Pressure distribution guided objective-constrained airfoil bayesian optimization method and apparatus

Abstract

The application discloses a kind of pressure distribution guide target constraint airfoil bayesian optimization method and device, belong to the technical field of aircraft design;It includes: constructing airfoil sample;Evaluate the aerodynamic performance of airfoil sample;Calculate airfoil sample target value and constraint violation value, and construct the sample set comprising airfoil sample, airfoil sample target value and constraint violation value;Using sample set trains Gaussian process proxy model, and exports airfoil sample target and constraint violation value prediction mean, prediction variance;Based on prediction mean and prediction variance, optimize the confidence boundary acquisition function with constraint, obtain the next airfoil sample to be evaluated;After iteration, select the feasible airfoil sample of best target performance as optimization solution.The application realizes the effective constraint of the sampling airfoil pressure distribution, guarantees the performance of final optimization airfoil at non-design point, more close to actual engineering demand.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aircraft design, and particularly relates to a wing profile Bayesian optimization method and device guided by pressure distribution and constrained by target. BACKGROUND

[0002] As a basic configuration of a wing, a wing profile is a direct factor affecting the aerodynamic efficiency and flight quality of an aircraft, and therefore, wing profile design is a basic link in aircraft design. At present, most wing profile design methods consider aerodynamic force coefficients as optimization targets, such as lift-drag force coefficients. Such single-point optimization results usually have superior target function values, but have poor performance at non-design points, and are difficult to cope with changing working conditions in the flight process. In fact, the wing profile surface pressure distribution curve has rich connotations, that is, some characteristics of the pressure distribution at the design point may indicate the performance at the non-design point. In theory, by optimizing or constraining multiple characteristic parameters, the optimization direction can be further guided, and the damage to the performance at the non-design point can be avoided. SUMMARY

[0003] The application aims to solve the problem that the existing wing profile optimization design does not combine multiple characteristic parameters or constraints, and has certain limitations.

[0004] To achieve the above-mentioned purpose, the technical scheme adopted by the application is as follows:

[0005] In a first aspect, a wing profile Bayesian optimization method guided by pressure distribution and constrained by target includes the following steps:

[0006] S1, constructing a wing profile sample;

[0007] S2, evaluating the aerodynamic performance of the wing profile sample to obtain aerodynamic force coefficients and a pressure distribution curve;

[0008] S3, extracting pressure distribution characteristics according to the pressure distribution curve, calculating wing profile sample target values and constraint violation values, and constructing a sample set containing the wing profile sample, the wing profile sample target values and the constraint violation values;

[0009] S4, training a Gaussian process surrogate model using the sample set, and outputting predicted mean values and predicted variance values of the wing profile sample target and the constraint violation values;

[0010] S5, based on the predicted mean values and the predicted variance values, optimizing a confidence boundary acquisition function with constraints to obtain a next wing profile sample to be evaluated;

[0011] S6, sending the next wing profile sample to be evaluated into S2, and executing S2-S5 until a preset iteration number is reached;

[0012] S7. Select the feasible sample with the best target performance from the evaluated airfoil samples as the optimization solution.

[0013] Furthermore, airfoil samples are constructed in S1, specifically including:

[0014] Represent the airfoil coordinate points using the Hicks-Henne parameter:

[0015]

[0016] In the formula, and These are the normalized ordinates of the upper surface and the lower surface of the new airfoil, respectively. , These are the normalized ordinates of the upper surface and the lower surface of the reference airfoil, respectively. To control the design variables of the airfoil shape; It is a shape function; k For designing variable numbers or shape function numbers; n To control the number of design variables on the upper surface of the airfoil or the number of design variables on the lower surface of the airfoil; The normalized x-coordinate of the airfoil chord;

[0017] Then, Latin hypercube sampling is performed in the user-defined parameter design space. The parameter design space is divided into sub-intervals of equal size according to the dimensions. Random sampling is performed from each sub-interval of each dimension, and then the scalar samples are randomly combined to form airfoil samples in the complete dimensions.

[0018] Furthermore, shape functions Represented as:

[0019]

[0020] In the formula, , express A specific chord coordinate of the airfoil.

[0021] Furthermore, S2 specifically includes:

[0022] Using the shape parameters of the airfoil sample and the design conditions input by the user as input, the aerodynamic coefficients and pressure distribution curves of the airfoil are obtained by airfoil aerodynamic simulation;

[0023] Based on the pressure distribution curve, extract the pressure distribution characteristics;

[0024] Among them, the aerodynamic coefficients include the lift coefficient and the drag coefficient;

[0025] Pressure distribution characteristics include wavefront wall Mach number, leading edge suction peak, highest pressure coefficient on the lower surface, pressure fluctuation on the suction plateau, post-loading, and pressure recovery gradient.

[0026] Furthermore, in S3, the target value for the airfoil sample is expressed as:

[0027]

[0028] In the formula, w 1. w 2 represents the weighting coefficient; C D This is the drag coefficient; The wavefront wall Mach number;

[0029] The constraint violation value is represented as:

[0030]

[0031] In the formula, The lift coefficient; The lift coefficient of the reference airfoil; This is the leading edge suction peak; This represents the highest pressure coefficient on the lower surface. For pressure fluctuations on the suction platform; Loaded later; For pressure recovery gradient; This represents the maximum thickness of the airfoil. The maximum thickness of the reference airfoil; U and L These are the upper and lower boundary vectors of the airfoil parameters, respectively; b 1,…, b 7 is the constraint threshold.

[0032] Furthermore, in S4, the posterior prediction distribution of the Gaussian process surrogate model is expressed as:

[0033]

[0034] In the formula, Values ​​that violate the target or constraint; for Hicks-Henne parameter column vector of airfoil samples The matrix formed; For the corresponding target or constraint, the function value is violated. The column vector consists of the objective or constraint that violates the function. Follows an infinite-dimensional Gaussian distribution In the formula, Represent a Gaussian process; This indicates that the objective or constraint of any airfoil sample violates the mean function. For expectation operators; This represents the covariance function between any two airfoil samples; For the objective or constraint violation function of another airfoil sample; The objective or constraint of the other airfoil sample violates the mean function; Represents any airfoil sample; This indicates the relationship between the current airfoil sample and all existing airfoil samples. The covariance matrix; This represents the variance of the current airfoil sample. This represents all existing airfoil samples and the current airfoil sample. The covariance matrix; This indicates that the target or constraint violates the column vector. The covariance matrix;

[0035] Among them, the predicted mean of the target or constraint violation value of the airfoil sample for:

[0036]

[0037] Prediction variance of airfoil sample target or constraint violation values for:

[0038]

[0039] In the formula, A simplified form representing the predicted mean of the target or constraint violation values; A simplified form representing the predicted variance of the target or constraint violation value.

[0040] Furthermore, in S5, the constrained confidence boundary acquisition function is expressed as:

[0041]

[0042] In the formula, This represents the value of the confidence boundary acquisition function with constraints. The number of constraints; b It is a positive number; Indicates the probability of satisfying the constraint; For the first A random variable with a posterior constraint violation value; Let represent the lower bound acquisition function based on the posterior prediction distribution of the Gaussian process, where This represents the posterior prediction mean of the Gaussian process; This represents the posterior prediction standard deviation of a Gaussian process; For the currently evaluated airfoil sample set, This indicates the currently assessed target or constraint violation value for the airfoil; This represents the multiple of the posterior prediction standard deviation of a Gaussian process, which determines... In the interval The confidence level is determined by specifying the confidence level. The airfoil sample with the smallest lower bound of the output confidence interval at the given confidence level is obtained by minimizing the lower bound of the confidence function based on the Gaussian process posterior prediction distribution, and then used as the next airfoil sample to be evaluated.

[0043] Secondly, an airfoil Bayesian optimization device for pressure distribution-guided target constraints includes:

[0044] The initial sample acquisition module is used to construct airfoil samples;

[0045] The sample aerodynamic evaluation module is used to evaluate the aerodynamic performance of airfoil samples and obtain aerodynamic coefficients and pressure distribution curves.

[0046] The target and constraint calculation module is used to extract pressure distribution characteristics, and calculate the target value and constraint violation value of the airfoil sample based on the aerodynamic coefficient and pressure distribution characteristics, and construct a sample set containing airfoil samples, airfoil sample target values ​​and constraint violation values;

[0047] The Gaussian process modeling module is used to train a Gaussian process surrogate model using a sample set and output the predicted mean and predicted variance of the airfoil sample target and constraint violation values.

[0048] The acquisition function optimization module is used to optimize the constrained confidence boundary acquisition function based on the predicted mean and predicted variance to obtain the next airfoil sample to be evaluated.

[0049] And for sending the next airfoil sample to be evaluated into the sample aerodynamic evaluation module, until the preset number of iterations is reached;

[0050] And to select the feasible sample with the best target performance from the evaluated airfoil sample as the optimization solution.

[0051] The airfoil Bayesian optimization method and apparatus for pressure distribution-guided target constraints provided by this invention have the following beneficial effects:

[0052] 1. Enhanced optimization effect: This invention uses the weighted sum of the wavefront wall Mach number, a characteristic parameter in the airfoil surface pressure distribution, and the drag coefficient as the objective term. It also constrains characteristic parameters such as the leading-edge suction peak, the highest pressure coefficient on the lower surface, the pressure fluctuation on the suction platform, post-loading, and the pressure recovery gradient. Furthermore, it integrates the constraint terms into the confidence boundary acquisition function to form a robust Bayesian optimization framework based on a constrained confidence boundary strategy. This enables the effective utilization of pressure distribution information, weakens shock waves to reduce drag, and maintains non-design point performance.

[0053] 2. Meets engineering requirements: By coupling the pressure distribution characteristic parameters such as the leading edge suction peak, the highest pressure coefficient on the lower surface, the pressure fluctuation of the suction platform, the post-loading, and the pressure recovery gradient with the Bayesian optimization confidence boundary acquisition function, the pressure distribution of the sampled airfoil is effectively constrained, ensuring the performance of the final optimized airfoil at non-design points, which is more in line with actual engineering requirements.

[0054] 3. Automated and efficient process: The Bayesian optimization framework utilizes the predicted mean and predicted variance of the Gaussian process surrogate model to avoid sampling in the low probability region of the global optimum, ensuring the efficiency of the optimization process. At the same time, the monotonicity of the designed constrained confidence boundary sampling function is not affected by the target confidence boundary value, and it automatically matches the constraint violation amount with the target amount and different constraint violation amounts, achieving a high degree of automated operation.

[0055] 4. Wide range of applications: Users can set different flight conditions and parameter spaces, and flexibly adjust the composition of pressure distribution characteristics in the target and constraints, which can meet diverse airfoil design needs. Attached Figure Description

[0056] Figure 1 This is a flowchart of the airfoil Bayesian optimization method with pressure distribution-guided target constraints in Embodiment 1 of the present invention.

[0057] Figure 2 This is a block diagram of the airfoil Bayesian optimization device for pressure distribution-guided target constraints in Embodiment 2 of the present invention. Detailed Implementation

[0058] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0059] Example 1

[0060] This embodiment presents a Bayesian optimization method for airfoil with pressure distribution-guided objective constraints. This method simultaneously considers the airfoil surface pressure distribution characteristics and aerodynamic coefficients in both the optimization objective and constraints, achieving effective constraints on the sampled airfoil pressure distribution and ensuring the performance of the final optimized airfoil at non-design points. (Refer to...) Figure 1 Specifically, it includes the following:

[0061] S1. Construct airfoil samples;

[0062] Representing the airfoil coordinate points using Hicks-Henne parameters, also known as the shape function linear perturbation method, involves applying a linear perturbation to the surface of the reference airfoil, specifically as follows:

[0063]

[0064] In the formula, and These are the normalized ordinates of the upper surface and the lower surface of the new airfoil, respectively. , These are the normalized ordinates of the upper surface and the lower surface of the reference airfoil, respectively. To control the design variables of the airfoil shape; It is a shape function; k For designing variable numbers or shape function numbers; n To control the number of design variables on the upper surface of the airfoil or the number of design variables on the lower surface of the airfoil; The normalized x-coordinate of the airfoil chord; for One design variable controls the amount of disturbance applied to the upper and lower surfaces. for A shape function;

[0065] Among them, shape function Represented as:

[0066]

[0067] In the formula, , express A specific chord coordinate of the airfoil.

[0068] Then, Latin hypercube sampling is performed in the user-defined parameter design space. The parameter design space is divided into sub-intervals of equal quantity to the sampling according to the dimensions. Random sampling is performed from each sub-interval of each dimension, and the scalar samples are randomly combined to form airfoil samples in the complete dimension. In this way, the airfoil samples can be fully covered in the entire design space with high efficiency.

[0069] S2. Evaluate the aerodynamic performance of the airfoil sample and obtain the aerodynamic coefficients and pressure distribution curves;

[0070] An external simulation program is called, using the shape parameters of the airfoil sample and the design conditions input by the user as input, and the aerodynamic coefficients and pressure distribution curves of the airfoil are obtained through airfoil aerodynamic simulation.

[0071] Based on the pressure distribution curve, extract the pressure distribution characteristics;

[0072] Among them, the aerodynamic coefficient includes the lift coefficient.C L drag coefficient C D ;

[0073] Pressure distribution characteristics include wavefront wall Mach number Ma wl Leading edge suction peak C P,suc Maximum pressure coefficient of the lower surface C P,low Suction platform pressure fluctuation Err Post-loading Load aft Pressure recovery gradient dC P Key feature parameter values, etc.

[0074] Among them, the Mach number of the wavefront wall Ma wl Shock wave location The Mach number at its maximum represents the shock wave intensity; shock wave location x sw The point of maximum slope near the abrupt change in shock wave pressure; the leading edge suction peak. C P,suc The largest | near the leading edge of the upper surface (within 15% of the chord length) C P |;Highest pressure coefficient on the lower surface C P,low The minimum pressure coefficient at the lower surface characterizes the highest flow velocity at the lower surface; pressure fluctuations at the suction platform. Err The pressure coefficient fluctuation area from the leading-edge suction peak to the wavefront range; post-loading Load aft The pressure coefficient distribution at the trailing edge of the lower surface (within 70%-100% of the chord length) is similar to... C P =0 area; pressure recovery gradient dC P The gradient of the highest pressure coefficient after the shock wave to the average pressure coefficient gradient of the trailing edge.

[0075] S3. Based on the pressure distribution curve, extract the pressure distribution characteristics, calculate the target value and constraint violation value of the airfoil sample, and construct a sample set containing the airfoil sample, the target value of the airfoil sample, and the constraint violation value.

[0076] This embodiment calculates the target value and constraint violation value of the airfoil sample based on the aerodynamic coefficient and pressure distribution characteristics of the airfoil sample, according to the target item composition and weight coefficient, constraint item and constraint threshold specified by the user;

[0077] The target value for the airfoil sample is expressed as:

[0078]

[0079] In the formula, w 1. w 2 represents the weighting coefficient; C D This is the drag coefficient; The wavefront wall Mach number; x It is the Hicks-Henne airfoil parameter vector;

[0080] The constraint violation value is represented as:

[0081]

[0082] In the formula, U and L These are the upper and lower boundary vectors of the airfoil parameters, respectively; b 1,…, b 7 is the constraint threshold.

[0083] S4. Train the Gaussian process surrogate model using the sample set, and output the predicted mean and predicted variance of the airfoil sample target and constraint violation values;

[0084] This embodiment adopts the Gaussian process assumption to establish functional mapping relationships between airfoil sample shape parameters and target values, and between airfoil sample shape parameters and constraint violation values, which can be used to quickly predict the target values ​​and constraint violation values ​​of any airfoil sample in the design space.

[0085] Gaussian process, assuming the objective or constraint violates the function Follows an infinite-dimensional Gaussian distribution The objective or constraint of any airfoil sample violates the mean function. The covariance function between any two airfoil samples is:

[0086] .

[0087] When used for predicting target or constraint violation values ​​for arbitrary airfoil samples in space, the sample size is assumed to be... sample set ,in for Hicks-Henne parameter column vector of the group of samples The matrix formed For the corresponding target or constraint, the function value is violated. The column vector is composed of these elements. The prior assumption of the target or constraint violation mean function is set to 0. Based on the prior assumption of the Gaussian process, the target or constraint violation column vector of this sample set... obey Meta-Gaussian distribution ,in For the target or constraint to violate the column vector Covariance matrix:

[0088]

[0089] For any sample Based on the prior assumptions of the Gaussian process, the model predicts the value of its objective or constraint violation. The target or constraints of the existing airfoil sample violate the observed values. The joint distribution is:

[0090]

[0091] in, This indicates the relationship between the current airfoil sample and all existing airfoil samples. The covariance matrix.

[0092] By marginalizing the joint distribution, the target or constraint violation value is obtained. The posterior prediction distribution is:

[0093]

[0094] Among them, the predicted mean of the target or constraint violation value of the airfoil sample for:

[0095]

[0096] Prediction variance of airfoil sample target or constraint violation values for:

[0097]

[0098] In the formula, A simplified form representing the predicted mean of the target or constraint violation values; A simplified form representing the predicted variance of the target or constraint violation value; For expectation operators; For the objective or constraint violation function of another airfoil sample; The objective or constraint of the other airfoil sample violates the mean function; This represents the variance of the current airfoil sample. This represents all existing airfoil samples and the current airfoil sample. The covariance matrix.

[0099] S5. Based on the predicted mean and predicted variance, optimize the constrained confidence boundary acquisition function to obtain the next airfoil sample to be evaluated.

[0100] This embodiment integrates the constraint violation prediction with the target prediction confidence boundary based on the designed constrained confidence boundary acquisition function, and obtains the shape parameters of the next sample to be evaluated by optimizing the function.

[0101] Specifically, the confidence boundary acquisition function is used to evaluate the best possible outcome for a given sample function value at a specific confidence level. The confidence lower bound acquisition function based on the Gaussian process posterior prediction distribution is defined as follows:

[0102]

[0103] in, This represents the posterior prediction mean of the Gaussian process; This represents the posterior prediction standard deviation of a Gaussian process; For the currently evaluated airfoil sample set, Decision made In the interval confidence level, This indicates the currently evaluated target or constraint violation value for the airfoil. (This is achieved by specifying...) By minimizing the lower bound of the confidence collection function based on the Gaussian process posterior prediction distribution, the sample with the smallest lower bound of the output confidence interval at that confidence level will be obtained as the next sample to be evaluated.

[0104] The constrained confidence boundary acquisition function is expressed as:

[0105]

[0106] In the formula, This represents the value of the confidence boundary acquisition function with constraints. The number of constraints; b It is a very small positive number; Indicates the probability of satisfying the constraint;

[0107] First, due to absolute value operations, negation operations, and positive constants... b The existence of, for Any value of , Follow The value increases and then strictly monotonically decreases; given the posterior derivative of the constraint term Gaussian process. The range is Supplement This guarantees and A monotonically positive correlation between them, regardless of Secondly, this coupling method automatically balances the positive and negative values. and The degree of influence on the new objective avoids overexploitation of regions with good confidence lower bounds but low feasibility probabilities, and by considering the probability of constraint satisfaction, it can tolerate the prediction bias of the constraint term model to a certain extent. In addition, the same weights for different constraint terms ensure that they have an equal degree of influence on the sampling results.

[0108] S6. Send the next airfoil sample to be evaluated into S2, and execute S2~S5 until the preset number of iterations is reached;

[0109] High-precision airfoil aerodynamic simulation evaluation is costly and requires a limited number of iterations based on available computing resources. Each iteration includes aerodynamic evaluation of the sampled airfoil, updating the corresponding Gaussian process surrogate model with the airfoil sample's shape parameters, target values, and constraint violation values ​​to improve the model accuracy of the globally optimal high-probability region, and determining the next sample to be evaluated based on the updated model.

[0110] S7. Select the feasible sample with the best target performance from the evaluated airfoil samples as the optimization solution;

[0111] The optimized solution in this embodiment corresponds to the target items and weights specified by the user. Different target item compositions and weight settings result in different optimized solutions, reflecting the importance attached to different optimization target components.

[0112] Example 2

[0113] This embodiment provides an airfoil Bayesian optimization device with pressure distribution-guided target constraints, referencing... Figure 2 It includes:

[0114] The initial sample acquisition module is used to construct airfoil samples;

[0115] Specifically, this module represents the airfoil coordinate points using Hicks-Henne parameters and performs Latin hypercube sampling in the user-defined parameter design space, so that the initial airfoil samples are evenly distributed in the design space. This module provides the initial airfoil sample shape parameters for the sample aerodynamic evaluation module.

[0116] The sample aerodynamic evaluation module is used to evaluate the aerodynamic performance of airfoil samples and obtain aerodynamic coefficients and pressure distribution curves; this module provides aerodynamic coefficients and pressure distribution curves for the target and constraint calculation module.

[0117] The target and constraint calculation module is used to extract pressure distribution features and calculate the target value and constraint violation value of the airfoil sample based on the aerodynamic coefficient and pressure distribution features. It also constructs a sample set containing airfoil samples, airfoil sample target values, and constraint violation values. This module provides target values ​​and constraint violation values ​​for the Gaussian process modeling module.

[0118] The Gaussian process modeling module is used to train a Gaussian process surrogate model using a sample set and output the predicted mean and variance of the target and constraint violation values ​​for the airfoil samples. This module provides the acquisition function optimization module with the predicted mean and variance of the target or constraint violation values ​​for any sample.

[0119] The acquisition function optimization module is used to optimize the constrained confidence boundary acquisition function based on the predicted mean and predicted variance to obtain the next airfoil sample to be evaluated; this module provides the shape parameters of the next airfoil sample to be evaluated to the sample aerodynamic evaluation module.

[0120] And for sending the next airfoil sample to be evaluated into the sample aerodynamic evaluation module, until the preset number of iterations is reached;

[0121] And to select the feasible sample with the best target performance from the evaluated airfoil sample as the optimization solution.

[0122] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A Bayesian optimization method for airfoils with pressure distribution-guided target constraints, characterized in that, Includes the following steps: S1. Construct airfoil samples; S2. Evaluate the aerodynamic performance of the airfoil sample, and obtain the aerodynamic coefficients and pressure distribution curves, which specifically includes: Using the shape parameters of the airfoil sample and the design conditions input by the user as input, the aerodynamic coefficients and pressure distribution curves of the airfoil are obtained by airfoil aerodynamic simulation; Based on the pressure distribution curve, extract the pressure distribution characteristics; Among them, the aerodynamic coefficients include the lift coefficient and the drag coefficient; Pressure distribution characteristics include wavefront wall Mach number, leading edge suction peak, highest pressure coefficient on the lower surface, pressure fluctuation on the suction plateau, post-loading, and pressure recovery gradient; S3. Based on the pressure distribution curve, extract the pressure distribution characteristics, calculate the target value and constraint violation value of the airfoil sample, and construct a sample set containing the airfoil sample, the target value of the airfoil sample, and the constraint violation value. The target value for the airfoil sample is expressed as: In the formula, w 1. w 2 represents the weighting coefficient; C D This is the drag coefficient; The Mach number of the wavefront wall; The constraint violation value is represented as: In the formula, The lift coefficient; The lift coefficient of the reference airfoil; This is the leading edge suction peak; This represents the highest pressure coefficient on the lower surface. For pressure fluctuations on the suction platform; Loaded later; For pressure recovery gradient; This represents the maximum thickness of the airfoil. The maximum thickness of the reference airfoil; U and L These are the upper and lower boundary vectors of the airfoil parameters, respectively; b 1,…, b 7 represents the constraint threshold; S4. Train the Gaussian process surrogate model using the sample set, and output the predicted mean and predicted variance of the airfoil sample target and constraint violation values; S5. Based on the predicted mean and predicted variance, optimize the constrained confidence boundary acquisition function to obtain the next airfoil sample to be evaluated. S6. Send the next airfoil sample to be evaluated into S2, and execute S2~S5 until the preset number of iterations is reached; S7. Select the feasible sample with the best target performance from the evaluated airfoil samples as the optimization solution.

2. The airfoil Bayesian optimization method with pressure distribution-guided target constraints according to claim 1, characterized in that, The construction of the airfoil sample in S1 specifically includes: Represent the airfoil coordinate points using the Hicks-Henne parameter: In the formula, and These are the normalized ordinates of the upper surface and the lower surface of the new airfoil, respectively. , These are the normalized ordinates of the upper surface and the lower surface of the reference airfoil, respectively. To control the design variables of the airfoil shape; It is a shape function; k For designing variable numbers or shape function numbers; n To control the number of design variables on the upper surface of the airfoil or the number of design variables on the lower surface of the airfoil; The normalized x-coordinate of the airfoil chord; Then, Latin hypercube sampling is performed in the user-defined parameter design space. The parameter design space is divided into sub-intervals of equal size according to the dimensions. Random sampling is performed from each sub-interval of each dimension, and then the scalar samples are randomly combined to form airfoil samples in the complete dimensions.

3. The airfoil Bayesian optimization method with pressure distribution-guided target constraints according to claim 2, characterized in that, The shape function Represented as: In the formula, , express A specific chord coordinate of the airfoil.

4. The airfoil Bayesian optimization method with pressure distribution-guided target constraints according to claim 1, characterized in that, In S4, the posterior prediction distribution of the Gaussian process surrogate model is expressed as: In the formula, Values ​​that violate the target or constraint; for Hicks-Henne parameter column vector of airfoil samples The matrix formed; For the corresponding target or constraint, the function value is violated. The column vector consists of the objective or constraint that violates the function. Follows an infinite-dimensional Gaussian distribution In the formula, Represent a Gaussian process; This indicates that the objective or constraint of any airfoil sample violates the mean function. For expectation operators; This represents the covariance function between any two airfoil samples; For the objective or constraint violation function of another airfoil sample; The objective or constraint of the other airfoil sample violates the mean function; Represents any airfoil sample; This indicates the relationship between the current airfoil sample and all existing airfoil samples. The covariance matrix; This represents the variance of the current airfoil sample. This represents all existing airfoil samples and the current airfoil sample. The covariance matrix; This indicates that the target or constraint violates the column vector. The covariance matrix; Among them, the predicted mean of the target or constraint violation value of the airfoil sample for: Prediction variance of airfoil sample target or constraint violation values for: In the formula, A simplified form representing the predicted mean of the target or constraint violation values; A simplified form representing the predicted variance of the target or constraint violation value.

5. The airfoil Bayesian optimization method with pressure distribution-guided target constraints according to claim 1, characterized in that, In S5, the constrained confidence boundary acquisition function is expressed as: In the formula, This represents the value of the confidence boundary acquisition function with constraints. The number of constraints; b It is a positive number; Indicates the probability of satisfying the constraint; For the first A random variable with a posterior constraint violation value; Let represent the lower bound acquisition function based on the posterior prediction distribution of the Gaussian process, where This represents the posterior prediction mean of the Gaussian process; This represents the posterior prediction standard deviation of a Gaussian process; For the currently evaluated airfoil sample set, This indicates the currently assessed target or constraint violation value for the airfoil; This represents the multiple of the posterior prediction standard deviation of a Gaussian process, which determines... In the interval The confidence level is determined by specifying the confidence level. The airfoil sample with the smallest lower bound of the output confidence interval at the given confidence level is obtained by minimizing the lower bound of the confidence function based on the Gaussian process posterior prediction distribution, and then used as the next airfoil sample to be evaluated.

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