CN116522769A - Pressure coefficient prediction method based on VAE-GAN and self-attention mechanism - Google Patents
Pressure coefficient prediction method based on VAE-GAN and self-attention mechanism Download PDFInfo
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Abstract
The invention relates to a pressure coefficient prediction method based on a VAE-GAN and a self-attention mechanism, which comprises the following steps: inputting the two-dimensional coordinates of the wing profile into a pressure prediction model, and outputting a corresponding prediction pressure coefficient curve; the pressure prediction model is constructed based on a VAE-GAN network; during training, the encoder of the VAE extracts airfoil geometric features, airfoil manifold features and airfoil environmental features based on airfoil two-dimensional coordinates, analyzes the mutual influence among the features, and then fuses the features to generate airfoil fusion features; the decoder of the VAE generates a corresponding predicted pressure coefficient curve and a corresponding false pressure coefficient curve based on the wing section fusion characteristic and the random noise respectively; the discriminator of the GAN calculates the corresponding loss function and updates the network parameters of the pressure prediction model until the model converges. The invention can extract a plurality of dimensional characteristics such as airfoil geometric characteristics, manifold characteristics, environmental characteristics and the like, and can analyze the interaction and correlation among different characteristics so as to better integrate the correlations among different characteristics.
Description
Technical Field
The invention relates to the technical field of aerodynamics, in particular to a pressure coefficient prediction method based on a VAE-GAN and a self-attention mechanism.
Background
Aerofoil aerodynamics is an important issue in aircraft design because it directly affects aircraft flight performance, maneuverability, and stability, and pressure coefficients are typical aerodynamic coefficients describing the relative pressure of the wing surfaces, with accurate predictions of pressure coefficients being significant to aircraft design.
Among them, the geometry of the airfoil greatly affects the aerodynamic performance of the airfoil, and a set of airfoil geometry parameters are generally used to characterize the geometry of the airfoil, such as chord length, thickness, etc., but the airfoil geometry can only be characterized approximately whether it is a manual design parameter or a polynomial characterization parameter, which is an urgent problem to be solved. Meanwhile, most aerodynamic performance researches neglect the influence of the coupling relation between the airfoil shape and the airfoil shape on aerodynamic performance, and only simply analyze the relation between the airfoil shape and the aerodynamic performance, so that the result is inaccurate, and therefore, how to balance the influence of the airfoil shape and the airfoil shape on aerodynamic prediction results is one of the problems of our researches.
With the advent of the information age, data has been explosively growing, and many excellent data analysis methods have been developed, and deep learning is the most blazed of them. Deep learning, namely DNN, is realized by designing a multi-layer neural network, so that neurons of each layer are deepened and widened continuously, and the neurons can be mapped to any function theoretically, so that the problem of complexity is solved, and the method is very outstanding in the fields of image recognition, face recognition and the like. In the hydrodynamic and aerodynamic fields such as aerodynamics analysis and flow field prediction of an airplane, deep learning also has remarkable potential, and the deep learning is used for feature extraction, feature fusion and the like, which are commonly used methods for hydrodynamic analysis. However, how to design a method that can implement feature extraction of an airfoil and prediction of a pressure coefficient curve based on a deep learning method is a technical problem to be solved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to solve the technical problems that: how to provide a pressure coefficient prediction method based on a VAE-GAN and a self-attention mechanism, multiple dimensional characteristics such as airfoil geometric characteristics, manifold characteristics, environmental characteristics and the like can be extracted, and the mutual influence and correlation among different characteristics can be analyzed, so that the mutual relations among different characteristics are better fused, the comprehensiveness and accuracy of wing pressure coefficient prediction can be improved, and a new thought is provided for the pneumatic prediction of the wing.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for predicting a pressure coefficient based on VAE-GAN and a self-attention mechanism, comprising:
s1: acquiring two-dimensional coordinates of an airfoil to be predicted;
s2: inputting the two-dimensional coordinates of the wing profile to be predicted into a trained pressure prediction model, and outputting a corresponding predicted pressure coefficient curve;
the pressure prediction model is constructed based on a VAE-GAN network;
during training, the two-dimensional coordinate of the wing profile and the true pressure coefficient curve which are used as training samples are used as model input of a pressure prediction model: firstly, an encoder of the VAE extracts corresponding airfoil geometric features, airfoil manifold features and airfoil environment features based on airfoil two-dimensional coordinates, analyzes the mutual influence among the airfoil geometric features, the airfoil manifold features and the airfoil environment features through a self-attention module, fuses the self-attention features output by the self-attention module through a feature fusion network, and generates corresponding airfoil fusion features; then, a decoder of the VAE generates a corresponding predicted pressure coefficient curve and a corresponding false pressure coefficient curve based on the wing profile fusion characteristic and the set random noise respectively; finally, the discriminator of the GAN calculates a corresponding loss function based on the predicted pressure coefficient curve and the false pressure coefficient curve generated by combining the real pressure coefficient curve, and further updates the network parameters of the pressure prediction model based on the loss function until the model converges;
s3: and taking the predicted pressure coefficient curve output by the pressure prediction model as a corresponding pressure coefficient prediction result.
Preferably, in step S2, the two-dimensional coordinates of the airfoil are encoded by a convolutional neural network, corresponding geometric features of the airfoil are extracted, and the geometric features of the airfoil are converted into data of a preset dimension.
Preferably, in step S2, first, the two-dimensional coordinate of the airfoil is extracted through a bezier curve to obtain the corresponding airfoil manifold feature; the airfoil manifold features are then encoded by a fully connected neural network to convert the airfoil manifold features into data of a preset dimension.
Preferably, the two-dimensional coordinates of the airfoil are expressed as a plurality of polynomials by using Bezier curves, and the inner product of two vertical vectors is calculated from the tangent space of each polynomial, so that the corresponding Riemann metric is extracted;
the formula is described as follows:
wherein: g vw (t) represents a Riemann metric for the airfoil at t;representing the direction of the partial derivative; />Representing that each segment of Bezier curve is biased for the parameter t; r (D; t) represents a function of a Bezier curve; p (P) i Representing airfoil coordinates; d represents the sample space in which the airfoil coordinates are located; t represents a parameter of a bezier curve; n represents the order of the Bessel curve;
the curvature is calculated by the following formula:
wherein: c represents curvature; r represents the radius of curvature, i.e. the inverse of the curvature; y' represents the first derivative of the airfoil ordinate y; y "represents the second derivative of the airfoil ordinate y.
Preferably, in step S2, the airfoil environmental characteristics include mach number, airfoil angle of attack, and reynolds number; and encoding the airfoil environmental characteristics through the fully connected neural network to convert the airfoil environmental characteristics into data with preset dimensions.
Preferably, in step S2, the working logic of the self-attention module is as follows:
s201: taking the characteristics extracted from the geometrical characteristics, manifold characteristics and environment characteristics of the wing profile through a neural network as input vectors of the self-attention module;
s202: for each input vector a i Respectively multiplied by three coefficients w q 、w k 、w v ；
The formula is described as follows:
q i ＝w q ·a i
k i ＝w k ·a i ；
v i ＝w v ·a i
wherein: q, k, v represent query, key, and value, respectively;
s203: calculating the correlation between two input vectors through q and k, namely calculating the value alpha of the Attention, wherein a matrix formed by all alpha is expressed as a correlation matrix A;
the formula is described as follows:
α i,j ＝q i ·k j ；
s204: performing softmax operation or relu operation on the correlation matrix A to obtain a corresponding relation matrix A';
s205: each input vector a is calculated by a relation matrix A i Output vector b of self-layer of (c) i Self-attention features as corresponding input vectors, i.e. corresponding features;
the formula is described as follows:
wherein: b i Representing input vector a i The self-attention feature of all input vectors interacting with each other is taken into account; v i ＝w v ·a i Representing the product of the input vector and the weight matrix; alpha' i,j Representing elements in the relationship matrix a'.
Preferably, in step S2, the encoder and decoder of the VAE are expressed by the following formula:
z～Enc(x)＝q(z|x),
wherein: enc (x) denotes an encoder, x being its input; z represents the output of the encoder; q (z|x) represents the distribution of the encoder output; dec (z) denotes a decoder, z being an input thereof;representing the output of the decoder; />Representing the distribution of the decoder output.
Preferably, in step S2, the loss function of the VAE is expressed by the following formula:
L VAE ＝L recon +L prior ；
L prior ＝D KL (q(z|x)||p(z))；
wherein: l (L) VAE Indicating a loss of VAE; l (L) recon Representing a predicted pressure coefficient curveDifferences from the true pressure coefficient curve; l (L) prior Represents KL divergence; d (D) KL (q (z|x) ||p (z)) represents KL divergence, used to calculate the gap between the q (z|x) and p (z) distributions; q (z|x) represents the distribution of the encoder output; p (z) specifies that the hidden variable z belongs to a gaussian distribution.
Preferably, in step S2, the loss function of GAN is expressed by the following formula:
wherein:indicating a loss of GAN; d (x) represents a discriminator that inputs the real data x to the GAN;representing random noise to be passed through the decoder +.>A discriminator input to the GAN; />Representing the discriminator that inputs the hidden variable z through the decoder to the GAN.
Preferably, in step S2, the model loss function of the pressure prediction model is expressed by the following formula:
L＝λ 0 L layer +λ 1 L GAN +λ 2 L recon +λ 3 L prior ；
wherein: l represents model loss of the pressure prediction model; l (L) recon Representing a predicted pressure coefficient curveDifferences from the true pressure coefficient curve; l (L) prior Represents KL divergence; l (L) GAN Indicating a loss of GAN; l (L) layer Representing boundary loss; d (D) l (x) Andrespectively representing the outputs of a certain layer of neural network and the neural network in the discriminator; lambda (lambda) 0 、λ 1 、λ 2 、λ 3 And a weight parameter representing the overall prediction result of each loss function.
Compared with the prior art, the pressure coefficient prediction method based on the VAE-GAN and the self-attention mechanism has the following beneficial effects:
the pressure prediction model extracts airfoil geometric features, airfoil manifold features and airfoil environment features, analyzes the mutual influence relationship among the airfoil geometric features, manifold features and environment features through the self-attention module, and then generates airfoil fusion features through feature fusion network fusion. On one hand, the method can extract the geometrical characteristics, manifold characteristics, environmental characteristics and other dimensional characteristics of the wing profile to be fused to generate the wing profile fusion characteristics, and can more comprehensively excavate the hidden characteristics of the wing profile, so that the comprehensiveness of the wing pressure coefficient prediction can be improved; on the other hand, the invention combines the self-attention mechanism and the feature fusion network, so that the pressure prediction model can analyze the mutual influence and correlation between different features and better fuse the mutual relation between different features, thereby improving the accuracy of wing pressure coefficient prediction, accelerating the convergence speed of model training through the self-attention mechanism and reducing the calculated amount.
According to the invention, the pressure prediction model is constructed based on the VAE-GAN network, so that the deep learning model VAE-GAN can be effectively combined with hydrodynamics and aerodynamics, and further, the hidden characteristics of the wing profile can be better excavated, so that the accurate prediction of the wing profile pressure coefficient curve can be realized; in addition, the problem of poor sample generation capability of the VAE can be solved by introducing a GAN discriminator, so that the convergence speed of the pressure prediction model and the quality of generated data can be improved.
According to the invention, when the pressure prediction model is trained, the loss function is calculated through the combination of the real pressure coefficient curve and the generated predicted pressure coefficient curve and the false pressure coefficient curve, so that the influences of the real sample, the reconstructed sample and the false sample can be considered in the training process, and the training effect and performance of the pressure prediction model can be further improved.
Drawings
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings, in which:
FIG. 1 is a frame diagram of a pressure coefficient prediction method and a pressure prediction model;
FIG. 2 is a logic block diagram of a pressure coefficient prediction method and a pressure prediction model;
FIG. 3 is a two-dimensional view of an airfoil reconstructed after extraction of airfoil manifold features;
FIG. 4 is a logical block diagram of a self-attention module and feature fusion network;
figure 5 is a schematic diagram of the architecture of a VAE-GAN network.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures. In the description of the present invention, it should be noted that, directions or positional relationships indicated by terms such as "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., are directions or positional relationships based on those shown in the drawings, or are directions or positional relationships conventionally put in use of the inventive product, are merely for convenience of describing the present invention and simplifying the description, and are not indicative or implying that the apparatus or element to be referred to must have a specific direction, be constructed and operated in a specific direction, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," "third," and the like are used merely to distinguish between descriptions and should not be construed as indicating or implying relative importance. Furthermore, the terms "horizontal," "vertical," and the like do not denote a requirement that the component be absolutely horizontal or overhang, but rather may be slightly inclined. For example, "horizontal" merely means that its direction is more horizontal than "vertical" and does not mean that the structure must be perfectly horizontal, but may be slightly tilted. In the description of the present invention, it should also be noted that, unless explicitly specified and limited otherwise, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
The following is a further detailed description of the embodiments:
examples:
in order to better introduce the technical solution of the present patent application, the following concepts are introduced:
1) Riemann metric: a Riemann metric g on M refers to the slaveIs a symmetrical positive cross-section. Equivalently, given the Riemann metric g, this is equivalent to the tangent space T at each point p p M designates an inner product g p The differential manifold that specifies the Riemann metric is called the Riemann manifold.
2) Curvature: the curvature of a curve is defined by differentiation for the rotation rate of the tangential angle to the arc length at a certain point on the curve, and indicates the degree to which the curve deviates from a straight line, and mathematically indicates the value of the degree to which the curve is curved at a certain point.
3) Airfoil geometry: refers to the chord length, thickness, etc. of the airfoil in Euclidean space.
4) Pressure coefficient: the pressure coefficient is a dimensionless number describing the relative pressure throughout the flow field in fluid dynamics, and applies to aerodynamic and hydrodynamic, with the pressure coefficient being different at each point in the fluid flow field.
5) VAE-GAN: VAE (variable Auto-Encoder) refers to the Encoder-decoder architecture, and this patent uses mainly the Encoder part of VAE, which is equivalent to the generator of GAN (Generative Adversarial Nets) network; GAN refers to a generator and a discriminator, wherein false data is generated by the generator, and the discriminator discriminates the false data and the true data, and plays with each other, so as to achieve the purpose of model convergence.
6) Self-attention mechanism: the self-attention mechanism mainly solves the correlation problem between different parts in the input without considering the latitude and the time, and solves the problem through key, value, query.
7) CNN: convolutional neural networks are a type of feedforward neural network that includes convolutional computation and has a deep structure, and are one of representative algorithms for deep learning. Convolutional neural networks have a characteristic learning capability and can perform translation-invariant classification on input information according to a hierarchical structure of the convolutional neural networks, so the convolutional neural networks are also called as 'translation-invariant artificial neural networks'.
The embodiment discloses a pressure coefficient prediction method based on a VAE-GAN and a self-attention mechanism.
A method of predicting pressure coefficients based on VAE-GAN and self-attention mechanisms, comprising:
s1: acquiring two-dimensional coordinates of an airfoil to be predicted;
s2: inputting the two-dimensional coordinates of the wing profile to be predicted into a trained pressure prediction model, and outputting a corresponding predicted pressure coefficient curve;
the pressure prediction model is constructed based on a VAE-GAN network; the pressure prediction model mainly comprises three parts of airfoil feature extraction, feature fusion and pressure coefficient curve prediction, which are shown in combination with fig. 1.
In combination with the illustration of fig. 2, during training, the two-dimensional coordinates of the airfoil profile and the true pressure coefficient curve used as training samples are input as a model of the pressure prediction model: firstly, an encoder of the VAE extracts corresponding airfoil geometric features, airfoil manifold features and airfoil environment features based on airfoil two-dimensional coordinates, analyzes the mutual influence among the airfoil geometric features, the airfoil manifold features and the airfoil environment features through a self-attention module, fuses the self-attention features output by the self-attention module through a feature fusion network, and generates corresponding airfoil fusion features; then, a decoder of the VAE generates a corresponding predicted pressure coefficient curve and a corresponding false pressure coefficient curve based on the wing profile fusion characteristic and the set random noise respectively; finally, the discriminator of the GAN calculates a corresponding loss function based on the predicted pressure coefficient curve and the false pressure coefficient curve generated by combining the real pressure coefficient curve, and further updates the network parameters of the pressure prediction model based on the loss function until the model converges;
s3: and taking the predicted pressure coefficient curve output by the pressure prediction model as a corresponding pressure coefficient prediction result.
The pressure prediction model extracts airfoil geometric features, airfoil manifold features and airfoil environment features, analyzes the mutual influence relationship among the airfoil geometric features, manifold features and environment features through the self-attention module, and then generates airfoil fusion features through feature fusion network fusion. On one hand, the method can extract the geometrical characteristics, manifold characteristics, environmental characteristics and other dimensional characteristics of the wing profile to be fused to generate the wing profile fusion characteristics, and can more comprehensively excavate the hidden characteristics of the wing profile, so that the comprehensiveness of the wing pressure coefficient prediction can be improved; on the other hand, the invention combines the self-attention mechanism and the feature fusion network, so that the pressure prediction model can analyze the mutual influence and correlation between different features and better fuse the mutual relation between different features, thereby improving the accuracy of wing pressure coefficient prediction, accelerating the convergence speed of model training through the self-attention mechanism and reducing the calculated amount.
According to the invention, the pressure prediction model is constructed based on the VAE-GAN network, so that the deep learning model VAE-GAN can be effectively combined with hydrodynamics and aerodynamics, and further, the hidden characteristics of the wing profile can be better excavated, so that the accurate prediction of the wing profile pressure coefficient curve can be realized; in addition, the problem of poor sample generation capability of the VAE can be solved by introducing a GAN discriminator, so that the convergence speed of the pressure prediction model and the quality of generated data can be improved.
According to the invention, when the pressure prediction model is trained, the loss function is calculated through the combination of the real pressure coefficient curve and the generated predicted pressure coefficient curve and the false pressure coefficient curve, so that the influences of the real sample, the reconstructed sample and the false sample can be considered in the training process, and the training effect and performance of the pressure prediction model can be further improved.
In the specific implementation process, the two-dimensional coordinates of the wing profile are encoded through a Convolutional Neural Network (CNN), the corresponding geometrical characteristics of the wing profile are extracted, and the geometrical characteristics of the wing profile are converted into data of preset dimensions.
In this embodiment, the airfoil geometry includes airfoil chord length, thickness, and the like.
The two-dimensional coordinates of the wing profiles are obtained from a UIUC wing profile database, after data processing, about 1000 wing profiles can be used, after each wing profile is processed by a B E zier curve, 192 two-dimensional coordinate points are taken to represent the geometric shape of each wing profile, namely the input characteristic size of CNN is 192 x 2 x 1. Wherein the CNN encoded airfoil geometry feature consists of a plurality of convolution layers, each followed by a BN layer, a Relu function, and a dropout function, the kernel size of all convolution layers being set to 4*2, the size of the last layer being 512-dimensional data, so that the airfoil geometry feature is represented using 512-dimensional data.
According to the invention, the two-dimensional coordinates of the wing profile are encoded by the CNN, so that the geometrical characteristics of the wing profile are extracted, the CNN is very prominent in aspects of image processing, characteristic extraction, dimension reduction and the like, and the extraction effect of the geometrical characteristics of the wing profile can be ensured.
In the implementation, the method is carried out by firstly passing a Bezier curve (hereinafter also referred to asCurve) to extract the two-dimensional coordinates of an airfoilMetrics and curvatures as corresponding airfoil manifold features; the airfoil manifold features are then encoded by a fully connected neural network to convert the airfoil manifold features into data of a preset dimension.
In this embodiment, the Bezier curve isA curve belongs to a mode of representing the curve in a parameter form. The Bezier curve is completely determined by its control points, n control points corresponding to the Bezier curve of order n-1, and can be plotted in a recursive manner. The generated Riemann metrics and curvatures are encoded using a fully connected neural network, the results of which are input to a self-attention module and feature fusion network. Wherein the Riemann metric, curvature, is composed of 192 dimensions of data, which each feature is extended to 512 dimensions of data by a fully connected network.
Specific:
using Bezier curve to represent airfoil two-dimensional coordinates as a plurality of polynomials, calculating the inner product of two vertical vectors from the tangent space of each polynomial, and further extracting the corresponding Riemann metric;
given a two-dimensional airfoil coordinate set d= { P i ＝(x i ,y i ) I=1, 2, …, M }, M represents the number of coordinate points, P represents a coordinate point, (x) i ,y i ) Representing the abscissa and the ordinate, D consists of 192 two-dimensional coordinates according to the actual coordinate set, by each airfoil coordinate set 3 degrees can be constructedA curve.
The formula is described as follows:
in the formula, n is 3 and is expressed as 3 degreesCurve, i.eThe section of curve is represented by 4 points, the two-dimensional airfoil consists of 192 points, i.e. 192/4=48 sections 3 degrees +.>The curvilinearity addition can obtain a corresponding polynomial;
the formula is the calculation formula of the inner product;
according to 3 degrees of constructionThe curve can be represented as a smooth curve with 4 points, then the entire two-dimensional airfoil coordinate set can be represented as multiple segments of 3 degrees +.>The curvilinear combination characterizes the entire airfoil, which can be obtained from +.>The wing profile curve is perceived through the control parameter t in the curve, and the Riemann metric at each t can be conveniently calculated, and the calculation formula is as follows:
wherein: g vw (t) represents a Riemann metric for the airfoil at t;representing the direction of the partial derivative; />Representing that each segment of Bezier curve is biased for the parameter t; r (D; t) represents a function of a Bezier curve; p (P) i Representing airfoil coordinates; d represents the sample space in which the airfoil coordinates are located; t represents BesselParameters of the Er curve; n represents the order of the Bessel curve;
since r (D; t) is a one-dimensional manifold, v=w, i.e
g vv (t)、g ww And (t) represents the Riemann measurement of the two-dimensional airfoil in different directions in the manifold space, and the two directions are consistent and equal due to the analysis of the two-dimensional airfoil.
Riemann metric g vw (t) represents the tangential space of r (D; t)The inner product of two vertical vectors of (a) and (b) constituting the inner product can be regarded as the basis of any vector in the tangent space of r (D; t). Thus, choose g vw (t) g as a geometric feature representing the tangential spatial feature of the airfoil curve vw (t) i.e. the number of Riemann metrics, is based on the number of points, each airfoil having 192 Riemann metrics.
The curvature is calculated by the following formula:
wherein: c represents curvature; r represents the radius of curvature, i.e. the inverse of the curvature; y' represents the first derivative of the airfoil ordinate y; y "represents the second derivative of the airfoil ordinate y; y' "represents the third derivative of the airfoil ordinate y where each coordinate point may take a curvature and each airfoil has 192 curvatures.
With reference to fig. 3, the airfoil combined by adding the Riemann metric and the curvature characteristic is smoother, only a small amount of airfoil errors occur, and the aerodynamic characteristics of the newly generated airfoil are better.
According to the invention, the characteristics of the airfoil profile such as Riemann measurement, curvature and the like are extracted through the Bezier curve, so that the model can better represent the geometric shape of the airfoil profile, and the accuracy of the prediction of the airfoil pressure coefficient can be improved in an auxiliary manner.
In the specific implementation process, the airfoil environmental characteristics comprise Mach numbers, airfoil attack angles and Reynolds numbers; and encoding the airfoil environmental characteristics through the fully connected neural network to convert the airfoil environmental characteristics into data with preset dimensions. The fully connected neural network is used for encoding the aerofoil environmental characteristics, the low-dimensional data is expanded into high-dimensional data, and the result is used as the input of the self-attention module and the characteristic fusion network.
In this embodiment, under real conditions, the Mach number has a value range of Ma E {0.1,0.2,0.3,0.4,0.5,0.6}, the airfoil attack angle has a value range of AOA E [ -10 °,10 ° ], and the Reynolds number has a value range of Re E {1e6,6e6,1e7}. The fully-connected network input of the coding environment features is data of three latitudes of Mach number, attack angle and Reynolds number, and the environment feature data is expanded into 512-dimensional data.
According to the invention, the environmental characteristics of the wing profile are better represented through Mach numbers, wing profile attack angles and Reynolds numbers, so that the accuracy of wing pressure coefficient prediction can be improved in an auxiliary manner.
In the implementation process, the self-attention module calculates the relation of different input features through a self-attention mechanism, and fuses the self-attention mechanism with a fully-connected network, so that the network can be enabled to notice the correlation between different parts in the whole input, the network can be enabled to converge more quickly, the calculated amount is reduced, and the model accuracy is increased.
The inputs to the self-attention module are airfoil geometry features, riemann features, curvature and environmental features, each of which is assumed to be a i Each feature is resized to maintain a 512-dimensional data size as input to the self-attention module. The working logic of the self-attention module, as shown in connection with fig. 4, is as follows:
s201: taking the characteristics extracted from the geometrical characteristics, manifold characteristics and environment characteristics of the wing profile through a neural network as input vectors of the self-attention module;
s202: for each input vector a i Respectively multiplied by three coefficients w q 、w k 、w v ；
The formula is described as follows:
q i ＝w q ·a i
k i ＝w k ·a i ；
v i ＝w v ·a i
wherein: q, k, v represent query, key, and value, respectively;
s203: calculating the correlation between two input vectors through q and k, namely calculating the value alpha of the Attention, wherein a matrix formed by all alpha is expressed as a correlation matrix A;
the formula is described as follows:
α i,j ＝q i ·k j the method comprises the steps of carrying out a first treatment on the surface of the The vector form is a=k T Q, each value in matrix a records the Attention size α of the corresponding two input vectors; k (K) T Represents k i ＝w k ·a i Is transposed of the set of (a); q represents Q i ＝w q ·a i Is a collection of (3);
s204: performing softmax operation or relu operation on the correlation matrix A to obtain a corresponding relation matrix A';
s205: through the relation matrix A ′ And V calculating each input vector a i Output vector b of self-layer of (c) i Self-attention features as corresponding input vectors, i.e. corresponding features;
the formula is described as follows:
the corresponding vector form is o=v·a';
wherein: b i Representing input vector a i The self-attention feature of all input vectors interacting with each other is taken into account; v i ＝w v ·a i Representing the product of the input vector and the weight matrix; o is conveyed by self-attention moduleOut of matrix combination, from b i Composition; v represents V i Is a collection of (3); a 'represents alpha' i,j Is a set of (3).
The purpose of the self-attention module is to introduce: the input received by the neural network is a plurality of vectors with different sizes, and different vectors have a certain relation, but the relation between the inputs cannot be fully exerted during actual training, so that the model training result is extremely poor. The problem of a fully connected neural network that does not establish a correlation for multiple correlated inputs is addressed by a self-attention mechanism, which is actually intended for the machine to notice the correlation between different parts of the entire input.
Working logic of the self-attention module: for a set of input length N vectors A, each input vector is denoted as a i After self-propagation, a set of vectors B of length N are output, each output vector being denoted B i I.e. any output vector b i All input vectors a are considered i Is obtained by the interaction of the above components.
In the implementation process, the feature fusion network is a fully-connected network.
The self-attention characteristics (namely, airfoil geometric characteristics, airfoil manifold characteristics and airfoil environment characteristics) obtained through processing of the self-attention module are taken as the input of a characteristic fusion network, and the input characteristics are compressed to a lower latitude through the fusion network and are taken as the input of a subsequent GAN network. The feature fusion network inputs 4 feature data of 512 dimensions, and outputs 256-dimension wing profile fusion features after the feature data passes through the feature fusion network, wherein the wing profile fusion features highly condense wing profile geometry, manifold and environment feature data and serve as input data of the GAN network.
According to the invention, by combining the self-attention mechanism and the feature fusion network, the pressure prediction model can analyze the mutual influence and correlation between different features and better fuse the mutual relation between different features, so that the accuracy of wing pressure coefficient prediction can be further improved, and meanwhile, the convergence speed of model training can be increased and the calculated amount can be reduced through the self-attention mechanism.
In an implementation, the predicted pressure coefficient curve is generated by a decoder of the VAE (i.e., a generator of GAN). The real data of the pressure coefficient curve of the airfoil is set as x and is used as the input of the discriminator. The input z of the generator is obtained according to a fusion network formed by a self-attention mechanism, and a newly generated pressure coefficient curve is obtained through a decoder formed by a deconvolution networkAs input to the discriminator. Setting random noise->And generates a false pressure coefficient curve, also as input to the discriminator. The encoder is constructed of deconvolution layers, and outputs as predicted pressure coefficient curve and dummy pressure coefficient curve data as shown in fig. 5.
The discriminator D discriminates the predicted pressure coefficient curve and the true pressure coefficient curve. And simultaneously inputting the real pressure coefficient curves into a discriminator together according to the predicted pressure coefficient curves and the false pressure coefficient curves, and respectively calculating the difference of the predicted pressure coefficient curves and the false pressure coefficient curves. The purpose of the discriminator is to discriminate, as far as possible, that the data generated by the generator is false.
First, the encoder and decoder of the VAE are expressed by the following formulas:
wherein: enc (x) denotes an encoder, x being its input; z represents the output of the encoder; q (z|x) represents the distribution of the encoder output; dec (z) denotes a decoder, z being an input thereof;representing the output of the decoder; />Representing the distribution of the decoder output.
The loss function of the VAE is expressed by the following formula:
L VAE ＝L recon +L prior ；
L prior ＝D KL (q(z|x)||p(z))；
wherein: l (L) VAE Indicating a loss of VAE; l (L) recon Representing a predicted pressure coefficient curveThe difference between the true pressure coefficient curves is compared with the mean square error MSE; l (L) prior Representing KL divergence for measuring the difference between the encoded representation vector and the gaussian distribution; d (D) KL (q (z|x) ||p (z)) represents KL divergence, used to calculate the gap between the q (z|x) and p (z) distributions; q (z|x) represents the distribution of the encoder output; p (z) specifies that the hidden variable z belongs to a Gaussian distribution, i.e. D KL (q (z|x) ||p (z)) also means that q (z|x) is fitting to gaussian distribution p (z).
In the implementation process, the capability of the VAE for generating samples is poor, so that a discriminator for introducing GAN accelerates model convergence and improves the quality of model generated data. Wherein the generator (i.e., encoder) attempts to generate spurious data to fool discriminator D, which continually sharpens its decision boundaries to determine a composite spurious sample from the true samples, its max-min game cross entropy loss function is as follows:
GAN generates samples purely from random noise, and it is difficult to obtain an explicit mapping from the data domain to the feature domain. Thus, we construct a pressure predictive model based on VAE-GAN. That is, as shown in fig. 2, the generator is replaced by the encoder-decoder structure of the VAE. Note that in VAE-GAN, the model generates a reconstructed sample (i.e., predicted pressure coefficient curve)Given the real sample x, a dummy sample is generated simultaneously>(i.e. a false pressure coefficient curve) which comes directly from random noise +.>Reconstructing a sampleAnd false sample->Should be classified as false by discriminator D, only x is considered as true by the discriminator, so the GAN loss function can be modified to the following equation:
wherein:indicating a loss of GAN; d (x) represents a discriminator that inputs the real data x to the GAN;representing random noise (Gaussian distribution variable) to be passed through decoder>A discriminator input to the GAN;representing a discriminator that inputs the airfoil fusion feature (hidden variable) z (z=enc (x), dec being the decoder, expressed as the airfoil fusion feature z through the decoder) through the decoder to the GAN; />Representing a false pressure coefficient curve; dec (Enc (x)) represents the reconstructed pressure coefficient curve of the true pressure coefficient curve reconstructed by the encoder and then by the decoder, and +.>The difference is that the former is the data of the true pressure coefficient curve reconstructed by the encoder and then by the decoder, the latter (i.e.)>) Only random data obtained by gaussian distribution, false pressure coefficient curves generated by a decoder.
Furthermore, in order to stabilize the training process and sharpen the decision boundaries of the discriminator D, a loss function L is introduced layer ：
In summary, the model loss function of the pressure prediction model is expressed by the following formula:
L＝λ 0 L layer +λ 1 L GAN +λ 2 L recon +λ 3 L prior ；
wherein: l represents model loss of the pressure prediction model; l (L) recon Representing a predicted pressure coefficient curveDifferences from the true pressure coefficient curve; l (L) prior Represents KL divergence; l (L) GAN Indicating a loss of GAN; l (L) layer Represents boundary loss, L layer Representing that a certain layer of neural network in GAN network is composed of x and +.>As input, calculate their distance, the purpose of which is to stabilize the training process, sharpening the decision boundary of the discriminator; d (D) l (x) And->Respectively representing the outputs of both neural networks of a certain layer in the discriminator (discriminator D has only one network, consists of a large number of layers, real data x and +.>The two inputs are used as the inputs of the discriminator, and the structures of the two inputs are consistent at the corresponding layer, but the physical meanings are different, and the divergence can be made, so that the model is more accurate); lambda (lambda) 0 、λ 1 、λ 2 、λ 3 And a weight parameter representing the overall prediction result of each loss function.
According to the invention, when the pressure prediction model is trained, the loss function is calculated through the combination of the real pressure coefficient curve and the generated predicted pressure coefficient curve and the false pressure coefficient curve, so that the influences of the real sample, the reconstructed sample and the false sample can be considered in the training process, and the training effect and performance of the pressure prediction model can be further improved.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the technical solution, and those skilled in the art should understand that modifications and equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the present invention, and all such modifications and equivalents are included in the scope of the claims.
Claims (10)
1. A method for predicting a pressure coefficient based on VAE-GAN and a self-attention mechanism, comprising:
s1: acquiring two-dimensional coordinates of an airfoil to be predicted;
s2: inputting the two-dimensional coordinates of the wing profile to be predicted into a trained pressure prediction model, and outputting a corresponding predicted pressure coefficient curve;
the pressure prediction model is constructed based on a VAE-GAN network;
during training, the two-dimensional coordinate of the wing profile and the true pressure coefficient curve which are used as training samples are used as model input of a pressure prediction model: firstly, an encoder of the VAE extracts corresponding airfoil geometric features, airfoil manifold features and airfoil environment features based on airfoil two-dimensional coordinates, analyzes the mutual influence among the airfoil geometric features, the airfoil manifold features and the airfoil environment features through a self-attention module, fuses the self-attention features output by the self-attention module through a feature fusion network, and generates corresponding airfoil fusion features; then, a decoder of the VAE generates a corresponding predicted pressure coefficient curve and a corresponding false pressure coefficient curve based on the wing profile fusion characteristic and the set random noise respectively; finally, the discriminator of the GAN calculates a corresponding loss function based on the predicted pressure coefficient curve and the false pressure coefficient curve generated by combining the real pressure coefficient curve, and further updates the network parameters of the pressure prediction model based on the loss function until the model converges;
s3: and taking the predicted pressure coefficient curve output by the pressure prediction model as a corresponding pressure coefficient prediction result.
2. The method for predicting pressure coefficients based on VAE-GAN and self-attention mechanisms of claim 1, wherein in step S2, two-dimensional coordinates of the airfoil are encoded by a convolutional neural network, corresponding geometric features of the airfoil are extracted, and the geometric features of the airfoil are converted into data of a preset dimension.
3. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 1, wherein: in the step S2, firstly, riemann measurement and curvature of two-dimensional coordinates of the airfoil are extracted through a Bezier curve to serve as corresponding airfoil manifold characteristics; the airfoil manifold features are then encoded by a fully connected neural network to convert the airfoil manifold features into data of a preset dimension.
4. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 3, wherein: using Bezier curve to represent airfoil two-dimensional coordinates as a plurality of polynomials, calculating the inner product of two vertical vectors from the tangent space of each polynomial, and further extracting the corresponding Riemann metric;
the formula is described as follows:
wherein: g vw (t) represents a Riemann metric for the airfoil at t;representing the direction of the partial derivative; />Representing that each segment of Bezier curve is biased for the parameter t; r (D; t) represents a function of a Bezier curve; p (P) i Representing airfoil coordinates; d represents the sample space in which the airfoil coordinates are located; t represents a parameter of a bezier curve; n represents the order of the Bessel curve;
the curvature is calculated by the following formula:
wherein: c represents curvature; r represents the radius of curvature, i.e. the inverse of the curvature; y' represents the first derivative of the airfoil ordinate y; y "represents the second derivative of the airfoil ordinate y.
5. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 1, wherein: in step S2, airfoil environmental characteristics include Mach number, airfoil angle of attack and Reynolds number; and encoding the airfoil environmental characteristics through the fully connected neural network to convert the airfoil environmental characteristics into data with preset dimensions.
6. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 1 wherein in step S2, the self-attention module operates as follows:
s201: taking the characteristics extracted from the geometrical characteristics, manifold characteristics and environment characteristics of the wing profile through a neural network as input vectors of the self-attention module;
s202: for each input vector a i Respectively multiplied by three coefficients w q 、w k 、w v ；
The formula is described as follows:
q i ＝w q ·a i
k i ＝w k .a i ；
v i ＝w v .a i
wherein: q, k, v represent query, key, and value, respectively;
s203: calculating the correlation between two input vectors through q and k, namely calculating the value alpha of the Attention, wherein a matrix formed by all alpha is expressed as a correlation matrix A;
the formula is described as follows:
α i，j ＝q i ·k j ；
s204: performing softmax operation or relu operation on the correlation matrix A to obtain a corresponding relation matrix A';
s205: each input vector a is calculated by a relation matrix A i Output vector b of self-layer of (c) i Self-attention features as corresponding input vectors, i.e. corresponding features;
the formula is described as follows:
wherein: b i Representing input vector a i The self-attention feature of all input vectors interacting with each other is taken into account; v i ＝w v .a i Representing the product of the input vector and the weight matrix; alpha' i，j Representing elements in the relationship matrix a'.
7. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 1, wherein in step S2, the encoder and decoder of the VAE are expressed by the following formulas:
wherein: enc (x) denotes an encoder, x being its input; z represents the output of the encoder; q (z|x) represents the distribution of the encoder output; dec (z) denotes a decoder, z being an input thereof;representing the output of the decoder; />Representing the distribution of the decoder output.
8. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 1 wherein in step S2, the VAE loss function is expressed by the following formula:
L VAE ＝L recon +L prior ；
L prior ＝D KL (q(z|x)||p(z))；
wherein: l (L) VAE Indicating a loss of VAE; l (L) recon Representing a predicted pressure coefficient curveDifferences from the true pressure coefficient curve; l (L) prior Represents KL divergence; d (D) KL (q (z|x) |p (z)) is used to calculate the gap between the q (z|x) and p (z) distributions; q (z|x) represents the distribution of the encoder output; p (z) specifies that the hidden variable z belongs to a gaussian distribution.
9. The method for predicting a pressure coefficient based on a VAE-GAN and self-attention mechanism as set forth in claim 8, wherein in step S2, a loss function of the GAN is expressed by the following formula:
wherein:indicating a loss of GAN; d (x) represents a discriminator that inputs the real data x to the GAN; />Representing random noise to be passed through the decoder +.>A discriminator input to the GAN; />A discriminator for inputting the airfoil fusion feature z passing through the decoder into the GAN; />Representing a false pressure coefficient curve; dec (Enc (x)) represents a reconstructed pressure coefficient curve in which a true pressure coefficient curve is reconstructed by an encoder and then a decoder.
10. The VAE-GAN and self-attention mechanism based pressure coefficient prediction method of claim 9, wherein in step S2, a model loss function of the pressure prediction model is expressed by the following formula:
L＝λ 0 L layer +λ 1 L GAN +λ 2 L recon +λ 3 L prior ；
wherein: l represents model loss of the pressure prediction model; l (L) recon Representing a predicted pressure coefficient curveDifferences from the true pressure coefficient curve; l (L) prior Represents KL divergence; l (L) GAN Indicating a loss of GAN; l (L) layer Representing boundary loss; d (D) l (x) Andrespectively representing the outputs of a certain layer of neural network and the neural network in the discriminator; lambda (lambda) 0 、λ 1 、λ 2 、λ 3 And a weight parameter representing the overall prediction result of each loss function.
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