Multi-fidelity discrete aerodynamic force modeling method for high-fidelity low-density sampling

Abstract

The invention discloses a multi-fidelity discrete aerodynamic modeling method for high-fidelity low-density sampling, and belongs to the field of multi-fidelity aerodynamic modeling. The method comprises the following steps: acquiring a small amount of wind tunnel test data as high-fidelity data; carrying out simulation calculation through XFoil software to obtain a large amount of low-fidelity data; the gradient of the high-fidelity data and the gradient of the low-fidelity data are calculated through the combination of spline interpolation and finite difference; a gradient enhanced Cokriging model is constructed through a small amount of high-fidelity data, a large amount of low-fidelity data and gradients calculated by the high-fidelity data and the low-fidelity data respectively. According to the invention, under the condition of low-density sampling of the high-fidelity data, the problem of low modeling precision caused by missing of the high-fidelity data information is solved by fusing additional gradient information.

Description

Technical Field

[0001] The invention belongs to the field of multi-fidelity aerodynamic modeling, and in particular relates to a multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling. Background Art

[0002] The accuracy and completeness of aerodynamic data directly determine the quality and credibility of flight simulation. The main source of aerodynamic data is wind tunnel testing, which is an experimental method that simulates the aerodynamic characteristics of an aircraft under different flight conditions under controlled conditions. Wind tunnel testing can provide a large amount of accurate aerodynamic data, laying the foundation for establishing a high-fidelity aerodynamic model. However, wind tunnel testing is expensive, and the limitations of test conditions and test equipment make it difficult to obtain comprehensive data under certain extreme flight conditions.

[0003] In addition to wind tunnel tests, aerodynamic data can also be obtained through theoretical calculations, empirical estimates and flight tests. Theoretical calculations are usually based on the basic principles of fluid mechanics and aerodynamics, and aerodynamic data is obtained through mathematical modeling and numerical calculations. However, the accuracy of theoretical calculations depends on the complexity of the model and the accuracy of the parameters, so there may be certain uncertainties under complex flight conditions. Empirical estimates are based on the design and test data of previous aircraft, and aerodynamic data is obtained through analogy and reasoning. The advantages of this method are fast and low cost, but the accuracy is low. Flight tests obtain aerodynamic data by testing actual aircraft under real flight conditions. The data of this method is the most real and reliable, but its cost is extremely high and the risk is relatively high.

[0004] Since aerodynamic data from different sources have their own advantages and disadvantages, a single method is difficult to cover the entire flight envelope of an aircraft. Therefore, it is necessary to comprehensively utilize multiple methods to fuse aerodynamic data and perform multi-fidelity modeling to improve the comprehensiveness and accuracy of the data.

[0005] The multi-fidelity modeling method is an effective method developed in recent years to improve the accuracy of aerodynamic data modeling. This method builds a multi-fidelity proxy model for data obtained from different channels, and fuses a small amount of high-fidelity data with a large amount of low-fidelity data to improve modeling efficiency and accuracy. The core idea of ​​this method is to make full use of the quantity advantage of low-fidelity data while ensuring the accuracy of high-fidelity data, so as to improve the accuracy and stability of the overall model.

[0006] Among the multi-fidelity modeling methods, the Cokriging model is a widely used technology. The model was originally developed in the field of geostatistics and aims to assist the prediction of high-fidelity data with low-fidelity data. The Cokriging model combines data of different fidelity by considering the correlation between different data sources, thereby improving the accuracy of prediction. Applying the Cokriging model to the field of aerodynamics can effectively improve the efficiency and accuracy of aerodynamic data modeling and provide more reliable data support for flight dynamics simulation. The literature "Deng Chen, Chen Gong, Wang Wenzheng, et al. Aerodynamic data fusion algorithm based on uncertainty and aerodynamic model [J]. Journal of Aerodynamics, 2022, 40(04): 117-123." In order to make up for the "defects" of multi-fidelity data, it is proposed to use the Cokriging fusion algorithm to establish an aircraft aerodynamic model. The experimental results show that compared with the modeling algorithm that uses only one type of precision data, the prediction accuracy of the multi-fidelity data fusion algorithm is greatly improved. Fusion data plays an important role in improving data accuracy and enhancing model prediction capabilities. Reference "Ning Chengjia, Wang Xu, Wang Wenzheng, et al. Data association fusion aerodynamic modeling method with high efficiency sampling [J]. Journal of Aerodynamics, 2022, 40(05): 39-49." Based on the Co-kriging model, an optimal association point selection method and a uniformity enhanced sequential sampling method are proposed to achieve efficient initialization and fastest convergence of the Co-kriging variable credibility model. The model is applied to the NACA0012 airfoil transonic aerodynamic engineering example. The results show that with a small number of high-fidelity samples, the proposed method can greatly improve the model convergence accuracy and modeling efficiency, and effectively reduce the sampling cost.

[0007] In addition, gradient information can reflect the changing trend of aerodynamic data. If it is integrated into the multi-fidelity proxy model, it can more accurately describe the aerodynamic characteristics of the aircraft under different flight conditions. Different from the existing multi-fidelity aerodynamic modeling methods, the main contribution of the present invention is to solve the problem of information loss caused by a small amount of high-fidelity data. Since the method only uses a small amount of high-fidelity data and a large amount of low-fidelity data for model training, no gradient information is added, the information of the high-fidelity data is not fully utilized, and the modeling efficiency is not high. The document "Deng, Yixiang, GuangLin, and Xiu Yang." Multifidelity data fusion via gradient-enhanced Gaussian process regression." arXiv preprint arXiv:2008.01066(2020)" proposes a data fusion method based on multi-fidelity Gaussian process regression, namely the gradient enhanced Cokriging algorithm (Gradient-enhanced CoKriging, GE-Cokriging), hereinafter referred to as GECok. The algorithm combines the quantity of interest (QoI) and its gradient information at different fidelity levels, and can provide approximation and uncertainty estimation of QoI and its gradient at the same time. Based on the algorithm, the present invention proposes a method for effectively extracting gradient information, that is, by combining spline fitting with finite difference calculation, and then constructing a gradient-enhanced Co-kriging model (i.e., GECok model) with the original multi-fidelity data and its gradient information to predict high-fidelity data.

[0008] The core idea of ​​the method provided by the present invention is to use the gradient information of high-fidelity and low-fidelity data as additional input variables and perform data fusion through the Gaussian process regression model. This can not only utilize the accuracy of high-fidelity data, but also improve the utilization efficiency of high-fidelity and low-fidelity data through gradient information, thereby improving the prediction accuracy of the overall model. Summary of the invention

[0009] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is as follows:

[0010] A multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling includes the following steps:

[0011] Obtain a small amount of wind tunnel test data as high-fidelity data (X h ,y h );

[0012] A large amount of low-fidelity data (X l ,y l );

[0013] Use Kriging to build a low-fidelity model K l , based on high-fidelity data using a low-fidelity model K l Interpolate to low-fidelity data (X l ,y l )middle;

[0014] Use spline interpolation combined with finite differences to calculate the gradient information of high and low fidelity data and

[0015] Through high and low fidelity data and their gradient information Build a GECok model and use it to make predictions on high-fidelity data.

[0016] The beneficial effects of the present invention are as follows: the present invention provides a high-fidelity, low-density sampling multi-fidelity discrete aerodynamic modeling method, and proposes a multi-fidelity fusion framework under the condition that the high-fidelity data is small in amount and the low-fidelity data has low accuracy and cannot provide complete data information. By integrating the gradient information of the two fidelity data, the problem of incomplete data information is solved, thereby improving the prediction accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments are briefly introduced below.

[0018] Figure 1 is a flowchart of the steps of the multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling described in the embodiment;

[0019] Figure 2 1 is a prediction result diagram (a) and a relative error diagram (b) of the lift coefficient of the NACA2414 airfoil in the embodiment;

[0020] Figure 3 1 is a diagram showing the predicted results of the drag coefficient of the NACA2414 airfoil in the embodiment (a) and a diagram showing the relative error (b). DETAILED DESCRIPTION

[0021] In order to make the technical solution of the present invention clearer, the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the invention. The described embodiments only use a part of the embodiments, rather than all the embodiments. The present invention is specifically implemented according to the following steps:

[0022] (1) Obtain a small amount of wind tunnel test data as high-fidelity data (X h ,y h ).

[0023] (2) A large amount of low-fidelity data (XFoil) is obtained through simulation calculation with XFoil software. l ,y l ).

[0024] Use Kriging to build a low-fidelity model based on low-fidelity data l , based on high-fidelity data using a low-fidelity model K l Interpolate to low-fidelity data (X l ,y l ). Note that this step is necessary because the high- and low-fidelity data may not be aligned, and the low-fidelity data will increase after interpolation;

[0025] (3) Based on the high-fidelity data set in S1 and the low-fidelity data set in S3, two spline functions are used to fit the two discrete data respectively. After interpolation, the forward difference method of finite difference is used to calculate the gradient information of the two data. and To obtain high-fidelity data gradients For example, this process is described by formulas (2) to (5):

[0026] S h =spline(X h ,y h ) (2)

[0027]

[0028] in, represents the data after dense sampling, represents the gradient of the i-th position, where i = 1, 2, ..., n-1, n represents the total number of data after dense sampling, n h Indicates the number of original high-fidelity data.

[0029] (4) Based on the data sets obtained in S1, S3 and S4 Construct the GECok model as follows:

[0030] Remember d =y h -wy l (X h ), where y l (X h ) is y l In with X h The value at the same position, then based on (X h ,y d ) Use Kriging to build the model difference model K d ;

[0031] (5) Based on model Kl and K d , build a high-fidelity model K h :

[0032] K h (x) = wK l (x)+K d (x) (1)

[0033] Among them, w is the weight coefficient, which is optimized by genetic algorithm during model training.

[0034] The present invention provides two embodiments, which are lift coefficient prediction and drag coefficient prediction experiments of NACA2414 airfoil when the Reynolds number is 60400. The high-fidelity data used in the experiments are derived from UIUC wind tunnel test data, and the low-fidelity data are derived from XFoil simulation calculation results.

[0035] Example 1: A multi-fidelity model is constructed for the aerodynamic data of the NACA2414 airfoil to predict the lift coefficient. The specific details are as follows:

[0036] This embodiment uses the wind tunnel test data in the UIUC public data set as high-fidelity data, and the results of simulation calculations by the XFoil software as low-fidelity data. This embodiment only uses a set of data with a Reynolds number of 60400 for the experiment, using the angle of attack as the input of the model and the output as the lift coefficient. There are 21 high-fidelity data and 35 low-fidelity data. In order to simulate engineering usage scenarios, only 8 high-fidelity data are sampled, and the sampling method is random sampling. All low-fidelity data are used for model training to prove the effectiveness and accuracy of the model. The result graph of the method of the present invention for predicting the lift coefficient of the NACA2414 airfoil and its corresponding relative error are shown in the figure. Figure 2 As shown in (a) and (b), the relative errors of the prediction results are both below 18%.

[0037] Example 2: Multi-fidelity modeling is performed on the aerodynamic data of the NACA2414 airfoil to predict the drag coefficient. The specific details are as follows:

[0038] The experimental data of this embodiment is the same as that of embodiment 1, except that the output of the model is changed to the drag coefficient. The prediction result diagram of the drag coefficient of the NACA2414 airfoil by the method of the present invention and its corresponding relative error are shown in FIG. Figure 3 As shown in (a) and (b), the relative errors of the prediction results are both below 5%.

[0039] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes.

Claims

1. A multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling, characterized in that: The steps include: Obtain a small amount of wind tunnel test data as high-fidelity data (X h ,y h ); A large amount of low-fidelity data (X l ,y l ); Use Kriging to build a low-fidelity model K l , based on high-fidelity data using a low-fidelity model K l Interpolate to low-fidelity data (X l ,y l )middle; Use spline interpolation combined with finite differences to calculate the gradient information of high- and low-fidelity data; A gradient-enhanced Cokriging model is constructed using high- and low-fidelity data and their gradient information, and the model is used to predict high-fidelity data.

2. A multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling according to claim 1, characterized in that: The high-fidelity data (X h ,y h ) is derived from the wind tunnel test data in the UIUC public data set, where X h is the Reynolds number and angle of attack, y h is the lift coefficient or drag coefficient.

3. The multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling according to claim 1 is characterized in that: The acquisition of a large amount of low-fidelity data (X l ,y l ), including: Identify a large amount of low-fidelity data dependent variable X l , namely the Reynolds number and the angle of attack; The corresponding lift coefficient or drag coefficient is obtained by simulation calculation using XFoil software as y l .

4. The multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling according to claim 1 is characterized in that: The use of Kriging to construct a low-fidelity model K l , based on high-fidelity data using a low-fidelity model K l Interpolate to low-fidelity data (X l ,y l ), specifically including: Based on low-fidelity data, Kriging is used to build a low-fidelity model K l ; Based on high-fidelity data, use low-fidelity model K l Interpolation (i.e. K l (X h )) to low-fidelity data (X l ,y l )middle.

5. The multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling according to claim 1 is characterized in that: The method of calculating the gradient information of high- and low-fidelity data by using spline interpolation combined with finite differences specifically includes: Spline fitting technology is used to smooth discrete high-fidelity data to improve the continuity of the data, and then interpolation is performed to calculate the gradient through finite differences to obtain high-fidelity gradients. Using the same method as described for S41, a low-fidelity gradient is obtained 6. The multi-fidelity discrete aerodynamic modeling method with high-fidelity and low-density sampling according to claim 1 is characterized in that: The use of high and low fidelity data and the gradients calculated from them Construct a gradient-enhanced Cokriging model, including: Remember d =y h -wy l (X h ), where y l (X h ) is y l In with X h The value at the same position, using (X h ,y d ) Construct Kriging model K d ; Based on the model K l and K d , build a high-fidelity model K h : K h (x)=wK l (x)+K d (x) (1) Among them, w is the weight coefficient, which is optimized by genetic algorithm during model training.

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