wing profile flow field database is constructed, and a steady compressible flow field is simulated under high Reynolds number conditions based on a Fluent solver of finite volume method to generate wing profile flow field data under various geometric and incoming flow conditions; an autoencoder model with a residual connection mechanism is used to extract wing profile geometric features: the black-and-white binary image is compressed into a low-dimensional geometric feature vector through the encoding module of the autoencoder model; the wing profile is reconstructed and the extraction effect is verified through the decoding module of the autoencoder model; a spectral domain residual perception neural network is constructed, Fourier transform and conditional position encoding mechanism are introduced into the spectral domain residual perception neural network and trained; the spatial coordinates are mapped into different scale domains through multi-scale projection, so that the spatial coordinates of the near-wall region and the far-field region are projected into different frequency bands; finally, the trained spectral domain residual perception neural network is used to predict the wing profile flow field. The airfoil flow field prediction module is configured to: construct a spectral domain residual perception neural network, introduce a Fourier transform and a conditional position coding mechanism into the spectral domain residual perception neural network and train the spectral domain residual perception neural network; map spatial coordinates into different scale domains through multi-scale projection, so that spatial coordinates of a near-wall region and a far-field region are projected into different frequency bands; and finally perform airfoil flow field prediction by using the trained spectral domain residual perception neural network.

9. A computer-readable storage medium having stored thereon a program, characterized in that, The program is executed by the processor to implement the steps in the airfoil flow field prediction method based on the spectral domain residual perception neural network according to any one of claims 1-7.

10. An electronic device comprising a memory, a processor, and a program stored in the memory and capable of running on the processor, characterized by The processor executes the program to implement the steps in the airfoil flow field prediction method based on the spectral domain residual perception neural network according to any one of claims 1-7.

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