An efficient engineering design method against numerical noise

Abstract

The present invention provides an efficient engineering design method for resisting numerical noise, including: optimizing the hyperparameters of a support vector regression model by using a hyperparameter optimization algorithm to obtain the optimal values of the hyperparameters; adding the optimal values of the hyperparameters to the diagonal of the correlation matrix during the training of the Kriging model to obtain the correlation matrix of the ε-Kriging model, and constructing the ε-Kriging model. It has the following advantages: When using the present invention for engineering design, the design cycle is greatly shortened, and it has stronger engineering practicability. The ε-Kriging surrogate model proposed by the present invention creatively introduces the hyperparameter ε in the support vector regression model into the training process of the Kriging model, improves the traditional Kriging model into a regression model, effectively filters out the influence of numerical noise in the data, and improves the noise filtering performance of the Kriging model.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering design, and particularly relates to an efficient engineering design method for resisting numerical noise. Background Art

[0002] At present, the design methods in the field of engineering design are deterministic design methods based on the accurate calculation of response values, without considering the influence of numerical noise in the response value calculation process. For example, in engineering design problems based on numerical simulation, irregular fluctuations may occur in the numerical simulation results due to grid discretization differences and inaccurate boundary condition settings, that is, numerical noise is introduced. Although slight numerical noise may not have a decisive impact on engineering design, strong numerical noise often has a serious impact on the design process. Therefore, how to design engineering problems considering the influence of numerical noise and improve the accuracy of engineering design is a technical problem that needs to be solved currently.

[0003] Currently, the methods that can handle numerical noise problems include polynomial fitting, deep neural network, "Nugget-effect" Kriging model, and support vector regression model (SVR), etc. (1) Polynomial fitting: Polynomial fitting is a linear model, and its goal is to construct an M-order polynomial of input x so that the polynomial can approximately represent the relationship between input x and output y. Research shows that when the model is more complex, the order of the polynomial model is more. If the data has numerical noise, a higher-order polynomial model needs to be constructed to fit the samples with numerical noise. Therefore, the calculation is very time-consuming and unacceptable in actual engineering problems. (2) Deep neural network: The deep neural network shows good performance in fields such as image recognition, object detection, semantic segmentation, and speech and natural language processing, but this method cannot effectively handle the problem of numerical noise in the dataset. (3) Support vector regression model: Due to the unique ε-band in its model, the support vector regression model can effectively weaken the influence of numerical noise on modeling. This model considers the sample points within the ε-band as correct sample points, allowing small fluctuations within a certain range of sample points without affecting the model itself. However, when the support vector regression model is established, there is no theoretical assumption of Gaussian process, and it is impossible to estimate the uncertainty of unknown points. Therefore, its application in engineering design is limited. (4) Kriging model: The Kriging model is an interpolation model based on the assumption of Gaussian process, and it is also the most widely used machine learning method in the current field of engineering design (such as aerodynamic performance design). However, when the samples contain numerical noise, the Kriging model will construct a non-smooth model along with the irregular fluctuations in the samples, resulting in modeling and design failures.

[0004] It can be seen that for engineering design problems with numerical noise in the response values, the existing anti-noise methods have limitations and cannot obtain a solution that meets the design requirements. Summary of the Invention

[0005] Aiming at the defects existing in the prior art, the present invention provides an efficient engineering design method for anti-numerical noise. Considering the influence of numerical noise on engineering design, the present invention can obtain the optimal design solution while ensuring relatively high design efficiency, thereby effectively solving the above problems.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The present invention provides an efficient engineering design method for anti-numerical noise, including the following steps:

[0008] Step 1, determine the design space X according to the specific engineering problem, and sample n sample points x (1) , x (2) ,..., x (n) within the design space X to form a sample point matrix S = [x (1) , x (2) ,..., x (n) T ;

[0009] Calculate the response value of each sample point to obtain the corresponding n response values y (1) , y (2) ,..., y (n) to form a response value matrix y s = [y (1) , y (2) ,..., y (n) T ;

[0010] The sample point matrix S and the response value matrix y s form a sample set W = (S, y s ) = [(x (1) , y (1) ), (x (2) , y (2) ),...,(x (n) , y (n) )] T ;

[0011] Step 2, establish a support vector regression model SVR, use the sample set W as the training sample, and optimize the hyperparameters of the support vector regression model SVR by using a hyperparameter optimization algorithm to obtain the optimal value of the hyperparameter ε, denoted as ε best ;

[0012] Step 3, according to the optimal value ε of the hyperparameter ε best ​​, construct the correlation matrix of the improved Kriging model The expression is:

[0013]

[0014] Where:

[0015] R(x (1) , x (n) ) represents the correlation function value between the sample point x (1) and the sample point x (n) ;

[0016] R(x (n) , x (1) ) represents the correlation function value between the sample point x (n) and the sample point x (1) ;

[0017] Step 4, according to the correlation matrix of the improved Kriging model constructed in Step 3 Using the sample set W as the training sample, construct an improved Kriging model, and call the improved Kriging model the ε-Kriging model. Adopt the maximum likelihood estimation or cross-validation method to train the hyperparameters of the ε-Kriging model to obtain the optimal values of the hyperparameters of the ε-Kriging model, where the optimal value of the hyperparameter θ l is denoted as θ lbest ;

[0018] Step 5, obtain the smooth prediction expression of the ε-Kriging model as:

[0019]

[0020] Where:

[0021] is the predicted value of the response value of the smooth prediction expression at the unknown point x;

[0022] β0 is a constant, representing the global trend of the ε-Kriging model,

[0023] r(x) represents the correlation vector composed of the correlation function values between the unknown point x and n sample points x (1) , x (2) ,..., x (n) respectively, and the expression is:

[0024]

[0025] Where: R(x (1) , x), R(x (2), x), …, R(x (n) , x), respectively represent the correlation function values between the unknown point x and the sample point x (1) The correlation function values between the unknown point x and the sample point x (2) The correlation function values between the unknown point x and the sample point x (n) ;

[0026] T represents the transpose of the matrix;

[0027] F represents the n-dimensional identity matrix, in the form of: F = [1 1 … 1] T ;

[0028] Step 6: Input the value of any unknown point x, and through the smooth prediction expression in Step 5, output the predicted value of the response value of the unknown point x Filter out the predicted value The influence of numerical noise in it to guide engineering design.

[0029] Preferably, in Step 1, the sampling method is the Latin hypercube sampling method or the uniform sampling method.

[0030] Preferably, in Step 2, the hyperparameter optimization algorithm adopted is the genetic algorithm, the covariance adaptive optimization method or the Bayesian optimization method.

[0031] Preferably, in Step 3, the correlation function value between two sample points represents the correlation between the two sample points and is a function of the distance between the two sample points.

[0032] Preferably, for the sample point x (1) and the sample point x (n) , the following formula is used to calculate the correlation function value:

[0033] R(x (1) , x (n) ) = exp(-θ lbest |x (1) - x (n) | p )

[0034] Where:

[0035] p represents the anisotropy parameter of the correlation function.

[0036] An efficient engineering design method for resisting numerical noise provided by the present invention has the following advantages:

[0037] (1) When using the present invention for engineering design, while meeting the design requirements, since the response value can be obtained by a low-confidence approximation calculation method, only the change trend of the response value with the design variables needs to be captured, greatly shortening the design cycle and having stronger engineering practicability.

[0038] (2) The ε-Kriging surrogate model proposed by the present invention creatively introduces the hyperparameter ε in the support vector regression model into the Kriging model training process, improves the traditional Kriging model into a regression model, effectively filters out the influence of numerical noise in the data, and improves the noise filtering performance of the Kriging model. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a comparison chart of the modeling errors of three models based on different noise levels provided by the present invention (R_Square is the R 2 mean value, representing the modeling accuracy, the same below);

[0040] Figure 2 It is a comparison chart of the model accuracies of three surrogate models in the case of small samples provided by the present invention;

[0041] Figure 3 It is a comparison chart of the model accuracies of three surrogate models in the case of large samples provided by the present invention;

[0042] Figure 4 It is a flowchart of an efficient engineering design method for resisting numerical noise provided by the present invention;

[0043] Figure 5 It is the numerical noise constructed in the airfoil design process of the present invention, and the curve graph of the drag coefficient of the RAE2822 airfoil changing with the maximum relative thickness;

[0044] Figure 6 It is a comparison chart of the designed airfoil and the reference airfoil obtained by the present invention;

[0045] Figure 7 It is the fitting and optimization result of the drag coefficient with numerical noise when the maximum relative thickness of the RAE2822 airfoil is changed. Among them, Samples represents the sample points, min real represents the position of the minimum value of the true function, min ε-Kriging represents the position of the minimum value of the true function, and ε-Kriging represents the modeling curve of the ε-Kriging model. DETAILED DESCRIPTION OF THE INVENTION

[0046] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer, the present 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 only used to explain the present invention and are not used to limit the present invention.

[0047] For engineering design problems with numerical noise in response values, traditional methods cannot effectively filter out the influence of numerical noise, and existing anti-noise methods have limitations and cannot obtain solutions that meet the design requirements. Therefore, the present invention proposes an efficient engineering design method for anti-numerical noise, which can be applied to aerodynamic design problems. The method of the present invention enables the engineering design process to be unaffected by numerical noise, and obtains solutions that meet the design requirements while ensuring the design efficiency.

[0048] Inspired by the ε-band in the support vector regression model SVR, the present invention improves the original Kriging model, proposes a new surrogate model, namely the ε-Kriging model, thereby developing an efficient engineering design method for anti-numerical noise. Taking the problem of reducing the cruise drag in the aerodynamic performance design of an airfoil as an example, the main content of the present invention is introduced. It should be noted that the present invention is a general method applied to engineering design. When implementing the embodiment, only the aerodynamic performance design problem is taken as an example, but the actual application scope of the present invention is not limited to this.

[0049] The present invention provides an efficient engineering design method for anti-numerical noise, referring to Figure 4 , and includes the following steps:

[0050] Step 1, determine a reasonable design space X according to the specific engineering problem, and sample n sample points x (1) , x (2) ,..., x (n) within the design space X to form a sample point matrix S = [x (1) , x (2) ,..., x (n) T ; The sampling method can be the Latin hypercube sampling method or the uniform sampling method.

[0051] Calculate the response value of each sample point, and thus obtain the corresponding n response values y (1) , y (2) ,..., y (n) to form a response value matrix y s = [y (1) , y (2) ,..., y (n) T ;

[0052] The sample point matrix S and the response value matrix y s form a sample set W = (S, y s ) = [(x (1) , y (1) ), (x (2) , y (2) ),...,(x (n) , y (n) )]​​T ;

[0053] When calculating the response value of each sample point, to improve the solution efficiency of engineering design, an approximate solution method is usually used to calculate the response value of the sample point. For example, in the field of aerodynamic design, a low-fidelity method is used to perform approximate CFD calculations on the sample point. Although the calculation accuracy of the response value will be lost, resulting in irregular fluctuations in the response value, it does not affect the trend characteristics of the design objective with respect to the design variables.

[0054] Step 2: Establish a support vector regression model SVR. Using the sample set W as the training sample, optimize the hyperparameters of the support vector regression model SVR using a hyperparameter optimization algorithm to obtain the optimal value of the hyperparameter ε, denoted as ε best ;

[0055] In this step, the hyperparameter optimization algorithm used can be a genetic algorithm, a covariance adaptive optimization method, or a Bayesian optimization method.

[0056] The quality of the hyperparameter ε of the support vector regression model SVR is evaluated by the generalization error. The generalization error estimation methods include cross-validation and the leave-one-out method. The research results of the inventors show that the hyperparameters obtained by the hyperparameter optimization method based on Bayesian optimization have a better fitting effect. Therefore, as a preferred method, the Bayesian optimization method is used to optimize the hyperparameter ε.

[0057] Step 3: According to the optimal value ε of the hyperparameter ε best , construct the correlation matrix R of the improved Kriging model εbest , and the expression is:

[0058]

[0059] Where:

[0060] R(x (1) , x (n) ) represents the correlation function value between the sample point x (1) and the sample point x (n) ;

[0061] R(x (n) , x (1) ) represents the correlation function value between the sample point x (n) and the sample point x (1) ;

[0062] Therefore, in the present invention, the optimal value ε of the hyperparameter ε of the support vector regression model SVR obtained in Step 2 best is added to the diagonal of the correlation matrix of the Kriging model, thereby obtaining the correlation matrix of the ε-Kriging model

[0063] The correlation function value between two sample points, representing the correlation between the two sample points, is a function of the distance between the two sample points. The selection of the correlation function must satisfy the Gaussian hypothesis and make the correlation matrix symmetric positive definite. The Gaussian exponential model and cubic spline function can be adopted.

[0064] As a specific implementation, for sample point x (1) and sample point x (n) , the following formula is used to calculate the correlation function value:

[0065] R(x (1) ,x (n) ) = exp(-θ lbest |x (1) - x (n) | p )

[0066] where:

[0067] p represents the anisotropic parameter of the correlation function.

[0068] Step 4, based on the correlation matrix of the improved Kriging model constructed in Step 3 Using the sample set W as the training samples, an improved Kriging model is constructed. The improved Kriging model is called the ε-Kriging model. The hyperparameters of the ε-Kriging model are trained using the maximum likelihood estimation or cross-validation method. During the training process, the mean and process variance of the ε-Kriging model can be analytically obtained, and the parameters in the correlation function are obtained through a numerical optimization algorithm, thereby obtaining the optimal values of the hyperparameters of the ε-Kriging model, where the optimal value of the hyperparameter θ l is denoted as θ lbest ;

[0069] Step 5, the smooth prediction expression of the ε-Kriging model is obtained as:

[0070]

[0071] where:

[0072] is the predicted value of the response value of the smooth prediction expression at the unknown point x;

[0073] β0 is a constant, representing the global trend of the ε-Kriging model,

[0074] r(x) represents the distances between the unknown point x and n sample points x (1) ,x (2) ,...,x(n) The correlation vector formed by the correlation function values between them, the expression is:

[0075]

[0076] Where: R(x (1) , x), R(x (2) , x), …, R(x (n) , x) respectively represent the correlation function values between the unknown point x and the sample point x (1) , the correlation function values between the unknown point x and the sample point x (2) , …, the correlation function values between the unknown point x and the sample point x (n) ;

[0077] T represents the transpose of the matrix;

[0078] F represents the n-dimensional identity matrix, in the form of: F = [1 1 … 1] T ;

[0079] Step 6, input the value of any unknown point x, and through the smooth prediction expression in Step 5, output the predicted value of the response of the unknown point x Filter out the influence of numerical noise in the predicted value , guide the engineering design, and obtain the best design scheme.

[0080] Through the smooth prediction expression of the ε-Kriging model, the influence of numerical noise existing in the sample set on modeling can be filtered out. Through the smooth prediction expression of the ε-Kriging model, the predicted value of the unknown point x can be obtained Moreover, while giving the predicted value of a certain unknown point x, the mean square error estimate of the corresponding predicted value can also be obtained

[0081] An engineering design method considering the influence of numerical noise provided by the present invention can obtain the best design scheme and ensure relatively high design efficiency at the same time.

[0082] The main innovation of the present invention is based on the numerical noise phenomenon that appears in the engineering design process and the problem of the weak ability of existing traditional methods to handle numerical noise. An engineering design method that is efficient and resistant to the influence of numerical noise is proposed. The surrogate model used is the smooth prediction expression of the ε-Kriging model proposed by the present invention. In specific engineering design problems, such as in the airfoil design process, if the response value is affected by numerical noise, traditional design methods cannot handle numerical noise. Although the response value is affected by numerical noise, it generally can correctly reflect the change trend of the design objective with the design variables. The ε-Kriging model provided by the present invention is based on the sample points affected by numerical noise to establish a relatively smooth mathematical model to achieve noise filtering processing of the sample points. Therefore, traditional methods can be used to solve the smooth prediction expression of the above ε-Kriging model, so as to obtain the predicted values of the design variables of the smooth prediction expression of the ε-Kriging model.

[0083] The following introduces an embodiment:

[0084] This embodiment is based on the RAE2822 airfoil standard example to carry out airfoil design with numerical noise. Usually, when evaluating the aerodynamic coefficients of an airfoil by CFD, the quality of grid discretization leads to numerical noise. To simulate the numerical noise phenomenon caused by grid quality in airfoil design, sparse grids are divided for the studied airfoil. Adopting inviscid fixed angle of attack calculation, the maximum relative thickness of the airfoil is used as the design variable for aerodynamic design.

[0085] This embodiment adopts the PARSEC airfoil parameterization method to describe the airfoil through 13 parameters. At the design state, the free-stream Mach number Ma is 0.734, AoA = 2.79deg, and the Reynolds number Re = 6.5×106. It is known that the maximum relative thickness of the basic airfoil is 0.1207078, and the variation range of the maximum relative thickness is set as [0.07, 0.19], that is: the design space X is [0.07, 0.19].

[0086] Step 1, when performing CFD evaluation on the sample points in the design space X[0.07, 0.19], solve the inviscid equation. For the computational grid, unstructured grids are used for calculation. The far-field boundary is outside 50 times the chord length from the object surface, and the number of grid cells is 15000 (the surface grid quantity is 512).

[0087] Uniform sampling is carried out within the design space X[0.07, 0.19], and a total of 86 sample points are selected to form a sample point matrix S = [x (1) , x (2) ,..., x (86) T ; perform CFD evaluation on the sample points to obtain the corresponding aerodynamic coefficient response values (drag coefficient), so as to construct a response value matrix y​s = [y (1) , y (2) ,..., y (86) T ;

[0088] The sample point matrix S and the response value matrix y s form a sample set W, specifically as Figure 5 shown. The abscissa t / c is the maximum relative thickness, and the ordinate Cd is the response value of the aerodynamic coefficient.

[0089] Step 2: Based on the sample set W in Step 1, use the support vector regression model SVR to model the sample set W. At the same time, use the Bayesian optimization algorithm to optimize the hyperparameters of the support vector model SVR itself, and obtain the optimal value ε best of the hyperparameter ε of the support vector regression model SVR is 0.008. In this process, the quality of the hyperparameters is evaluated based on the generalization error of cross-validation.

[0090] Step 3: Extract the optimal value ε best of the hyperparameter ε of the support vector regression model SVR in Step 2. Based on the sample set W in Step 1, add the optimal value ε best to the diagonal of the Kriging correlation matrix during the surrogate model training stage to form the correlation matrix of the ε-Kriging model In addition, select the Gaussian exponential model as the correlation function to calculate the correlation function value between two sample points.

[0091] Step 4: Train the hyperparameters of the ε-Kriging model according to the maximum likelihood estimation. During the training process, the mean and process variance of ε-Kriging can be analytically obtained, and the parameters in the correlation function are obtained by the quasi-Newton method.

[0092] Step 5: Establish a smooth prediction expression of the ε-Kriging model to filter out the possible numerical noise in the sample set. The predicted value of the response value of a certain sample point (whose design variable is x) by the smooth prediction expression of the ε-Kriging model is The smooth prediction expression of the ε-Kriging model can also obtain the mean square error estimate of the corresponding predicted value while giving the predicted value of the response value of a certain sample point

[0093] Step 6: Use the genetic algorithm to solve the smooth prediction expression of the ε-Kriging model established in Step 5. The predicted value of the response value predicted by the smooth prediction expression of the ε-Kriging model has filtered out the influence of numerical noise, so an airfoil that meets the design requirements can be obtained through the genetic algorithm.​

[0094] The airfoil design effects obtained by the method of the present invention are as follows:

[0095] The comparison of the baseline airfoil and the optimum airfoil after design is as follows Figure 6 As shown, the maximum relative thickness of the baseline airfoil is 0.1218, and the maximum relative thickness of the airfoil after design is 0.1064. Therefore, the maximum relative thickness of the airfoil after design is slightly less than that of the baseline airfoil, and the shock wave intensity on the upper airfoil surface is reduced for the airfoil after design.

[0096] To verify the quality of the design results, the performances of the airfoils before and after design were evaluated. Table 1 comparatively shows the aerodynamic coefficients of the baseline airfoil and the airfoil after design.

[0097] Table 1 Design results of the drag coefficient of the RAE2822 airfoil with variable maximum relative thickness including numerical noise

[0098]

[0099] As can be seen from Table 1, under the condition of meeting the design requirements, the method proposed by the present invention has a relatively excellent drag reduction effect, can accurately find the design point with the best performance, and the relative error from the position of the actual optimal point is controlled within 2%.

[0100] Figure 7 The fitting results of the ε-Kriging model provided by the present invention and the final design results are given. As Figure 7 can be seen, the position of the ε-Kriging optimal solution is basically the same as that of the true optimal solution. Therefore, the noise filtering effect of the noise-filterable ε-Kriging model proposed by the present invention is good, and the best solution can be designed relatively accurately.

[0101] The present invention also conducts a comparative test on the model accuracies of the ε-Kriging model provided by the present invention, the traditional "Nugget-effect" Kriging model, and the traditional SVR model.

[0102] As Figure 1 shown, it is the comparison of the modeling errors of the three models based on different noise levels (R_Square is the R 2 mean value, representing the modeling accuracy, the same below); as Figure 2 shown, it is the comparison of the model accuracies of the three surrogate models in the case of small samples; as Figure 3 shown, it is the comparison of the model accuracies of the three surrogate models in the case of large samples.

[0103] By comparing Figure 1 , Figure 2 and Figure 3, it can be seen that the ε-Kriging surrogate model proposed by the present invention has high modeling accuracy in general, small sample cases, and large sample cases. The modeling accuracy of the ε-Kriging surrogate model is higher than that of the SVR and "Nugget-effect" Kriging models; in the case of medium and low amplitude noise, the modeling accuracy of SVR is higher than that of the "Nugget-effect" Kriging model, but in the case of high amplitude noise, the modeling accuracy of the "Nugget-effect" Kriging model is higher than that of the SVR model.

[0104] An efficient engineering design method for resisting numerical noise provided by the present invention has the following advantages:

[0105] (1) When using the present invention for engineering design, while meeting the design requirements, since the response value can be obtained by a low-confidence approximation calculation method, only the change trend of the response value with the design variables needs to be captured, greatly shortening the design cycle and having stronger engineering practicability.

[0106] (2) The ε-Kriging surrogate model proposed by the present invention creatively introduces the hyperparameter ε in the support vector regression model into the Kriging model training process, improves the traditional Kriging model into a regression model, effectively filters out the influence of numerical noise in the data, and improves the noise filtering performance of the Kriging model.

[0107] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. An efficient engineering design method against numerical noise, characterized in that, Including the following steps: Step 1, determine the design space X according to specific engineering problems, and obtain n sample points x within the design space X (1) , x (2) ,..., x (n) , forming a sample point matrix S = [x (1) , x (2) ,..., x (n) T ;​ Calculate the response value of each sample point, and thus obtain the corresponding n response values y (1) , y (2) ,..., y (n) , and form the response value matrix y s = [y (1) , y (2) ,..., y (n) T ;​ Sample point matrix S and response value matrix y s Form a sample set W = (S, y s ) = [(x (1) , y (1) ), (x (2) , y (2) ),..., (x (n) , y (n) )] T ; Step 2, establish a support vector regression model SVR. Using the sample set W as the training samples, optimize the hyperparameters of the support vector regression model SVR by using a hyperparameter optimization algorithm to obtain the optimal value of the hyperparameter ε, denoted as ε best ; Step 3, according to the optimal value ε of the hyperparameter ε best , construct the correlation matrix of the improved Kriging model The expression is as follows: Wherein: R(x (1) ,x (n) ) represents the correlation function value between the sample points x (1) and the sample point x (n) ; R(x (n) ,x (1) ) represents the correlation function value between the sample points x (n) and the sample point x (1) ; Step 4, according to the correlation matrix of the improved Kriging model constructed in Step 3 Using the sample set W as the training sample, an improved Kriging model is constructed, and the improved Kriging model is called the ε-Kriging model. The maximum likelihood estimation or cross-validation method is used to train the hyperparameters of the ε-Kriging model to obtain the optimal values of the hyperparameters of the ε-Kriging model, where the hyperparameter θ l The optimal value of is denoted as θ lbest ; In step 5, the smooth prediction expression of the ε-Kriging model is: Wherein: is the estimated value of the response value of the smooth prediction expression at the unknown point x; β0 is a constant, representing the global trend of the ε-Kriging model, β0 = (F T R εbest -1 F) -1 F T R εbest -1 y s ; r(x) represents the correlation vector composed of the correlation function values between the unknown point x and n sample points x (1) , x (2) ,..., x (n) , and the expression is: Where: R(x (1) , x), R(x (2) , x), …, R(x (n) , x) respectively represent the correlation function values between the unknown point x and the sample point x (1) , the correlation function values between the unknown point x and the sample point x (2) , …, the correlation function values between the unknown point x and the sample point x (n) ; T represents the transpose of a matrix; F represents an n-dimensional identity matrix in the form: F = [1 1 … 1] T ; Step 6: Input the value of any unknown point x, and through the smooth prediction expression in Step 5, output the predicted value of the response value of the unknown point x. Filter the predicted value to eliminate the influence of numerical noise and guide engineering design.

2. An efficient engineering design method for resisting numerical noise according to claim 1, characterized in that In step 1, the sampling method is the Latin hypercube sampling method or the uniform sampling method.

3. An efficient engineering design method for resisting numerical noise according to claim 1, characterized in that In step 2, the hyperparameter optimization algorithm adopted is the genetic algorithm, the covariance adaptive optimization method or the Bayesian optimization method.

4. An efficient engineering design method for resisting numerical noise according to claim 1, characterized in that, In step 3, the correlation function value between two sample points represents the correlation between the two sample points and is a function of the distance between the two sample points.

5. An efficient engineering design method for resisting numerical noise according to claim 4, characterized in that For the sample point x (1) and the sample point x (n) , the following formula is used to calculate the relevant function value: R(x (1) , x (n) ) = exp(-θ lbest |x (1) - x (n) | p ) Wherein: p represents the anisotropy parameter of the correlation function.

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