Wing flow field area decomposition rapid prediction method

Abstract

The invention discloses a rapid prediction method for wing flow field area decomposition. According to the method, a k-means clustering decomposition method is adopted, effective decomposition of a flow field area is achieved, area sampling is carried out based on area decomposition, main modal energy extraction is carried out on a sampled flow field data set through a model order reduction method, a basis matrix of flow field data is obtained, the basis matrix is trained through a machine learning method, and the flow field data is obtained. And finally, a wing flow field region decomposition rapid prediction framework is realized. According to the method, the calculation efficiency of a traditional numerical simulation method is remarkably improved, and the method has wide applicability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerospace vehicle wing performance evaluation, in particular to a wing flow field region decomposition rapid prediction method. BACKGROUND

[0002] Subsonic airfoils have important engineering application value in the fields of aerospace engineering and energy power. Traditional methods based on computational fluid dynamics (CFD) (such as Navier-Stokes equation solving) often have high computational cost and long time consumption when simulating airfoil pressure distribution, which is difficult to support real-time design and optimization requirements. SUMMARY

[0003] The application aims to provide a wing flow field region decomposition rapid prediction method, which has fast calculation speed, high calculation accuracy and effectively improves the prediction efficiency of the wing flow field.

[0004] In order to achieve the purpose of the application, the application provides a wing flow field region decomposition rapid prediction method, which comprises the following steps:

[0005] Step 1, obtaining a data set; obtaining a parameterized wing flow field data set through CFD simulation of the wing flow field coming flow conditions obtained by random sampling; arranging the wing flow field data set to obtain a wing flow field snapshot matrix, each column of the wing flow field snapshot matrix corresponding to the wing flow field data under the wing flow field coming flow conditions;

[0006] Step 2, determining a region decomposition scheme for the wing flow field: according to the parameterized wing flow field data set generated in step 1, setting the wing pressure value as the wing flow field region decomposition index by selecting the wing pressure field data from the parameterized wing flow field data set;

[0007] Step 3, carrying out region decomposition of a single wing flow field: obtaining a group of wing flow field data by randomly selecting the wing flow field snapshot matrix, carrying out region decomposition of the wing flow field data by means of k-means clustering algorithm, and dividing the flow field region into high feature region, medium feature region and low feature region;

[0008] Step 4, carrying out batch region decomposition: repeating step 3 to obtain a plurality of region decomposition results with repeated times;

[0009] Step 5, generating a global region decomposition scheme: according to the plurality of region decomposition results, obtaining a global region decomposition scheme of the wing flow field data set by taking the union of the feature regions of each group, the global region decomposition scheme mainly including the coordinates of the wing flow field sample points contained in the high feature region, the medium feature region and the low feature region;

[0010] Step 6, constructing a region decomposition sampling scheme to form a machine learning data set: obtaining a region decomposition sampling scheme suitable for the whole data set of the flow field by differentiating the sampling ratio of the global region decomposition scheme, and sampling the wing flow field snapshot matrix according to the region decomposition sampling scheme suitable for the whole data set of the flow field to obtain a machine learning data set;

[0011] Step 7, carrying out model reduction processing based on modal decomposition: carrying out model reduction processing on the machine learning data set by eigenvalue orthogonal decomposition to obtain wing flow field model reduction coefficients;

[0012] Step 8, establishing a wing profile flow field reduction prediction model based on a neural network: setting the wing flow field incoming flow condition as an input layer and setting the wing flow field model reduction coefficient as an output layer, and constructing a full-connection neural network through the input layer and the output layer; obtaining a trained neural network through machine learning on the neural network;

[0013] Step 9, rapid prediction of the wing flow field: obtaining the neural network output predicted flow field model reduction coefficient by inputting the working condition parameters of the flow field to be predicted under a specific working condition into the trained neural network, and then reconstructing the wing flow field prediction result through eigenvalue orthogonal decomposition.

[0014] Compared with the prior art, the significant progress of the present application is that:

[0015] (1) The flow field is divided into high, medium and low characteristic regions by the region decomposition technology, and the first three order principal modes are reserved only by combining the POD reduction model, so that the data dimension is significantly reduced. The neural network quickly maps the working condition parameters and the modal coefficients, so that the prediction time is shortened from several hours of traditional CFD to seconds, and the calculation efficiency is greatly improved;

[0016] (2) A hierarchical sampling strategy (80% for high characteristic region, 50% for medium characteristic region, and 20% for low characteristic region) is adopted to retain the details of the flow field in the key region; the POD reduction algorithm combines the modal energy matrix to ensure that the prediction error of the pressure, velocity and other physical fields is less than, and the flow field can be effectively predicted within a reasonable error;

[0017] (3) The region is dynamically divided based on k-means clustering (k=3), and the parameter k can be adjusted according to the complexity of the flow field, supporting rapid generalization across working conditions (such as different Mach numbers and angles of attack). 50% of the data are randomly extracted to construct the decomposition scheme, which enhances the robustness of the model to noise and abnormal flow;

[0018] (4) The region decomposition and neural network are fused to construct a nonlinear mapping relationship between the input working condition and the basis matrix. Compared with the traditional proxy model, this method reduces the input variable dimension through POD reduction, effectively reduces the memory occupancy rate while improving the training efficiency, and supports multi-physical field coupling prediction;

[0019] (5) The technical solution is realized in steps, forming a closed loop from data preparation to model training; each module (such as regional decomposition, POD reduction, and neural network) can be independently optimized, facilitating integration into an existing CFD process or expansion to complex scenarios such as turbulence and shock waves, and having potential for industrial-level application.

[0020] To more clearly illustrate the functional characteristics and structural parameters of the present application, the following further describes the present application with reference to the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0021] The accompanying drawings, which are included to provide a further understanding of the present application, constitute a part of this application, and the illustrative embodiments of the present application and their description serve to explain the present application, and do not limit the present application in any manner. In the drawings:

[0022] Figure 1 is a step flow chart of the present application;

[0023] Figure 2 is a wing profile flow field regional decomposition and modal acquisition process schematic diagram of the present application;

[0024] Figure 3 is a machine learning reduced-order model prediction flow field flow characteristic schematic diagram of the present application;

[0025] Figure 4 is a flow field regional decomposition process schematic diagram based on k-means clustering of the present application. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments of the present application; based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0027] The present application is a wing flow field regional decomposition rapid prediction method, which combines Figure 1 , and includes the following steps:

[0028] Step 1, obtaining a data set; 100 groups of wing flow field inflow conditions obtained by random sampling are simulated by CFD to obtain a parameterized wing flow field data set; the wing flow field data set is sorted to obtain a wing flow field snapshot matrix, each column of the wing flow field snapshot matrix corresponding to wing flow field data under the wing flow field inflow condition;

[0029] Step 2, determine the regional decomposition scheme for the wing flow field: set the wing pressure value as the wing flow field regional decomposition index by selecting the wing pressure field data from the parameterized wing flow field data set generated in step 1;

[0030] Step 3, carry out regional decomposition of single wing flow field: obtain a set of wing flow field data by randomly selecting the wing flow field snapshot matrix, carry out regional decomposition of the wing flow field data by means of k-means clustering algorithm, and divide the flow field region into high feature region, medium feature region and low feature region;

[0031] Step 4, carry out batch regional decomposition: repeat step 3 for 20 times to obtain 20 sets of regional decomposition results;

[0032] Step 5, generate global regional decomposition scheme: obtain the global regional decomposition scheme of the wing flow field data set by taking the union of the feature regions of each group according to the 20 sets of regional decomposition results, which mainly includes the coordinates of the wing flow field sample points in the high feature region, medium feature region and low feature region;

[0033] Step 6, construct regional decomposition sampling scheme and form machine learning data set: obtain the regional decomposition sampling scheme suitable for the whole flow field data set by differentiating the sampling ratio of the global regional decomposition scheme, and sample the wing flow field snapshot matrix according to the regional decomposition sampling scheme suitable for the whole flow field data set to obtain the machine learning data set;

[0034] Step 7, carry out model reduction based on modal decomposition: carry out model reduction of the machine learning data set by proper orthogonal decomposition (POD) to obtain wing flow field model reduction coefficients;

[0035] Step 8, establish wing profile flow field reduction prediction model based on neural network: set the wing flow field incoming flow condition as the input layer and the wing flow field model reduction coefficient as the output layer, and construct a fully connected neural network; train the neural network to obtain the trained neural network;

[0036] Step 9, rapid prediction of wing flow field: input the trained neural network with the working condition parameters of the flow field to be predicted under a specific working condition to obtain the neural network output prediction of the flow field model reduction coefficient, and then reconstruct the wing flow field prediction result by proper orthogonal decomposition.

[0037] The data set obtained in step 1 includes wing flow field data: sample point coordinates, wing flow field velocity, wing flow field pressure; wing flow field incoming flow condition: incoming Mach number, angle of attack.

[0038] The Mach number working condition ranges from [0.68Ma, 0.73Ma], and the attack angle working condition ranges from [2.40°, 3.20°].

[0039] In combination Figure 4 , the k-means clustering algorithm of step 3 specifically includes the following steps:

[0040] Step 3-1, determine the number of sample clusters, set it to 3, randomly select k sample points as initial cluster centers, determine the distance of each sample point to each cluster center, where the distance dist is the Euclidean distance used as the basis for judgment;

[0041] ;

[0042] Where x is a data point, c i is the i-th cluster center, d is the dimension of the data, x j and c ij are the values of the data point x and the cluster center c i in the j-th dimension;

[0043] Step 3-2, distribute the sample points to the cluster where each cluster center is located according to the distance, and then recalculate the mean of the sample points in each cluster to obtain new cluster centers ;

[0044] ;

[0045] Where C i is the number of samples in the cluster, and x is the value corresponding to the sample point in the cluster;

[0046] Step 3-3, based on the new cluster centers, continue to calculate the distance of each sample point to the cluster center, repeat the above steps until the change value of the cluster center is less than the set convergence value or the maximum iteration step is reached.

[0047] Each feature area of step 5 is a high feature area and a low feature area.

[0048] The differential sampling ratio of step 6 is: the sampling ratio of the high feature area is set to 80%, the sampling ratio of the medium feature area is set to 50%, and the sampling ratio of the low feature area is set to 20%.

[0049] The eigenvalue orthogonal decomposition of step 7 is a method of reducing high-dimensional sample data to low-dimensional space, in combination Figure 2 , specifically as follows:

[0050] Calculate the sample mean and standardize it:

[0051] ;

[0052] ;

[0053] wherein, is the flow field data matrix that we need to reduce the order of the model, is the sample flow field data mean, is the standardized sample flow field data;

[0054] According to the standardized data, the covariance matrix C is calculated :

[0055] ;

[0056] wherein, the size of the C matrix becomes n x n, n is the degree of freedom of the flow field data; the eigenvalues and eigenvectors of the C matrix are calculated, and the eigenvalues and eigenvectors are sorted according to the size of the eigenvalues;

[0057] In order to ensure the accuracy of the reduction, it is usually necessary to ensure that the sum of the proportions of the first m eigenvalues to the total eigenvalues is not less than 0.999, as follows:

[0058] ;

[0059] The first m eigenvalues and eigenvectors are constructed into a mapping matrix and a coefficient matrix:

[0060] ;

[0061] ;

[0062] wherein, U is the POD mapping matrix, with a shape of n x m; Y is the coefficient matrix.

[0063] In combination with Figure 3 , the full connection neural network constructed in step 8 is specifically as follows:

[0064] ;

[0065] wherein, Y' is the flow field model reduction coefficient matrix under a specific working condition output by the neural network, Ma is the Mach number of the wing flow field incoming flow condition, and a is the airfoil attack angle; w is the neural network weight, and b is the bias of the neuron; Y w ' is the wing flow field model reduction coefficient matrix.

[0066] The eigenvalue orthogonal decomposition reconstruction of step 9 is specifically as follows:

[0067] ;

[0068] wherein X p is the flow field wing flow field data matrix under the specific working condition to be predicted; U + is the pseudo-inverse matrix of the mapping matrix U; Y’ is the flow field model reduced order coefficient matrix under the specific working condition; is the sample flow field mean matrix.

[0069] It should be noted that the relational terms herein such as first and second and the like are used solely to distinguish one entity or action from another, without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus.

[0070] While the embodiments of the application have been illustrated and described, it will be understood by those skilled in the art that various changes, modifications, substitutions, and alterations can be made therein without departing from the spirit and scope of the application, which is defined by the appended claims and their equivalents.

Claims

1. A method for fast prediction of a flow field region decomposition of an airfoil, characterized in that, The method comprises the following steps: Step 1, obtaining a data set; obtaining a parameterized wing flow field data set through CFD simulation of wing flow field obtained by random sampling; The wing flow field data set is sorted to obtain a wing flow field snapshot matrix, each column of the wing flow field snapshot matrix corresponding to the wing flow field data under the wing flow field incoming flow condition; Step 2, determining the regional decomposition scheme for the wing flow field: according to the parameterized wing flow field data set, the wing pressure value is set as the wing flow field regional decomposition index by selecting the wing pressure field data from the parameterized wing flow field data set; Step 3, carrying out regional decomposition of a single wing flow field: a group of wing flow field data is obtained by randomly selecting the wing flow field snapshot matrix, and the wing flow field data is regionally decomposed by means of k-means clustering algorithm; Step 4, carrying out batch regional decomposition: repeating step 3 to obtain a plurality of regional decomposition results of repeated times; Step 5, generating a global regional decomposition scheme: according to the plurality of regional decomposition results, the feature regions of each group are taken and the global regional decomposition scheme of the wing flow field data set is obtained; Step 6, constructing a regional decomposition sampling scheme to form a machine learning data set: the global regional decomposition scheme is obtained by differentiating the sampling ratio to obtain a regional decomposition sampling scheme suitable for the whole data set of the flow field, and the wing flow field snapshot matrix is sampled according to the regional decomposition sampling scheme suitable for the whole data set of the flow field to obtain a machine learning data set; Step 7, carrying out model reduction processing based on modal decomposition: the machine learning data set is subjected to model reduction processing by proper orthogonal decomposition to obtain wing flow field model reduction coefficients; Step 8, establishing a neural network-based airfoil flow field reduction prediction model: the wing flow field incoming flow condition is set as the input layer, and the wing flow field model reduction coefficient is set as the output layer, and the input layer and the output layer are connected to form a fully connected neural network; the neural network is trained by machine learning to obtain a trained neural network; Step 9, rapid prediction of wing flow field: the trained neural network is used to input the working condition parameters of the flow field under the specific working condition to be predicted to obtain the flow field model reduction coefficient predicted by the neural network output, and then the wing flow field prediction result is obtained by proper orthogonal decomposition reconstruction.

2. The method of claim 1, wherein, The data set obtained in step 1 includes wing flow field data: sample point coordinates in flow field, wing flow field velocity, wing flow field pressure; wing flow field incoming flow condition: incoming Mach number, angle of attack.

3. The method of claim 2, wherein, The range of Mach number condition is [0.68Ma, 0.73Ma], and the range of angle of attack condition is [2.40°, 3.20°].

4. The method of claim 1, wherein The number of flow field region division in step 3 is three, which are high feature region, medium feature region and low feature region.

5. The method of claim 4, wherein, The k-means clustering algorithm of step 3 specifically comprises the following steps: Step 3-1, determining the number of divided sample clusters, randomly selecting k sample points as initial clustering centers, and determining the distance of each sample point to each clustering center; Step 3-2, distributing the sample points to the cluster according to the distance, and then recalculating the mean value of the sample points in each cluster to obtain a new cluster center; Step 3-3, based on the new cluster center, continue to calculate the distance of each sample point to the cluster center, repeat the above steps until the change value of the cluster center is less than the set convergence value or the maximum iteration step is reached.

6. The method of claim 4, wherein, Each feature area of the step 5 is a high feature area and a low feature area, and the global area decomposition scheme includes coordinates of the wing flow field sample points in the high feature area, the medium feature area and the low feature area.

7. The method of claim 4, wherein, The differential sampling ratio of the step 6 is that the sampling ratio of the high feature area is set to 80%, the sampling ratio of the medium feature area is set to 50%, and the sampling ratio of the low feature area is set to 20%.

8. The method of claim 1, wherein, The proper orthogonal decomposition of the step 7 is a method for reducing the order of high-dimensional sample data to a low-dimensional space, and is specifically as follows: Calculate the sample mean and standardize it: ； ； wherein, is the flow field data matrix for which we need to perform model reduction, is the mean of the sample flow field data, is the normalized sample flow field data; computing a covariance matrix from the standardized data : ； Wherein, the size of the C matrix becomes n x n, n is the degree of freedom of the flow field data; calculate the eigenvalue and eigenvector of the C matrix, and sort the eigenvalue and eigenvector according to the size of the eigenvalue; The first m eigenvalues and eigenvectors are constructed into a mapping matrix and a coefficient matrix: ； ； Wherein, U is the POD mapping matrix, and the shape is n x m; Y is the coefficient matrix.

9. The method of claim 1, wherein The fully connected neural network constructed in the step 8 is specifically as follows: ； Wherein, Y' is the reduced order coefficient matrix of the flow field model under the specific working condition output by the neural network, Ma is the Mach number of the wing flow field incoming flow condition, and a is the airfoil angle of attack; w is the neural network weight, and b is the bias of the neuron; Y w ' is the reduced order coefficient matrix of the wing flow field model.

10. The method of claim 1, wherein, The proper orthogonal decomposition reconstruction of the step 9 is specifically as follows: ； wherein X p is the flow field wing flow field data matrix under the specific working condition to be predicted; U + is the pseudo-inverse matrix of the mapping matrix U; Y' is the flow field model reduced order coefficient matrix under the specific working condition; is the sample flow field mean matrix.

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