A multi-confidence proxy optimization method capable of reducing numerical noise interference and computing bad point influence

Abstract

The application belongs to the field of engineering optimization design, and provides a multi-confidence proxy optimization method capable of reducing numerical noise interference and computing bad point influence, comprising: obtaining a multi-level original sample set arranged in descending order of confidence; establishing a SVR-MHK proxy model capable of filtering noise, including a support vector regression model, an abnormal response value identification model, an epsilon-Kriging model and a multi-confidence MHK model; based on the SVR-MHK proxy model, using an optimization adding point criterion to guide the addition of new sample points; using the updated sample set to reconstruct the SVR-MHK proxy model, and continuously repeating the reconstruction until an optimization convergence criterion is reached. The application combines a dynamic filtering strategy and a multi-confidence modeling framework to realize filtering of numerical noise and bad points in high-dimensional optimization design, and can be applied to airfoil optimization design and other problems, reducing the influence of numerical noise in optimization design, and obtaining an optimization result meeting design requirements while ensuring optimization efficiency.

Description

Technical Field

[0001] This invention belongs to the field of engineering optimization design technology, specifically involving a multi-credibility proxy optimization method that can reduce numerical noise interference and the impact of computational bad points. Background Technology

[0002] Numerical noise and bad spots exist in the field of aerodynamic design. Numerical noise refers to the random fluctuations of the objective or constraint function around the true function as design variables change during the optimization process. Bad spots refer to response values ​​that significantly exceed the true range and are difficult to correct using conventional methods. Affected by factors such as incomplete convergence, mesh discretization, turbulence models, inaccurate boundary condition settings, and unreasonable model shapes, numerical noise and bad spots inevitably occur during CFD calculations, leading to inaccurate optimization results or even optimization failure, severely impacting the efficiency of aerodynamic optimization design. Therefore, numerical noise, along with the curse of dimensionality, complex numerical analysis, and continuous / discrete design spaces, has become a key scientific problem hindering research on efficient global aerodynamic optimization design.

[0003] Future refined optimization design will develop towards high performance, multi-task and multi-disciplinary coupling, exhibiting significant characteristics such as more design variables, more complex design spaces, and more time-consuming numerical simulations. Specifically, high-dimensional aerodynamic optimization problems under complex conditions face the following challenges: 1) The contradiction between the need for large samples and the enormous computational load. Constructing a sufficiently comprehensive sample set in a high-dimensional space requires an exponentially increasing number of samples. However, due to the limitations of CFD computational costs, engineering projects typically only have a limited number of samples, leading to the surrogate model being underconstrained in most regions, further amplifying the impact of numerical noise on model predictions. 2) Increased risk of correlation modeling failure. Surrogate models based on correlation functions, such as Kriging's, require the estimation of a large number of hyperparameters in high-dimensional cases. Numerical noise and bad points can severely interfere with the hyperparameter optimization process, causing the correlation structure to degenerate and even resulting in ill-conditioned covariance matrices, leading to model instability or failure. 3) Reduced robustness of the addition criteria. In the context of high-dimensional noise, addition criteria based on uncertainty or expected improvement criteria are easily misled by local noise peaks, producing "false optimal points" or overexploring high-frequency numerical noise regions, thereby severely reducing global optimization efficiency. Therefore, high-dimensional problems are not simply a matter of "increasing number of variables," but rather a systemic challenge resulting from the superposition of multiple factors such as noise, bad points, model complexity, and computational cost. There is an urgent need to develop noise-resistant proxy optimization methods that take into account both robustness and the ability to cope with high-dimensional problems.

[0004] To address the complex situation of numerical noise and dead pixels coexisting in high-dimensional aerodynamic design, researchers have proposed a series of high-dimensional noise-resistant optimization strategies, which can be broadly categorized into two approaches: gradient enhancement methods and multi-confidence methods. Gradient enhancement methods reduce the number of high-confidence samples by introducing gradient information, but the curse of dimensionality becomes more pronounced. Multi-confidence methods significantly reduce computational costs by introducing samples of different confidence levels and solving the relationships between different confidence functions, but there is still room for improvement: 1) Existing multi-confidence noise-resistant surrogate optimization algorithms mainly address problems around ten dimensions, and further research is needed for high-dimensional problems; 2) Existing methods primarily focus on numerical noise and cannot handle the simultaneous existence of numerical noise and dead pixels, thus their application scenarios need further expansion; 3) Hyperparameter training time is long, and as the ability to handle heteroscedasticity or other types of noise improves, the number of introduced hyperparameters also increases, further increasing the difficulty of hyperparameter optimization and modeling costs.

[0005] Therefore, developing a multi-credibility noise-resistant surrogate optimization method to solve high-dimensional optimization design problems with numerical noise and bad points in engineering is of great significance to the development of surrogate model theory and provides methodological support for future high-dimensional noise-resistant optimization design. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a multi-credibility proxy optimization method that can reduce numerical noise interference and the impact of computational bad points, effectively solving the aforementioned problems.

[0007] The technical solution adopted in this invention is as follows:

[0008] This invention provides a multi-confidence proxy optimization method that can reduce numerical noise interference and the impact of computational bad points, comprising the following steps:

[0009] Step S1: Based on the optimization problem, obtain the results in descending order of credibility. Hierarchical original sample set ,in, Representative level The original sample set; ; Representative level The set of sample points; Representative sample point set The resulting hierarchy The set of response values;

[0010] Step S2: Establish a noise-filterable SVR-MHK proxy model; the SVR-MHK proxy model includes a support vector regression model. Anomaly response value identification model, ε-Kriging model, and multi-confidence MHK model;

[0011] Step S3, based on the support vector regression model To obtain each level sample point set The corresponding predicted response value set ;

[0012] Step S4, for each level response value set Numerical noise and bad pixel correction were performed on all samples to obtain a set of predicted response values ​​after numerical noise and bad pixel correction, which were then combined with the sample point set. To obtain this level The sample set after numerical noise and bad pixel repair; the repair method is as follows:

[0013] Using the aforementioned abnormal response value identification model, based on the predicted response value set Identify each level response value set Are there any abnormal response values?

[0014] If abnormal response values ​​exist, the predicted response value set will be used. Consider as a set of response values Predicted response value set after repairing numerical noise and bad pixels;

[0015] If no abnormal response value exists, then based on the ε-Kriging model, the values ​​for each level are obtained. sample point set The corresponding predicted response value set , regarded as a set of response values Predicted response value set after repairing numerical noise and bad pixels;

[0016] Step S5, for each level The numerical noise and the sample set after bad pixel repair are used to implement the hierarchy of the multi-confidence MHK model. The MHK sub-model yields the hierarchy. Predicted response value set and mean squared error estimation This serves as the output of the SVR-MHK proxy model.

[0017] Step S6: Based on the mean squared error estimate of the SVR-MHK surrogate model, the optimization addition criterion is used to guide the addition of new sample points to obtain new sample points. ;

[0018] Step S7, evaluate the new sample points response value New samples were obtained Then add it to the original sample set in step S1, and use the updated sample set to reconstruct the SVR-MHK surrogate model. Repeat this process until the optimization convergence criterion is met.

[0019] Furthermore, in step S1, the sample point set have sample points ,therefore, ; Response value set have Response value ,therefore, ;therefore, .

[0020] Furthermore, step S3 specifically includes:

[0021] Using the original sample set Training the support vector regression model For the support vector regression model The hyperparameters are optimized to obtain the hyperparameters. The value of and the sample point set Make predictions to obtain a set of predicted response values. .

[0022] Furthermore, in step S4, the abnormal response value identification model is used, based on the predicted response value set. Identify each level response value set Are there any abnormal response values? Specifically:

[0023] right Use the T-multiple comparison method to identify each level. response value set Are there any abnormal response values?

[0024] Furthermore, in step S4, if no abnormal response value exists, then based on the ε-Kriging model, the values ​​for each level are obtained. sample point set The corresponding predicted response value set ,include:

[0025] ①Based on hyperparameters The values ​​of are used to construct the correlation matrix of the ε-Kriging model. The expression is:

[0026] (1)

[0027] in: for Square matrix; Representative sample points and sample points The relevant function values ​​between them; Representative sample points and sample points The relevant function values ​​between them;

[0028] ②Based on the correlation matrix With sample set Using training samples, a trained ε-Kriging model is obtained; the expression for the predicted response value of the trained ε-Kriging model is:

[0029] (2)

[0030] in: The constant represents the global trend of the ε-Kriging model. ; represent A unit vector of dimension 1 has the following form: ; Represents the transpose of a matrix;

[0031] Representative sample point set Each currently computed sample point respectively with sample points The correlation vector, formed by the correlation function values ​​between them, is expressed as:

[0032] (3)

[0033] in: ; This represents the value of the relevant function.

[0034] Furthermore, in step S5, the hierarchy Predicted response value set for:

[0035] (4)

[0036] In formula (4), The value range is 1~ ,according to get ,according to get And so on, according to get By recursion, the set of predicted response values ​​for level 1, which represents the highest level of confidence, can be obtained. The expression is:

[0037] (5)

[0038] in: It is a constant. ; for The correlation matrix of order 1 is expressed as:

[0039] (6)

[0040] Represents the relevant function value;

[0041] hierarchical The predicted response set output by the MHK sub-model is expressed as follows:

[0042] (7)

[0043] in: express 3D space;

[0044] It is a correction value for the predicted response value. ;

[0045] hierarchy Mean squared error estimation for:

[0046] (8)

[0047] in: hierarchical The variance of a credible static random process.

[0048] Furthermore, step S6 specifically involves:

[0049] Based on the mean squared error estimation of the SVR-MHK surrogate model, an optimization addition criterion is used to guide the addition of new sample points, thereby improving the accuracy of the SVR-MHK surrogate model. A traditional optimization algorithm is employed to solve the corresponding optimization problem, obtaining new sample points with minimal computational cost. .

[0050] Furthermore, in step S7, after obtaining the new sample... Then, it is added to the original sample set with the highest confidence level in step S1. middle.

[0051] The multi-confidence proxy optimization method provided by this invention, which can reduce numerical noise interference and the impact of computational bad points, has the following advantages:

[0052] By combining dynamic noise filtering strategies and a multi-confidence modeling framework, this invention achieves the filtering of numerical noise and bad points in high-dimensional optimization design, and can be applied to problems such as airfoil optimization design. The method of this invention can reduce the impact of numerical noise in optimization design, obtaining optimization results that meet design requirements while ensuring optimization efficiency. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 A flowchart of a multi-confidence proxy optimization method provided by the present invention to reduce numerical noise interference and the impact of computational bad points;

[0055] Figure 2 The diagram shows the noise filtering method based on SVR-MHK compared to the traditional HK-based method, along with the EI function distribution.

[0056] Figure 3 Space diagram for the RAE2822 baseline airfoil and optimized design;

[0057] Figure 4 The convergence curve is shown during the optimization process of the RAE2822 airfoil.

[0058] Figure 5 Comparison of geometric shapes of the RAE2822 airfoil with numerical noise optimization results;

[0059] Figure 6 A comparison of the pressure distribution of the RAE2822 airfoil with numerical noise optimization results. Detailed Implementation

[0060] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the invention.

[0061] For high-dimensional optimization design problems where numerical noise and bad pixels exist in the response values, traditional methods are unable to obtain optimization results that meet design requirements due to the influence of numerical noise and bad pixels. Therefore, this invention proposes a multi-confidence noise-resistant proxy optimization method that can reduce the impact of numerical noise and bad pixels. Combining a dynamic noise filtering strategy and a multi-confidence modeling framework, it achieves the filtering of numerical noise and bad pixels in high-dimensional optimization design, and can be applied to problems such as airfoil optimization design. The method of this invention can reduce the influence of numerical noise in optimization design, and obtain optimization results that meet design requirements while ensuring optimization efficiency.

[0062] This invention provides an optimization design method for reducing numerical noise and the impact of bad pixels in high-dimensional problems, achieving the optimal design solution while ensuring high design efficiency.

[0063] Based on the SVR-MHK model, a noise-resistant surrogate optimization method that can reduce the impact of numerical noise, was developed. The main content of the invention is briefly introduced using the airfoil drag reduction optimization design problem as an example. It should be noted that this invention is a general method applied to surrogate optimization. This invention is only illustrated using the airfoil drag reduction optimization design problem as an example, but its actual application scope is not limited to this. See also... Figure 1 A multi-confidence proxy optimization method that can reduce numerical noise interference and the impact of computational bad points mainly includes the following steps:

[0064] Step S1: Based on the optimization problem, obtain the results in descending order of credibility. Hierarchical original sample set ,in, Representative level The original sample set; ; Representative level The set of sample points; Representative sample point set The resulting hierarchy The set of response values;

[0065] In this step, the sample point set have sample points ,therefore, ; Response value set have Response value ,therefore, ;therefore, It is important to emphasize that each sample point and each response value in this step can be a multidimensional variable.

[0066] For example, for hierarchy Determine the hierarchy based on the specific engineering problem. Credibility Design Space In the design space Internal sampling sample points To form a sample point set The sampling method can be either Latin hypercube sampling or uniform sampling. The response value at each sample point is calculated, thereby obtaining the corresponding... Response value , obtain the response value set Sample point set and response value set A sample set containing numerical noise and corresponding credibility levels is formed to construct the proxy model.

[0067] Step S2: Establish a noise-filterable SVR-MHK proxy model; the SVR-MHK proxy model includes a support vector regression model. Anomaly response value identification model, ε-Kriging model, and multi-confidence MHK model;

[0068] Step S3, based on the support vector regression model To obtain each level sample point set The corresponding predicted response value set ;

[0069] Using the original sample set The support vector regression model is trained using training samples. For the support vector regression model The hyperparameters are optimized to obtain the hyperparameters. The value of and the sample point set Make predictions to obtain a set of predicted response values. .

[0070] In this step, the SVR hyperparameter optimization algorithms that can be used include genetic algorithms, covariance matrix adaptive evolution strategies, and Bayesian optimization algorithms. The hyperparameters of the SVR model (insensitive loss parameter ε, outlier penalty factor C, kernel function parameter σ) are determined by the generalization error assessment, and the generalization error estimation methods include cross-validation and leave-one-bound methods.

[0071] Step S4, for each level response value set Numerical noise and bad pixel correction were performed on all samples to obtain a set of predicted response values ​​after numerical noise and bad pixel correction, which were then combined with the sample point set. To obtain this level The sample set after numerical noise and bad pixel repair; the repair method is as follows:

[0072] Using the aforementioned abnormal response value identification model, based on the predicted response value set Identify each level response value set Are there any abnormal response values?

[0073] If abnormal response values ​​exist, the predicted response value set will be used. Consider as a set of response values Predicted response value set after repairing numerical noise and bad pixels;

[0074] If no abnormal response value exists, then based on the ε-Kriging model, the values ​​for each level are obtained. sample point set The corresponding predicted response value set , regarded as a set of response values Predicted response value set after repairing numerical noise and bad pixels;

[0075] In this step, the abnormal response value identification model is used, based on the predicted response value set. Identify each level response value set Are there any abnormal response values? Specifically: for Use the T-multiple comparison method to identify each level. response value set Are there any abnormal response values?

[0076] In this step, if no abnormal response value exists, then based on the ε-Kriging model, the values ​​for each level are obtained. sample point set The corresponding predicted response value set ,include:

[0077] ①Based on hyperparameters The values ​​of are used to construct the correlation matrix of the ε-Kriging model. The expression is:

[0078] (1)

[0079] in: for A square matrix of order 1, where all elements on the diagonal are 1. ; Representative sample points and sample points The relevant function values ​​between them; Representative sample points and sample points The relevant function values ​​between them;

[0080] ②Based on the correlation matrix With sample set Using training samples, a trained ε-Kriging model is obtained; the expression for the predicted response value of the trained ε-Kriging model is:

[0081] (2)

[0082] in: The constant represents the global trend of the ε-Kriging model. ; represent A unit vector of dimension 1 has the following form: ; Represents the transpose of a matrix;

[0083] Representative sample point set Each currently computed sample point respectively with sample points The correlation vector, formed by the correlation function values ​​between them, is expressed as:

[0084] (3)

[0085] in: ; This represents the value of the relevant function.

[0086] Step S5, for each level The numerical noise and the sample set after bad pixel repair are used to implement the hierarchy of the multi-confidence MHK model. The MHK sub-model yields the hierarchy. Predicted response value set and mean squared error estimation This serves as the output of the SVR-MHK proxy model.

[0087] In this step, the hierarchy Predicted response value set for:

[0088] (4)

[0089] In formula (4), The value range is 1~ ,according to get ,according to get And so on, according to get By recursion, the set of predicted response values ​​for level 1, which represents the highest level of confidence, can be obtained. The expression is:

[0090] (5)

[0091] in: It is a constant. ; for The correlation matrix of order 1 is expressed as:

[0092] (6)

[0093] Represents the relevant function value;

[0094] hierarchical The predicted response set output by the MHK sub-model is expressed as follows:

[0095] (7)

[0096] in: express 3D space;

[0097] It is a correction value for the predicted response value. ;

[0098] hierarchy Mean squared error estimation for:

[0099] (8)

[0100] in: hierarchical The variance of a credible static random process.

[0101] Step S6: Based on the mean squared error estimate of the SVR-MHK surrogate model, use an optimization point addition criterion (such as maximizing the EI function) to guide the addition of new sample points, improve the accuracy of the noise filtering model, and obtain new sample points. ;

[0102] Specifically, based on the mean squared error estimation of the SVR-MHK surrogate model, an optimization point addition criterion is used to guide the addition of new sample points, thereby improving the accuracy of the SVR-MHK surrogate model. Traditional optimization algorithms (quasi-Newton algorithm, genetic algorithm, and Hooke-Jeeves pattern search method) are employed to solve the corresponding optimization problem, obtaining new sample points with minimal computational cost. .

[0103] Step S7, evaluate the new sample points response value New samples were obtained The updated sample set is then added to the original sample set in step S1. The SVR-MHK surrogate model is reconstructed using the updated sample set. This process is repeated until the optimization convergence criterion is met, thereby obtaining the optimization result that meets the design requirements.

[0104] As a specific implementation method, after obtaining a new sample Then, it is added to the original sample set with the highest confidence level in step S1. middle.

[0105] It should be noted that the description of numerical noise and bad pixel repair in the steps of this invention has the same meaning as filtering out numerical noise and bad pixels, which means repairing the response value of numerical noise and bad pixels to the predicted response value obtained by this invention.

[0106] The main innovation of this invention is based on the numerical noise and bad pixels that occur during engineering optimization design, and the weak ability of existing optimization methods to handle numerical noise and bad pixels. It proposes a multi-confidence noise-resistant surrogate optimization method to reduce the impact of numerical noise and bad pixels. The surrogate model used is the innovative noise-filtering surrogate model SVR-MHK proposed in this invention. In specific optimization design problems, such as airfoil aerodynamic optimization design, if the response value is affected by numerical noise and bad pixels, it will mislead the point-addition process of the surrogate model, leading to optimization failure. Existing optimization methods cannot effectively handle numerical noise and bad pixels. Although these response values ​​are affected by numerical noise, they generally correctly reflect the changing trend of the design objective with design variables. The noise-resistant optimization method proposed in this invention can adaptively filter out the influence of numerical noise and bad pixels during the construction of the surrogate model and point-addition process, achieving efficient and accurate optimization. Figure 2 As shown, the noise reduction optimization method developed in this invention achieves both noise filtering and precise point addition compared to the traditional Kriging-based method.

[0107] Based on the RAE2822 airfoil standard example, the inventors conducted airfoil optimization design with numerical noise, the source of which was incomplete convergence. In this case, an 8th-order CST parameterization method was used, with 18 design variables. Under the design conditions, the free-flow Mach number was 0.734, and the Reynolds number was... The lift coefficient is 0.824.

[0108] Step 1: Define the specific optimization problem; the optimization design objective is the drag coefficient. Minimum, constrained by lift coefficient Torque coefficient and airfoil area Airfoil area not less than the initial airfoil The optimized mathematical model is as follows:

[0109]

[0110] The design space is taken as 0.5 times the lower limit and 1.5 times the upper limit of the initial airfoil design variables, such as... Figure 3 As shown, the noise-resistant proxy optimization algorithm proposed in this invention is used for optimization design. The CFD calculation based on the Navier-Stokes equations is considered as high-confidence, and a 512×256 grid is selected as its computational grid, with a far-field of 120c (c being the chord length). The grid height of the first layer is 5.0×10⁻⁶. -6 The grid size is approximately 130,000. Treating the CFD calculation based on the Euler equations as low-confidence, a 256×128 grid was chosen for its computation, with a far-field of 120c (where c is the chord length). The first layer's grid height is 1.0×10⁻⁶. -3 The number of grid cells is approximately 33,000.

[0111] Step 2: Within the design space, use Latin hypercube sampling to select 30 high-confidence initial sample points and 300 low-confidence initial sample points, and perform CFD calculations on the initial sample points to obtain the corresponding aerodynamic coefficient response values ​​(drag coefficient, lift coefficient, and moment coefficient), thereby constructing a sample set (including numerical noise).

[0112] Therefore, this embodiment =2, level =1,2, meaning there are two sample sets with different levels of credibility; where, the sample set This is a high-confidence sample set, containing 30 high-confidence samples. Sample set This is a low-confidence sample set, containing 300 low-confidence samples. .

[0113] Step 3, for each level sample point set Based on the aforementioned support vector regression model The corresponding predicted response value set is obtained. ;

[0114] Therefore, using the sample set of level 1 SVR models for design variables with respect to drag coefficient, lift coefficient, and moment coefficient were established and predictions were made. A Bayesian optimization algorithm was used, and generalization error estimation was performed based on cross-validation to obtain the predicted response sets. and optimal hyperparameter values .

[0115] Similarly, using the sample set of level 2 SVR models for design variables with respect to drag coefficient, lift coefficient, and moment coefficient were established and predictions were made. A Bayesian optimization algorithm was used, and generalization error estimation was performed based on cross-validation to obtain the predicted response sets. and optimal hyperparameter values .

[0116] Step 4, for each level response value set All of them use the aforementioned abnormal response value identification model to identify whether an anomaly exists.

[0117] Therefore, for the response value set of level 1 Each response value is three-dimensional data, including the drag coefficient, lift coefficient, and moment coefficient; therefore, the SVR predicts the response values ​​for the drag coefficient, lift coefficient, and moment coefficient, respectively. With sample response value The squared difference is used to identify the set of response values ​​using the T-multiple comparison method. Is there any anomaly?

[0118] If outliers are found, the response value will be predicted. The predicted response value is considered after repairing numerical noise and bad pixels;

[0119] If no outliers are found, then based on ε-Kriging models were established separately, and the predicted response values ​​of the ε-Kriging models were... It is considered as the predicted response value after repairing numerical noise and bad pixels.

[0120] For the response value set of level 2 The same process will be performed, and will not be repeated here.

[0121] Step 5: Therefore, for level 1, we obtain the sample set after numerical noise and bad pixel repair; for level 2, we obtain the sample set after numerical noise and bad pixel repair.

[0122] Based on the predicted response values ​​of drag coefficient, lift coefficient, and moment coefficient after numerical noise repair using Level 1 and Level 2 confidence levels, a multi-confidence MHK model is established, consisting of two levels of MHK sub-models. Each level of the MHK sub-model outputs a set of predicted response values. and mean squared error estimation Simultaneously, it serves as the set of predicted response values ​​for each level output by the SVR-MHK surrogate model. and mean squared error estimation .

[0123] At this point, the predicted values ​​of the SVR-MHK surrogate model are respectively The SVR-MHK surrogate model, while providing predicted values ​​of aerodynamic coefficients for a given sample point, can also estimate the mean square error of those predicted values. .

[0124] Step 6: When searching for sample points to be added to the SVR-MHK surrogate model, the point addition method of maximizing the EI function is used. When solving this sub-optimization problem, the quasi-Newton algorithm, genetic algorithm and Hooke-Jeeves pattern search method are used in combination to find the objective function on the surrogate model, and sample points that improve the accuracy of the surrogate model are obtained. One sample point is added in each iteration.

[0125] Step 7: Perform CFD calculations on the new sample point obtained in Step 6 to obtain the corresponding aerodynamic coefficient response value, and add it to the sample set.

[0126] Step 8: Reconstruct the SVR-MHK surrogate model using the updated sample set, and repeat steps 2 to 7. After 270 iterations, the number of high-confidence sample points was expanded from 30 to 300. CFD analysis was performed on the 300 high-confidence sample points and the 300 low-confidence sample points to obtain the airfoil with the best drag reduction effect.

[0127] The airfoil design effect obtained by the method of the present invention is as follows:

[0128] Figure 4 The figure shows the convergence curve during the optimization process, demonstrating a more stable and faster convergence based on the method of this invention. A comparison of the initial and optimized airfoil shapes is also provided. Figure 4 As shown in Table 1, to verify the quality of the optimization results, the performance of the airfoil before and after optimization was evaluated. Table 1 compares the results of the initial airfoil, the optimized airfoil obtained using the conventional method, and the optimized airfoil obtained using the present invention. As can be seen from Table 1, under the condition of satisfying design constraints, the noise-resistant optimization design method proposed in this invention has a significant drag reduction effect, and the drag coefficient of the optimized airfoil is significantly lower than that of the optimized airfoil obtained by the conventional method. Figure 5 To compare the geometry and pressure distribution of a baseline airfoil with those optimized using different methods, from... Figure 5 It can be seen that the geometry of the optimized airfoil is slightly different, indicating that there may be multiple extreme points in this aerodynamic optimization example, while the traditional method gets stuck in a local optimum. In addition, the optimized airfoil is thinner near the leading edge, while the thickness of the middle and rear sections of the airfoil is increased, which weakens the shock wave on the upper surface, and is the main reason for drag reduction.

[0129] Table 1. Optimization Design Results of RAE2822 with Noise Reduction

[0130] Cd(counts) Reduction of Cd (%) Baseline airfoil 198.02 / SVR-MHK based method 120.00 39.40 Kriging-based method 126.58 36.08

[0131] The multi-confidence proxy optimization method provided by this invention, which can reduce numerical noise interference and the impact of computational bad points, has the following advantages:

[0132] (1) The proxy optimization method based on the SVR-MHK proxy model proposed in this invention can achieve efficient collaborative filtering of numerical noise and bad points in high-dimensional space by fusing dynamic noise filtering strategy and multi-confidence information, and then develop a corresponding noise-resistant proxy optimization method, which effectively reduces the impact of numerical noise in response value on optimization results.

[0133] (2) When using the present invention for airfoil drag reduction optimization design, significant drag reduction optimization can be achieved even when the response value contains numerical noise, which has a good engineering application prospect.

[0134] (3) The proxy optimization method based on the SVR-MHK proxy model proposed in this invention has a strong ability to filter out numerical noise during the optimization process. Its optimization results are better than those based on the traditional Kriging model. The specific results are shown in the example in the figure.

[0135] 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 multi-confidence proxy optimization method that can reduce numerical noise interference and the impact of computational bad points, characterized in that, Includes the following steps: Step S1: Based on the optimization problem, obtain the results in descending order of credibility. Hierarchical original sample set ,in, Representative level The original sample set; ; Representative level The set of sample points; Representative sample point set The resulting hierarchy The set of response values; Step S2: Establish a noise-filterable SVR-MHK proxy model; the SVR-MHK proxy model includes a support vector regression model. Anomaly response value identification model, ε-Kriging model, and multi-confidence MHK model; Step S3, based on the support vector regression model To obtain each level sample point set The corresponding predicted response value set ; Step S4, for each level response value set Numerical noise and bad pixel correction were performed on all samples to obtain a set of predicted response values ​​after numerical noise and bad pixel correction, which were then combined with the sample point set. To obtain this level The sample set after numerical noise and bad pixel repair; the repair method is as follows: Using the aforementioned abnormal response value identification model, based on the predicted response value set Identify each level response value set Are there any abnormal response values? If abnormal response values ​​exist, the predicted response value set will be used. Consider as a set of response values Predicted response value set after repairing numerical noise and bad pixels; If no abnormal response value exists, then based on the ε-Kriging model, the values ​​for each level are obtained. sample point set The corresponding predicted response value set , regarded as a set of response values Predicted response value set after repairing numerical noise and bad pixels; Step S5, for each level The numerical noise and the sample set after bad pixel repair are used to implement the hierarchy of the multi-confidence MHK model. The MHK sub-model yields the hierarchy. Predicted response value set and mean squared error estimation This serves as the output of the SVR-MHK proxy model. Step S6: Based on the mean squared error estimate of the SVR-MHK surrogate model, the optimization addition criterion is used to guide the addition of new sample points to obtain new sample points. ; Step S7, evaluate the new sample points response value New samples were obtained Then add it to the original sample set in step S1, and use the updated sample set to reconstruct the SVR-MHK surrogate model. Repeat this process until the optimization convergence criterion is met.

2. The multi-confidence proxy optimization method according to claim 1, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that, In step S1, the sample point set have sample points ,therefore, ; Response value set have Response value ,therefore, ;therefore, .

3. The multi-confidence proxy optimization method according to claim 2, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that... Step S3 is as follows: Using the original sample set Training the support vector regression model For the support vector regression model The hyperparameters are optimized to obtain the hyperparameters. The value of and the sample point set Make predictions to obtain a set of predicted response values. .

4. The multi-confidence proxy optimization method according to claim 3, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that... In step S4, the abnormal response value identification model is used, based on the predicted response value set. Identify each level response value set Are there any abnormal response values? Specifically: right Use the T-multiple comparison method to identify each level. response value set Are there any abnormal response values? 5. The multi-confidence proxy optimization method according to claim 3, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that... In step S4, if no abnormal response value exists, then based on the ε-Kriging model, the values ​​for each level are obtained. sample point set The corresponding predicted response value set ,include: ①Based on hyperparameters The values ​​of are used to construct the correlation matrix of the ε-Kriging model. The expression is: （1） in: for Square matrix; Representative sample points and sample points The relevant function values ​​between them; Representative sample points and sample points The relevant function values ​​between them; ②Based on the correlation matrix With sample set Using training samples, a trained ε-Kriging model is obtained; the expression for the predicted response value of the trained ε-Kriging model is: （2） in: The constant represents the global trend of the ε-Kriging model. ; represent A unit vector of dimension 1 has the following form: ; Represents the transpose of a matrix; Representative sample point set Each currently computed sample point respectively with sample points The correlation vector, formed by the correlation function values ​​between them, is expressed as: （3） in: ; This represents the value of the relevant function.

6. The multi-confidence proxy optimization method according to claim 3, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that... In step S5, the hierarchy Predicted response value set for: （4） In formula (4), The value range is 1~ ,according to get ,according to get And so on, according to get By recursion, the set of predicted response values ​​for level 1, which represents the highest level of confidence, can be obtained. The expression is: （5） in: It is a constant. ; for The correlation matrix of order 1 is expressed as: （6） Represents the relevant function value; hierarchical The predicted response set output by the MHK sub-model is expressed as follows: （7） in: express 3D space; It is a correction value for the predicted response value. ; hierarchy Mean squared error estimation for: （8） in: hierarchical The variance of a credible static random process.

7. The multi-confidence proxy optimization method according to claim 1, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that... Step S6 is as follows: Based on the mean squared error estimation of the SVR-MHK surrogate model, an optimization addition criterion is used to guide the addition of new sample points, thereby improving the accuracy of the SVR-MHK surrogate model. A traditional optimization algorithm is employed to solve the corresponding optimization problem, obtaining new sample points with minimal computational cost. .

8. The multi-confidence proxy optimization method according to claim 1, which can reduce numerical noise interference and the impact of computational bad points, is characterized in that... In step S7, after obtaining the new sample Then, it is added to the original sample set with the highest confidence level in step S1. middle.

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