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

Abstract

The application provides an airfoil flow field prediction method and system based on a spectral domain residual perception neural network, and belongs to the technical field of aircraft design; the method comprises the following steps: constructing an airfoil geometry database containing coordinate information of multiple standard airfoils; constructing an airfoil flow field database; based on a finite volume method Fluent solver, simulating a steady compressible flow field under a high Reynolds number condition to generate airfoil flow field data; extracting airfoil geometry features by using a self-encoder model with a residual connection mechanism; constructing a spectral domain residual perception neural network and introducing a Fourier transform and a conditional position coding mechanism; and predicting the airfoil flow field by using the trained spectral domain residual perception neural network. Through a segmented modeling framework, the application decouples the geometry feature extraction and flow field prediction processes, can realize efficient modeling under different types of grids and data distributions, and realizes accurate prediction of the airfoil flow field.

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 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 experiment and numerical simulation. Although the wind tunnel experiment 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 appeared. 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, which significantly reduces 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:

[0005] (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.

[0006] (2) Current researches mainly focus on low Reynolds number (laminar flow) flow field, and have poor adaptability to high Reynolds number conditions, with significantly decreased prediction accuracy, and some models may even fail, which cannot meet the actual engineering needs.

[0007] (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

[0008] 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 wing profile flow field.

[0009] In order to achieve the above object, one or more embodiments of the present application provide the following technical solutions:

[0010] The present application provides a wing profile flow field prediction method based on a spectral domain residual perception neural network in the first aspect.

[0011] The wing profile flow field prediction method based on a spectral domain residual perception neural network comprises:

[0012] A wing profile geometry database containing coordinate information of multiple standard wing profiles is constructed, and the contours of each standard wing profile are pixelated to generate corresponding black and white binary images;

[0013] 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 multiple geometric and incoming flow conditions;

[0014] An autoencoder model with residual connection mechanism is used to extract wing profile geometric features: the autoencoder model is used to compress the black and white binary image into a low-dimensional geometric feature vector through the encoding module of the autoencoder model; the decoding module of the autoencoder model is used to reconstruct the wing profile and verify the extraction effect;

[0015] 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; through multi-scale projection, the spatial coordinates are mapped to different scale domains, 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 to predict the wing profile flow field.

[0016] Further, the control equation set of the Fluent solver is based on the Reynolds averaged RANS equation system, which specifically includes the continuity equation, momentum equation and energy equation.

[0017] 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.

[0018] Further, the balance between the transition of the boundary layer flow and the simulation accuracy of the high Reynolds number turbulent flow region is achieved by using a Transition SST model, and the steady equation set in the Transition SST model includes a turbulent kinetic energy equation, a specific dissipation rate equation, an intermittency factor equation and a momentum thickness Reynolds number equation.

[0019] Further, the auto-encoder model uses a ReLU activation function and takes the mean square error as a loss function.

[0020] Further, the spectral domain residual perception neural network takes the geometric features extracted by the auto-encoder model, the incoming flow conditions, the grid node coordinates and the unsigned distance function as inputs, and outputs the velocity components and the pressure coefficients of the corresponding nodes; wherein the incoming flow conditions include the Mach number and the angle of attack.

[0021] Further, the amplitude and bias modulation of the Fourier transform are performed by using conditional position coding, including: first, obtaining adjustment parameters based on the incoming flow conditions, and then generating the modulated position coding by channel-by-channel modulation.

[0022] The second aspect of the present application provides a wing profile flow field prediction system based on a spectral domain residual perception neural network.

[0023] The wing profile flow field prediction system based on the spectral domain residual perception neural network comprises:

[0024] The wing profile geometry database construction module is configured to: construct a wing profile geometry database containing coordinate information of a plurality of standard wing profiles, and perform pixelization processing on the profiles of the standard wing profiles to generate corresponding black-and-white binary images;

[0025] The wing profile flow field database construction module is configured to: construct a wing profile flow field database, and perform steady compressible flow field simulation under high Reynolds number conditions based on a Fluent solver of the finite volume method to generate wing profile flow field data under a plurality of geometric and incoming flow conditions;

[0026] The wing profile geometry feature extraction module is configured to: extract wing profile geometry features by using an auto-encoder model with a residual connection mechanism; compress the black-and-white binary images into low-dimensional geometry feature vectors by using the encoding module of the auto-encoder model; and reconstruct the wing profile and verify the extraction effect by using the decoding module of the auto-encoder model.

[0027] The wing profile 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 by 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 perform wing profile flow field prediction by using the trained spectral domain residual perception neural network.

[0028] The third aspect of the present application provides a computer readable storage medium, which stores a program, and 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.

[0029] The fourth aspect of the present application provides an electronic device, which comprises a memory, a processor and a program stored in the memory and executable on the processor, and the processor executes the program 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.

[0030] The above one or more technical solutions have the following beneficial effects:

[0031] (1) The present application first extracts airfoil geometric features by 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, which decouples the airfoil geometric feature extraction and the flow field prediction process. First, the autoencoder is used to extract low-dimensional and dense geometric feature vectors from the airfoil binary image, which realizes efficient compression and representation of the original geometric data. Then, the spectral domain residual perception neural network uses the feature vectors, combined with a small amount of input such as flow conditions and spatial coordinates, to directly predict the point-to-point flow field physical quantity. 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 the computational cost and time cost of model construction.

[0032] (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 near-wall region and leading edge shock, and low-frequency flow characteristics in far-field region; the conditional position encoding enables the model to adaptively modulate frequency feature responses based on 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.

[0033] (3) The spectral domain residual perception neural network directly takes the flow field grid node coordinates and corresponding geometric features, inflow conditions and the like as inputs, and outputs the flow field physical quantity of the node, thereby being naturally applicable to non-uniform data distribution such as a non-structured grid. The method avoids information distortion that may be introduced by a pretreatment process such as flow field projection, and can accurately retain flow details in key areas such as a near-wall area. At the same time, since the model learns a continuous function mapping in a physical space, the prediction result is more physically consistent, effectively avoids the problem of generating non-physical numerical solutions inside the airfoil, and ensures the physical reasonableness and reliability of the prediction result.

[0034] Advantages of the additional aspects of the present application will be partially given in the following description, partially will become apparent from the following description, or will be learned by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0035] The accompanying drawings, which form a part of the specification, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of the present application, and their

[0036] Figure 1 A structured flow chart of the airfoil flow field prediction method based on the spectral domain residual perception neural network in the embodiment one of the present application.

[0037] Figure 2 A schematic diagram of the airfoil black and white binary graph in the embodiment one of the present application; wherein, Figure 2 (a) in the figure represents the airfoil black and white binary graph of NACA0021, Figure 2 (b) in the figure represents the airfoil black and white binary graph of A18, Figure 2 (c) in the figure represents the airfoil black and white binary graph of 2032C.

[0038] Figure 3 A structure diagram of the auto-encoder model in the embodiment one of the present application.

[0039] Figure 4 A structure diagram of the spectral domain residual perception neural network in the embodiment one of the present application.

[0040] Figure 5 A comparison schematic diagram of the distribution characteristics of the x-direction velocity of the airfoil flow field under a specific working condition in the embodiment one of the present application; wherein, Figure 5 (a) in the figure represents the distribution characteristics of the x-direction velocity of the airfoil flow field by CFD, Figure 5 (b) in the figure represents the distribution characteristics of the x-direction velocity of the airfoil flow field by the spectral domain residual perception neural network, Figure 5 (c) in the figure represents the absolute error distribution of the x-direction velocity of the airfoil flow field by CFD and the spectral domain residual perception neural network.

[0041] Figure 6 FIG. 1 is a schematic diagram of the distribution characteristics of the y-direction velocity of the airfoil flow field under a specific working condition in the embodiment of the present application; wherein, Figure 6 (a) in FIG. 1 represents the distribution characteristics of the y-direction velocity of the airfoil flow field by CFD, Figure 6 (b) in FIG. 1 represents the distribution characteristics of the y-direction velocity of the airfoil flow field by the spectral-domain residual-aware neural network, Figure 6 (c) in FIG. 1 represents the absolute error distribution of the y-direction velocity of the airfoil flow field by CFD and the spectral-domain residual-aware neural network.

[0042] Figure 7 FIG. 2 is a schematic diagram of the distribution characteristics of the pressure coefficient of the airfoil flow field under a specific working condition in the embodiment of the present application; wherein, Figure 7 (a) in FIG. 2 represents the distribution characteristics of the pressure coefficient of the airfoil flow field by CFD, Figure 7 (b) in FIG. 2 represents the distribution characteristics of the pressure coefficient of the airfoil flow field by the spectral-domain residual-aware neural network, Figure 7 (c) in FIG. 2 represents the absolute error distribution of the pressure coefficient of the airfoil flow field by CFD and the spectral-domain residual-aware neural network. DETAILED DESCRIPTION

[0043] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, 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 application belongs.

[0044] It should be noted that the terms used herein are only intended to describe specific embodiments and are not intended to limit exemplary embodiments according to the present application.

[0045] In the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0046] Embodiment I

[0047] The present embodiment discloses an airfoil flow field prediction method based on a spectral-domain residual-aware neural network.

[0048] The airfoil flow field prediction method based on the spectral-domain residual-aware neural network comprises:

[0049] Step S1, constructing an airfoil geometry database containing coordinate information of a plurality of standard airfoils, and performing pixelization processing on the profile of each standard airfoil to generate a corresponding black-and-white binary image;

[0050] Step S2, constructing an airfoil flow field database, based on the Fluent solver of the finite volume method, simulating steady compressible flow fields under high Reynolds number conditions to generate airfoil flow field data under a plurality of geometric and incoming flow conditions;

[0051] Step S3, extracting airfoil geometric features by using an autoencoder model with a residual connection mechanism: compressing the black and white binary graph into a low-dimensional geometric feature vector through the encoding module of the autoencoder model; reconstructing the airfoil profile through the decoding module of the autoencoder model and verifying the extraction effect;

[0052] Step S4, constructing a spectral domain residual perception neural network, introducing Fourier transform and conditional position encoding mechanism in the spectral domain residual perception neural network and training; mapping 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; finally, using the trained spectral domain residual perception neural network to predict the airfoil flow field.

[0053] Based on the above process, the present application 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 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 its calculation speed is nearly 1000 times higher than that of existing CFD solvers. 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.

[0054] 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 agent 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 agent model together with the incoming flow condition to realize fast prediction of the target two-dimensional flow field; the overall process reflects the use of CFD high-fidelity data to drive the deep learning model, which greatly improves the flow field prediction efficiency while maintaining accuracy.

[0055] In step S1, a geometric database of airfoils containing coordinate information of multiple standard airfoils is constructed, and the profiles of each standard airfoil are pixelated to generate corresponding black and white binary graphs.

[0056] A large number of standard airfoil data are selected from the published kinetic database, and an airfoil coordinate database is constructed accordingly. On this basis, the geometric profile of each airfoil is pixelated. Specifically, a uniform pixel grid with a size of 216x216 is generated in a smaller circumscribed rectangular region that can completely contain the airfoil profile; then, it is determined whether each pixel center point is located on the airfoil profile or its adjacent region according to the airfoil geometric shape. If the pixel center point falls within the airfoil profile 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, a black and white binary graph for training and performance verification can be obtained. Figure 2 Three typical airfoils in the airfoil database are shown, wherein, Figure 2 (a) in (a) represents the airfoil black and white binary graph of NACA0021, Figure 2 (b) in (b) represents the airfoil black and white binary graph of A18, Figure 2 (c) in (c) represents the airfoil black and white binary graph of 2032C. The 216x216 binary result formed under the above method, wherein the white pixels correspond to the airfoil profile area, and the black pixels correspond to the background area. Such binary graph can accurately reflect the geometric characteristics of different airfoils in terms of leading edge shape, thickness distribution, camber change and trailing edge shape, etc., providing a reliable data basis for subsequent geometric feature extraction of the auto-encoder model.

[0057] In step S2, an airfoil flow field database is constructed, and based on the Fluent solver of the finite volume method, steady compressible flow field simulation is carried out under high Reynolds number conditions to generate airfoil flow field data under various geometric and incoming flow conditions.

[0058] 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.:

[0059] ;

[0060] ;

[0061] ;

[0062] wherein, represents the average density; and represent the mass-weighted average velocity components, and the subscript , can be 1, 2 or 3, respectively representing x axis, yAxis and z Axis direction; And Indicates the spatial coordinate component; Indicates the average static pressure; And Indicates the velocity fluctuation component; Indicates the density-weighted velocity fluctuation correlation term; Indicates the total energy per unit mass; Indicates the effective thermal conductivity; Indicates the mass-weighted average value of temperature. Indicates the effective stress tensor, defined as follows:

[0063] ;

[0064] Wherein, Indicates the molecular dynamic viscosity of air; Indicates the turbulent eddy viscosity; Indicates the mass-weighted average velocity component, subscript Can be 1, 2, 3, respectively indicating x Axis, y Axis and z Axis direction; Indicates the Kronecker symbol, when 1, otherwise 0.

[0065] Total energy per unit mass , defined as:

[0066] ;

[0067] Wherein, Indicates the specific internal energy. Effective thermal conductivity , defined as:

[0068] ;

[0069] Wherein, Indicates the molecular thermal conductivity; Indicates the turbulent thermal conductivity; Indicates the specific heat capacity at constant pressure, Indicates the effective Prandtl number.

[0070] To achieve the thermodynamic closure relationship 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:

[0071] ;

[0072] Wherein, RR represents the gas constant, and 287.0 J / (kg·K) is taken for air. The molecular dynamic viscosity of air is described by Sutherland law, and its mathematical definition is as follows:

[0073]

[0074] wherein, represents the reference viscosity; represents the reference temperature; represents the Sutherland constant. The Reynolds stress term in the RANS equation should be closed by the turbulent viscosity hypothesis:

[0075]

[0076] wherein, represents the turbulent kinetic energy; S ij represents the average strain rate tensor, and can be specifically defined as:

[0077]

[0078] In order to simultaneously consider the simulation accuracy of the transition of the boundary layer flow and the high Reynolds number turbulent flow region, the application selects the Transition SST model based on the improved SST. k - ω The model introduces a transition-related additional control variable on the basis of the traditional SST turbulent model, so that it can simultaneously describe the transition process from laminar flow to turbulent flow and the flow characteristics in the mature turbulent flow region. The control equation of the turbulent kinetic energy k - ω is used to represent the kinetic energy of the turbulent fluctuation and reflect the evolution process of the turbulent intensity; the control equation of the specific dissipation rate k is used to describe the rate of dissipation of turbulent kinetic energy to small scales, so as to determine the turbulent viscosity and energy dissipation characteristics. The combination of the two can be used to calculate the effective eddy viscosity, so as to realize the accurate prediction of the turbulent shear stress. The steady control equation set of the model includes the turbulent kinetic energy equation, the specific dissipation rate equation, the intermittency factor equation and the momentum thickness Reynolds number equation, and its specific form is as follows: ω

[0079]

[0080]

[0081]

[0082]

[0083] wherein, represents the density;​​​​​​​​k is the turbulent kinetic energy; is the specific dissipation rate; and is an SST model empirical constant; , and are diffusion coefficient constants for the cross-diffusion terms of the k , equations and ; F 1 is an SST blending function to adjust the weight of near-wall and free-stream regions; is an intermittency factor, with "0" representing laminar flow and "1" representing fully turbulent flow; and are the production and dissipation terms of the k equation, respectively; and are the source and dissipation terms of the equation, respectively; represents the transition momentum thickness Reynolds number; represents the source term of the equation; and are the diffusion coefficient constants of the and equations, respectively.

[0084] In step S3, a self-encoder 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 self-encoder model; the airfoil profile is reconstructed and the extraction effect is verified through the decoding module of the self-encoder model.

[0085] The present application designs a self-encoder model with a residual connection mechanism for extracting airfoil geometric features. As shown in Figure 3 , 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 by the self-encoder.

[0086] The self-encoder constructed in the present application uses a ReLU activation function, and the loss function is the mean square error, which is specifically defined as follows:

[0087] ;

[0088] wherein, Ndenotes the number of samples in a training batch, subscript , , respectively denote the values of pixels in the height and width directions; denotes the pixel value, superscript , respectively denote the true value and the predicted value.

[0089] In step S4, a spectral domain residual perception neural network is constructed, a Fourier transform and a conditional position coding mechanism are introduced in the spectral domain residual perception neural network, and the spectral domain residual perception neural network is trained.

[0090] The spectral domain residual perception neural network is designed for airfoil flow field proxy modeling, and the model architecture is shown in Figure 4 . Specifically, the network input includes the incoming Mach number Ma , the angle of attack AOA, the spatial coordinates x , y , the geometric code G , and the wall distance d . First, the spatial coordinates x , y are subjected to a Fourier transform module for frequency domain feature mapping to enhance the network's ability to perceive high-frequency changes in the flow field. At the same time, the geometric code G and the incoming flow parameters L (such as Ma , AOA, d ) are sent to the conditional coding module to generate conditional modulation information that matches the deep residual blocks of the network. The above-mentioned Fourier-transformed features and conditional coding outputs are jointly fed into the feature concatenation layer of the main network, and are fed into multiple serially arranged residual blocks to realize step-by-step feature extraction and cross-layer information transmission through the residual structure. Finally, the network outputs the velocity components U , V of the airfoil flow field and the pressure coefficient C p . Through the synergistic effect of Fourier mapping and conditional coding, the spectral domain residual perception network of the present application effectively improves the learning ability and generalization performance of the proxy model. The network can be formally represented as the following function:

[0091] ;

[0092] 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, the random projection matrix is represented as:

[0093] ;

[0094] where, denotes the number of random basis vectors at the th scale, subscript denotes the row index of the projection matrix (represents a certain random frequency), subscript denotes the column index of the random matrix (consistent with the coordinate dimension), denotes the th scale corresponding variance (control frequency range). Then, the coordinates are projected into the frequency space using the projection matrix and the corresponding sine and cosine features are constructed:

[0095] ;

[0096] where, denotes the th random basis vector at the th scale; denotes the transpose. For each projection result the sine and cosine are calculated, resulting in two features at each frequency:

[0097] ;

[0098] Finally, all the features at all frequencies and all scales are concatenated to obtain the final representation:

[0099] ;

[0100] The present application maps the spatial coordinates into different scale domains, so that the coordinates of the near-wall region and the far-field region are projected into different frequency bands, respectively. Through such multi-scale Fourier expansion, the model can better represent the flow with high frequency or local steep characteristics, such as the front edge rapid transition, the tail edge backflow, and the boundary layer thin layer structure.

[0101] To make the model adaptive to the incoming flow conditions, the conditional positional encoding is used to amplitude / bias modulate the above Fourier transform. First, the adjustment parameters are obtained based on the incoming flow conditions L = [ Ma , AOA]:

[0102] ;

[0103] The adjustment parameters are obtained through a two-layer feedforward neural network. Among them, W 1 and W 2 are the weight matrices of the two layers, respectively; b 1 and b2denote the corresponding bias vectors. These parameters are continuously updated during the training process. It is noted that, F = 2 K r , i.e. each Fourier encoding corresponds to two tuning parameters γ and β . Subsequently, the is modulated channel by channel, resulting in the modulated position encoding of the l layer:

[0104] ;

[0105] The conditional position encoding enables the model to adaptively amplify or suppress the corresponding spatial frequency band by channel under different flow conditions Ma and AoA, so as to cover multiple flow patterns in the same network and avoid relying on "flow condition specific network", further improving the generalization ability of the model to incoming flow conditions.

[0106] To further illustrate the significant progress of the present application, this embodiment carries out training and testing within a limited range of incoming flow parameters, while aiming at high Reynolds number flow of multiple airfoils. The training and verification of the spectral domain residual-aware neural network considers seven airfoils, namely NACA0006, NACA1410, NACA2410, NACA4421, NACA6412, RAE5213 and S4083. Ma The range of is set to 0.2 to 0.6 (interval 0.1), and the range of AOA is (interval ). This parameter setting not only covers the typical Mach number range of subsonic flow, but also includes the common angle of attack range in engineering applications. Among them, for NACA0006, NACA1410 and RAE5213 airfoils, Ma and AOA take even values in their ranges respectively, and each airfoil contains 15 working conditions, a total of 45 working conditions; the remaining four kinds of airfoils take odd values in the range, and each airfoil contains 12 working conditions, a total of 48 working conditions. Therefore, the training and test working conditions are 93 in total, of which 80% are used for training, 10% are used for cross-validation during the training process, and the remaining 10% are used for generalization test after the training is completed.

[0107] 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. The selected test working condition is the test working condition of the NACA4421 airfoil under Ma=0.5, AOA= . Among them, Figure 5 (a) in (a) represents the distribution characteristics of the x-direction velocity of the CFD in the airfoil flow field,Figure 5 In the diagram, (b) represents the velocity in the x-direction of the spectral domain residual sensing neural network in the airfoil flow field. The distribution characteristics of ) Figure 5 In the figure, (c) represents the velocity in the x-direction of the CFD and the spectral domain residual sensing neural network in the airfoil flow field. The absolute error distribution of ).

[0108] like Figure 6 The diagram shows a comparison of the y-direction velocity distribution characteristics of the airfoil flow field under specific operating conditions. The selected test conditions are for the NACA4421 airfoil at Ma=0.5 and AOA= Testing conditions under various environmental conditions. Among them, Figure 6 In the figure, (a) represents the velocity in the y-direction of the CFD in the airfoil flow field. The distribution characteristics of ) Figure 6 In the diagram, (b) represents the velocity in the y-direction of the spectral domain residual sensing neural network in the airfoil flow field. The distribution characteristics of ) Figure 6 In the figure, (c) represents the velocity in the y-direction of the CFD and the spectral domain residual sensing neural network in the airfoil flow field. The absolute error distribution of ).

[0109] like Figure 7 The diagram shows a comparison of the pressure coefficient distribution characteristics of the airfoil flow field under specific operating conditions in Embodiment 1 of the present invention. The selected test conditions are for the NACA4421 airfoil at Ma=0.5 and AOA= Testing conditions under various environmental conditions. Among them, Figure 7 In the figure, (a) represents the pressure coefficient of CFD in the airfoil flow field. The distribution characteristics of ) Figure 7 In the figure, (b) represents the pressure coefficient of the spectral domain residual sensing neural network in the airfoil flow field. The distribution characteristics of ) Figure 7 In the figure, (c) represents the pressure coefficient in the airfoil flow field obtained by CFD and spectral domain residual sensing neural network. The absolute error distribution of ).

[0110] Figure 5 , Figure 6 , Figure 7 All data are presented in the form of two-dimensional cloud maps. The horizontal and vertical coordinates of the two-dimensional cloud maps correspond to the x and y coordinates of discrete points in the airfoil flow field, respectively. The discrete flow field values ​​at each point in the two-dimensional cloud maps can be determined by the color gradient on the right side of the corresponding image. Furthermore, this invention... Figure 5 , Figure 6 , Figure 7 The x and y coordinates in the figure are both dimensionless, that is, they are normalized to the range [-1, 1] by comparing them with the maximum absolute value.

[0111] according to Figure 5 It can be seen that the model of this invention 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 morphology is highly consistent with the CFD results, and the error is mainly located in the far-field region with a small amplitude. According to Figure 6 It can be seen that the predicted field can effectively capture the velocity gradient change characteristics on both the upper and lower surfaces of the airfoil, and the overall distribution trend is in good consistency with CFD; the error only increases slightly in local flow inflection points and small-scale shear regions, but the overall magnitude is low. According to Figure 7 It can be seen that the model of the present invention not only accurately reproduces the changes in pressure gradient between the leading edge low-pressure zone and the upper surface, but also correctly captures the trend of pressure recovery at the trailing edge; the error is mainly concentrated in the high gradient region where the pressure change is more dramatic, and its overall deviation remains within a small range.

[0112] comprehensive Figures 5-7 The results show that the modeling framework proposed in this invention still exhibits stable and reliable prediction capabilities under geometric shapes and incoming flow parameter combinations not seen in the training set, fully verifying the generalization performance of the network structure. Furthermore, in predicting operating conditions for single airfoils, the model of this invention can complete the reconstruction of the velocity and pressure fields in milliseconds, improving computational efficiency by approximately three orders of magnitude compared to traditional CFD solutions, greatly meeting the timeliness requirements for rapid aerodynamic performance evaluation in engineering.

[0113] Example 2

[0114] This embodiment discloses an airfoil flow field prediction system based on a spectral domain residual sensing neural network.

[0115] An airfoil flow field prediction system based on spectral domain residual sensing neural networks includes:

[0116] The airfoil geometry database construction module is configured to: 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;

[0117] The airfoil flow field database construction module is configured to: construct an airfoil flow field database, perform steady compressible flow field simulation under high Reynolds number conditions using the Fluent solver based on the finite volume method, and generate airfoil flow field data under various geometric and incoming flow conditions;

[0118] The airfoil geometric feature extraction module is configured to: extract airfoil geometric features using an autoencoder model with a 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; and reconstruct the airfoil profile and verify the extraction effect through the decoding module of the autoencoder model.

[0119] 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.

[0120] Embodiment three

[0121] An object of this embodiment is to provide a computer-readable storage medium.

[0122] A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the airfoil flow field prediction method based on a spectral domain residual perception neural network according to Embodiment One of the present disclosure.

[0123] Embodiment four

[0124] An object of this embodiment is to provide an electronic device.

[0125] An electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, wherein the processor implements the steps of the airfoil flow field prediction method based on a spectral domain residual perception neural network according to Embodiment One of the present disclosure when executing the program.

[0126] The steps and methods involved in the above embodiments two, three and four correspond to Embodiment One, and the specific implementation can be seen from the relevant description of Embodiment One. The term "computer-readable storage medium" should be understood to include a single medium or multiple media of one or more instruction sets; it should also be understood to include any medium capable of storing, encoding or carrying instruction sets for execution by a processor and causing the processor to perform any of the methods in the present disclosure.

[0127] Those skilled in the art should understand that each module or step of the present disclosure described above can be implemented by a general computer device, and alternatively, they can be implemented by program code executable by a computing device, so that they can be stored in a storage device for execution by a computing device, or they can be made into individual integrated circuit modules, or a plurality of modules or steps among them can be made into a single integrated circuit module. The present disclosure is not limited to any specific combination of hardware and software.

[0128] The above describes the specific embodiments of the present disclosure in conjunction with the accompanying drawings, but is not a limitation on the scope of protection of the present disclosure. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present disclosure without inventive labor are still within the scope of protection of the present disclosure.

Claims

1. A method for predicting the flow field of an airfoil based on a spectral domain residual sensing neural network, characterized in that, include: A geometric database containing coordinate information of multiple standard airfoils is constructed, and the outline of each standard airfoil is pixelated to generate the corresponding black and white binary image. An airfoil flow field database was constructed, and steady compressible flow field simulations were carried out under high Reynolds number conditions using the Fluent solver based on the finite volume method, generating airfoil flow field data under various geometric and incoming flow conditions. An autoencoder model with residual connection mechanism is used to extract airfoil geometric features: the encoding module of the autoencoder model compresses the black-and-white binary image into a low-dimensional geometric feature vector; the decoding module of the autoencoder model reconstructs the airfoil profile and verifies the extraction effect. A spectral domain residual sensing neural network is constructed, and Fourier transform and conditional position encoding mechanisms are introduced and trained within the network. 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 respectively. Finally, the trained spectral domain residual sensing neural network is used to predict the airfoil flow field. The spectral domain residual sensing 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. The incoming flow conditions include Mach number and angle of attack.

2. The airfoil flow field prediction method based on spectral domain residual sensing neural network as described in claim 1, characterized in that, The governing equations of the Fluent solver are based on the Reynolds-averaged RANS equations, specifically including the continuity equation, momentum equation, and energy equation.

3. The airfoil flow field prediction method based on spectral domain residual sensing neural network as described in claim 2, characterized in that, An ideal gas law is used to represent the relationship between pressure, density, and temperature, so as to realize the thermodynamic closure relationship of the Reynolds-averaged RANS equation system.

4. The airfoil flow field prediction method based on spectral domain residual sensing neural network as described in claim 1, characterized in that, The Transition SST model is used to achieve a balance between the transition of boundary layer flow and the simulation accuracy of the high Reynolds number turbulent region. The steady equations in the Transition SST model include the turbulent kinetic energy equation, the specific dissipation rate equation, the intermittent factor equation, and the momentum-thickness Reynolds number equation.

5. The airfoil flow field prediction method based on spectral domain residual sensing neural network as described in claim 1, characterized in that, The autoencoder model uses the ReLU activation function and the mean squared error as the loss function.

6. The airfoil flow field prediction method based on spectral domain residual sensing neural network as described in claim 1, characterized in that, The Fourier transform is modulated by conditional position coding, including: first, obtaining the adjustment parameters based on the incoming flow conditions, and then generating the modulated position code by channel-by-channel modulation.

7. An airfoil flow field prediction system based on a spectral domain residual sensing neural network, characterized in that, include: The airfoil geometry database construction module is configured to: 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; The airfoil flow field database construction module is configured to: construct an airfoil flow field database, perform steady compressible flow field simulation under high Reynolds number conditions using the Fluent solver based on the finite volume method, and generate airfoil flow field data under various geometric and incoming flow conditions; The airfoil geometric feature extraction module is configured to: extract airfoil geometric features using an autoencoder model with a 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; and reconstruct the airfoil profile and verify the extraction effect through the decoding module of the autoencoder model. The airfoil flow field prediction module is configured to: construct a spectral domain residual sensing neural network, introduce Fourier transform and conditional position encoding mechanisms 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; the spectral domain residual sensing 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 Mach number and angle of attack.

8. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the airfoil flow field prediction method based on spectral domain residual sensing neural network as described in any one of claims 1-6.

9. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the airfoil flow field prediction method based on spectral domain residual sensing neural network as described in any one of claims 1-6.

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