CN116306044A

CN116306044A - Uncertainty analysis method of full turbulence configuration and gradient optimization design method thereof

Info

Publication number: CN116306044A
Application number: CN202310580483.6A
Authority: CN
Inventors: 史亚云; 杨体浩; 陈艺夫; 兰夏毓
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2023-05-23
Filing date: 2023-05-23
Publication date: 2023-06-23

Abstract

The invention discloses an uncertainty analysis method of a full turbulence configuration and a gradient optimization design method thereof, which belong to the technical field of aircraft design, and in order to improve the design precision and efficiency of the full turbulence configuration, the method comprises the following steps: according to the initial full turbulence configuration, a grid is established and the initial value of a full turbulence configuration design variable is determined; parameterizing and deforming the grid by a free deformation parameterization method according to the initial value of the design variable to obtain a surface grid; deforming the surface grid by utilizing a dynamic grid technology based on inverse distance weight to obtain a deformed space grid; sampling a preset uncertainty variable in a random space to obtain a plurality of sampling points; according to the deformed space grid, carrying out deterministic analysis on each sampling point in a full turbulence state by utilizing a solver to obtain a flow field result; determining the mean value and the variance of the uncertainty variable according to the flow field result; and obtaining an analysis result of the uncertainty variable according to the uncertainty variable, the mean value and the variance.

Description

Uncertainty analysis method of full turbulence configuration and gradient optimization design method thereof

Technical Field

The invention relates to the technical field of aircraft design, in particular to an uncertainty analysis method of a full turbulence configuration and a gradient optimization design method thereof.

Background

The performance of all engineering systems is affected by some degree of uncertainty. The performance of the aircraft is susceptible to large changes due to numerous uncertainty factors such as manufacturing or flight conditions and environment. Traditional pneumatic designs belong to deterministic designs, and can cause that the pneumatic performance is extremely sensitive to uncertain factors, and even certain potential safety hazards can be brought. Therefore, in the aircraft design phase, attention is paid to developing a robust optimization design that takes uncertainty into account, and the uncertainty needs to be represented first. Research has found that probabilistic methods remain the most popular theory of uncertainty. In uncertainty analysis, an important step is the process of converting the characteristics of an uncertainty source into an estimate of the uncertainty of the output variable, known as propagation of the uncertainty. This requires the establishment of an efficient and accurate uncertainty propagation method. In recent years, polynomial chaotic expansion method is more and more popular due to its higher flexibility and computational efficiency. However, when the input uncertainty variable dimension is high, there is a dimension disaster problem, and the calculation cost is high. Therefore, the calculation cost of uncertainty analysis needs to be further reduced by numerical technical means.

Gradient optimization algorithms have significant advantages in terms of efficiency of the optimization algorithm. The use of gradient optimization algorithms is still one of the most effective ways to solve the problem of pneumatic optimization design of large-scale design variables, and the benefits of the design are more obvious for analysis design considering uncertainty. At present, the gradient optimization design method based on the accompanying has been successfully applied to deterministic optimization design, which lays a foundation for the application of the accompanying method to robust design considering uncertainty. In the gradient optimization design, it is particularly important to solve gradient information efficiently and accurately, so that the statistical moment of the uncertainty analysis method needs to be subjected to gradient solution. The influence of uncertainty factors on the performance of an aircraft is particularly important.

Disclosure of Invention

The invention aims to provide an uncertainty analysis method of a full turbulence configuration and a gradient optimization design method thereof, so as to solve the problem of higher calculation cost in the existing uncertainty analysis method of the full turbulence configuration, and greatly reduce the number of sample points on the premise of ensuring the solving precision, thereby greatly reducing the calculation amount in the airfoil robustness optimization design process.

The technical scheme for solving the technical problems is as follows:

the invention provides an uncertainty analysis method of a full turbulence configuration, which comprises the following steps:

s1: according to the initial full turbulence configuration, a grid is established and the initial value of a full turbulence configuration design variable is determined;

s2: parameterizing and deforming the grid by a free deformation parameterization method according to the initial value of the design variable to obtain a surface grid;

s3: deforming the surface grid by utilizing a dynamic grid technology based on inverse distance weight to obtain a deformed space grid;

s4: sampling uncertainty variables of the full turbulence configuration in random space to obtain a plurality of sampling points;

s5: according to the deformed space grid, carrying out deterministic analysis on each sampling point in a full turbulence state by utilizing a solver to obtain a flow field result;

s6: determining the mean value and the variance of the uncertainty variable according to the flow field result;

s7: and obtaining an analysis result of the uncertainty variable according to the uncertainty variable and the mean value and the variance of the uncertainty variable.

Optionally, the S3 includes:

according to the surface grid and the deformation geometry, calculating normal torsion angles and corresponding translation distances before and after each sub-grid unit in the surface grid changes;

and obtaining the deformed space grid according to the normal torsion angles before and after the change of each sub-grid unit and the corresponding translation distance.

Optionally, in the step S4, the uncertainty variable of the full turbulence configuration includes a mach number

And/or angle of attack

And/or geometric deformation;

the number of sampling points is determined by the number of uncertainty variables, the order of the independent basis function polynomial and the oversampling rate

The method comprises the following steps:

wherein,,

indicating the oversampling rate, +.>

Representing the order of the independent basis function polynomial, < +.>

Representing the number of random variables +.>

Representing the number of sampling points.

Optionally, the S6 includes:

s61: decomposing the uncertainty variable into a determining part and a random part to obtain an infinite series expression of the uncertainty variable;

s62: carrying out normalization derivation and chaotic expansion on an infinite series expression of the uncertainty variable to obtain a chaotic expansion result;

s63: constructing a linear equation set according to the chaos expansion result;

s64: according to the flow field result, solving a coefficient matrix of the linear equation set;

s65: and obtaining the mean value and standard deviation of the random variable according to the coefficient of the linear equation set.

Alternatively, in said S61,

the infinite series expression of the uncertainty variable is:

wherein,,

designing a variable vector for certainty +.>

Is an uncertainty variable vector, ++>

Is the firstjDeterministic portion of the order->

Is->

The random part of the step.

Optionally, in S63, the system of linear equations is:

wherein,,

representing a matrix of basis functions, the matrix size being +.>

，/>

For the number of sampling points, +.>

For the number of basis functions +.>

A coefficient matrix of a linear equation set, the matrix size is +.>

，/>

To output the number of random variables, +.>

Is a flow field result matrix with the size of +.>

。

Optionally, in the step S65, a mean value of the uncertainty variable

The method comprises the following steps:

standard deviation of the uncertainty variable

The method comprises the following steps:

wherein,,

for the first coefficient of the coefficient matrix of the linear system of equations>

Indicate->

Deterministic portion of the order->

Indicate->

Basis function of order>

Representing the number of sampling points.

The invention also provides a gradient optimization design method based on the uncertainty analysis method of the full turbulence configuration, which comprises the following steps:

a1: establishing an objective function according to the mean value and the variance of the uncertainty variable;

a2: calculating the gradient of the uncertainty variable to the design variable based on the flow field result;

a3: calculating the gradient of the objective function according to the gradient;

a4: updating the design variable by using a sequence quadratic programming algorithm according to the gradient of the objective function to obtain an updated design variable;

a5: judging whether the updated design variable converges or not, if so, optimizing the current full turbulence configuration by using the updated design variable; otherwise, the initial values of the design variables are changed and the uncertainty analysis is performed again.

Alternatively, in the A1,

the target function

The method comprises the following steps:

in the A3, the gradient of the objective function

The method comprises the following steps:

wherein,,

and->

Respectively representing uncertainty objective function combination weight coefficients, < ->

Mean value representing uncertainty variable, +.>

Standard deviation of uncertainty variable +.>

Representing deterministic design variable vectors,/->

Is an uncertainty variable vector.

The invention has the following beneficial effects:

on the one hand, the uncertainty analysis method of the full turbulence configuration can solve the problem of higher calculation cost in the existing uncertainty analysis method of the full turbulence configuration, and can greatly reduce the number of sample points on the premise of ensuring the solving precision by chaos expansion of a polynomial, thereby greatly reducing the calculation amount in the airfoil robustness optimization design process; on the other hand, by the aid of the gradient optimization design method, calculation accuracy and calculation cost can be effectively improved, and therefore the full turbulence configuration can meet requirements more under the condition of lower calculation cost.

Drawings

FIG. 1 is a flow chart of a method of uncertainty analysis of a full turbulence configuration of the present invention;

FIG. 2 is a schematic diagram of a RAE2822 airfoil optimized FFD control frame in embodiment 2 of the present invention;

FIG. 3 is a graph showing a comparison of low subsonic deterministic and uncertainty optimized airfoils in accordance with example 2 of the present invention;

FIG. 4 is a graph showing the comparison of low subsonic deterministic and uncertainty optimized pressure distributions in example 2 of the present invention;

FIG. 5 is a graph showing a random distribution of low subsonic deterministic and uncertainty optimized drag coefficients in example 2 of the present invention;

FIG. 6 (a) is a standard deviation cloud plot of the spatial flow field pressure coefficient of the initial airfoil optimized for initial, deterministic, and uncertainty results in consideration of Mach number and angle of attack uncertainty in example 2 of the present invention; FIG. 6 (b) is a standard deviation cloud plot of the spatial flow field pressure coefficient of the initial, deterministic, and uncertainty optimization results for deterministic analysis airfoils taking Mach number and angle of attack uncertainty into account; FIG. 6 (c) is a standard deviation cloud plot of the spatial flow field pressure coefficient of the initial, deterministic, and uncertainty optimization results for uncertainty analysis airfoils taking Mach number and angle of attack uncertainty into account;

FIG. 7 is a low subsonic deterministic and uncertainty optimization history of example 2 of the present invention;

FIG. 8 is a graph showing a comparison of transonic deterministic and uncertainty optimized airfoils in accordance with embodiment 3 of the present invention;

FIG. 9 is a graph showing a comparison of a transonic deterministic and uncertainty optimized pressure distribution in example 3 of the present invention;

FIG. 10 is a graph showing a random distribution of transonic deterministic and uncertainty-optimized drag coefficients in example 3 of the present invention;

FIG. 11 is a cross-sound velocity deterministic and uncertainty optimization process in example 3 of the present invention.

Detailed Description

The principles and features of the present invention are described below with reference to the drawings, the examples are illustrated for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.

Example 1

The technical scheme for solving the technical problems is as follows:

the invention provides an uncertainty analysis method of a full turbulence configuration, which is shown by referring to fig. 1, and comprises the following steps:

s2: parameterizing and deforming the grid by a free deformation parameterization method to obtain a surface grid;

the step S2 comprises the following steps:

establishing a FFD (Free Form Deform) control box wrapping the grid;

establishing a mapping relation between the control frame and the full turbulence configuration; namely:

wherein,,

global coordinate vector representing any point on the design outline, < >>

Representing its parameter coordinate vector, ">

Weight coefficient representing each control point in control box, < ->

Three control directions are indicated and are shown,

indicating that the control body is +>

Control points in three control directions, < ->

、/>

And->

Respectively indicate->

And->

B-spline basis functions of (2).

Solving local coordinates of the middle points of the grids according to the mapping relation;

disturbing control points in the FFD control frame by using the current design variables;

and obtaining global coordinates of the disturbed surface grid according to the mapping relation.

optionally, the S3 includes:

alternatively, the uncertainty variable of the full turbulence configuration includes Mach number

And/or angle of attack->

And/or geometric deformation; the sampling points may be randomly extracted from the uncertainty of the full-clique flow laminar wing by random sampling or Latin hypercube sampling methods.

The number of sampling points is determined by the number of uncertainty variables, the order of independent basis function polynomials and the oversampling rate

The method comprises the following steps:

wherein,,

indicating the oversampling rate, +.>

Representing the order of the independent basis function polynomial, < +.>

Representing the number of random variables +.>

Representing the number of sampling points.

the invention solver adopts a RANS solver, and a RANS equation solving part can be expressed as follows:

wherein,,

flow field residual representing RANS solution, +.>

Is a flow field conservation variable and is a state variable of the RANS equation.

optionally, the S6 includes:

the infinite series expression of the uncertainty variable is:

wherein,,

designing a variable vector for certainty +.>

Is an uncertainty variable vector, ++>

Is the firstjDeterministic portion of the order->

Is->

The random part of the step.

the result of chaotic expansion is as follows:

the chaos expansion result is linearly expressed as a linear equation set, wherein the linear equation set is as follows:

wherein,,

representing a matrix of basis functions, the matrix size being +.>

，/>

For the number of sampling points, +.>

For the number of basis functions +.>

A coefficient matrix of a linear equation set, the matrix size is +.>

，/>

To output the number of random variables, +.>

Is a flow field result matrix with the size of +.>

。

based on the linear equation set, as the flow field result is known, the basis function matrix can be determined through selection, and then the coefficient matrix of the linear equation set can be obtained through solving.

Mean value of the uncertainty variable

The method comprises the following steps:

standard deviation of the uncertainty variable

The method comprises the following steps:

wherein,,

Indicate->

Deterministic portion of the order->

Indicate->

Basis function of order>

Representing the number of sampling points.

S7: and obtaining an analysis result of the uncertainty variable according to the uncertainty variable of the full turbulence configuration and the mean value and the variance of the uncertainty variable.

The uncertainty variable in the full turbulence configuration is Mach number

And/or angle of attack->

In the case of (a), the analysis of the uncertainty variable results in the lift coefficient and/or drag coefficient.

Based on the above, compared with a deterministic optimization design, the uncertainty optimization design can improve the capability of resisting Mach number and attack angle uncertainty disturbance by reasonably balancing deterministic performance and uncertainty performance, and optimize performance mean and standard deviation.

Alternatively, in the A1,

the target function

The method comprises the following steps:

in the A3, the gradient of the objective function

The method comprises the following steps:

wherein,,

and->

Mean value representing uncertainty variable, +.>

Standard deviation of uncertainty variable +.>

Representing deterministic design variable vectors,/->

Is an uncertainty variable vector.

Example 2

The initial airfoil selection RAE2822, referred to the Cessna design state, is:

，

，/>

。

the FFD control point is shown in fig. 2, and the control frame is encrypted at the airfoil head to better control the profile of the airfoil leading edge. Definition of deterministic and uncertainty analysis problems:

the total number of design variables in the optimization process is 16, and the design variables are geometric design variables. The uncertainty analysis assumes that the Mach number and the angle of attack respectively satisfy

Normal distribution and->

The airfoil lift coefficient at this time in the mean state is 0.3. In the optimization process, a 3-step enhancement type polynomial chaos method is used, and the prediction error can be kept at about 0.1%.

Table 1 shows deterministic and uncertainty force coefficient results for low subsonic airfoil optimization, eachDeterministic force coefficients are reference flow field results, i.e

，/>

. Deterministic analysis airfoil designation DeOpt (Deterministic Optimization); the uncertainty analysis airfoil was named UMOpt (Uncertainty Multiple factor Optimization). From the deterministic force coefficients in Table 1, it can be seen that the deterministic optimization results in a drag reduction of 10.03counts, about 10.15%. Wherein the pressure differential resistance is mainly reduced, while the frictional resistance remains almost unchanged. The uncertainty analysis total drag reduction was 9.33counts, slightly less than the deterministic optimization. On the other hand, from the uncertainty statistical response result of the resistance coefficient, the uncertainty analysis, whether the mean value or the standard deviation, is smaller than the initial configuration and the deterministic optimization result. The mean value of the resistance coefficient of the uncertainty analysis result is reduced by about 17% and the standard deviation of the resistance coefficient is reduced by about 80% compared with the initial configuration. Combining the above two aspects, it can be concluded that: uncertainty analysis sacrifices the performance of the deterministic reference field in exchange for robustness of performance over the perturbation range.

TABLE 1 Low subsonic aerofoil optimization results (resistance coefficient in counts)

The results of the deterministic and non-deterministic are compared, see fig. 3 and fig. 4. The thickness of the front edge of the upper surface of the UMOpt airfoil is increased compared with that of the DeOpt airfoil, the front loading phenomenon of the front edge of the lower surface disappears, and the thickness increase is reflected in the pressure distribution as the forward pressure gradient of the upper surface and the lower surface is increased compared with that of the DeOpt airfoil, and the suction peak position is moved forward.

And sampling in random space by adopting a Monte Carlo method and carrying out deterministic analysis, wherein the obtained random sample point resistance coefficient distribution is shown in figure 5. The violin graph represents the distribution characteristic of the resistance coefficient of the sample points, and the more plump parts in the graph have higher probability density, the more sample points fall in the interval. The black thick solid line in the center of each violin diagram represents the upper and lower quartile intervals, and the middle point represents the median of the overall data. Intuitively, therefore, the upper and lower positions of the violin diagram can approximate the height of the average value of the representative resistance coefficient, and the lower the representative average resistance coefficient is; the shape of the violin graph represents the robustness of the resistance performance, and the slimmer violin graph shows that the standard deviation of the resistance coefficient is larger and the robustness is worse, the shorter and thicker the standard deviation of the resistance coefficient is smaller, the performance is more concentrated, and the robustness is better. Comparing violin map results for three airfoils, the UMOpt airfoil was found to have significant advantages. The initial configuration is less robust in both average performance and performance, and both the denopt airfoil and the UMOpt airfoil significantly reduce the average value of the drag coefficient, but compared to the UMOpt performance is more concentrated toward the average value.

The initial configuration Initial, deOpt airfoil, UMOpt airfoil, is subject to standard deviation cloud image comparison of spatial flow field pressure coefficients affected by Mach number and angle of attack uncertainty. From fig. 6 ((a) Initial airfoil, (b) deterministic analysis airfoil, (c) uncertainty analysis airfoil) it can be seen that the flow field pressure coefficient standard deviation magnitudes at the upper surface leading edge locations are ordered as UMOpt < denopt < Initial. Therefore, compared with a deterministic optimization design, the uncertainty of the pressure coefficient in the space flow field can be effectively reduced by the analysis design considering the uncertainty under the full turbulence, and the advantages of the uncertainty analysis design are reflected.

The deterministic and uncertainty analysis processes are shown in fig. 7. The deterministic optimization process is marked in a triangle line, the uncertainty analysis process is marked in a circle line, and the deterministic reference field resistance coefficient is marked in a gray line in the uncertainty analysis process. Since the objective function in the uncertainty analysis is

The difference between the gray circle marking line and the black circle standard line can thus approximately represent the magnitude of the standard deviation. The key node positions in the uncertainty analysis process are respectively marked by different colors in the figure, and the mean value and standard deviation response result of the pressure distribution are displayed beside the key node positions to show the mean value and the standard deviation response result of the pressure distributionAnd airfoil variations. Each key iteration step in the pressure distribution map can compare the pressure distribution mean value with the previous key step, and can also always compare the pressure distribution mean value and the standard deviation response range with the initial airfoil.

The uncertainty analysis goes through the main iteration 8 times, and finally meets constraint and objective function convergence conditions. The first steps of main iteration objective functions in the optimization process are obviously reduced, the last steps of objective functions are smaller in change, and the adjustment and the fairing of the pressure distribution are mainly completed, so that the standard deviation of the resistance coefficient in the optimization process is greatly reduced. The main optimization direction of uncertainty analysis design is to slightly improve the suction peak value of the head of the upper surface and continuously delay the appearance position of the suction peak; reducing the forward pressure gradient of the lower surface. The optimized end result UMOpt airfoil reference field drag coefficient is slightly greater than the DeOpt airfoil, but the standard deviation response near the airfoil head is significantly less than the DeOpt airfoil.

Example 3

Referring to the Honda Jet design state, an established full turbulence configuration uncertainty analysis method and a gradient optimization design method (figure 1) are adopted to conduct optimization design research. The Honda Jet design state is:

，

，/>

. The initial airfoil selection RAE2822, FFD control frame, is consistent with the low subsonic conditions of FIG. 2. And respectively carrying out single-point deterministic optimization design and analysis design considering Mach number and angle of attack uncertainty on the airfoil. The torque constraint is increased compared to the low subsonic optimization to control the low head torque. The optimization problem is defined as follows:

mach number is assumed in analysis considering Mach number and angle of attack uncertaintyAnd the attack angles respectively satisfy

And->

The airfoil lift coefficient at this point in the mean state is 0.38. According to PCE verification results, a 3-step degree enhanced polynomial chaotic method is selected to be used in transonic optimization design, and the error can be controlled below 1%.

Table 2 shows deterministic and uncertain force coefficient results for transonic airfoil optimization, where each deterministic force coefficient is a reference flow field result, i.e

，/>

. The deterministic optimization design airfoil is named DeOpt (Deterministic Optimization); uncertainty analysis design airfoil was named UMOpt (Uncertainty Multiple factor Optimization). The UMOpt airfoil deterministic reference field resistance is slightly greater than the DeOpt airfoil, but the UMOpt airfoil mean resistance coefficient (89.19 counts) is reduced by about 6% from the initial airfoil as seen from the uncertainty result, slightly less than the DeOpt airfoil mean resistance coefficient (91.44 counts). The difference is more pronounced in the drag coefficient standard deviation response, with UMOpt airfoils of only 1.6counts, comparable to the original airfoils. Whereas the drag coefficient standard deviation of the denopt airfoil is 5.11counts, even higher than the initial airfoil, indicating that optimization results considering only deterministic performance may lead to poor performance robustness.

TABLE 2 transonic airfoil optimization results (resistance coefficient in counts)

FIGS. 8 and 9 are airfoil result and pressure distribution comparisons for deterministic optimization and uncertainty analysis, respectively. The radius of the head of the DeOpt airfoil is increased, the position of the maximum thickness of the upper surface is moved forward, and the thickness of the front edge of the lower surface is reduced. The surface suction peaks increase on the corresponding pressure profile. To meet the moment constraint, the trailing edge is unloaded, the original aft loading is removed, and the lift load moves toward the head.

The UMOpt airfoil is seen to have significant advantages in the violin diagram of fig. 10. The DeOpt airfoil has a worse drag performance robustness than the original airfoil under the uncertainty perturbations of mach number and angle of attack. In contrast, the UMOpt airfoil further reduces the average value of the drag coefficient while maintaining the initial configuration robustness substantially unchanged.

Transonic deterministic and uncertainty analysis histories as shown in fig. 11, the uncertainty analysis goes through the main iteration 8 times, and finally, the constraint and objective function convergence conditions are satisfied. The first half objective function in the optimization process is fast in decline, the second half objective function is small in change, the adjustment and the fairing of the pressure distribution are mainly completed, the standard deviation of the resistance coefficient in the optimization process is small in change, and the analysis of the total turbulence considering Mach number and angle of attack uncertainty only reduces average resistance performance and does not obviously optimize robustness. The main optimization direction of uncertainty analysis design is to continuously increase the peak value of head suction force, reduce the lift load at the rear part and move the load towards the front edge.

The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims

1. A method for uncertainty analysis of a full turbulence configuration, the method comprising:

s4: sampling a preset uncertainty variable in a random space to obtain a plurality of sampling points;

2. The method for uncertainty analysis of a full turbulence configuration according to claim 1, wherein S3 comprises:

3. The method of uncertainty analysis of a full turbulence configuration according to claim 1, wherein in S4, the predetermined uncertainty variable includes a mach number

And/or angle of attack->

And/or geometric deformation;

The method comprises the following steps:

wherein,,

indicating the oversampling rate, +.>

Representing the order of the independent basis function polynomial, < +.>

Representing the number of random variables that are to be used,

representing the number of sampling points.

4. The method for uncertainty analysis of a fully turbulent flow configuration according to claim 1, wherein S6 comprises:

5. The method for analyzing uncertainty of a full turbulence configuration according to claim 4, wherein in S61, the infinite series expression of the uncertainty variable is:

wherein,,

designing a variable vector for certainty +.>

Is an uncertainty variable vector, ++>

Is the firstjDeterministic portion of the order->

Is->

The random part of the step.

6. The method for analyzing the uncertainty of the full turbulence configuration according to claim 4, wherein in S63, the system of linear equations is:

wherein,,

representing a matrix of basis functions, the matrix size being +.>

，/>

For the number of sampling points, +.>

For the number of basis functions +.>

A coefficient matrix of a linear equation set, the matrix size is +.>

，/>

To output the number of random variables, +.>

Is a flow field result matrix with the size of +.>

。

7. The method for analyzing uncertainty of full turbulence configuration according to claim 4, wherein in S65, the mean value of the uncertainty variable

The method comprises the following steps:

standard deviation of the uncertainty variable

The method comprises the following steps:

wherein,,

Indicate->

Deterministic portion of the order->

Indicate->

Basis function of order>

Representing the number of sampling points.

8. A gradient optimization design method based on the uncertainty analysis method of the full turbulence configuration according to any one of claims 1 to 7, characterized in that the gradient optimization design method comprises:

9. The gradient optimization design method according to claim 8, wherein in the A1,

the objective function