Machine learning-driven airfoil design methods, devices, media, and program products

Abstract

This invention discloses a machine learning-driven airfoil design method, device, medium, and program product, including: (1) constructing a mathematical model of the float and lift-drag ratio of airfoil nodes with weight and stiffness as constraints; (2) establishing an airfoil population based on space-filled Latin hypercube sampling; (3) using uniformly distributed random numbers to call DE mutation operation and maximum-minimum distance screening method to generate the first generation of subpopulation; (4) using interior point optimization to generate the second generation of subpopulation; (5) using a proxy model-assisted error-driven adaptive screening strategy to select airfoil offspring, evaluating the airfoil offspring and selecting the best individual from them through feasibility rules, judging whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments, if so, outputting the optimal variable parameters, otherwise returning to step (3). This invention designs an evolutionary mechanism that adapts to the differences in airfoil constraint calculation to reduce computational cost, thereby shortening the design cycle of airfoil lift-drag ratio optimization.

Description

Technical Field

[0001] This invention relates to the fields of general artificial intelligence technology and swarm intelligence, and more specifically, to machine learning-driven airfoil design methods, devices, media, and program products. Background Technology

[0002] Lift-to-drag ratio is a key indicator of an aircraft's aerodynamic efficiency. A higher lift-to-drag ratio can significantly reduce drag, decrease fuel consumption, and effectively extend range. In the field of airfoil performance design, improving the lift-to-drag ratio is one of the core requirements. The optimization goal is to maximize the lift-to-drag ratio while ensuring lightweight and high rigidity requirements. However, airfoil structure optimization design usually relies on computationally intensive simulations. Traditional algorithms are inefficient and computationally resource-intensive, making it difficult to effectively achieve this optimization goal in practical engineering applications.

[0003] Machine learning models can learn the complex nonlinear mapping relationships and trends of real functions based on evaluated historical data, thereby constructing high-precision surrogate models. These models not only accurately reflect the relationships between optimization objectives, constraints, and design variables, but also quickly establish predictive mathematical models that combine accuracy and efficiency. Compared to traditional numerical simulation methods (such as finite element analysis), the time consumed in the prediction process is almost negligible.

[0004] However, existing optimization methods fail to distinguish between the high cost of lift-to-drag ratio evaluation and the low-cost characteristics of weight and stiffness constraints in actual optimization, treating them uniformly. This leads to excessive waste of computational resources on inexpensive constraints, while severely neglecting the exploration of expensive objectives, significantly reducing algorithm search efficiency and constraint satisfaction quality. Furthermore, the limited prediction accuracy of ordinary machine learning models makes it even more difficult for classical algorithms to handle such constraint optimization problems where the cost of objective and constraint evaluation is unbalanced. Summary of the Invention

[0005] To address the limitations of existing technologies or the need for improved technologies, this invention proposes a machine learning-driven airfoil design method, device, medium, and program product, which effectively solves the constraint optimization problem of the imbalance between the airfoil lift-to-drag ratio objective function and the two constraints of airfoil weight and airfoil stiffness in evaluating cost.

[0006] In a first aspect, the present invention provides a machine learning-driven airfoil design method, comprising the following steps:

[0007] (1) Taking the floating amount of each key node of the airfoil as the design variable, weight and stiffness as constraints, and lift-to-drag ratio as the target, the design domain of each design variable is constructed according to the geometric constraints of the airfoil structure, and a mathematical model is constructed through geometric analysis;

[0008] (2) Within the design domain of the design variables, an airfoil population is established based on space-filled Latin hypercube sampling;

[0009] (3) Evaluate the weight of each design variable in the airfoil population and save it to the database. Use uniformly distributed random numbers to call DE mutation operation and maximum-minimum distance screening method to generate the first generation of subpopulation;

[0010] (4) Evaluate the stiffness of each design variable in the first generation subpopulation and save it to the database. Use the interior point method to optimize the stiffness of each design variable to generate the second generation subpopulation.

[0011] (5) Evaluate the lift-to-drag ratio of each design variable in the second generation subpopulation, establish a radial basis function model for the objective function, use an error-driven adaptive screening strategy assisted by a surrogate model to select airfoil offspring, evaluate the airfoil offspring and select the best individual from them through feasibility rules, determine whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments, if so, output the optimal variable parameters, otherwise return to step (3).

[0012] Optionally, in step (1), the design domain of each design variable is constructed based on the geometric constraints of the airfoil structure, and a mathematical model is constructed through geometric analysis. The specific steps include the following:

[0013] The first step is to determine the number of design variables and, based on the geometric constraints of the airfoil structure, construct a design domain consisting of the float values ​​of each key node.

[0014] The second step is to construct a mathematical model through geometric analysis, the mathematical expression of which is as follows:

[0015] ,

[0016] In the above formula, Solve represents the optimal variable parameters for solving the airfoil structure optimization problem. It is a vector composed of various design variables. For the design variables in the airfoil structure optimization problem, n The number of design variables is given, T is the transpose of the matrix, and Max is the maximum value of the airfoil's lift-to-drag ratio. L and D These represent lift and drag, respectively, and St is the constraint that needs to be satisfied. G For airfoil stiffness, For Herveside functions, Let f be the topological description function of the airfoil structure, and t be the Neumann boundary Γ. t The volume force density and the preset surface traction force, where u is the displacement field. V It is a random variable representing the volume of the airfoil structure. S It is a random variable representing the displacement of the airfoil structure. It is the lower limit of airfoil design stiffness. M For airfoil weight, It is the density of the airfoil material. This is the upper limit of the airfoil weight. The design domain for design variables.

[0017] Optionally, the specific steps of step (2) are as follows:

[0018] A space-filled Latin hypercube sampling method was used to establish an wing population to reduce the randomness and uneven distribution of sampling points. d 1, d 2,…, d m For sampling plan The distances between all pairwise sample points are calculated, and then sorted in ascending order of distance values. ,in, m This represents the total number of pairwise distances between sample points in sampling plan X. n Given the number of sample points, the mathematical expression for calculating the distance is as follows:

[0019] ,

[0020] In the above formula, and The index of the sample point, and , For the first sample points and the sample points Between p -norm distance, p For the norm order, when p =1 For rectangular distance, when p =2 For Euclidean distance, k The dimension of the sample points, i.e., each sample point consists of... k It consists of several design variables. for The j One design variable, for The j One design variable;

[0021] set up J 1, J 2,…, J m This represents the number of sample point pairs corresponding to the same distance, each... d i One Ji Space-filling Latin hypercubes introduce scalar discriminant functions. Maximize the minimum distance between sample points d i And minimize the number of distance-related sample point pairs. J i To take into account d i and J i The size of the sample affects the sampling, therefore, when The smaller the value, the more uniform the distribution of sample points in space, the higher the quality of the sampling plan X, and the better the scalar discriminant function. The mathematical expression is as follows:

[0022] ,

[0023] In the above formula, X is the sampling plan. d i It is the first i The distance between sample points J i The distance is d i The number of sample point pairs corresponding to the time. m It is the total number of pairwise distances between sample points in sampling plan X. q This is a parameter used to adjust the sensitivity to the influence of distance, and it is usually taken as a positive value.

[0024] Optionally, the specific steps of step (3) are as follows:

[0025] The first step is to evaluate the airfoil weights of the design variables at each key node in the airfoil population and save the design variables and airfoil weight data of each key node to the database.

[0026] The second step is to use all individuals in the database as the parent population, and to call the DE mutation operation on the parent population using uniformly distributed random numbers. That is, to generate an intermediate subpopulation by gradually executing DE evolution, feasibility criterion screening, replacement mechanism and mutation strategy.

[0027] First, DE evolution is performed on the parent population to balance exploration and exploitation capabilities. The mutation method is selected using random numbers. The expression used in DE evolution is as follows:

[0028] when R <0.5,DE / current-to-rand / 1: ,

[0029] when R >0.5, DE / rand-to-best / 1: ,

[0030] In the above formula, R Here, `DE` represents differential evolution, `current` indicates that the starting point of evolution is a specific parent individual, and `to` indicates the direction of differential evolution. In `DE / current-to-rand / 1`, `rand` indicates that the evolution is guided by random individuals from the parent population, and "1" indicates the number of random differential terms. In `DE / rand-to-best / 1`, `rand` indicates that the starting point of evolution is a random individual, and `best` indicates that the evolution is guided by the best individual from the parent population. The airfoil design variables obtained after differential mutation, x c It is the parent population vector. F It is a scaling factor design variable, x r1 x r2 and x r3 These are three airfoil design variables randomly selected from the parent population, x best It is the best design variable in the parent population;

[0031] Secondly, the offspring population obtained through DE evolution will be screened against its parent population using feasibility criteria. The screening rules are as follows:

[0032] If the constraint violation value of the offspring is small, it directly replaces the parent individual;

[0033] If both are feasible, the individual with the smaller target value will remain.

[0034] If a child individual is not feasible to enter the next generation, but the objective function value of the child individual is better than that of its parent individual, then the child individual is stored in the predefined file A.

[0035] Next, a replacement mechanism is used to replace some individuals in the population that have passed the feasibility criterion with individuals from file A to mitigate the greediness of the feasibility criterion. The specific rules of the replacement mechanism are as follows:

[0036] Individuals in the population that have been screened by the feasibility criterion are sorted in descending order according to the objective function value, and then divided into multiple parts of the same size.

[0037] Select the individual with the largest constraint violation value from the first part. a Select the individual with the smallest constraint violation value from file A. b ;if f ( a )< f ( b ), then the individual a Replace with individual b And delete the individuals in file A. b ;

[0038] Repeat the above replacement process for all parts except the first part until each part is updated or file A becomes an empty set;

[0039] Furthermore, when all individuals in the population formed after the replacement mechanism become infeasible, a mutation strategy is used to help them escape the infeasible region and prevent them from getting trapped in local optima. The specific operation of the mutation strategy is as follows:

[0040] If no feasible solution exists in the population formed after the replacement mechanism, select the individual with the largest constraint violation value. c Randomly select one design variable dimension of the individual and replace it with a random value within the feasible region of that dimension to generate a mutant individual. e ;

[0041] Reassess mutant individuals e The target value, if f ( c )< f ( e ), then the individual c Replace with mutant individuals e ;

[0042] Through the aforementioned DE evolution, feasibility criterion screening, replacement mechanism, and mutation strategy, an intermediate subpopulation is generated from the parent population.

[0043] The third step involves using the maximum-minimum distance screening method to select the first-generation subpopulation that has diversity and satisfies the weight constraint from the intermediate subpopulation. The steps are as follows:

[0044] First, select the first individual from the intermediate subpopulation as the seed individual and store it in the selected subpopulation. P In step 1, the first individual of the intermediate subpopulation is removed and updated to the candidate population Ω1;

[0045] Secondly, in the k During the rotation, the remaining candidate population Ω k Each individual in the process undergoes iterative selection, where... ,calculate In the selected population P k The Euclidean distance between all individuals in the group, where, It is the first k Remaining candidate population Ω during round selection k The first in j Individual, , It is the remaining candidate population Ω k The number of individuals; the minimum Euclidean distance among all individuals is obtained. The formula is shown below:

[0046] ,

[0047] In the above formula, min is the expression for... In the selected population P k The minimum Euclidean distance among all individuals in the group. It is the first k Selected population during round selection P k The t Individual, , It is the European distance. L 2-norm;

[0048] Next, find the remaining candidate population Ω. k Zhongyu P k The individual with the maximum and minimum distances among all individuals. The formula is shown below:

[0049] ,

[0050] In the above formula, arg represents the individual that makes the subsequent function reach its maximum value;

[0051] Then, Save to the selected population and update the selected population. P k+1 = P k And in the remaining candidate population Ω k Remove individuals Updated to Ω k+1 When the number of iterations reaches k = N -1, selected population P N The scale has reached the target value NP At that time, the screening process ends and the first-generation offspring population with high diversity is finally output.

[0052] Optionally, the specific steps of step (4) are as follows:

[0053] The first step is to evaluate the airfoil stiffness of the design variables at each key node of all airfoils in the first generation of offspring, and save the design variables and airfoil stiffness data of each key node of the airfoil to the database;

[0054] The second step is to use the interior point method to optimize the stiffness of the design variables of all key nodes of the airfoil in the first generation subpopulation in order to find the second generation subpopulation that satisfies the airfoil design stiffness.

[0055] Optionally, the specific steps of step (5) are as follows:

[0056] The first step is to evaluate the lift-to-drag ratio of the design variables of each key node in the second-generation subpopulation, evaluate the weight and stiffness constraints, and store the design variables of the subpopulation, the corresponding weight and stiffness constraints, and the target lift-to-drag ratio in the database.

[0057] The second step involves establishing a lift-to-drag ratio and radial basis function model for the design variables of each key node using the evaluated data in the database. The design variables of each key node in the evaluated data serve as the training point set. The lift-to-drag ratio of the design variables at each key node is used as the response set. Then the expression for the radial basis function model is as follows:

[0058] ,

[0059] ,

[0060] In the above formula, When the input is the prediction point The predicted value output at that time. K It is the number of training samples. It is the first i The weights corresponding to each basis function As basis functions, It is the first i The center point of each basis function It is a prediction point and The Euclidean distance between them It is a polynomial function relating to x. It is a dimension of design variables. It is the coefficient of the 0th polynomial. It is the first i polynomial coefficients yes The i One component;

[0061] To solve for the weight vector w=[ w 1, w 2,…, w K ] T and polynomial coefficient matrix By solving the block matrix equations, a radial basis function model of the design variables and target values ​​is established. The specific formula is as follows:

[0062] ,

[0063] In the above formula, For the training point set The relevant polynomial matrix, It is a 0 matrix. It is a Gram matrix, where T denotes the transpose of the matrix. The specific formula is as follows:

[0064] ;

[0065] In the above formula, As basis functions, It is the first design variable. It is the first K One design variable;

[0066] The third step is to use the established radial basis function model to predict the target and constraint values ​​of the airfoil lift-to-drag ratio for the first and second generation subpopulations.

[0067] Fourth step, set the number of individuals to be selected. N An error-driven adaptive screening strategy assisted by a proxy model is used to select wing-shaped offspring from the merged first and second generation subpopulations.

[0068] The fifth step is to evaluate the lift-to-drag ratio of the selected airfoil offspring and evaluate the weight and stiffness constraints. The best individual is selected from the airfoil offspring through the feasibility rule. It is then determined whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments. If so, the optimal variable parameters corresponding to the best individual are output. Otherwise, the radial basis function model is updated and the airfoil offspring is updated to enter step (3) to participate in the next cycle.

[0069] Optionally, the screening steps for the surrogate model-assisted error-driven adaptive screening strategy include:

[0070] Remove duplicate individuals from the merged first and second generation subpopulations;

[0071] Calculate the constraint violation value for each deduplicated individual to determine whether the individual is feasible;

[0072] If no feasible individuals are found, the minimum distance from each infeasible individual to other infeasible individuals is calculated to assess diversity. A non-dominated ranking method is used, with a comprehensive ranking based on minimizing constraint violations and maximizing minimum distances. Individuals are selected sequentially from highest to lowest Pareto front level. Within the same Pareto front level, individuals are ranked in descending order of airfoil lift-to-drag ratio target value, and the highest-ranking individuals are selected. This process continues until all infeasible individuals are selected. N Individual;

[0073] If the number of feasible individuals is insufficient NIf there are 10 feasible individuals, first select all feasible individuals, then calculate the minimum distance for the remaining infeasible individuals, and use the non-dominated sorting method to sort the infeasible individuals based on the criteria of minimizing constraint violations and maximizing the minimum distance. Select infeasible individuals in descending order of Pareto front level until all are selected. N Individual;

[0074] If the number of feasible individuals is exactly equal to N One, directly select all feasible individuals;

[0075] If the number of feasible individuals exceeds N If there are only a few feasible individuals, then only feasible individuals are selected; calculate the minimum distance from each feasible individual to other feasible individuals; use a non-dominated sorting method, sorting individuals based on maximizing the target value and maximizing the minimum distance, selecting individuals in descending order of Pareto front level, and sorting individuals within the same Pareto front level in descending order of airfoil lift-to-drag ratio target value, selecting the top-ranked individuals, until all are selected. N Individual.

[0076] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the aforementioned machine learning-driven airfoil design method.

[0077] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the aforementioned machine learning-driven airfoil design method.

[0078] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned machine learning-driven airfoil design method.

[0079] In summary, compared with the prior art, the machine learning-driven airfoil design method, device, medium, and program products provided by this invention have the following advantages:

[0080] 1. By constructing a mathematical model of the float and lift-to-drag ratio of the airfoil node, considering the correlation between structural geometry and design variables, an airfoil population is established through space-filled Latin hypercube sampling to ensure that the initial population is evenly distributed in the design space, laying a foundation for subsequent optimization;

[0081] 2. Using uniformly distributed random numbers to invoke the DE mutation operation increases the direction of population evolution and guides the population into the feasible region; through the replacement mechanism and mutation strategy in this DE mutation operation, the diversity of the population is improved, avoiding premature entry into local optima, expanding the optimization exploration space, and obtaining a first-generation subpopulation with high diversity and satisfying weight constraints.

[0082] 3. The interior point method is used to optimize the population stiffness constraints to generate the second generation subpopulation. Since the interior point method has good global convergence, it can quickly locate the feasible region, laying the foundation for subsequent population selection.

[0083] 4. To address the shortcomings of existing airfoil structure optimization design methods, which suffer from long simulation calculation times, and considering the actual engineering application requirements for lift-to-drag ratio optimization, this invention designs a novel optimization framework and adaptive screening strategy. Specifically, it improves the efficiency of algorithm optimization by providing accurate prediction results through machine learning models, thereby reducing the number of time-consuming actual evaluations; and it selects airfoil offspring that meet the design requirements through an error-driven adaptive screening method, balancing the optimization between objectives and constraints, and increasing the probability of finding a feasible solution.

[0084] 5. This invention can effectively solve complex optimization problems involving time-consuming simulation models, has stronger robustness, and significantly improves optimization efficiency. It is not only suitable for handling expensive constrained optimization problems and provides a systematic solution for airfoil lift-to-drag ratio design problems, but also provides a usable algorithm structure for the performance design of other complex structures, and has broad application prospects. Attached Figure Description

[0085] Figure 1 A simplified flowchart of the machine learning-driven airfoil design method provided by this invention. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0087] Please see Figure 1 The machine learning-driven airfoil design method provided by this invention is applicable to the airfoil lift-to-drag ratio optimization problem. Specifically, the method includes steps (1) to (5).

[0088] (1) Taking the floating amount of each key node of the airfoil as the design variable, weight and stiffness as constraints, and lift-to-drag ratio as the target, the design domain of each design variable is constructed according to the geometric constraints of the airfoil structure, and a mathematical model is constructed through geometric analysis.

[0089] Step (1) involves constructing the design domain for each design variable based on the geometric constraints of the airfoil structure, and building a mathematical model through geometric analysis. The specific steps include the following:

[0090] The first step is to determine the number of design variables and, based on the geometric constraints of the airfoil structure, construct a design domain consisting of the float values ​​of each key node.

[0091] The second step is to construct a mathematical model through geometric analysis, the mathematical expression of which is as follows:

[0092] ,

[0093] In the above formula, Solve represents the optimal variable parameters for solving the airfoil structure optimization problem. It is a vector composed of various design variables. For the design variables in the airfoil structure optimization problem, n The number of design variables is given, T is the transpose of the matrix, and Max is the maximum value of the airfoil's lift-to-drag ratio. L and D These represent lift and drag, respectively, and St is the constraint that needs to be satisfied. G For airfoil stiffness, For Herveside functions, Let f be the topological description function of the airfoil structure, and t be the Neumann boundary Γ. t The volume force density and the preset surface traction force, where u is the displacement field. V It is a random variable representing the volume of the airfoil structure. S It is a random variable representing the displacement of the airfoil structure. It is the lower limit of airfoil design stiffness. M For airfoil weight, It is the density of the airfoil material. This is the upper limit of the airfoil weight. The design domain for design variables.

[0094] (2) Within the design domain of the design variables, an airfoil population is established based on space-filled Latin hypercube sampling.

[0095] The specific steps of step (2) are as follows:

[0096] A space-filled Latin hypercube sampling method was used to establish an wing population to reduce the randomness and uneven distribution of sampling points. d 1, d 2,…, dm For sampling plan The distances between all pairwise sample points are calculated, and then sorted in ascending order of distance values. ,in, m This represents the total number of pairwise distances between sample points in sampling plan X. n Given the number of sample points, the mathematical expression for calculating the distance is as follows:

[0097] ,

[0098] In the above formula, and The index of the sample point, and , For the first sample points and the sample points Between p -norm distance, p For the norm order, when p =1 For rectangular distance, when p =2 For Euclidean distance, k The dimension of the sample points, i.e., each sample point consists of... k It consists of several design variables. for The j One design variable, for The j One design variable.

[0099] set up J 1, J 2,…, J m This represents the number of sample point pairs corresponding to the same distance, each... d i One J i Space-filling Latin hypercubes introduce scalar discriminant functions. Maximize the minimum distance between sample points d i And minimize the number of distance-related sample point pairs. J i To take into account d i and J i The size of the sample affects the sampling, therefore, when The smaller the value, the more uniform the distribution of sample points in space, the higher the quality of the sampling plan X, and the better the scalar discriminant function. The mathematical expression is as follows:

[0100] ,

[0101] In the above formula, X is the sampling plan. d i It is the first i The distance between sample points J i The distance is d i The number of sample point pairs corresponding to the time. m It is the total number of pairwise distances between sample points in sampling plan X. q This is a parameter used to adjust the sensitivity to the influence of distance, and it is usually taken as a positive value.

[0102] (3) Evaluate the weight of each design variable in the airfoil population and save it to the database. Use uniformly distributed random numbers to call DE mutation operation and maximum-minimum distance screening method to generate the first generation of subpopulation.

[0103] The specific steps of step (3) are as follows:

[0104] The first step is to evaluate the airfoil weights of the design variables at each key node in the airfoil population and save the design variables and airfoil weight data of each key node to the database.

[0105] The second step is to use all individuals in the database as the parent population and call the DE mutation operation on the parent population using uniformly distributed random numbers. That is, by gradually executing DE evolution, feasibility criterion screening, replacement mechanism and mutation strategy, an intermediate subpopulation is generated.

[0106] First, DE evolution is performed on the parent population to balance exploration and exploitation capabilities. The mutation method is selected using random numbers. The expression used in DE evolution is as follows:

[0107] when R <0.5,DE / current-to-rand / 1: ,

[0108] when R >0.5, DE / rand-to-best / 1: ,

[0109] In the above formula, RHere, `DE` represents differential evolution, `current` indicates that the starting point of evolution is a specific parent individual, and `to` indicates the direction of differential evolution. In `DE / current-to-rand / 1`, `rand` indicates that the evolution is guided by random individuals from the parent population, and "1" indicates the number of random differential terms. In `DE / rand-to-best / 1`, `rand` indicates that the starting point of evolution is a random individual, and `best` indicates that the evolution is guided by the best individual from the parent population. The airfoil design variables obtained after differential mutation, x c It is the parent population vector. F It is a scaling factor design variable, x r1 x r2 and x r3 These are three airfoil design variables randomly selected from the parent population, x best It is the best design variable in the parent population.

[0110] Secondly, the offspring population obtained through DE evolution will be screened against its parent population using feasibility criteria. The screening rules are as follows:

[0111] If the constraint violation value of the offspring is small, it directly replaces the parent individual;

[0112] If both are feasible, the individual with the smaller target value will remain.

[0113] If a child individual is not feasible to enter the next generation, but the objective function value of the child individual is better than that of its parent individual, then the child individual is stored in a predefined file A.

[0114] Next, a replacement mechanism is used to replace some individuals in the population that have passed the feasibility criterion with individuals from file A to mitigate the greediness of the feasibility criterion. The specific rules of the replacement mechanism are as follows:

[0115] Individuals in the population that have been screened by the feasibility criterion are sorted in descending order according to the objective function value, and then divided into multiple parts of the same size.

[0116] Select the individual with the largest constraint violation value from the first part. a Select the individual with the smallest constraint violation value from file A. b ;if f ( a )< f ( b ), then the individual a Replace with individual b And delete the individuals in file A. b ;

[0117] Repeat the above replacement process for all parts except the first part until each part is updated or file A becomes an empty set.

[0118] Furthermore, when all individuals in the population formed after the replacement mechanism become infeasible, a mutation strategy is used to help them escape the infeasible region and prevent them from getting trapped in local optima. The specific operation of the mutation strategy is as follows:

[0119] If no feasible solution exists in the population formed after the replacement mechanism, select the individual with the largest constraint violation value. c Randomly select one design variable dimension of the individual and replace it with a random value within the feasible region of that dimension to generate a mutant individual. e ;

[0120] Reassess mutant individuals e The target value, if f ( c )< f ( e ), then the individual c Replace with mutant individuals e ;

[0121] Through the execution of DE evolution, the feasibility criterion screening, the replacement mechanism, and the mutation strategy, an intermediate subpopulation is generated from the parent population.

[0122] The third step involves using the maximum-minimum distance screening method to select the first-generation subpopulation that has diversity and satisfies the weight constraint from the intermediate subpopulation. The steps are as follows:

[0123] First, select the first individual from the intermediate subpopulation as the seed individual and store it in the selected subpopulation. P In step 1, the first individual of the intermediate subpopulation is removed and updated to the candidate population Ω1;

[0124] Secondly, in the k During the rotation, the remaining candidate population Ω k Each individual in the process undergoes iterative selection, where... ,calculate In the selected population P k The Euclidean distance between all individuals in the group, where, It is the first k Remaining candidate population Ω during round selection k The first in j Individual, , It is the remaining candidate population Ω k The number of individuals; the minimum Euclidean distance among all individuals is obtained. The formula is shown below:

[0125] ,

[0126] In the above formula, min is the expression for... In the selected population P k The minimum Euclidean distance among all individuals in the group. It is the first k Selected population during round selection P k The t Individual, , It is the European distance. L 2-norm;

[0127] Next, find the remaining candidate population Ω. k Zhongyu P k The individual with the maximum and minimum distances among all individuals. The formula is shown below:

[0128] ,

[0129] In the above formula, arg represents the individual that makes the subsequent function reach its maximum value;

[0130] Then, Save to the selected population and update the selected population. P k+1 = P k And in the remaining candidate population Ω k Remove individuals Updated to Ω k+1 When the number of iterations reaches k = N -1, selected population P N The scale has reached the target value NP At that time, the screening process ends and the first-generation offspring population with high diversity is finally output.

[0131] (4) Evaluate the stiffness of each design variable in the first generation subpopulation and save it to the database. Use the interior point method to optimize the stiffness of each design variable to generate the second generation subpopulation.

[0132] It should be noted that the interior point method involved in step (4) is currently the most robust and commonly used method for solving general nonlinear constraint optimization. It has good global convergence and is suitable for large-scale, sparse nonlinear problems. Specifically, by simultaneously solving for the original and dual variables, a barrier function is used to handle the inequality constraints, and a series of perturbation KKT points that gradually approach the optimal solution are solved using Newton's method.

[0133] The specific steps of step (4) are as follows:

[0134] The first step is to evaluate the airfoil stiffness of the design variables at each key node of all airfoils in the first generation of offspring, and save the design variables and airfoil stiffness data of each key node of the airfoil to the database.

[0135] The second step is to use the interior point method to optimize the stiffness of the design variables of all key nodes of the airfoil in the first generation subpopulation in order to find the second generation subpopulation that satisfies the airfoil design stiffness.

[0136] (5) Evaluate the lift-to-drag ratio of each design variable in the second generation subpopulation, establish a radial basis function model for the objective function, use an error-driven adaptive screening strategy assisted by a surrogate model to select airfoil offspring, evaluate the airfoil offspring and select the best individual from them through feasibility rules, determine whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments, if so, output the optimal variable parameters, otherwise return to step (3).

[0137] The specific steps of step (5) are as follows:

[0138] The first step is to evaluate the lift-to-drag ratio of the design variables of each key node in the second-generation subpopulation, evaluate the weight and stiffness constraints, and store the design variables of the subpopulation, the corresponding weight and stiffness constraints, and the target lift-to-drag ratio in the database.

[0139] The second step involves establishing a lift-to-drag ratio and radial basis function model for the design variables of each key node using the evaluated data in the database. The design variables of each key node in the evaluated data serve as the training point set. The lift-to-drag ratio of the design variables at each key node is used as the response set. Then the expression for the radial basis function model is as follows:

[0140] ,

[0141] ,

[0142] In the above formula, When the input is the prediction point The predicted value output at that time. K It is the number of training samples. It is the first i The weights corresponding to each basis function As basis functions, It is the first i The center point of each basis function It is a prediction point and The Euclidean distance between them It is a polynomial function relating to x. It is a dimension of design variables. It is the coefficient of the 0th polynomial. It is the first i polynomial coefficients yes The i One component;

[0143] To solve for the weight vector w=[ w 1, w 2,…, w K ] T and polynomial coefficient matrix By solving the block matrix equations, a radial basis function model of the design variables and target values ​​is established. The specific formula is as follows:

[0144] ,

[0145] In the above formula, For the training point set The relevant polynomial matrix, It is a 0 matrix. It is a Gram matrix, where T denotes the transpose of the matrix. The specific formula is as follows:

[0146] .

[0147] In the above formula, As basis functions, It is the first design variable. It is the first K One design variable.

[0148] The third step is to use the established radial basis function model to predict the target and constraint values ​​of the airfoil lift-to-drag ratio for the first and second generation subpopulations.

[0149] Fourth step, set the number of individuals to be selected. N An error-driven adaptive selection strategy assisted by a surrogate model is used to select wing-shaped offspring from the merged first and second generation subpopulations.

[0150] In the fourth step, the screening steps for the surrogate model-assisted error-driven adaptive screening strategy include:

[0151] Remove duplicate individuals from the merged first and second generation subpopulations;

[0152] Calculate the constraint violation value for each deduplicated individual to determine whether the individual is feasible;

[0153] If no feasible individuals are found, the minimum distance from each infeasible individual to other infeasible individuals is calculated to assess diversity. A non-dominated ranking method is used, with a comprehensive ranking based on minimizing constraint violations and maximizing minimum distances. Individuals are selected sequentially from highest to lowest Pareto front level. Within the same Pareto front level, individuals are ranked in descending order of airfoil lift-to-drag ratio target value, and the highest-ranking individuals are selected. This process continues until all infeasible individuals are selected. N Individual;

[0154] If the number of feasible individuals is insufficient N If there are 10 feasible individuals, first select all feasible individuals, then calculate the minimum distance for the remaining infeasible individuals, and use the non-dominated sorting method to sort the infeasible individuals based on the criteria of minimizing constraint violations and maximizing the minimum distance. Select infeasible individuals in descending order of Pareto front level until all are selected. N Individual;

[0155] If the number of feasible individuals is exactly equal to N One, directly select all feasible individuals;

[0156] If the number of feasible individuals exceeds N If there are only a few feasible individuals, then only feasible individuals are selected; calculate the minimum distance from each feasible individual to other feasible individuals; use a non-dominated sorting method, sorting individuals based on maximizing the target value and maximizing the minimum distance, selecting individuals in descending order of Pareto front level, and sorting individuals within the same Pareto front level in descending order of airfoil lift-to-drag ratio target value, selecting the top-ranked individuals, until all are selected. N Individual.

[0157] The fifth step is to evaluate the lift-to-drag ratio of the selected airfoil offspring and evaluate the weight and stiffness constraints. The best individual is selected from the airfoil offspring through the feasibility rule. It is then determined whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments. If so, the optimal variable parameters corresponding to the best individual are output. Otherwise, the radial basis function model is updated and the airfoil offspring is updated to enter step (3) to participate in the next cycle.

[0158] Example 1, please refer to Figure 1This embodiment uses the benchmark function CEC2017 C14 to illustrate the optimization performance of the proposed machine learning-driven airfoil design method. The expression of the benchmark function CEC2017 C14 is as follows:

[0159] ,

[0160] In the above formula, Min represents minimizing the objective function. It is the objective function that needs to be minimized. x It is the original vector. y It is the transformed vector, by Definition, where o For offset vector, D It is a variable y Dimensions y i yes y The first vector i One element, e St is the base of the natural logarithm, and St is the constraint that needs to be satisfied. g ( x ) is the inequality constraint function. y 1 is y The first element of the vector, h ( x ) is the equality constraint function, where represents the range of values ​​and the variable transformation formula.

[0161] The above benchmark functions are processed through steps (1) to (5) of the machine learning-driven airfoil design method provided by this invention to obtain experimental results.

[0162] To further illustrate this embodiment, the machine learning-driven airfoil design method of this embodiment is compared with another algorithm, LSHADE44. The maximum number of simulation evaluations in this embodiment is set to 500, the dimension of the optimized design parameter variables is 30D, and the population size is 60 (i.e., twice the dimension). The experimental results are shown in Table 1. Under the same variable dimension and population size, the method of this embodiment achieves a near-global optimal solution and outperforms LSHADE44. This demonstrates the optimization efficiency of the machine learning-driven airfoil design method of this embodiment, and it can be considered that the method of this embodiment has good performance in the airfoil structure lift-to-drag ratio optimization problem.

[0163] Table 1 Comparison of optimization results of different methods

[0164]

[0165] The machine learning-driven airfoil design method provided by this invention designs a novel optimization framework and adaptive screening strategy. Considering the differences in the time consumption of constraint conditions and target evaluation, it applies DE mutation operation and interior point method optimization to lightweight and stiffness constraints, respectively. It provides accurate prediction results through machine learning models and selects airfoil progeny that meet design requirements through an error-driven adaptive screening strategy assisted by surrogate models. This provides a systematic solution to the airfoil lift-to-drag ratio optimization problem.

[0166] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a machine learning-driven airfoil design method of the foregoing embodiments.

[0167] The memory can be volatile or non-volatile, or a combination of both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory of this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0168] The processor can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the processor's hardware or by software instructions. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0169] The method steps of this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0170] Software implementation can be achieved by executing functional modules (such as procedures, functions, etc.). Software code can be stored in memory and executed by the processor. Memory can be implemented in the processor or outside the processor.

[0171] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a machine learning-driven airfoil design method according to the foregoing embodiments.

[0172] Computer storage media can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0173] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of a machine learning-driven airfoil design method according to the foregoing embodiments.

[0174] Specifically, computer program products include: data signals and data signals embodied in a carrier wave.

[0175] It should be noted that the technical solutions described in this invention can be combined arbitrarily without conflict.

[0176] Those skilled in the art will readily understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A machine learning-driven airfoil design method, characterized in that, Including the following steps: (1) Taking the floating amount of each key node of the airfoil as the design variable, weight and stiffness as constraints, and lift-to-drag ratio as the target, the design domain of each design variable is constructed according to the geometric constraints of the airfoil structure, and a mathematical model is constructed through geometric analysis; (2) Within the design domain of the design variables, an airfoil population is established based on space-filled Latin hypercube sampling; (3) Evaluate the weight of each design variable in the airfoil population and save it to the database. Use uniformly distributed random numbers to call DE mutation operation and maximum-minimum distance screening method to generate the first generation of subpopulation; (4) Evaluate the stiffness of each design variable in the first generation subpopulation and save it to the database. Use the interior point method to optimize the stiffness of each design variable to generate the second generation subpopulation. (5) Evaluate the lift-to-drag ratio of each design variable in the second generation subpopulation, establish a radial basis function model for the objective function, use the error-driven adaptive screening strategy assisted by the surrogate model to select the airfoil subpopulation, evaluate the airfoil subpopulation and select the best individual from them through the feasibility rules, determine whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments, if so, output the optimal variable parameters, otherwise return to step (3). Among them, the design variables of each key node of the evaluated data are used as the training point set. The lift-to-drag ratio of the design variables at each key node is used as the response set. Then the expression for the radial basis function model is as follows: ， ， In the above formula, When the input is the prediction point The predicted value output at that time. K It is the number of training samples. It is the first i The weights corresponding to each basis function As basis functions, It is the first i The center point of each basis function It is a prediction point and The Euclidean distance between them It is a polynomial function relating to x. It is a dimension of design variables. It is the coefficient of the 0th polynomial. It is the first i polynomial coefficients yes The i One component; To solve for the weight vector w=[ w 1, w 2,…, w K ] T and polynomial coefficient matrix By solving the block matrix equations, a radial basis function model of the design variables and target values ​​is established. The specific formula is as follows: ， In the above formula, For the training point set The relevant polynomial matrix, It is a 0 matrix. It is a Gram matrix, where T denotes the transpose of the matrix. The specific formula is as follows: ； In the above formula, As basis functions, It is the first design variable. It is the first K One design variable; The screening steps for the surrogate model-assisted error-driven adaptive screening strategy include: Remove duplicate individuals from the merged first and second generation subpopulations; Calculate the constraint violation value for each deduplicated individual to determine whether the individual is feasible; If no feasible individuals are found, the minimum distance from each infeasible individual to other infeasible individuals is calculated to assess diversity. A non-dominated ranking method is used, with a comprehensive ranking based on minimizing constraint violations and maximizing minimum distances. Individuals are selected sequentially from highest to lowest Pareto front level. Within the same Pareto front level, individuals are ranked in descending order of airfoil lift-to-drag ratio target value, and the highest-ranking individuals are selected. This process continues until all infeasible individuals are selected. N Individual; If the number of feasible individuals is insufficient N If there are 10 feasible individuals, first select all feasible individuals, then calculate the minimum distance for the remaining infeasible individuals, and use the non-dominated sorting method to sort the infeasible individuals based on the criteria of minimizing constraint violations and maximizing the minimum distance. Select infeasible individuals in descending order of Pareto front level until all are selected. N Individual; If the number of feasible individuals is exactly equal to N One, directly select all feasible individuals; If the number of feasible individuals exceeds N If there are only a few feasible individuals, then only feasible individuals are selected; calculate the minimum distance from each feasible individual to other feasible individuals; use a non-dominated sorting method, sorting individuals based on maximizing the target value and maximizing the minimum distance, selecting individuals in descending order of Pareto front level, and sorting individuals within the same Pareto front level in descending order of airfoil lift-to-drag ratio target value, selecting the top-ranked individuals, until all are selected. N Individual.

2. The method as described in claim 1, characterized in that, Step (1) involves constructing the design domain for each design variable based on the geometric constraints of the airfoil structure, and building a mathematical model through geometric analysis. The specific steps include the following: The first step is to determine the number of design variables and, based on the geometric constraints of the airfoil structure, construct a design domain consisting of the float values ​​of each key node. The second step is to construct a mathematical model through geometric analysis, the mathematical expression of which is as follows: ， In the above formula, Solve represents the optimal variable parameters for solving the airfoil structure optimization problem. It is a vector composed of various design variables. For the design variables in the airfoil structure optimization problem, n The number of design variables is given, T is the transpose of the matrix, and Max is the maximum value of the airfoil's lift-to-drag ratio. L and D These represent lift and drag, respectively, and St is the constraint that needs to be satisfied. G For airfoil stiffness, For Herveside functions, Let f be the topological description function of the airfoil structure, and t be the Neumann boundary Γ. t The volume force density and the preset surface traction force, where u is the displacement field. V It is a random variable representing the volume of the airfoil structure. S It is a random variable representing the displacement of the airfoil structure. It is the lower limit of airfoil design stiffness. M For airfoil weight, It is the density of the airfoil material. This is the upper limit of the airfoil weight. The design domain for design variables.

3. The method as described in claim 1, characterized in that, The specific steps of step (2) are as follows: A space-filled Latin hypercube sampling method was used to establish an wing population to reduce the randomness and uneven distribution of sampling points. d 1, d 2,…, d m For sampling plan The distances between all pairwise sample points are calculated, and then sorted in ascending order of distance values. ,in, m This represents the total number of pairwise distances between sample points in sampling plan X. n Given the number of sample points, the mathematical expression for calculating the distance is as follows: ， In the above formula, and The index of the sample point, and , For the first sample points and the sample points Between p -norm distance, p For the norm order, when p =1 For rectangular distance, when p =2 For Euclidean distance, k The dimension of the sample points, i.e., each sample point consists of... k It consists of several design variables. for The j One design variable, for The j One design variable; set up J 1, J 2,…, J m This represents the number of sample point pairs corresponding to the same distance, each... d i Corresponding to one J i Space-filling Latin hypercubes introduce scalar discriminant functions. Maximize the minimum distance between sample points d i And minimize the number of distance-related sample point pairs. J i To take into account d i and J i The size of the sample affects the sampling, therefore, when The smaller the value, the more uniform the distribution of sample points in space, the higher the quality of the sampling plan X, and the better the scalar discriminant function. The mathematical expression is as follows: ， In the above formula, X is the sampling plan. d i It is the first i The distance between sample points J i The distance is d i The number of sample point pairs corresponding to the time. m It is the total number of pairwise distances between sample points in sampling plan X. q It is a parameter used to adjust the sensitivity to the influence of distance. q Take the positive value.

4. The method as described in claim 1, characterized in that, The specific steps of step (3) are as follows: The first step is to evaluate the airfoil weights of the design variables at each key node in the airfoil population and save the design variables and airfoil weight data of each key node to the database. The second step is to use all individuals in the database as the parent population, and to call the DE mutation operation on the parent population using uniformly distributed random numbers. That is, to generate an intermediate subpopulation by gradually executing DE evolution, feasibility criterion screening, replacement mechanism and mutation strategy. First, DE evolution is performed on the parent population to balance exploration and exploitation capabilities. The mutation method is selected using random numbers. The expression used in DE evolution is as follows: When R <0.5, DE / current-to-rand / 1: , Current R >0.5, DE / rand-to-best / 1: , In the above formula, R Here, `DE` represents differential evolution, `current` indicates that the starting point of evolution is a specific parent individual, and `to` indicates the direction of differential evolution. In `DE / current-to-rand / 1`, `rand` indicates that the evolution is guided by a random individual from the parent population, and "1" indicates the number of random difference terms. In `DE / rand-to-best / 1`, `rand` indicates that the starting point of evolution is a random individual, and `best` indicates that the evolution is guided by the best individual from the parent population. The airfoil design variables obtained after differential mutation, x c It is the parent population vector. F It is a scaling factor design variable, x r1 x r2 and x r3 These are three airfoil design variables randomly selected from the parent population, x best It is the best design variable in the parent population; Secondly, the offspring population obtained through DE evolution will be screened against its parent population using feasibility criteria. The screening rules are as follows: If the constraint violation value of the offspring is small, it directly replaces the parent individual; If both are feasible, the individual with the smaller target value will remain. If a child individual is not feasible to enter the next generation, but the objective function value of the child individual is better than that of its parent individual, then the child individual is stored in the predefined file A. Next, a replacement mechanism is used to replace some individuals in the population that have passed the feasibility criterion with individuals from file A to mitigate the greediness of the feasibility criterion. The specific rules of the replacement mechanism are as follows: Individuals in the population that have been screened by the feasibility criterion are sorted in descending order according to the objective function value, and then divided into multiple parts of the same size. Select the individual with the largest constraint violation value from the first part. a Select the individual with the smallest constraint violation value from file A. b ; if f ( a )< f ( b ), then the individual a Replace with individual b And delete the individuals in file A. b ; Repeat the above replacement process for all parts except the first part until each part is updated or file A becomes an empty set; Furthermore, when all individuals in the population formed after the replacement mechanism become infeasible, a mutation strategy is used to help them escape the infeasible region and prevent them from getting trapped in local optima. The specific operation of the mutation strategy is as follows: If no feasible solution exists in the population formed after the replacement mechanism, select the individual with the largest constraint violation value. c Randomly select one design variable dimension of the individual and replace it with a random value within the feasible region of that dimension to generate a mutant individual. e ; Reassess mutant individuals e The target value, if f ( c )< f ( e ), then the individual c Replace with mutant individuals e ; Through the aforementioned DE evolution, feasibility criterion screening, replacement mechanism, and mutation strategy, an intermediate subpopulation is generated from the parent population. The third step involves using the maximum-minimum distance screening method to select the first-generation subpopulation that has diversity and satisfies the weight constraint from the intermediate subpopulation. The steps are as follows: First, select the first individual from the intermediate subpopulation as the seed individual and store it in the selected subpopulation. P In step 1, the first individual of the intermediate subpopulation is removed and updated to the candidate population Ω1; Secondly, in the k During the rotation, the remaining candidate population Ω k Each individual in the process undergoes iterative selection, where... ,calculate In the selected population P k The Euclidean distance between all individuals in the group, where, It is the first k Remaining candidate population Ω during round selection k The first in j Individual, , It is the remaining candidate population Ω k The number of individuals; the minimum Euclidean distance among all individuals is obtained. The formula is shown below: ， In the above formula, min is the expression for... In the selected population P k The minimum Euclidean distance among all individuals in the group. It is the first k Selected population during round selection P k The t Individual, , It is the European distance. L 2-norm; Next, find the remaining candidate population Ω. k Zhongyu P k The individual with the maximum and minimum distances among all individuals. The formula is shown below: ， In the above formula, arg represents the individual that makes the subsequent function reach its maximum value; Then, Save to the selected population and update the selected population. P k+1 = P k And in the remaining candidate population Ω k Remove individuals Updated to Ω k+1 When the number of iterations reaches k = N -1, selected population P N The scale has reached the target value NP At that time, the screening process ends and the first-generation offspring population with high diversity is finally output.

5. The method as described in claim 1, characterized in that, The specific steps of step (4) are as follows: The first step is to evaluate the airfoil stiffness of the design variables at each key node of all airfoils in the first generation of offspring, and save the design variables and airfoil stiffness data of each key node of the airfoil to the database; The second step is to use the interior point method to optimize the stiffness of the design variables of all key nodes of the airfoil in the first generation subpopulation in order to find the second generation subpopulation that satisfies the airfoil design stiffness.

6. The method as described in claim 1, characterized in that, The specific steps of step (5) are as follows: The first step is to evaluate the lift-to-drag ratio of the design variables of each key node in the second-generation subpopulation, evaluate the weight and stiffness constraints, and store the design variables of the subpopulation, the corresponding weight and stiffness constraints, and the target lift-to-drag ratio in the database. The second step is to establish a lift-to-drag ratio and radial basis function model of the design variables for each key node using the evaluated data in the database. The third step is to use the established radial basis function model to predict the target and constraint values ​​of the airfoil lift-to-drag ratio for the first and second generation subpopulations. Fourth step, set the number of individuals to be selected. N An error-driven adaptive screening strategy assisted by a proxy model is used to select wing-shaped offspring from the merged first and second generation subpopulations. The fifth step is to evaluate the lift-to-drag ratio of the selected airfoil offspring and evaluate the weight and stiffness constraints. The best individual is selected from the airfoil offspring through the feasibility rule. It is then determined whether the optimization result of the best individual meets the standard or whether the current number of judgments has reached the maximum number of judgments. If so, the optimal variable parameters corresponding to the best individual are output. Otherwise, the radial basis function model is updated and the airfoil offspring is updated to enter step (3) to participate in the next cycle.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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