An aircraft aerodynamic data fusion method based on MCOK agent model

Abstract

The application provides an aircraft aerodynamic data fusion method based on an MCOK agent model, comprising the following steps: determining design variables and a design space; defining CFD calculation models with different levels of credibility; constructing a training sample set; constructing a large correlation matrix and correcting the same; and obtaining a fused aerodynamic data response prediction value of the sample according to the MCOK agent model. The application introduces additional model parameters in front of the cross terms of the correlation matrix to quantify the correlation between multiple sources of complex data, and realizes efficient and high-precision fusion of any multiple aerodynamic data with different levels of credibility. The aircraft aerodynamic data fusion method based on the MCOK agent model provided by the application not only overcomes the defect that the fusion precision is affected by the inaccuracy of low-credibility models, but also considers the correlation between low-credibility models, greatly improves the precision of the fusion prediction, and makes the model more robust, and has good engineering application potential.

Description

Technical Field

[0001] This invention belongs to the field of aircraft aerodynamic data fusion technology, specifically relating to an aircraft aerodynamic data fusion method based on the MCOK proxy model. Background Technology

[0002] High-precision aerodynamic data is the basis for aircraft aerodynamic shape design. Currently, methods for acquiring aircraft aerodynamic data mainly include numerical calculation, wind tunnel testing, and flight testing. Numerical calculation methods are often less accurate due to factors such as computational grids, turbulence models, and transitions. Wind tunnel testing simulates a certain range of flight conditions and environments, but ground-based test conditions can never fully reflect real flight conditions, nor can they completely correct for the effects of tunnel walls and supports, thus limiting accuracy. Flight testing methods provide the closest approximation of aerodynamic data under actual flight conditions, but are often costly and lack sufficient coverage of different flight conditions and environments. To overcome the shortcomings of these single methods, aerodynamic data fusion technology can theoretically be used to obtain high-precision aerodynamic data for aircraft.

[0003] Currently, the commonly used aerodynamic data fusion method for aircraft in engineering is the multi-confidence surrogate model-based aerodynamic data fusion method, which can be mainly divided into the following three categories: ① Aerodynamic data fusion method based on scaling function correction multi-confidence surrogate model, which introduces low-confidence sample data through multiplication, addition, or mixed scaling functions to construct a multi-confidence surrogate model. However, the final fusion accuracy of the model depends excessively on the accuracy of the scaling function. ② Aerodynamic data fusion method based on spatial mapping multi-confidence surrogate model, which maps the high-confidence design space (or low-confidence output space) to the low-confidence design space (or high-confidence output space), and then constructs a multi-confidence surrogate model through a suitable transformation function. Its drawback is that the transformation function is usually difficult to determine easily. ③ Aerodynamic data fusion method based on Co-Kriging multi-confidence surrogate model, which, according to Bayesian theory, uses low-confidence sample data to provide the global trend of the model, and then uses high-confidence sample data for interpolation correction to establish a multi-confidence surrogate model. Compared with the previous two fusion models, this type of method often has higher fusion accuracy and better engineering applicability. It is currently widely used in fields such as aerodynamic modeling and data fusion of aircraft, and layout and shape optimization design.

[0004] However, current Co-Kriging-based multi-confidence surrogate model methods still have the following shortcomings: ① The relative accuracy relationships between different low-confidence data need to be known in advance to determine the order of recursive modeling "from low to high"; ② An additional surrogate model needs to be built for the low-confidence data and a predicted value needs to be provided as a global trend, so the final fusion accuracy will largely depend on the accuracy of the low-confidence surrogate model; ③ Only the correlation between high-confidence data and each low-confidence data is considered, and the correlation between different low-confidence data has not been considered, thus limiting the accuracy of the fusion result. Therefore, it is urgent to develop a new multi-confidence surrogate model method to achieve efficient and high-precision fusion of multi-source aerodynamic data of aircraft. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for aircraft aerodynamic data fusion based on the MCOK proxy model, which can effectively solve the above-mentioned problems.

[0006] The technical solution adopted in this invention is as follows:

[0007] This invention provides a method for fusion of aerodynamic data of aircraft based on the MCOK proxy model, comprising the following steps:

[0008] Step 1: Determine the design variable x of the aircraft and the range of values ​​for the design variable x to obtain the design space, and let the number of design variables be m;

[0009] Step 2: Define L+1 layers of CFD computation models with different confidence levels; where layer 0 is a high-confidence CFD model y0(x), and layers 1 to L are all low-confidence CFD models, represented as: layer 1 low-confidence CFD model y1(x), layer 2 low-confidence CFD model y2(x), ..., layer L low-confidence CFD model y L (x); where any low-confidence CFD model at layer k is represented as y k (x), k = 1, 2, ..., L;

[0010] Step 3: Construct a training sample set, which includes a set of high-confidence samples. and the corresponding set of high-confidence aerodynamic data response values. Low-confidence sample set S k and the corresponding set of low-confidence aerodynamic data response values. The method is as follows:

[0011] Step 3.1: Randomly select one set of values ​​for the design variable x in the design space to form one sample;

[0012] Therefore, n0 samples are randomly selected from the design space as high-confidence samples, thus forming the high-confidence sample set of layer 0. in, These are the individual samples in the high-confidence sample set S0;

[0013] Randomly select n from the design space k Each sample is considered a low-confidence sample in the k-th layer, thus forming the low-confidence sample set in the k-th layer. in, S represents the set of low-confidence samples at layer k. k Each sample in the sample;

[0014] Step 3.2: Set the high-confidence sample set of layer 0. High-confidence samples The data is input into a high-confidence CFD model y0(x), which outputs the aerodynamic data response value corresponding to each high-confidence sample, thus obtaining the set of high-confidence aerodynamic data response values. in, They are respectively The corresponding aerodynamic data response value;

[0015] The set of low-confidence samples at layer k. Each low-confidence sample The input is fed into the corresponding k-th layer low-confidence CFD model y k In (x), the k-th layer low-confidence CFD model y k (x) Output the aerodynamic data response value corresponding to each low confidence sample, thereby obtaining the set of low confidence aerodynamic data response values ​​for the k-th layer. in, They are respectively The corresponding aerodynamic data response value;

[0016] Step 4: Construct a large correlation matrix

[0017] Set of high-confidence samples and low-confidence sample sets Construct a total sample set S0, S1, ..., S1 of layer L+1. L ;

[0018] In the total sample set S0, S1,...,S L In the process, calculate the sample set of the j-th layer. Samples in and the l-th layer sample set Samples in Spatial correlation Where p = 1, 2, ..., n j ; q = 1, 2, ..., n l j,l=0,1,…,L;n j ,n l They represent the sample set of the j-th layer, respectively. and the l-th layer sample set The number of samples in the sample;

[0019] The formula for spatial correlation is as follows:

[0020]

[0021] in:

[0022] θ i The value to be determined represents the model hyperparameter corresponding to the i-th design variable in design variable x; i = 1, 2, ..., m;

[0023] and Representing samples respectively and The value of the i-th design variable;

[0024] Thus, the sample set S of the j-th layer is obtained. j and the l-th layer sample set S l Correlation matrix between

[0025]

[0026] After the correlation matrices between all sample sets have been calculated, the correlation matrices form a large, dense, and symmetric correlation matrix as follows.

[0027]

[0028] Step 5: Construct the corrected large correlation matrix

[0029] In large correlation matrices In this context, the multiplier γ is introduced. jl Where j,l=0,1,…,L, and multiplier γ jl Represents the correlation matrix R (jl) The multipliers yield the corrected large correlation matrix.

[0030]

[0031] in:

[0032] γ jl The value to be determined;

[0033] Step 6, in the corrected large correlation matrix In the above equation, the hyperparameter matrix θ = [θ1, θ2, ..., θ] is obtained by maximizing the likelihood function. m ] T The sum of the multiplier matrix γ = [γ 00 ,γ 01 ,γ 02 ,…,γ LL ] T :

[0034]

[0035] wrtθ,γ

[0036] in:

[0037] n0, n1, n2, ..., n L , representing the sample set S0, S1, ..., S L The number of samples;

[0038] Represents the set of high-confidence aerodynamic data response values ​​y from layer 0. S,0 The first layer of low-confidence aerodynamic data response value set y S,1 The set of low-confidence aerodynamic data response values ​​y at layer L. S,L The response value matrix is ​​composed of;

[0039] Representative size is The regression matrix;

[0040] Represents the trend vector;

[0041] Step 7: Randomly sample the values ​​of design variable x within the design space to form sample x′, and establish the MCOK model equation as follows, based on the training sample set and the corrected large correlation matrix. The model hyperparameter matrix θ = [θ1, θ2, ..., θ m ] T The sum of the multiplier matrix γ = [γ 00 ,γ 01 ,γ 02 ,…,γ LL ] T The predicted aerodynamic response value after fusion of sample x′ is obtained by calculation:

[0042]

[0043] in:

[0044] The fused aerodynamic data response prediction value represents sample x′;

[0045] This represents a regression vector of length L+1;

[0046] Let r0 represent the correlation vector of the high-confidence samples in layer 0, expressed as: The meaning is: each high-confidence sample in the high-confidence sample set S0 Spatial correlation between sample x′ and The high-confidence sample correlation vector formed by the 0th layer; r1,...,r L Represent the correlation vectors of low-confidence samples in layer 1, ..., layer L, respectively; where r1, ..., r L any r in k Let k = 1, 2, ..., L, be the relevance vector of the low-confidence samples in the k-th layer, expressed as: Meaning: The set of low-confidence samples at level k, S k Each low-confidence sample Spatial correlation between sample x′ and The correlation vector of the low-confidence samples in the k-th layer;

[0047] This outputs the predicted aerodynamic data response value after fusion of sample x′.

[0048] Preferably, in step 1, the design variable x is a multi-dimensional design variable.

[0049] Preferably, the different dimensional components of the design variable x include the component obtained after parameterizing the body geometry, and the flight state component.

[0050] The aerodynamic data fusion method for aircraft based on the MCOK proxy model provided by this invention has the following advantages:

[0051] Compared with other aerodynamic data fusion methods based on Co-Kriging-type multi-credibility proxy models, the beneficial effects of this invention are as follows:

[0052] (1) The MCOK model can integrate any number of low-reliability datasets with unknown relative accuracy relationships, which expands its engineering application scope and makes it more versatile.

[0053] (2) The MCOK model avoids recursive modeling of each low-confidence data, which not only reduces the complexity of modeling, but also reduces the loss of accuracy of the final model caused by the inaccurate prediction of the low-confidence proxy model.

[0054] (3) The additional hyperparameter γ can be used to quantify the correlation between data at different confidence levels, so that the MCOK model can not only consider the correlation between high confidence data and each low confidence data, but also the correlation between different low confidence data, which greatly improves the fusion accuracy.

[0055] (4) The estimated value expression of the MCOK model is very close to that of the traditional Kriging model, so it is easy to program and has engineering applicability. Attached Figure Description

[0056] Figure 1 A flowchart illustrating an aircraft aerodynamic data fusion method based on the MCOK proxy model provided by this invention;

[0057] Figure 2 A parameterized schematic diagram of the geometric shape of the FDL-5A hypersonic vehicle;

[0058] Figure 3 This is a schematic diagram showing how aerodynamic coefficients calculated using the RANS solver vary with mesh size.

[0059] Figure 4 This is a schematic diagram showing how aerodynamic coefficients calculated using the Euler solver vary with mesh size.

[0060] Figure 5 Calculate the grid for a RANS with 2 million grid points;

[0061] Figure 6 Calculate the grid for a RANS with a grid size of 500,000;

[0062] Figure 7 Calculate the grid for Euler with a grid size of 2 million;

[0063] Figure 8 Calculate the grid for Euler with a grid size of 1 million;

[0064] Figure 9 To obtain the R-value of the fused lift coefficient results of the FDL-5A aircraft using three different multi-confidence models. 2 Box plot;

[0065] Figure 10 Box plot of RMSE index for the fusion results of lift coefficient of FDL-5A aircraft using three different multi-confidence models;

[0066] Figure 11 Box plot of MAE index for the fusion results of lift coefficient of FDL-5A aircraft using three different multi-confidence models;

[0067] Figure 12To obtain the R-value of the fusion results of the drag coefficient of the FDL-5A aircraft using three different multi-confidence models. 2 Box plot;

[0068] Figure 13 Box plot of RMSE index for the fusion results of drag coefficient of FDL-5A aircraft using three different multi-confidence models;

[0069] Figure 14 Box plot of MAE index for the fusion results of drag coefficient of FDL-5A aircraft using three different multi-confidence models;

[0070] Figure 15 To evaluate the R-values ​​of the fused torque coefficients of the FDL-5A aircraft using three different multi-confidence models. 2 Box plot;

[0071] Figure 16 Box plot of RMSE index for the fusion results of the moment coefficient of the FDL-5A aircraft using three different multi-confidence models;

[0072] Figure 17 Box plot of MAE index for the fusion results of moment coefficient of FDL-5A aircraft using three different multi-confidence models;

[0073] Figure 18 A heatmap showing the correlation between different confidence levels of the MCOK model for the lift coefficient;

[0074] Figure 19 A heatmap of correlation between different confidence levels of the MCOK model was obtained for the drag coefficient.

[0075] Figure 20 A heatmap of correlation between different confidence levels of the MCOK model was obtained for the torque coefficient. Detailed Implementation

[0076] To more clearly illustrate the objectives, technical methods, and advantages of this invention, specific embodiments are described below in detail with reference to specific examples and accompanying drawings. Furthermore, the described embodiments are merely a subset of examples of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this application.

[0077] This invention addresses the shortcomings of traditional Co-Kriging multi-fidelity surrogate models by proposing a new aircraft aerodynamic data fusion method based on the MCOK surrogate model. The MCOK surrogate model is a novel multi-fidelity Co-Kriging surrogate model that directly incorporates the correlations between all high and low fidelity data into a single correlation matrix. This avoids recursive modeling of low-fidelity data at each layer and eliminates the need for prior knowledge of the relative accuracy relationships between different low-fidelity data. Furthermore, by introducing an additional model parameter γ before the cross-covariance of the correlation matrix, the correlation between data of any different fidelity levels is quantified, significantly improving the model's fusion prediction accuracy.

[0078] This invention provides a method for fusion of aerodynamic data of aircraft based on the MCOK surrogate model. By establishing an MCOK surrogate model that can fuse aerodynamic data of different confidence levels, it replaces the high-confidence CFD model y0(x) and achieves high-precision and rapid prediction of aerodynamic data of aircraft under different shapes and different flow state parameters.

[0079] refer to Figure 1 This invention provides a method for fusion of aerodynamic data of aircraft based on the MCOK proxy model, comprising the following steps:

[0080] Step 1: Determine the design variable x of the aircraft and the range of values ​​for the design variable x to obtain the design space, and let the number of design variables be m;

[0081] The design variable x is a multi-dimensional design variable. The different dimensional components of the design variable x include the component obtained after parameterizing the body geometry, as well as the flight state component.

[0082] Specifically, for the target aircraft, a parametric method is used to parameterize the aerodynamic shape of the aircraft, obtaining design components that can control the geometry. Then, the flow state variables of the aircraft are selected as design components, resulting in a total of m design components, which form the design variable x = [x1, x2, ... x]. m ] T This refers to the fusion of m-dimensional aerodynamic data. The baseline value of each design component of the design variable is perturbed by 30% up and down to obtain the upper and lower limits of the design variable, which are then used as the design space.

[0083] Step 2: Define L+1 layers of CFD computation models with different confidence levels; where layer 0 is a high-confidence CFD model y0(x), and layers 1 to L are all low-confidence CFD models, represented as: layer 1 low-confidence CFD model y1(x), layer 2 low-confidence CFD model y2(x), ..., layer L low-confidence CFD model yL (x); where any low-confidence CFD model at layer k is represented as y k (x), k = 1, 2, ..., L;

[0084] Step 3: Construct a training sample set, which includes a set of high-confidence samples. and the corresponding set of high-confidence aerodynamic data response values. Low-confidence sample set S k and the corresponding set of low-confidence aerodynamic data response values. The method is as follows:

[0085] Step 3.1: Randomly select one set of values ​​for the design variable x in the design space to form one sample;

[0086] Therefore, n0 samples are randomly selected from the design space as high-confidence samples, thus forming the high-confidence sample set of layer 0. in, These are the individual samples in the high-confidence sample set S0;

[0087] Randomly select n from the design space k Each sample is considered a low-confidence sample in the k-th layer, thus forming the low-confidence sample set in the k-th layer. in, S represents the set of low-confidence samples at layer k. k Each sample in the sample;

[0088] In practical applications, the Latin hypercube experimental design method can be used to randomly and uniformly sample within the design space to obtain high-confidence samples and low-confidence samples.

[0089] Step 3.2: Set the high-confidence sample set of layer 0. High-confidence samples The data is input into a high-confidence CFD model y0(x), which outputs the aerodynamic data response value corresponding to each high-confidence sample, thus obtaining the set of high-confidence aerodynamic data response values. in, They are respectively The corresponding aerodynamic data response value;

[0090] The set of low-confidence samples at layer k. Each low-confidence sample The input is fed into the corresponding k-th layer low-confidence CFD model y k In (x), the k-th layer low-confidence CFD model y k(x) Output the aerodynamic data response value corresponding to each low confidence sample, thereby obtaining the set of low confidence aerodynamic data response values ​​for the k-th layer. in, They are respectively The corresponding aerodynamic data response value;

[0091] Step 4: Construct a large correlation matrix

[0092] Set of high-confidence samples and low-confidence sample sets Construct a total sample set S0, S1, ..., S1 of layer L+1. L ;

[0093] In the total sample set S0, S1,...,S L In the process, calculate the sample set of the j-th layer. Samples in and the l-th layer sample set Samples in Spatial correlation Where p = 1, 2, ..., n j ; q = 1, 2, ..., n l j,l=0,1,…,L;n j ,n l They represent the sample set of the j-th layer, respectively. and the l-th layer sample set The number of samples in the sample;

[0094] The formula for spatial correlation is as follows:

[0095]

[0096] in:

[0097] θ i The value to be determined represents the model hyperparameter corresponding to the i-th design variable in design variable x; i = 1, 2, ..., m;

[0098] and Representing samples respectively and The value of the i-th design variable;

[0099] Thus, the sample set S of the j-th layer is obtained. j and the l-th layer sample set S l Correlation matrix between

[0100]

[0101] After the correlation matrices between all sample sets have been calculated, the correlation matrices form a large, dense, and symmetric correlation matrix as follows.

[0102]

[0103] Step 5: Construct the corrected large correlation matrix

[0104] In large correlation matrices In this context, the multiplier γ is introduced. jl Where j,l=0,1,…,L, and multiplier γ jl Represents the correlation matrix R (jl) The multipliers yield the corrected large correlation matrix.

[0105]

[0106] in:

[0107] γ jl The value to be determined;

[0108] In this invention, to quantify the correlation between data of different confidence levels, an additional model parameter "γ" is introduced before the interaction term, and γ∈(0,1). If γ jl The closer γ is to 1, the stronger the correlation between the j-th layer samples and the l-th layer samples; conversely, if γ is closer to 1, the stronger the correlation between the j-th layer samples and the l-th layer samples .... jl The closer the correlation is to 0, the weaker the correlation between the two.

[0109] Furthermore, in practical applications, when j = l, γ jl =1.

[0110] Step 6, in the corrected large correlation matrix In the above equation, the hyperparameter matrix θ = [θ1, θ2, ..., θ] is obtained by maximizing the likelihood function. m ] T Sum of multiplier matrices

[0111]

[0112] wrtθ,γ

[0113] in:

[0114] n0, n1, n2, ..., n L , representing the sample set S0, S1, ..., S L The number of samples;

[0115] Represents the set of high-confidence aerodynamic data response values ​​y from layer 0. S,0 The first layer of low-confidence aerodynamic data response value set y S,1 The set of low-confidence aerodynamic data response values ​​y at layer L. S,L The response value matrix is ​​composed of;

[0116] Representative size is The regression matrix;

[0117] Represents the trend vector;

[0118] Step 7: Randomly sample the values ​​of design variable x within the design space to form sample x′, and establish the MCOK model equation as follows, based on the training sample set and the corrected large correlation matrix. The model hyperparameter matrix θ = [θ1, θ2, ..., θ m ] T The sum of the multiplier matrix γ = [γ 00 ,γ 01 ,γ 02 ,…,γ LL ] T The predicted aerodynamic response value after fusion of sample x′ is obtained by calculation:

[0119]

[0120] in:

[0121] The fused aerodynamic data response prediction value represents sample x′;

[0122] This represents a regression vector of length L+1;

[0123] Let r0 represent the correlation vector of the high-confidence samples in layer 0, expressed as: The meaning is: each high-confidence sample in the high-confidence sample set S0 Spatial correlation between sample x′ and The high-confidence sample correlation vector formed by the 0th layer; r1,...,r L Represent the correlation vectors of low-confidence samples in layer 1, ..., layer L, respectively; where r1, ..., r L any r in k Let k = 1, 2, ..., L, be the relevance vector of the low-confidence samples in the k-th layer, expressed as: v = 1, 2, ..., n k The meaning is: the set of low-confidence samples S in the kth layer.k Each low-confidence sample Spatial correlation between sample x′ and The correlation vector of the low-confidence samples in the k-th layer;

[0124] This outputs the predicted aerodynamic data response value after fusion of sample x′.

[0125] The MCOK surrogate model established in this invention optimizes the model hyperparameter θ of the relevant function and the additionally introduced model parameter γ, thereby establishing a more accurate MCOK model and improving the prediction performance of the MCOK model.

[0126] This invention provides a pneumatic data fusion method that fully considers the correlation between data of different confidence levels, and introduces additional model hyperparameters to quantify this correlation. Furthermore, this invention avoids the process of modeling individual low-confidence data, resulting in a significant improvement in the accuracy of the final fusion result and greatly enhanced model robustness, demonstrating good potential for engineering applications.

[0127] The following is an example:

[0128] This invention example focuses on data fusion of the aerodynamic coefficients of the FDL-5A hypersonic vehicle from the Flight Dynamics Laboratory.

[0129] To integrate the aerodynamic coefficients of the FDL-5A under different configurations and flight conditions, this example uses a 26-dimensional design variable x. Specifically, the airframe planar shape is defined using 5 geometric parameters, and the upper and lower control lines of the midsection are defined using the Common Shape Transformation (CST) method, along with 3 thickness parameters, 4 trailing edge rudder parameters, and 4 vertical tail parameters, as shown below. Figure 2 As shown in Table 1. Additionally, this example considers four quantities defining the flight state as design components. Therefore, a total of 26 design components are used to establish the multi-credibility surrogate model. Finally, to avoid abnormal configurations and difficulties in aerodynamic calculations, the range of the 26 design components is limited, as shown in Table 1.

[0130] Table 1

[0131]

[0132] In this example, to construct sample sets with different confidence levels for aerodynamic data fusion, the flow around the surface of the FDL-5A hypersonic vehicle was solved using RANS and Euler equations based on unstructured computational grids of varying coarseness. Furthermore, to facilitate demonstrating the effectiveness of this invention, real gas effects were not considered in the numerical simulation. To determine the high-confidence and low-confidence CFD models, grid convergence was studied on the baseline configuration using RANS and Euler solvers, with flow conditions of Ma = 7.98, H = 24.5 km, and α = 10°. Figure 3 and Figure 4 The diagrams show the variations of aerodynamic coefficients with mesh size calculated using the RANS solver and the Euler solver, respectively. Figure 3 The results also show the lift coefficient, drag coefficient, and moment coefficient obtained using the Richardson extrapolation method under an infinitely dense grid. It can be seen that the force coefficients obtained by both solvers exhibit approximately linear changes with the grid size, indicating good grid convergence. In this example, the RANS solver was ultimately used to perform CFD simulations on L1 (2 million) and L2 (500,000) grids, defining them as a high-confidence CFD model and a Level 1 low-confidence CFD model, respectively. The Euler solver was used to perform CFD simulations on L3 (2 million) and L4 (1 million) grids, defining them as Level 2 and Level 3 low-confidence CFD models, respectively. The specific four sets of grids are as follows: Figures 5-8 As shown in Table 2, the aerodynamic coefficients of the baseline configuration calculated by CFD models of different confidence levels are compared with wind tunnel test data, with the relative errors in parentheses. It can be seen from the table that among the four different confidence levels of CFD models, the RANS result using the L1 grid has the smallest relative error and should therefore be a high-confidence CFD model. The relative errors for each aerodynamic coefficient differ for the other three CFD models, making it impossible to uniformly determine their relative accuracy levels. This invention can handle such non-hierarchical low-confidence datasets, and only requires that the high-confidence CFD model be determined, without needing to know the relative accuracy relationships between the low-confidence CFD models in advance.

[0133] Table 2

[0134]

[0135] By using Latin hypercube sampling in the design space specified in Table 1, 150 high-confidence samples and 600 low-confidence samples were randomly and uniformly generated, establishing a training sample set of 1950 samples in total. Then, an additional 450 high-confidence samples were generated to test the model's accuracy. To avoid the influence of the initial samples on modeling accuracy, the experiment was repeated five times, with each experiment using different multi-confidence sample sets for both training and testing. To fully explore the advantages and benefits of this invention, it was compared with other existing multi-confidence surrogate models, such as the NHLF-COK multi-confidence surrogate model for non-hierarchical low-precision data and the LR-MFS multi-confidence surrogate model based on linear regression.

[0136] Table 3 presents a comparison of the average accuracy indicators of the fusion of aerodynamic data of the FDL-5A hypersonic vehicle using three multi-confidence CFD models in this experiment.

[0137] Table 3

[0138]

[0139] As can be seen from Table 3, the MCOK model of this invention has the best average value of the three accuracy indicators, the largest R2, and the smallest RMSE and MAE, indicating that its fusion accuracy is the highest and it is superior to other multi-trust proxy models in terms of both local and global accuracy. Figure 9 , 10 and Figure 11 The R values ​​are obtained by fusing the lift coefficient of the FDL-5A aircraft using three different multi-confidence CFD models. 2 Box charts for indicators, RMSE indicator box chart, and MAE indicator box chart. Figure 12 , 13 and Figure 14 The R values ​​are obtained by fusing the drag coefficient of the FDL-5A aircraft using three different multi-confidence CFD models. 2 Box charts for indicators, RMSE indicator box chart, and MAE indicator box chart. Figure 15 , 16 and Figure 17 The R values ​​are obtained by fusing the moment coefficients of the FDL-5A aircraft using three different multi-confidence CFD models. 2 Box plots of indicators, RMSE indicator box plot, and MAE indicator box plot. As can be seen from the figures, the interquartile range of the present invention is smaller than that of the other two multi-confidence CFD models, indicating that the dispersion of the results of five repeated predictions is lower. The robustness of the MCOK model of the present invention is significantly better than other multi-confidence surrogate models. Figure 18 , 19 and Figure 20The figures show the correlation heatmaps of CFD models with different confidence levels obtained using the MCOK model for lift, drag, and moment coefficients. It can be seen that the correlation between the first low-confidence CFD model and the high-confidence CFD model is much higher than the correlation between the other two low-confidence CFD models and the high-confidence CFD models. In other words, CFD results calculated using the same flow control equations on different grid coarseness are closer to each other, and have a higher correlation than CFD results calculated using different flow control equations on grids of the same magnitude.

[0140] In summary, this invention discloses an aerodynamic data fusion method for aircraft based on the MCOK surrogate model. This method quantifies the correlation between multi-source and complex data by introducing additional model parameters before the covariance term of the correlation matrix, achieving efficient and high-precision fusion of aerodynamic data with arbitrarily high confidence levels. Compared with other aerodynamic data fusion methods based on multi-confidence surrogate models (such as the NHLF-COK multi-confidence surrogate model for non-hierarchical low-precision data and the LR-MFS multi-confidence surrogate model based on linear regression), the aircraft aerodynamic data fusion method based on the MCOK surrogate model proposed in this invention not only overcomes the defect of loss of fusion accuracy caused by the inaccuracy of low-confidence models, but also considers the correlation between low-confidence models, significantly improving the accuracy of fusion prediction and making the model more robust, thus possessing good engineering application potential.

[0141] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for fusion of aerodynamic data of aircraft based on the MCOK surrogate model, characterized in that, The MCOK proxy model is a novel multi-fidelity Co-Kriging proxy model, referred to as MCOK, which includes the following steps: Step 1: Determine the design variables of the aircraft and design variables The range of values ​​for is used to obtain the design space, and the number of design variables is set to . ; Step 2, Define CFD computational models with different confidence levels at each layer; where layer 0 is a high-confidence CFD model. , from the 1st floor to the All layers are low-confidence CFD models, represented as follows: Layer 1 low-confidence CFD model Layer 2 low-confidence CFD model ,…, No. Low-confidence CFD model ; among which, any number of The low-confidence CFD model is represented as , ; Step 3: Construct a training sample set, which includes a set of high-confidence samples. and the corresponding set of high-confidence aerodynamic data response values. Low-confidence sample set and the corresponding set of low-confidence aerodynamic data response values. The method is as follows: Step 3.1: Randomly select one set of design variables from the design space. The value of is used to form 1 sample; Therefore, randomly select from the design space Each sample is designated as a high-confidence sample, thus forming the high-confidence sample set of layer 0. ;in, High-confidence sample sets Each sample in the sample; Randomly selected in the design space The nth sample is the first The low-confidence samples of the layer form the first layer. Low-confidence sample set ;in, The first Low-confidence sample set Each sample in the sample; Step 3.2: Set the high-confidence sample set of layer 0. High-confidence samples Input into a high-confidence CFD model In the middle, high-confidence CFD model Output the aerodynamic data response value corresponding to each high-confidence sample, thereby obtaining the set of high-confidence aerodynamic data response values. ;in, They are respectively The corresponding aerodynamic data response value; The first Low-confidence sample set Each low-confidence sample Enter into the corresponding number Low-confidence CFD model In the middle, the first Low-confidence CFD model Output the aerodynamic data response value corresponding to each low-confidence sample, thereby obtaining the first... Low-confidence aerodynamic data response value set ;in, They are respectively The corresponding aerodynamic data response value; Step 4: Construct a large correlation matrix : Set of high-confidence samples and low-confidence sample sets Construction Total sample set of the layer ; In the total sample set In the middle, calculate the first Layer sample set Samples in and the Layer sample set Samples in Spatial correlation ,in, ; Representing the first Layer sample set and the Layer sample set The number of samples in the sample; The formula for spatial correlation is as follows: in: The value to be determined represents the design variable. The Middle The model hyperparameters corresponding to each design variable; ; and Representing samples respectively and The The values ​​of the design variables; Therefore, we obtain the first... Layer sample set and the Layer sample set Correlation matrix between , ; After the correlation matrices between all sample sets have been calculated, the correlation matrices form a large, dense, and symmetric correlation matrix as follows. : ； Step 5: Construct the corrected large correlation matrix : In large correlation matrices In the middle, multipliers are introduced. ,in, , ride Represents the correlation matrix The multipliers yield the corrected large correlation matrix. : ； in: The value to be determined; Step 6, in the corrected large correlation matrix In this process, the hyperparameter matrix of the model is obtained by maximizing the likelihood function according to the following formula. Sum of multiplier matrices : ； in: , representing the sample set The number of samples; This represents the set of high-confidence aerodynamic data response values ​​from layer 0. The first layer of low-confidence aerodynamic data response value set ,…,No. Low-confidence aerodynamic data response value set The response value matrix is ​​composed of; , representing a scale of The regression matrix; , representing the trend vector; Step 7: Randomly select design variables within the design space. The value forms a sample The MCOK model equation is established based on the training sample set and the corrected large correlation matrix. Model hyperparameter matrix Sum of multiplier matrices The sample was obtained through calculation. The fused aerodynamic data response prediction values: in: Representative sample The predicted value of the fused aerodynamic data response; The representative length is The regression vector; Represents the relevant vector. The relevance vector representing the high-confidence samples at layer 0 is expressed as: , The meaning is: a set of highly reliable samples. Each high-confidence sample and samples Spatial correlation between The high-confidence sample correlation vector formed by the 0th layer; These represent the correlation vectors of the low-confidence samples in the first layer, ..., the ... The correlation vector of low-confidence samples in the layer; where, any of , , for the first The correlation vector of low-confidence samples in the layer is represented as: , The meaning is: the first Low-confidence sample set Each low-confidence sample and samples Spatial correlation between The first Relevance vectors of low-confidence samples in the layer; This outputs a sample. The fused aerodynamic data response prediction value.

2. The method for fusion of aircraft aerodynamic data based on the MCOK proxy model according to claim 1, characterized in that, In step 1, design variables Design variables for multiple dimensions.

3. The method for fusion of aircraft aerodynamic data based on the MCOK proxy model according to claim 1, characterized in that, Design variables The different dimensional components include the components obtained after parameterizing the body geometry, as well as the flight state components.

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