Blade robustness aerodynamic design optimization method with aerodynamic reliability constraint

Abstract

The invention provides a blade robustness aerodynamic design optimization method with aerodynamic reliability constraint. The method comprises the following steps: firstly, determining a blade RADO problem mathematical description with aerodynamic reliability constraint; thirdly, providing a pneumatic uncertainty quantification method, coupling the method with an adaptive Gaussian process, and constructing an optimization model; and finally, performing multi-objective optimization on the optimization model by adopting an NSGA-II algorithm to obtain an optimal solution. According to the method disclosed by the invention, the uncertainty influence of the uncertainty parameters on the constraint aerodynamic performance parameters and the target aerodynamic performance parameters of the blade is comprehensively considered, so that the reliability of the constraint aerodynamic performance parameters of the optimized blade and the robustness of the target aerodynamic performance parameters can be remarkably improved; the pneumatic design optimization thought can be widely applied to robustness optimization design of turbomachinery blades.

Description

Technical Field

[0001] The present invention belongs to the field of uncertainty quantification and optimization design, and particularly relates to a robust aerodynamic design optimization method for blades with aerodynamic reliability constraints. This method is applicable to the robust optimization design of impeller machine blades, and can significantly improve the reliability of the constrained aerodynamic performance parameters of the optimized blades and the robustness of the target aerodynamic performance parameters. Background Art

[0002] In order to further improve the aerodynamic performance of aeroengine blades, it is necessary to perform aerodynamic design optimization (ADO) on the blades. Traditional blade ADO has been relatively mature, and its objective function and constraint function are deterministic results, ignoring the influence of the uncertainty of geometric design parameters and operating conditions. Such ADO is called deterministic aerodynamic design optimization (DADO). However, with the continuous improvement of the requirements for blade performance and reliability in the industrial community, the influence of uncertain parameters on blade performance has become increasingly prominent, and the limitations of traditional DADO have gradually emerged. The geometric deviation uncertainty and aerodynamic boundary perturbation uncertainty of the blades will inevitably affect the aerodynamic performance during the actual service process of the blades. Although the optimized blades obtained by DADO can achieve good aerodynamic performance without considering the influence of uncertain parameters, in actual situations, the optimized blades will be affected by uncertain parameters and the aerodynamic performance will be scattered, that is, the standard deviation of the aerodynamic performance is relatively large. In engineering practical problems, the optimized blades by DADO may experience a rapid decline in aerodynamic performance under a small perturbation of uncertain parameters, that is, the aerodynamic robustness is poor. Summary of the Invention

[0003] In view of the limitations in traditional DADO, the present invention proposes a new robust aerodynamic design optimization (RAD0) method for blades with aerodynamic reliability constraints. Due to the randomness of uncertain parameters, the objective aerodynamic function of the optimal blade will depend on whether the statistical performance of the blade geometry in the uncertain parameter perturbation space is optimal, and the corresponding aerodynamic constraint conditions will depend on whether the aerodynamic reliability constraints of the blade geometry in the uncertain parameter perturbation space are met.

[0004] Robustness generally refers to the characteristic of a system to maintain the stability of its output under certain perturbations of system parameters or input parameters. In the RADO study, robustness can be understood as the sensitivity of the target aerodynamic function to uncertain parameters. The basic idea of reliability in RADO is to ensure that the system can meet the required performance standards during its service life by limiting the system failure probability or failure risk. Specifically, the aerodynamic reliability constraint can be expressed as the failure probability of a certain aerodynamic performance index not exceeding a certain probability threshold at a given confidence level. The limit state function g characterizing the failure of aerodynamic constraint parameters can be expressed as a function of uncertain parameters x. The failure domain is represented by F = {x; g(x) < 0}, the safety domain is represented by S = {x; g(x) > 0}, and the limit surface, i.e., the boundary of F, is represented by G = {x; g(x) = 0}. In the process of RADO, solving the magnitude of the failure probability of a certain aerodynamic constraint parameter is a complex process. For the sake of convenience in operation, the probability constraint can be converted into an approximate statistical moment constraint, and the aerodynamic reliability constraint at a certain confidence probability can be achieved by evaluating the statistical mean and standard deviation of aerodynamic constraint parameters.

[0005] The method proposed by the present invention mainly includes the following steps: First, determine the mathematical description of the blade RADO problem with aerodynamic reliability constraints; for comparison, in the process of clarifying the basic principle of RADO, the basic principle of DADO is also conceptually clarified. Then, propose a method for quantifying aerodynamic uncertainty, couple this method with the Adaptive Gaussian process (ADGP), and construct an optimization model. Finally, use the NSGA-II algorithm to obtain the optimal solution of multi-objective optimization.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A robust aerodynamic design optimization method with aerodynamic reliability constraints, which specifically includes:

[0008] (1) Conduct a mathematical description of the blade RADO problem with aerodynamic reliability constraints, and the specific method is as follows:

[0009] The RADO problem is extended on the basis of the DADO problem. In the DADO problem, for the optimization of a system with deterministic flow conditions and blade geometry, DADO ignores the uncertainty of blade aerodynamic performance and only considers deterministic aerodynamic objectives and aerodynamic constraints. For a constrained minimization deterministic optimization problem, its mathematical description is:

[0010]

[0011] Where: I represents the target aerodynamic performance parameter, ω and v represent the flow field state, input variables, and design variables respectively; p i is the aerodynamic performance parameter of the inequality constraint, q i is the aerodynamic performance parameter of the equality constraint; and n c are the numbers of the aerodynamic performance parameters of the inequality constraint and the equality constraint respectively. It should be noted that the input variable ω usually refers to the boundary conditions of the flow numerical simulation or the parameters related to the blade geometry, and the design variable v usually refers to the design parameters of the parametric modeling of the blade.

[0012] Different from DADO, RADO no longer focuses on a certain definite result, but considers the statistical result affected by the uncertainty parameters. The mathematical description of the blade RADO problem with aerodynamic reliability constraints is specifically as follows:

[0013] Considering the uncertainty in the n-dimensional input variable ω, the statistical mean of the input variable ω is μ ω ={μ ω1 ,…,μ ωn}, and all elements in μ ω are independent of each other and follow the normal distribution. The objective function will also be given in the way of probability statistics. The statistical mean of the target aerodynamic performance parameter I is μ I , and the standard deviation is σ I . The equality constraint needs to hold under the and the expected conditions of ω, that is, it holds for and μ ω . The inequality constraint is transformed into a probability statement: the probability that the constraint holds is greater than or equal to the specified confidence probability P k . Under the assumption that the relevant variables follow the normal distribution, this probability statement is transformed into the constraints of the statistical mean and standard deviation of the parameters. The mathematical description of RADO is:

[0014]

[0015] where, is the statistical mean of the aerodynamic performance parameter p i of the inequality constraint, is the statistical mean of the aerodynamic performance parameter of the original designed blade constraint , is the standard deviation of the aerodynamic performance parameter p i of the inequality constraint; is the statistical mean of the aerodynamic performance parameter q j of the equality constraint, is the statistical mean of the aerodynamic performance parameter of the original designed blade constraint ; k represents the standard deviation by which the statistical mean of the aerodynamic performance parameter of the inequality constraint must be displaced The quantity to achieve the specified confidence probability P k 。

[0016] In the actual application process, the inequality constraints or equality constraints can also be considered separately according to specific problems without strict restrictions.

[0017] (2) To quickly implement RADO, an optimization model is constructed based on the Adaptive Gaussian process (ADGP), which specifically includes:

[0018] Step S1: In the optimization design space, the initial training sample set X is generated by Latin hypercube sampling. X is used as the input of the optimization model, and the pneumatic uncertainty quantification method is used to evaluate the statistics of the target pneumatic performance parameters and constraint pneumatic performance parameters of each training sample, specifically including the statistical mean and standard deviation, denoted as Y. Y is used as the output of the optimization model. And a large number of test point sets X * are generated in the optimization design space for use in subsequent Step S3;

[0019] Step S2: Based on X and Y, a Gaussian process (GP) model is trained to obtain the optimization model;

[0020] Step S3: Based on the optimization model, predict the statistics of the target pneumatic performance parameters and constraint pneumatic performance parameters corresponding to the test point set X * , calculate the acquisition function values of each test point, select the test point corresponding to the maximum acquisition function value, and add the test point and the corresponding prediction result to the covariance matrix of the optimization model. Repeat this process until a sufficient number of new sample points are selected. In this step, the optimization model does not need to be retrained.

[0021] Step S4: First, use the blade parametric modeling method to perform blade parametric modeling on the selected new sample points to obtain the blade geometric shapes corresponding to the new sample points; then, based on the blade geometric shapes of the new sample points, use the pneumatic uncertainty quantification method to accurately evaluate the statistics of the target pneumatic performance parameters and constraint pneumatic performance parameters of the new sample points, add the accurately evaluated new sample points to the training samples, and retrain the optimization model.

[0022] Step S5: Repeat Steps S3 and S4 until the maximum value of the acquisition function converges to obtain the final optimization model.

[0023] (3) In the optimization design space, based on the optimization model, the NSGA-II algorithm is used to solve the optimal solution of the multi-objective optimization, which specifically includes:

[0024] Step S1: Set the constraint conditions in the NSGA-II algorithm based on the inequality constraints and equality constraints in the RADO problem;

[0025] Step S2: Use the NSGA-II algorithm to perform multi-objective optimization on the optimization model and solve to obtain the Pareto optimal solution set.

[0026] Step S3: Analyze and select the solutions in the Pareto optimal solution set to obtain the final optimal solution.

[0027] In the above technical solution, further, in step S3 of step (2), calculating the acquisition function values of each test point specifically includes the following steps:

[0028] 1) Evaluate the model standard deviation of each test point in the test point set X * It is the square root of the model variance It is the model variance The square root; the definition of the model variance is as follows:

[0029]

[0030] Among them, x * represents a new test point, K is the covariance matrix of the optimization model, k(x * , x * ) represents the autocorrelation value of the test point, and k(x * , X) represents the covariance vector between the test point x * and the training sample set X.

[0031] 2) Calculate the acquisition function f acq corresponding to each test point of the optimization model:

[0032]

[0033] Among them: n obj represents the number of objectives of the optimization model, and the objectives of the optimization model specifically include the target aerodynamic performance parameters and the statistics of the constrained aerodynamic performance parameters; λ j represents the weight coefficient corresponding to each objective.

[0034] Further, during the loop of step S3 in step (2), it is necessary to determine whether the maximum value of the acquisition function converges. If it converges, the optimization model is established; if it does not converge, it is further determined whether the number of newly added samples allowed for each iteration reaches a given number, such as a limit of 2. If the number of new samples does not reach the given number, the test point corresponding to the maximum value of the acquisition function is continuously added to the covariance matrix of the optimization model, and the optimization model updated with the covariance matrix is used for prediction. If the number of new samples has reached the given number, the process of selecting new sample points is completed. It should be noted that this process does not require retraining the optimization model, but only updating the covariance matrix.

[0035] Further, the test point at the position of the maximum value of the acquisition function is considered as a new sample point, and its model prediction solution is regarded as the true solution, and this process does not require pneumatic uncertainty quantification.

[0036] Further, in steps S1 and S4 of step (2), the pneumatic uncertainty quantification method is used to accurately evaluate the statistics of the target pneumatic performance parameters and the constraint pneumatic performance parameters of the training samples or new sample points, specifically including the following steps:

[0037] Step 1) For the pneumatic performance parameters (specifically including the target pneumatic performance parameters and the constraint pneumatic performance parameters) affected by N independent uncertainty parameter perturbations, it can be Taylor-expanded as the following expression:

[0038]

[0039] Among them, f(b + Δb) is the pneumatic performance parameter, f0(b) represents the deterministic pneumatic performance parameter corresponding to the uncertainty parameter b, G = (g i ) N and H = (h ij ) N×N are the first-order sensitivity (FO) vector and the second-order sensitivity (SO) matrix respectively. The FO vector and the SO matrix are specifically calculated based on the blade geometric shape corresponding to the sample point using the FDM method (finite difference method); Δb is the perturbation amount of the uncertainty parameter, and O(Δ 2 ) is the high-order term of the Taylor formula and can be ignored.

[0040] Step 2) Within the perturbation range of the uncertainty parameter, the change amount Δf of the pneumatic performance parameter can be approximately evaluated by the following formula:

[0041]

[0042] It should be noted that once the perturbation amount Δb of the uncertainty parameter is given, the change amount of the aerodynamic performance parameter can be directly calculated without additional CFD flow field calculation, which greatly reduces the calculation cost.

[0043] Step 3) Based on the results of Step 1) and 2), calculate the change amount of the aerodynamic performance parameter for all training samples or new sample points, and then calculate the statistics of the target aerodynamic performance parameter and the constraint aerodynamic performance parameter for each training sample or new sample point.

[0044] The beneficial effects of the present invention are as follows:

[0045] 1. The present invention proposes a robust aerodynamic design optimization method for blades with aerodynamic reliability constraints, gives a mathematical description of the robust aerodynamic design optimization of blades with aerodynamic reliability constraints, and provides a new idea for the robust aerodynamic design optimization of blades.

[0046] 2. The present invention uses the aerodynamic uncertainty quantification method to efficiently quantify the uncertainty influence of uncertainty parameters on the aerodynamic performance parameters and constraint aerodynamic performance parameters of the blades, greatly reducing the calculation cost. A robust optimization model is constructed by using the adaptive Gaussian process coupled with the aerodynamic uncertainty quantification method, and the optimization design of the blades is efficiently realized.

[0047] 3. The method of the present invention can significantly improve the reliability of the constraint aerodynamic performance parameters and the robustness of the target aerodynamic performance parameters of the optimized blades. This aerodynamic design optimization idea can be widely applied to the robust optimization design of impeller machine blades. Description of the Drawings

[0048] Figure 1 is the flow chart of the robust aerodynamic design optimization framework of the present invention;

[0049] Figure 2 is the iterative convergence curve of the maximum value of the acquisition function of the ADGP model;

[0050] Figure 3 is the optimal solution set under different confidence probability aerodynamic constraints;

[0051] Figure 4 is the optimized blade geometry under different confidence probability aerodynamic constraints. Detailed Embodiments

[0052] The present invention will be described in detail below with reference to the drawings.

[0053] Figure 1 is the flow chart of the robust aerodynamic design optimization framework of the present invention.

[0054] In this example, a certain type of low-pressure turbine rotor blade is taken as the research object, and the robust aerodynamic design optimization problem with aerodynamic reliability constraints considering geometric deviation uncertainty is studied. The target aerodynamic performance parameter is the total pressure loss coefficient ζ, and the constraint aerodynamic performance parameter is the mass flow rate Under the aerodynamic reliability constraints with a certain confidence probability, improve the average aerodynamic performance of the optimized blade and reduce the sensitivity of the total pressure loss coefficient ζ of the optimized blade to geometric deviations. The aerodynamic constraint is the flow rate in the blade passage Statistical mean Under certain reliability requirements, it is not lower than the statistical mean of the flow rate of the original design blade of

[0055] (1) The mathematical description of the blade RADO problem with aerodynamic reliability constraints is as follows:

[0056]

[0057] Among them, k takes three cases of 1, 2, and 3 respectively, and μ ζ and σ ζ are the mean and standard deviation of the total pressure loss coefficient respectively, is the flow rate in the blade passage of the standard deviation. Among them, equality constraints are not considered in this example problem

[0058] (2) In order to quickly implement RADO, an optimization model is constructed based on the Adaptive Gaussian process (ADGP), which specifically includes:

[0059] Step S1: In the optimization design space, use Latin hypercube sampling to generate an initial training sample set X, and use the aerodynamic uncertainty quantification method to evaluate the statistical means and standard deviations (denoted as Y) of the target aerodynamic performance parameters and constraint aerodynamic performance parameters of each training sample. Take X as the input of the optimization model and Y as the output of the optimization model; and generate a large number of test point sets X * ;

[0060] Among them, the aerodynamic uncertainty quantification UQ (Uncertainty Quantification) method is used to evaluate the statistical means and standard deviations of the target aerodynamic performance parameters and constraint aerodynamic performance parameters of each training sample, which specifically includes the following steps:

[0061] 1) For the aerodynamic performance parameter f affected by 14 geometric deviation characteristic modes, it can be Taylor-expanded into the following expression:

[0062]

[0063] Among them, f(b + Δb) is the aerodynamic performance parameter, f0(b) represents the deterministic aerodynamic performance parameter corresponding to the uncertainty parameter b, G = (g i ) N and H = (h ij ) N×B are the first-order sensitivity (First order sensitivity, FO) vector and the second-order sensitivity (Second order sensitivity, SO) matrix respectively. The FO vector and SO matrix at a given sample point are specifically calculated using the FDM method, that is, sensitivity calculation; Δb is the perturbation amount of the uncertainty parameter, and O(Δ 2 ) is the high-order term of the Taylor formula and can be ignored.

[0064] 2) Within the perturbation range of the uncertainty parameter, the change amount Δf of the aerodynamic performance parameter can be approximately evaluated by the following formula:

[0065]

[0066] It should be noted that once the perturbation amount Δb of the uncertainty parameter is given, the change amount of the aerodynamic performance parameter can be directly calculated without additional CFD flow field calculation, greatly reducing the calculation cost.

[0067] 3) Based on steps 1) and 2), the change amounts of the aerodynamic performance parameters of all training samples are calculated, and thus the statistics of the target aerodynamic performance parameters and the constraint aerodynamic performance parameters of each training sample are calculated to achieve sensitivity-based aerodynamic uncertainty quantification UQ (i.e., sensitivity aerodynamic UQ), as Figure 1 shown. The number of training samples needs to be determined according to the convergence of the actual situation.

[0068] Step S2: Based on X and Y, Gaussian process (GP) model training is performed to obtain an optimized model.

[0069] Step S3: Evaluate the model standard deviation * of each test point in the test point set X which is the square root of the model variance , and the definition of is as follows:

[0070]

[0071] Among them, x * represents a new test point, K is the covariance matrix of the optimized model, k(x * , x * ) represents the autocorrelation value of the test point, and k(x * , X) represents the test point x* The covariance vector with the training sample set X.

[0072] Step S4: Calculate the acquisition function f of the optimization model corresponding to each test point acq , and select the maximum value of the acquisition function; the acquisition function f acq Specifically:

[0073]

[0074] Where: n obj represents the number of objectives of the optimization model, and λ q represents the weight coefficients corresponding to each objective.

[0075] Step S5: Determine whether the maximum value of the acquisition function converges. If it converges, the global optimization model is established. If it does not converge, further determine whether the number of newly added samples allowed for each iteration reaches a given number, such as a limit of 2. If the number of new samples does not reach the given number, go to step S6; if the number of new samples has reached the given number, go to step S7.

[0076] Step S6: Incorporate the sample point at the position of the maximum value of the acquisition function into the training samples, update the covariance matrix of the GP model, and perform model prediction. Repeat steps S3 to S5 in this way.

[0077] Step S7: Perform blade parametric modeling on the newly obtained sample points (such as 2). Subsequently, use the aerodynamic uncertainty quantification method to accurately evaluate the target aerodynamic performance parameters and constraint aerodynamic performance parameters of the new sample points.

[0078] Step S8: Re-add the newly obtained samples after accurate evaluation to the training samples, update the covariance matrix of the GP model, and retrain the GP model; repeat steps S2 to S7 until the maximum value of the acquisition function converges in step S5.

[0079] In the said step S6, the sample point at the position of the maximum value of the acquisition function is regarded as a new sample point, and its model prediction solution is regarded as the true solution. This process does not require aerodynamic uncertainty quantification.

[0080] In the said step S7, the new sample points come from step S6. The purpose of step S7 is to accurately evaluate the true solutions of the new sample points.

[0081] Figure 2 The iteration convergence curve of the maximum value of the acquisition function for the optimization model is given, and it converges after 30 outer iterations. The results show that the robust optimization model proposed by the present invention can converge quickly, thus realizing the rapid construction of the optimization model.

[0082] (3) Within the optimized design space, based on the optimized model, the NSGA-II algorithm is used to obtain the optimal solutions for multi-objective optimization, specifically including:

[0083] Step S1: Based on the inequality constraints and equality constraints in the RADO problem, set the constraint conditions in the NSGA-II algorithm;

[0084] Step S2: Use the NSGA-II algorithm to perform multi-objective optimization on the optimized model and solve to obtain the Pareto optimal solution set.

[0085] Step S3: Analyze and select the solutions in the Pareto optimal solution set to obtain the final optimal solutions, namely Figure 3 Opt-I, Opt-III, and Opt-IV in

[0086] Figure 3 are the optimal solution sets under different confidence probability aerodynamic constraints, where the three cases are k = 1, k = 2, and k = 3 respectively. The results show that as the confidence probability of the aerodynamic constraint increases, the optimal solution set moves upward and to the right. At the same standard deviation of the total pressure loss coefficient, the statistical mean of the total pressure loss coefficient increases and the target aerodynamic performance weakens.

[0087] Figure 4 are the optimized blade geometric shapes under different confidence probability aerodynamic constraints. It can be seen from the figure that compared with the original design blade, the included angle of the center line of the RADO optimized blade decreases, the curvature of the leading edge of the suction surface increases, and the curvature in the middle of the suction surface decreases.

[0088] Table 1 gives the comparison results of the target aerodynamic performance parameters and constrained aerodynamic performance parameters between the optimized blade and the original design blade. Among them, Δζ represents the change in the total pressure loss coefficient, Δμ L represents the change in the statistical mean of the total pressure loss coefficient, Δσ ζ represents the change in the standard deviation of the total pressure loss coefficient, represents the change in the mass flow rate, represents the change in the statistical mean of the mass flow rate, represents the change in the standard deviation of the mass flow rate. Overall, compared with the original design blade, the statistical quantities of the total pressure loss coefficient of the optimized blade all decrease and the aerodynamic robustness all improves. Compared with the original design blade, as the confidence probability of the flow constraint increases, the standard deviation of the total pressure loss coefficient of the RADO optimized blade increases, the dispersion degree of the target aerodynamic performance of the blade increases, and the aerodynamic robustness weakens. As the flow is the aerodynamic reliability constraint of RADO, as the constraint strengthens, the statistical mean of the flow rate of the optimized blade increases, and the flow rate standard deviation decreases compared with the original design blade, indicating that the flow reliability of the blade increases.

[0089] Table 1

[0090]

Claims

1. A blade robust aerodynamic design optimization method with aerodynamic reliability constraints, characterized in that: The following steps are involved: (1) The RADO problem of blades with aerodynamic reliability constraints is mathematically described. The specific method is as follows: Considering the uncertainty in the n-dimensional input variable ω, the statistical mean of the input variable ω is μ ω ={μ ω1 ,…,μ ωn }, and μ ω All elements in are independent and follow a normal distribution; the objective function is given in a probability statistical way, and the statistical mean of the target aerodynamic performance parameter I is μ I , with standard deviation σ I ; Equality constraints on flow field state and the expectation of the input variable ω and μ ω The inequality constraint is a probability statement: the probability that the constraint is true is greater than or equal to the specified confidence probability P k , assuming that the relevant variables follow a normal distribution, this probability statement is converted into constraints on the statistical mean and standard deviation of the parameters; the equality constraints and inequality constraints contain constraints on aerodynamic performance parameters; the mathematical description of the RADO problem is: Where v represents the design variable, is the inequality constraint aerodynamic performance parameter p i The statistical mean of Constrain aerodynamic performance parameters for the original blade design The statistical mean, σ pi is the inequality constraint aerodynamic performance parameter p i The standard deviation of The aerodynamic performance parameter q is constrained by equation j The statistical mean of Constrain aerodynamic performance parameters for the original blade design The statistical mean of c* and n c are the number of aerodynamic performance parameters constrained by inequality and the number of aerodynamic performance parameters constrained by equality, respectively; k represents the standard deviation of the required displacement of the statistical mean of the aerodynamic performance parameters constrained by inequality The number of, so as to achieve the specified confidence probability P k ; In practical applications, inequality constraints or equality constraints can be considered separately according to specific problems; (2) In order to quickly implement RADO, an optimization model is constructed based on an adaptive Gaussian process. The specific method is as follows: Step S1: In the optimization design space, Latin hypercube sampling is used to generate an initial training sample set X, X is used as the input of the optimization model, and the aerodynamic uncertainty quantification method is used to evaluate the statistics of the target aerodynamic performance parameters and the constrained aerodynamic performance parameters of each training sample, including the statistical mean and standard deviation, which is recorded as Y, and Y is used as the output of the optimization model; and a large number of test point sets X are generated in the optimization design space. * ; Step S2: Perform Gaussian process model training based on X and Y to obtain an optimized model; Step S3: Predict the test point set X based on the optimization model * The corresponding statistics of the target aerodynamic performance parameters and the constrained aerodynamic performance parameters are calculated, and the acquisition function value of each test point is calculated. The test point corresponding to the maximum value of the acquisition function is selected, and the test point and the corresponding prediction result are added to the covariance matrix of the optimization model; this cycle is repeated until a sufficient number of test points are selected as new sample points; Step S4: firstly, the selected new sample points are subjected to blade parameter modeling to obtain the blade geometric shape corresponding to the new sample points, and then based on the blade geometric shape of the new sample points, the statistics of the target aerodynamic performance parameters and the constrained aerodynamic performance parameters of the new sample points are accurately evaluated using an aerodynamic uncertainty quantification method, the accurately evaluated new sample points are added to the training samples, and the optimization model is retrained; Step S5: Repeat steps S3 and S4 until the maximum value of the acquisition function converges to obtain the final optimization model; (3) In the optimization design space, based on the optimization model, the NSGA-II algorithm is used to solve the optimal solution of the multi-objective optimization, specifically including: Step S1: Based on the inequality constraints and equality constraints in the RADO problem, set the constraints in the NSGA-II algorithm; Step S2: Use NSGA-II algorithm to perform multi-objective optimization on the optimization model and obtain the Pareto optimal solution set; Step S3: Analyze and select the solutions in the Pareto optimal solution set to obtain the final optimal solution.

2. The blade robust aerodynamic design optimization method with aerodynamic reliability constraints according to claim 1 is characterized in that: In step S3 of step (2), the acquisition function value of each test point is calculated, which specifically includes the following steps: 1) Evaluate the test point set X * The model standard deviation of each test point in is the model variance square root of is defined as follows: Among them, x * represents a new test point, K is the covariance matrix of the optimized model, k(x * ,x * ) represents the autocorrelation value of the test point, k(x * ,X) represents the test point x * The covariance vector between the training sample set X; 2) Calculate the acquisition function f of the optimization model corresponding to each test point acq : Where: n obj Indicates the number of targets for the optimization model; j Represents the weight coefficient corresponding to each target.

3. The blade robust aerodynamic design optimization method with aerodynamic reliability constraints according to claim 1 is characterized in that: In step S1 and step S4 of step (2), the statistics of the target aerodynamic performance parameters and the constrained aerodynamic performance parameters of the training samples or new sample points are accurately evaluated by using an aerodynamic uncertainty quantification method, which specifically includes the following steps: Step 1) Taylor expansion is performed on the aerodynamic performance parameter f(b+Δb) affected by N independent uncertainty parameter disturbances: Where f0(b) represents the deterministic aerodynamic performance parameter corresponding to the uncertainty parameter b, G = (g i ) N and H=(h ij ) n×n are the first-order sensitivity vector and the second-order sensitivity matrix, Δb is the disturbance of the uncertainty parameter, O(Δ 2 ) is the higher-order term of Taylor’s formula; Step 2) Within the disturbance range of the uncertainty parameter, the aerodynamic performance parameter change Δf is calculated by the following formula: Step 3) calculates the aerodynamic performance parameter changes of all training samples or new sample points based on steps 1) and 2), thereby calculating the statistics of the target aerodynamic performance parameters and constrained aerodynamic performance parameters of each training sample or new sample point.

Images