Active optimization design method for axial flow fan blade

Abstract

The invention relates to an active optimization design method of an axial flow fan blade, which comprises the following steps of: defining a blade profile construction line by adopting seven parameters such as a leading edge radius, and parameterizing and representing two-dimensional blade profile geometric characteristics based on NURBS curve control points; a two-dimensional blade profile and three-dimensional fan coordinate system is constructed, and control point coordinate mapping is achieved through matrix transformation; the method comprises the following steps: acquiring an initial sample based on Latin hypercube sampling, and establishing a Gaussian process proxy model by combining two-dimensional CFD calculation data; a K-RVEA algorithm is applied, maximization of a worst attack angle lift-drag ratio and minimization of a resistance coefficient are taken as double targets, Pareto optimization is carried out in combination with geometry and performance constraints, and iteration is terminated through a hyper-volume convergence criterion; and the optimized two-dimensional blade profile parameters are converted into NURBS description, and stacking is carried out in the spanwise direction to generate a three-dimensional blade entity. The grid sensitive effect in three-dimensional optimization is overcome, the flow field analysis precision is improved, invalid calculation is reduced, the blade profile curvature continuity and the process feasibility are guaranteed, and the design period of the axial flow fan is shortened.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fluid machinery aerodynamic optimization, in particular to an active optimization design method of an axial flow fan blade. BACKGROUND

[0002] As a core fluid equipment in the fields of energy, heating, ventilation, aerospace, etc., the improvement of the aerodynamic efficiency of the axial flow fan has great strategic significance for energy saving and emission reduction. Studies have shown that the aerodynamic efficiency of modern axial flow fans still has 15%-20% of the improvement space from the theoretical limit (92%). However, the average annual efficiency growth rate of actual products in the past decade is less than 0.5%. This bottleneck is mainly due to the defects of the existing design method.

[0003] The current axial flow fan relies on fine-tuning design, which makes small-range geometric adjustments (such as installation angle ± 2°, chord length ± 3%) on the baseline blade profile, and verifies through the following ways:

[0004] (1) Test method: it needs to open a full-size mold for the designed fan, which has low error but high mold cost;

[0005] (2) CFD simulation method: although it avoids physical prototype, the time and calculation cost of one high-level CDF calculation are still not low, and the calculation error is far from that of the test method. SUMMARY

[0006] In view of the problems existing in the prior art, the purpose of the present application is to provide an active optimization design method of an axial flow fan blade, which solves the core contradiction between high cost of traditional three-dimensional optimization calculation and two-dimensional simulation deviating from reality, and realizes the coordinated breakthrough of efficiency improvement and design cycle.

[0007] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0008] An active optimization design method of an axial flow fan blade, comprising the following steps:

[0009] Two-dimensional blade profile parameterization: the two-dimensional blade profile of the axial flow fan is parameterized and reconstructed, seven parameters of leading edge radius, trailing edge radius, arch height, chord length, maximum thickness, thickness position ratio and camber position ratio are used to completely describe the two-dimensional blade profile construction line, a seven-degree-of-freedom control parameter set is defined, and a geometric mapping function is established based on NURBS curve control points (non-uniform rational B-spline curve);

[0010] Establishing an aerodynamic coordinate system: based on the NURBS curve control points, the two-dimensional blade profile coordinate system and the three-dimensional fan coordinate system are constructed, and the control point coordinates in the two-dimensional blade profile coordinate system are mapped to the three-dimensional fan coordinate system through matrix transformation;

[0011] The Latin hypercube sampling obtains an initial sample set: based on a seven-degree-of-freedom control parameter set, an initial sample set with high spatial representation is generated through a stratified uniform coverage and random arrangement strategy, and each sample in the initial sample set contains the values of the seven parameters;

[0012] Two-dimensional airfoil aerodynamic calculation: for each sample, a corresponding two-dimensional airfoil geometric model is generated using a geometric mapping function, and two-dimensional CFD calculation (fluid numerical simulation method) is performed, outputting aerodynamic performance indicators including lift coefficient, drag coefficient and lift-drag ratio, and the results are associated with the corresponding seven-degree-of-freedom control parameter set;

[0013] Gaussian process construction of proxy model: after data normalization, a multi-output Gaussian process model is constructed by using a Matern 5 / 2 kernel function (describing the similarity between random processes or functions) with the aerodynamic performance indicators and the corresponding sample parameters as inputs, and the proxy model is obtained through hyperparameter optimization and k-fold cross-validation;

[0014] K-RVEA algorithm optimization: based on the proxy model, the seven-degree-of-freedom control parameters are taken as design variables, the K-RVEA algorithm is applied, the key angle of attack is calculated as the objective function, the reference vector is generated combined with geometric and performance constraints and iterative optimization is performed, the iteration is terminated using the hyper volume convergence criterion, and the Pareto solution set is output;

[0015] Generation of three-dimensional blade entity: the two-dimensional airfoil parameters of the optimal individual are selected from the Pareto solution set, which are converted into mathematical description of NURBS curve through geometric mapping function, and the three-dimensional blade entity is generated by stacking along the span direction based on three-dimensional fan coordinate system.

[0016] Further, the geometric mapping function is

[0017]

[0018] where C(u) is a two-dimensional airfoil construction line function, P i =(x i ,y i ) is the coordinate of the control point, w i is the weight coefficient, and N i,p (u) is the p-th B-spline basis function.

[0019] Further, the two-dimensional CFD calculation adopts unstructured triangular mesh and adds a boundary layer on the airfoil surface, and through grid independence verification, the lift-drag ratio calculation results of different grid numbers based on the same parameter set are used to train the proxy model.

[0020] Further, the matrix transformation formula is

[0021]

[0022] In the formula, β is the installation angle of the blade.

[0023] Further, in the two-dimensional airfoil aerodynamic calculation, the boundary condition is set as: the angle between the speed inlet direction and the chord line is the attack angle α, and the residual convergence standard is: the continuity, momentum, turbulent flow energy and specific dissipation rate are reduced to 10 -3 In the following, the energy residual is reduced to 10 -6 In the following.

[0024] Further, the formula for data normalization processing is

[0025]

[0026] In the formula, x i is the original parameter value, respectively, the upper and lower limits of the parameters, and the sample parameters are mapped to the [0, 1] interval.

[0027] Further, the hyperparameters of the proxy model are obtained by maximum likelihood estimation, and the determination coefficient is ensured to be ≥0.98 and the coverage probability is ensured to be ≥95% through k-fold cross-validation.

[0028] Further, the objective function is

[0029]

[0030] In the formula, x=[R1, R2, h, t, L, x t ,x c ] T is a set of 7-degree-of-freedom control parameters, C l and C d are aerodynamic performance indicators, and the key attack angle

[0031] Further, the K-RVEA algorithm generates uniformly distributed reference vectors by using the Das-Dennis method (reference vector generation technology) to ensure the convergence and distribution of the Pareto front.

[0032] Further, in the iteration process of the K-RVEA algorithm, the optimal individual selected from the Pareto solution set is verified by CFD in the full attack angle range, and meets the engineering threshold C l / C d ≥45, C d ≤0.025; if the verification finds that the performance in the uncovered area does not meet the standard, the attack angle is included in the key attack angle for re-optimization.

[0033] Overall, the present application has the following advantages:

[0034] 1) Through the two-dimensional airfoil parameterization reconstruction mechanism, the grid sensitivity effect in three-dimensional optimization can be overcome, and the flow field analysis accuracy is improved;

[0035] 2) The method uses the Bayesian optimization framework to drive the proxy model iteration, which greatly reduces the invalid calculation.

[0036] 3) NURBS parameterization embeds manufacturing constraints into control point boundaries, automatically ensuring airfoil curvature continuity and process feasibility;

[0037] 4) The proxy model driven parallel optimization mechanism can greatly shorten the design cycle of axial flow fans. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 It is a three-dimensional model diagram of Z670W-7A axial flow fan;

[0039] Figure 2 It is a two-dimensional airfoil flattening diagram of the cross section of Z670W-7A axial flow fan;

[0040] Figure 3 It is a flow rate-static pressure comparison diagram of three-dimensional CFD aerodynamic performance calculation of Z670W-7A axial flow fan before and after optimization;

[0041] Figure 4 It is a flow rate-power comparison diagram of three-dimensional CFD aerodynamic performance calculation of Z670W-7A axial flow fan before and after optimization;

[0042] Figure 5 It is a flow rate-efficiency comparison diagram of three-dimensional CFD aerodynamic performance calculation of Z670W-7A axial flow fan before and after optimization. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical scheme and advantages of the present application more clear and definite, the following will combine with the example of axial flow fan Z670W-7A, as shown in the drawings, and further describe the present application in detail. Figure 1

[0044] (1) Two-dimensional airfoil parameterization:

[0045] The two-dimensional airfoil of the axial flow fan is parameterized and reconstructed, and the seven parameters shown in Table 1 are used to completely describe the two-dimensional airfoil construction line.

[0046] Table 1 Two-dimensional airfoil parameter table

[0047]

[0048] x1 and x2 are the horizontal coordinate values of the maximum thickness and the maximum arch height position, respectively.

[0049] ​Define seven degrees of freedom control parameter set: θ = [R1, R2, h, t, L, x t ,x c ] T .

[0050] Two-dimensional airfoil parameterization: based on NURBS curve control point to establish geometric mapping function.

[0051]

[0052] Where P i = (x i ,y i ) is the control point coordinate, w i is the weight coefficient, and N i,p (u) is the p-th B-spline basis function. This function is used to convert the parameters of the two-dimensional airfoil into control point coordinates. The complex three-dimensional blade problem is reduced to a two-dimensional airfoil, which can be uniquely determined by seven key geometric parameters, and the curvature is kept continuous by NURBS curve, which lays a low-dimensional and manufacturable geometric foundation for subsequent optimization.

[0053] (2) Establish the aerodynamic coordinate system:

[0054] (a) Two-dimensional airfoil coordinate system: take the leading edge circle as the origin o1, the chord line direction as the X1 axis (pointing to the trailing edge circle), and the airfoil normal direction as the Z1 axis (pointing to the suction surface), and the Y1 axis is determined by the right-hand rule; (b) Three-dimensional fan coordinate system: take the hub center as the origin o2, the axial direction as the Z2 axis (pointing to the outlet), the radial direction as the X2 axis (pointing to the blade tip), and the circumferential direction as the Y2 axis. The control point coordinates are defined in the O1 system, and the control point coordinates are mapped to the O2 system through matrix transformation.

[0055]

[0056] Map the two-dimensional airfoil control points to the three-dimensional fan coordinate system through matrix transformation to ensure that the two-dimensional optimization results can be directly used for three-dimensional blade reconstruction, avoiding the traditional two-dimensional / three-dimensional iterative iteration, greatly shortening the design cycle.

[0057] (3) Latin hypercube sampling to obtain the initial sample set:

[0058] Through the strategy of hierarchical uniform coverage and random arrangement, an initial sample set with high spatial representation is generated. The specific steps are as follows:

[0059] First, determine the sample number N, balance the spatial coverage and computational efficiency. The empirical formula of Latin hypercube sampling is:

[0060] N = max (10d, 50) (3)

[0061] where d is the number of parameters, 10d can ensure enough hierarchy in each parameter dimension, and 50 is the minimum sample size (to avoid under sampling). The scheme selects 70 samples.

[0062] Second, the value range of each parameter is evenly divided into N=70 layers, and the length of each layer is:

[0063]

[0064] where are the upper and lower limits of the i-th parameter, respectively.

[0065] For each parameter dimension, generate a random permutation of 1 to N, ensuring that each layer is selected only once in each parameter dimension, avoiding sample aggregation in a certain dimension.

[0066] Third, calculate the sample coordinates, and check whether the generated 70 samples meet the correlation constraints between parameters. Finally, organize the sample data to form the initial sample set X={x (1) ,x (2) ,...,x (70)}, where each sample contains the values of 7 parameters, taking into account spatial coverage and computational efficiency, providing a high-quality initial data set for subsequent proxy models.

[0067] (4) Two-dimensional airfoil aerodynamic calculation:

[0068] First, parameterized geometric modeling: UG (industrial design software) script establishes a two-dimensional airfoil;

[0069] Second, meshing: unstructured triangular mesh is used, and a boundary layer is added to the airfoil surface (to accurately capture the turbulence generation and dissipation process in the near-wall region).

[0070] The boundary layer selection needs to meet the minimum layer requirement of y + +1

[0071]

[0072] where y + is a dimensionless parameter that quantifies the distance of the near-wall region grid node to the wall surface, used to evaluate the resolution of the CFD grid to the wall boundary layer flow; u τ is the friction velocity, (u τ ≈0.1u in , U in is the incoming flow velocity); y is the first layer grid height; v is the fluid viscosity (air viscosity v≈1.5×10 -5 m 2 / s);

[0073] Grid independence verification: select 3 groups of different grid numbers (e.g. 50,000, 100,000, 150,000), calculate the lift-drag ratio C l / C d of the same parameter set l , if the C d of adjacent grid numbers changes less than 1%, select 100,000 grid numbers as the reference.

[0074] Third step, flow field solution: turbulence model: select k-omega-SST model (suitable for simulating boundary layer separation, transition and adverse pressure gradient flow, consistent with the flow characteristics of axial fan blade profile); Discrete scheme: first-order upwind difference format (initialization, accelerate convergence speed), second-order upwind difference format (final calculation, improve accuracy); Pressure-velocity coupling: SIMPLEC algorithm (suitable for incompressible flow); Boundary condition definition: velocity inlet: given incoming flow velocity, direction is the angle of attack a (included angle with chord line of blade profile); Pressure outlet: set to atmospheric pressure; Residual convergence: energy residual drops to 10 -6 -4 below; -3 ;

[0075] After calculation, output aerodynamic performance indicators: lift coefficient C l , drag coefficient C d , lift-drag ratio C l / C d ; export the results as CSV file (common pure text table data storage format), associate the corresponding parameter set θ = [R1, R2, h, t, L, x t , x c ] T .

[0076] (5) Gaussian process to build surrogate model:

[0077] Surrogate model can realize efficient and high-precision prediction from parameters to performance, and provide key support for subsequent Bayesian optimization. The specific steps are as follows:

[0078] First step, define the input and output of the surrogate model. Input: 7 degrees of freedom control parameter set x =

[0079] [R1, R2, h, t, L, x t , x c ] T . Among them, the physical meaning and value range of each parameter are shown in Table 1. Output: two-dimensional blade profile aerodynamic performance indicators, lift coefficient: y1 = C l , drag coefficient: y2 = C d , and lift-drag ratio: y3 = C l / C d .

[0080] The nonlinear mapping relationship from the input parameter x to the output performance index y = [y1, y2, y3] is established by the Gaussian model: T

[0081] y = f(x) + ε (6)

[0082] where f(x) is an unknown true performance function, is a Gaussian noise (measurement error).

[0083] Second step, data preprocessing. Since the dimensions and value ranges of the parameters in the parameter set are quite different, the input data needs to be normalized to ensure that the parameters are on the same scale and to avoid the dimension sensitivity of the kernel function. Linear scaling is used to map each parameter to the interval [0, 1]:

[0084]

[0085] where x i is the original parameter value, are the upper and lower limits of the parameters, respectively.

[0086] Third step, Gaussian process model construction. Gaussian process is a non-parametric Bayesian model that describes the uncertainty of the function through prior distribution (kernel function) and posterior distribution (data update). This scheme uses a multi-output Gaussian process to simultaneously predict multiple aerodynamic performance indicators (C l , C d , C l / C d ).

[0087] For the 7-degree-of-freedom high-dimensional parameter set, the Matern 5 / 2 kernel function (suitable for modeling smooth functions and has good robustness for high-dimensional data) is selected:

[0088]

[0089] where r = ||x-x ′ || is the Euclidean distance between the input parameter x and x ′ ; is the signal variance (control function fluctuation amplitude); is the length scale parameter (each dimension corresponds to a length scale, which controls the influence of the parameter on the output).

[0090] Fourth step, hyperparameter optimization. Before training the model, hyperparameter optimization is needed. Because the value of the hyperparameter directly determines the prediction accuracy of the model, if it is not optimized, the model may be overfitting or underfitting, which cannot support subsequent Bayesian optimization. The hyperparameters include: signal variance ​Time scale Noise variance The hyperparameters are optimized using maximum likelihood estimation, aiming to maximize the likelihood function of the training data:

[0091]

[0092] where, is the hyperparameter vector, K is the kernel matrix (K ij = k(x i , x j )), n is the number of training samples, and y is the output performance vector of the training samples.

[0093] Step 5, model training. The 70 initial samples generated by Latin hypercube sampling in (4) (x (k) , y (k) , k = 1, 2,..., 70) are input into the Gaussian process model for model training.

[0094] Step 6, model validation. To ensure the generalization ability of the surrogate model, k-fold cross-validation is used. The prediction error indicators include:

[0095] Root mean square error (RMSE): (reflecting the deviation between predicted and true values);

[0096] Coefficient of determination (R 2 ): (reflecting the model's ability to explain data, R 2 closer to 1, the higher the model accuracy, ≥98%);

[0097] Coverage probability (CP): (reflecting the coverage ability of the uncertainty interval, ≥95%).

[0098] (6) K-RVEA algorithm optimization.

[0099] Step 1, determine the design variables, objective functions, and constraints. Design variables: 7-degree-of-freedom control parameter set x = [R1, R2, h, t, L, x t , x c ] T ; design conditions: select three key attack angles To ensure the stability of the two-dimensional airfoil performance in the full operating range, the algorithm aims to maximize the lift-drag ratio f1 at the worst attack angle and minimize the drag coefficient f2 at the worst attack angle, the objective function:

[0100]

[0101] where, x = [R1, R2, h, t, L, xt x c ] T is the set of 7-DOF control parameters.

[0102] Constraints: (a) the value range of each parameter is shown in Table 1 in (1); (b) geometric constraints: the blade profile curve needs to satisfy the curvature continuity requirement: c(u) is the parametric equation of the blade profile curve; (c) performance constraints:

[0103] In the second step, in order to ensure that the solution set generated by the evolutionary algorithm converges to the Pareto front and guarantee the distribution, a reference vector needs to be generated. The present application uses the Das-Dennis method to generate uniformly distributed reference vectors: input: target number m = 2 (f1, f2), resolution p = 20 (control reference vector density); calculate the number of reference vectors: Generate reference vectors: the kth reference vector is Output: reference vector set

[0104] In the third step, the Latin hypercube is used to generate the initial population ( is the design variable value of the ith sample).

[0105] In the fourth step, the real performance of the initial population is evaluated by the two-dimensional blade profile aerodynamic calculation method (the two-dimensional blade profile aerodynamic calculation method can be seen in (5)), and the real performance set of the initial population is output ( in the formula ).

[0106] In the fifth step, iteration is performed. The surrogate model M constructed by (6) is used to predict the target value of the current population P g-1 (g is the current iteration number), When the change rate of the hypervolume HV of 5 consecutive generations is less than or equal to 1%, stop iteration:

[0107]

[0108] In the formula, HV is the hypervolume, which represents the size of the solution set covering the target space, and comprehensively reflects the convergence and distribution; is the target vector set of the solution set; f * is the reference point (for example, f * = (0.3, 10) T represents C d = 10) ; is the m-dimensional real number space, and m is the target number (the target number in this optimization is 2); I is an indicator function, which takes 1 when the condition is met, and 0 otherwise.

[0109] Sixth step, when the iteration is terminated, output the Pareto solution set with the Pareto front

[0110] Seventh step, for the optimal individual in the Pareto solution set, CFD verification is carried out in the full range of attack angle (α = 0° ~ 15°), and it is confirmed that the performance of the design condition and the non-design condition meets the engineering threshold C l / C d ≥ 45, C d ≤ 0.025; if the verification finds that the performance of the uncovered area (such as 6°) does not meet the standard, the attack angle needs to be included in the key attack angle re-optimization.

[0111] (7) Convert the two-dimensional blade profile parameters obtained by optimization into mathematical description (control points, weights, node vectors) of NURBS curve (non-uniform rational B-spline curve); read the NURBS data of each span section through the parametric modeling script of UG, and automatically stack the sections along the span (the installation angle remains the original blade profile) to generate a three-dimensional blade entity.

[0112] (8) The axial flow fan before and after optimization is respectively subjected to CFD aerodynamic performance calculation, and the results are shown in Figure 3 、 Figure 4 、 Figure 5 The optimization degree of performance index is compared with reference table 2.

[0113] Table 2 Aerodynamic performance index change of Z670W-7A before and after optimization

[0114]

[0115] The above examples are the preferred embodiments of the present application, but the embodiments of the present application are not limited by the above examples, and any changes, modifications, substitutions, combinations and simplifications made without departing from the spirit and principles of the present application should be equivalent replacement methods, and all are included in the protection scope of the present application.

Claims

1. An active optimization design method for axial flow fan blades, characterized in that: Includes the following steps: Two-dimensional blade parameterization: The two-dimensional blade of the axial flow fan is parametrically reconstructed. The construction line of the two-dimensional blade is completely described by seven parameters: leading edge radius, trailing edge radius, camber height, chord length, maximum thickness, thickness position ratio and camber position ratio. A set of seven degrees of freedom control parameters is defined, and a geometric mapping function is established based on NURBS curve control points. Establishing an aerodynamic coordinate system: Based on NURBS curve control points, construct a two-dimensional blade coordinate system and a three-dimensional wind turbine coordinate system, and map the coordinates of the control points in the two-dimensional blade coordinate system to the three-dimensional wind turbine coordinate system through matrix transformation; Latin hypercube sampling to obtain the initial sample set: Based on the seven-degree-of-freedom control parameter set, a high spatial representative initial sample set is generated through a hierarchical uniform coverage and random arrangement strategy. Each sample in the initial sample set contains the values ​​of the seven parameters. Two-dimensional airfoil aerodynamic calculation: For each sample, a corresponding two-dimensional airfoil geometric model is generated using a geometric mapping function, and two-dimensional CFD calculation is performed to output aerodynamic performance indicators, including lift coefficient, drag coefficient and lift-to-drag ratio, and the results are associated with the corresponding seven-degree-of-freedom control parameter set; Gaussian process surrogate model construction: Aerodynamic performance indicators and corresponding sample parameters are used as inputs. After data normalization, a multi-output Gaussian process model is constructed using the Matern 5 / 2 kernel function. The surrogate model is obtained through hyperparameter optimization and k-fold cross-validation. K-RVEA Algorithm Optimization: Based on the surrogate model, using the seven-degree-of-freedom control parameters as design variables, the K-RVEA algorithm is applied to select the key angle of attack to calculate the objective function, and a reference vector is generated by combining geometric and performance constraints and iterative optimization is performed. The iteration is terminated by using the hypervolume convergence criterion, and the Pareto solution set is output. Generating 3D blade entities: Select the 2D blade profile parameters of the optimal individual from the Pareto solution set, convert them into the mathematical description of NURBS curves through a geometric mapping function, and generate 3D blade entities by stacking them along the span based on the 3D wind turbine coordinate system.

2. The method according to claim 1, characterized in that: The geometric mapping function is Where C(u) is the two-dimensional leaf-shaped construction line function, P i =(x i ,y i ) represents the coordinates of the control point, w i N represents the weighting coefficient. i,p (u) is a p-th degree B-spline basis function.

3. The method according to claim 1, characterized in that: Two-dimensional CFD calculations employ unstructured triangular meshes and add boundary layers to the airfoil surface. Mesh independence is verified, and the lift-to-drag ratio is calculated based on the same parameter set with different mesh counts. The performance metrics output from the flow field solution are used for surrogate model training.

4. The method according to claim 1, characterized in that: The matrix transformation formula is In the formula, β is the blade installation angle.

5. The method according to claim 1, characterized in that: In the two-dimensional blade aerodynamic calculation, the boundary conditions are set as follows: the angle between the velocity inlet direction and the chord is the angle of attack α, and the residual convergence criteria are: continuity, momentum, turbulent kinetic energy, and specific dissipation rate decrease to 10. -3 Below, the energy residual decreases to 10. -6 the following.

6. The method according to claim 1, characterized in that: The formula for data normalization is: In the formula, x i These are the original parameter values. These are the upper and lower limits of the parameters, respectively, mapping the sample parameters to the [0,1] interval.

7. The method according to claim 1, characterized in that: The hyperparameters of the surrogate model were obtained through maximum likelihood estimation, and k-fold cross-validation was used to ensure that the coefficient of determination was ≥0.98 and the coverage probability was ≥95%.

8. The method according to claim 1, characterized in that: The objective function is In the formula, x = [R1,R2,h,t,L,x] t ,x c ] T For a 7-DOF control parameter set, C l and C d For aerodynamic performance indicators, key angle of attack 9. The method according to claim 1, characterized in that: The K-RVEA algorithm uses the Das-Dennis method to generate uniformly distributed reference vectors to ensure the convergence and distribution of the Pareto front.

10. The method according to claim 1, characterized in that: During the iterative process, the optimal individual selected from the Pareto solution set by the K-RVEA algorithm undergoes CFD verification across the entire angle of attack range, satisfying the engineering threshold C. l / C d ≥45,C d ≤0.025; If the verification finds that the performance of the uncovered area is not up to standard, then the angle of attack will be included in the critical angle of attack for re-optimization.

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