A learning-based compressor airfoil proxy-assisted evolutionary optimization method and system

Abstract

This invention provides a learning-based surrogate-assisted evolutionary optimization method and system for compressor airfoil design. By introducing manifold learning theory, this invention maps high-dimensional compressor airfoil design variables to a low-dimensional discriminative subspace that preserves the Pareto front geometry, effectively mitigating the curse of dimensionality. A manifold Gaussian process surrogate model incorporating Riemannian geometric regularization, constructed on this low-dimensional subspace, significantly improves the prediction accuracy and robustness of the surrogate model under sparse samples. Geodesic crossover and Riemannian gradient mutation operators conforming to manifold constraints are proposed to ensure that the search process always proceeds along an effective manifold, improving search efficiency and quality. Filling solutions are selected through hypervolume contribution to ensure that the selected solutions have excellent aerodynamic performance on the actual airfoil. Compared with existing technologies, this invention can solve the optimization problem of high-dimensional, expensive compressor airfoils more efficiently and accurately, obtaining airfoils with superior aerodynamic performance.

Description

Technical Field

[0001] This invention relates to the field of compressor blade optimization technology, and more specifically, to a learning-based surrogate-assisted evolutionary optimization method and system for compressor blades. Background Technology

[0002] The compressor is a core component of aero-engines and gas turbines, and its performance directly determines the efficiency and stability of the entire power plant. The aerodynamic design of compressor blades is a typical high-dimensional, expensive, multi-objective optimization problem. To obtain better aerodynamic performance (such as reducing the total pressure loss coefficient and increasing the total pressure ratio), design variables typically include hundreds of parameters describing the blade geometry (such as controlling the coordinates of the apex using the FFD method). Realistic aerodynamic performance evaluation of these design variable combinations requires simulations using high-precision computational fluid dynamics (CFD), with single simulations potentially taking anywhere from a few minutes to several hours, resulting in extremely high computational costs.

[0003] To reduce optimization costs, surrogate-assisted evolutionary algorithms have emerged. These methods approximate expensive CFD simulations by constructing computationally inexpensive surrogate models, guiding the evolutionary algorithm to search for the optimal airfoil within a vast design space. However, existing surrogate-assisted methods face severe challenges when dealing with compressor airfoil optimization problems with high-dimensional variables: First, the curse of dimensionality. As the dimensionality of design variables increases, the search space grows exponentially, resulting in extremely sparse samples for training the surrogate model and a significant decrease in model prediction accuracy. Second, geometric distortion. Complex nonlinear coupling relationships exist between high-dimensional design variables, and the true optimal airfoil is often distributed on a potential low-dimensional manifold. Most existing dimensionality reduction methods rely on linear projection or statistical properties, neglecting the intrinsic geometric structure between variables. This leads to a mismatch between the reduced subspace and the Pareto front topology of the original high-dimensional space, resulting in structural distortion. Consequently, the optimal solution found in the low-dimensional space, when mapped back to the high-dimensional space, exhibits significantly different aerodynamic performance than expected. Third, the accuracy of surrogate modeling. Traditional surrogate models (such as Gaussian processes) typically rely on Euclidean distance to measure sample similarity. However, in high-dimensional spaces, the Euclidean distance between samples tends to be consistent, making it difficult to effectively capture the impact of subtle changes in airfoil geometry on aerodynamic performance.

[0004] Therefore, a compressor airfoil optimization method is needed that can effectively reduce dimensionality in high-dimensional design spaces, preserve Pareto front geometry, and achieve high-precision surrogate modeling, in order to improve the solution efficiency and effectiveness of high-dimensional and expensive aerodynamic optimization problems. Therefore, a learning-based compressor airfoil surrogate-assisted evolutionary optimization method and system are proposed. Summary of the Invention

[0005] The purpose of this invention is to address the problems identified in the existing background technology. To achieve the above-mentioned objective, this invention provides the following technical solution: a learning-based surrogate-assisted evolutionary optimization method for compressor blade profiles, comprising the following steps: S1. Several initial airfoil samples are generated through experimental design methods, and the aerodynamic performance of each initial airfoil sample is evaluated by real CFD to obtain an initial sample library containing design variables and their corresponding aerodynamic performance. S2. Based on the initial sample library, the Riemannian manifold optimization method is used to learn the discriminant subspace to obtain a low-dimensional discriminant subspace that can maintain the Pareto front topology and its corresponding optimal mapping matrix. S3. In the low-dimensional discriminant subspace, a manifold Gaussian process surrogate model is constructed for each aerodynamic performance target using data from the sample library; during the training process of the manifold Gaussian process surrogate model, a Riemannian geometric regularization term is introduced to enhance the smoothness and generalization ability of the model. S4. In the low-dimensional discriminant subspace, a manifold-constrained multi-objective evolutionary algorithm is executed to generate a candidate solution set; wherein, the evolutionary algorithm adopts a geodesic-based crossover operator and a Riemann gradient-guided mutation operator to ensure that the generated offspring individuals are always located on a potential effective manifold; S5. Map the candidate solution set back to the original high-dimensional space through the inverse of the optimal mapping matrix to obtain high-dimensional candidate solutions; adopt a filling solution selection strategy based on hypervolume contribution to select the most promising individuals from the high-dimensional candidate solutions for real CFD aerodynamic performance evaluation, and add the newly evaluated samples to the sample library to update the sample library. S6. Repeat steps S2 to S5 until the preset maximum number of real evaluations is reached, and output the Pareto optimal solution set in the sample library as the optimized compressor blade profile.

[0006] As a preferred technical solution of the present invention, the discriminative subspace learning using the Riemannian manifold optimization method in step S2 specifically includes: assigning different class labels to non-dominated solutions, dominated solutions, and other solutions according to the dominance relationship of samples in the sample library; constructing a discriminative optimization problem based on the class labels to minimize intra-class divergence and maximize inter-class divergence in order to find the optimal mapping matrix; modeling the discriminative optimization problem as an unconstrained optimization problem on a Stiefel manifold and solving it using the Riemannian trust field algorithm to obtain the optimal mapping matrix.

[0007] As a preferred technical solution of the present invention, the manifold Gaussian process surrogate model in step S3 has a kernel function constructed based on the geodesic distance on the low-dimensional discriminant subspace, which is used to measure the similarity of samples on the manifold.

[0008] As a preferred technical solution of the present invention, in step S3, when training the manifold Gaussian process surrogate model, a sharpness-aware minimization strategy is introduced to enhance the robustness of the model to inverse mapping perturbations by finding a flat minimum on the prediction surface. The geodesic-based crossover operator in step S4 specifically includes: in the low-dimensional discriminant subspace, interpolation is performed along the geodesic connecting two parent individuals to generate new child individuals.

[0009] As a preferred technical solution of the present invention, the mutation operator guided by the Riemann gradient in step S4 specifically includes: calculating the Riemann gradient of the current individual under the manifold Gaussian process surrogate model, and determining the variable length and direction based on the gradient direction and random perturbation, and generating new offspring individuals.

[0010] As a preferred technical solution of the present invention, the filling solution selection strategy based on residual correction in step S5 specifically includes: constructing a residual surrogate model in the original high-dimensional space to learn the systematic deviation between the predicted value of the manifold Gaussian process surrogate model and the actual CFD evaluation value; correcting the predicted value of the high-dimensional candidate solution using the residual surrogate model; performing non-dominated sorting on the corrected high-dimensional candidate solutions to select a candidate solution pool; and selecting the most promising individual from the candidate solution pool based on the hypervolume Sharpe ratio index for actual evaluation.

[0011] As a preferred technical solution of the present invention, a learning-based compressor blade profile proxy-assisted optimization system is provided, comprising: The initialization module is used to generate several initial airfoil samples through experimental design methods, and to perform real CFD aerodynamic performance evaluation on each initial airfoil sample to obtain an initial sample library containing design variables and their corresponding aerodynamic performance. The subspace learning module is used to learn the discriminative subspace based on the initial sample library using the Riemann manifold optimization method, so as to obtain a low-dimensional discriminative subspace that can preserve the Pareto front topology and its corresponding optimal mapping matrix. The surrogate modeling module is used to construct a manifold Gaussian process surrogate model for each aerodynamic performance target using data from the sample library in the low-dimensional discriminant subspace; during the training process of the manifold Gaussian process surrogate model, a Riemannian geometric regularization term is introduced to enhance the smoothness and generalization ability of the model. The evolutionary search module is used to execute a manifold-constrained multi-objective evolutionary algorithm to generate a candidate solution set in the low-dimensional discriminant subspace; wherein the evolutionary algorithm employs a geodesic-based crossover operator and a Riemann gradient-guided mutation operator to ensure that the generated offspring individuals always lie on a potential effective manifold; The filling solution selection module is used to map the candidate solution set back to the original high-dimensional space through the inverse of the optimal mapping matrix to obtain high-dimensional candidate solutions; based on the filling solution selection strategy of hypervolume contribution, the most promising individuals are selected from the high-dimensional candidate solutions for real CFD aerodynamic performance evaluation, and the newly evaluated samples are added to the sample library to update the sample library. The loop control module is used to repeatedly execute the subspace learning module, surrogate modeling module, evolutionary search module, and fill solution selection module until the preset maximum number of real evaluations is reached, and outputs the Pareto optimal solution set in the sample library as the optimized compressor blade profile.

[0012] As a preferred technical solution of the present invention, an electronic device is provided, the electronic device including a processor and a memory, the memory storing at least one instruction, the at least one instruction being loaded and executed by the processor to implement the above-mentioned learning-based compressor blade profile proxy-assisted optimization method.

[0013] As a preferred technical solution of the present invention, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the above-mentioned learning-based compressor blade profile proxy-assisted optimization method.

[0014] Compared with existing technologies, the advantages of this invention are as follows: By introducing manifold learning theory, this invention maps high-dimensional compressor blade design variables to a low-dimensional discriminant subspace that preserves the Pareto front geometry, effectively alleviating the curse of dimensionality. The manifold Gaussian process surrogate model constructed on this low-dimensional manifold significantly improves the prediction accuracy and robustness of the surrogate model under sparse samples by employing geodesic distance and Riemannian geometric regularization. Furthermore, geodesic crossover and Riemannian gradient mutation operators that conform to manifold constraints are designed in the evolutionary search to ensure that the search process always proceeds along the effective manifold, improving search efficiency and quality. Finally, by selecting and filling solutions using hypervolume contribution, the selected solutions are ensured to have excellent aerodynamic performance on the actual blade profile. Compared with existing technologies, this invention can solve the high-dimensional, expensive compressor blade optimization problem more efficiently and accurately, obtaining blade profiles with superior aerodynamic performance. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the MLDSAEA algorithm framework provided by the present invention; Figure 2 Schematic diagram of the results obtained by different algorithms provided in this invention on the airfoil optimization model; Figure 3 A comparative diagram of airfoil geometry corresponding to the non-dominated solution with the maximum hyperbody contribution provided by the present invention; Figure 4The maximum HV data frame diagram obtained by MLDSAEA and 8 comparative algorithms for the airfoil optimization problem provided by this invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0017] Therefore, the following detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely illustrates some embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments and features and technical solutions in the embodiments of the present invention can be combined with each other. It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0018] Example 1: A learning-based agent-assisted evolutionary optimization method and system for compressor blade profiles. This method can be implemented using electronic devices, such as terminals or servers. The processing flow of this method may include the following steps: S1. Initialization: Several initial airfoil samples are generated using experimental design methods, and the aerodynamic performance of each initial airfoil sample is evaluated using real CFD, resulting in an initial sample library containing design variables and their corresponding aerodynamic performance. Specifically, Latin hypercube sampling can be used to generate N0 initial samples in the design variable space. Each sample represents a set of airfoil design parameters; for example, if the FFD parameterization method is used, the design variables can be the normal offsets of each control vertex, etc. A high-performance computing cluster is used to parallelly call CFD solvers (such as NUMECA, ANSYS CFX, etc.) to perform real evaluations on these N0 samples, obtaining the aerodynamic performance corresponding to each sample, such as the total pressure loss coefficient and total pressure ratio. The design variable vector x of each sample and its corresponding aerodynamic performance vector F(x) are stored as a complete sample in the sample library.

[0019] S2. Discriminant Subspace Learning: Based on the initial sample library, the Riemannian manifold optimization method is used to learn the discriminant subspace, obtaining a low-dimensional discriminant subspace Z that preserves the Pareto front topology and its corresponding optimal mapping matrix U. Step S2 specifically includes the following sub-steps: S201. Class Label Construction: For all samples in the sample library, sort them according to their objective function values ​​(such as ω and π) to determine their non-dominated status. If a sample x is a Pareto non-dominated solution, assign it a class label L=1; if it is a dominated solution, assign it L=0; otherwise (e.g., not dominated by other solutions), assign it L=-1. This yields the label for each sample.

[0020] S202. Modeling the Discriminant Optimization Problem: The goal is to find a mapping matrix. (d is the dimension of the original variable, The dimension after dimensionality reduction, and Mapping a high-dimensional sample x to a low-dimensional space. To preserve the class structure of the samples as well as possible in this low-dimensional space, an objective function is constructed that simultaneously minimizes intra-class divergence and maximizes inter-class divergence. The intra-class divergence matrix is ​​defined. and inter-class scatter matrix The optimization problem can then be expressed as: This constraint This indicates that U lies in the Stiefel manifold superior.

[0021] S203, Solving Riemannian manifold optimization problems: Transform the above problem into an unconstrained optimization problem on a Stiefel manifold. The Riemann trust region algorithm is used to solve the problem. This algorithm constructs a quadratic model on the tangent space of the manifold, maps the tangent vectors back to the manifold through a shrinking operation, and iteratively updates U until convergence. The final optimal mapping matrix U is the desired result, and the low-dimensional discriminant subspace is... .

[0022] S3. Manifold Gaussian Process Proxy Modeling: In the low-dimensional discriminant subspace Z, a manifold Gaussian process proxy model is constructed for each aerodynamic performance target (such as the total pressure loss coefficient) using data from the sample library.

[0023] Optionally, step S3 specifically includes the following sub-steps: S301. Kernel Function Based on Geodesic Distance: Traditional geodesic (GP) uses Euclidean distance, which cannot accurately measure the distance between two points on a manifold. This invention uses geodesic distance. To measure sample points on a low-dimensional manifold and The similarity is used to construct kernel functions, for example: S302. Model Training with Geometric Regularization: To enhance the smoothness of the model under sparse samples, a Riemann gradient regularization term is introduced in addition to maximizing the traditional logarithmic marginal likelihood during MGP training. This regularization term penalizes the gradient change of the model's predicted values ​​on the manifold, forcing the model to maintain geometric smoothness on the manifold. The final optimization objective is: S303, Sharpness-Aware Minimization: To further enhance the model's robustness to inverse mapping perturbations, a sharpness-aware minimization strategy is introduced. For any candidate solution z, its robust prediction is not simply the mean prediction μ(z) of the MGP, but rather the worst-case prediction within its local neighborhood, i.e.: This can be achieved by utilizing first-order gradient information. An approximate solution is used. This strategy tends to select solutions located in flat regions of the prediction surface, whose predictive performance changes less when subjected to perturbations (such as inverse mapping errors).

[0024] S4. Manifold-constrained multi-objective evolutionary search: In the low-dimensional discriminant subspace Z, the manifold-constrained multi-objective evolutionary algorithm is executed to generate a candidate solution set.

[0025] Step S4 specifically includes the following sub-steps: S401, Geodesic-based Crossover Operator: To ensure that offspring individuals lie on the manifold, select two parent individuals from the current population. Offspring are generated by interpolation along the geodesic lines connecting them, and the offspring individuals... ,in These are the interpolation parameters.

[0026] S402, Riemann gradient-guided mutation operator: To guide the search towards more promising regions, first-order information provided by the MGP model is utilized. For the current individual z, its Riemann gradient on the manifold is calculated. The mutation direction is formed by the gradient descent direction and a random perturbation vector. The mutated vector lies in the tangent space of z. By mapping back to the manifold through a shrinking operation, new offspring individuals are obtained.

[0027] S403. Environmental Selection: After merging the parent and offspring populations, the predicted fitness vector for each individual is calculated using the MGP model combined with a sharpness-perceived minimization strategy. Based on these predicted fitness values, environmental selection is performed using non-dominated ordination based on geodesic distance and crowding distance to select a new generation of population. This process is repeated until a predetermined number of generations is reached, resulting in a set of Pareto optimal candidate solutions. .

[0028] S5. Filling the solution set and updating the sample: This involves filling the candidate solution set with... Through inverse mapping Returning to the original high-dimensional space, we obtain high-dimensional candidate solutions. We selected q individuals with the highest potential based on the hypervolume contribution index for real-world CFD evaluation and updated the sample database.

[0029] Step S5 specifically includes the following sub-steps: S501, Candidate Solution Selection: Based on the corrected prediction values ​​of the surrogate model All candidate solutions are sorted by non-dominated order, and the non-dominated solutions are selected to form a candidate solution pool. .

[0030] S502, Batch Selection Based on HVI: Calculate the hypervolume contribution index for each solution in the candidate solution pool. Select the q solutions with the highest HVI values. As the final filled solution, it is submitted to the high-performance computing cluster for real CFD evaluation. The new evaluation results... Add to the sample library.

[0031] S6. Loop Check: Determine whether the current total number of real evaluations has reached the preset maximum number of evaluations. If the target is not reached, return to step S2, and use the updated sample library to re-perform the discriminant subspace learning, surrogate modeling, and evolutionary search to start a new round of iterative optimization; if the target has been reached, stop the optimization, and output all Pareto non-dominated solutions in the current sample library. The blade profiles corresponding to these solutions are the optimal candidate compressor blade profiles obtained through optimization.

[0032] This invention also provides a learning-based compressor blade profile proxy-assisted optimization system, the system comprising: The initialization module 710 is used to generate several initial airfoil samples through experimental design methods, and to perform real CFD aerodynamic performance evaluation on each initial airfoil sample to obtain an initial sample library containing design variables and their corresponding aerodynamic performance. Subspace learning module 720 is used to learn the discriminative subspace based on the initial sample library using the Riemann manifold optimization method, to obtain a low-dimensional discriminative subspace that can maintain the Pareto front topology and its corresponding optimal mapping matrix. The surrogate modeling module 730 is used to construct a manifold Gaussian process surrogate model for each aerodynamic performance target using data from the sample library in the low-dimensional discriminant subspace; during the training process of the manifold Gaussian process surrogate model, a Riemannian geometric regularization term is introduced to enhance the smoothness and generalization ability of the model. The evolutionary search module 740 is used to execute a manifold-constrained multi-objective evolutionary algorithm to generate a candidate solution set in the low-dimensional discriminant subspace; wherein the evolutionary algorithm employs a geodesic-based crossover operator and a Riemann gradient-guided mutation operator to ensure that the generated offspring individuals always lie on a potential effective manifold; The filling selection module 750 is used to map the candidate solution set back to the original high-dimensional space through the inverse mapping of the optimal mapping matrix to obtain high-dimensional candidate solutions; adopting the filling solution selection strategy of hypervolume contribution, the most promising individuals are selected from the high-dimensional candidate solutions for real CFD aerodynamic performance evaluation, and the newly evaluated samples are added to the sample library to update the sample library. The loop control module 760 is used to repeatedly execute the subspace learning module, the surrogate modeling module, the evolutionary search module, and the filling selection module until the preset maximum number of real evaluations is reached, and outputs the Pareto optimal solution set in the sample library as the optimized compressor blade profile.

[0033] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described herein. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, as well as all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.

Claims

1. A learning-based compressor airfoil proxy-assisted evolutionary optimization method, characterized in that, Includes the following steps: S1. Collect several initial airfoil samples through experimental design methods, and conduct real CFD aerodynamic performance evaluation on each initial airfoil sample to obtain an initial sample library containing design variables and their corresponding aerodynamic performance. S2. Based on the initial sample library, the Riemannian manifold optimization method is used to learn the discriminant subspace to obtain a low-dimensional discriminant subspace that can maintain the Pareto front topology and its corresponding optimal mapping matrix. S3. In the low-dimensional discriminant subspace, a manifold Gaussian process surrogate model is constructed for each aerodynamic performance target using data from the sample library; during the training process of the manifold Gaussian process surrogate model, a Riemannian geometric regularization term is introduced to enhance the smoothness and generalization ability of the model. S4. In the low-dimensional discriminant subspace, a manifold-constrained multi-objective evolutionary algorithm is executed to generate a candidate solution set; wherein, the evolutionary algorithm adopts a geodesic-based crossover operator and a Riemann gradient-guided mutation operator to ensure that the generated offspring individuals are always located on a potential effective manifold; S5. Map the candidate solution set back to the original high-dimensional space through the inverse of the optimal mapping matrix to obtain high-dimensional candidate solutions; adopt a filling solution selection strategy based on hypervolume contribution to select the most promising individuals from the high-dimensional candidate solutions for real CFD aerodynamic performance evaluation, and add the newly evaluated samples to the sample library. S6. Repeat steps S2 to S5 until the preset maximum number of real evaluations is reached, and output the Pareto optimal solution set in the sample library as the optimized compressor blade profile.

2. The learning-based compressor airfoil proxy-assisted evolutionary optimization method of claim 1, wherein, In step S2, the Riemannian manifold optimization method is used for discriminative subspace learning, specifically including: assigning different class labels to non-dominated solutions, dominated solutions, and other solutions according to the dominance relationship of samples in the sample library; constructing a discriminative optimization problem based on the class labels, aiming to minimize intra-class divergence and maximize inter-class divergence, in order to find the optimal mapping matrix; modeling the discriminative optimization problem as an unconstrained optimization problem on a Stiefel manifold, and solving it using the Riemannian trust field algorithm to obtain the optimal mapping matrix.

3. The learning-based compressor airfoil proxy-assisted evolutionary optimization method of claim 1, wherein, The manifold Gaussian process surrogate model in step S3 has a kernel function constructed based on the geodesic distance on the low-dimensional discriminant subspace, which is used to measure the similarity of samples on the manifold.

4. The learning-based compressor airfoil proxy-assisted evolutionary optimization method of claim 1, wherein, In step S3, when training the manifold Gaussian process surrogate model, a sharpness-aware minimization strategy is introduced to enhance the model's robustness to inverse mapping perturbations by finding flat minima on the prediction surface.

5. The learning-based compressor airfoil proxy-assisted evolutionary optimization method of claim 1, wherein, The geodesic-based crossover operator in step S4 specifically includes: interpolating along the geodesic connecting two parent individuals in the low-dimensional discriminant subspace to generate new child individuals.

6. The learning-based compressor airfoil proxy-assisted evolutionary optimization method of claim 1, wherein, The mutation operator guided by the Riemann gradient in step S4 specifically includes: calculating the Riemann gradient of the current individual under the manifold Gaussian process surrogate model, and determining the variable length and direction based on the gradient direction and random perturbation to generate new offspring individuals.

7. The learning-based compressor airfoil proxy-assisted evolutionary optimization method of claim 1, wherein, The filling solution selection strategy based on hypervolume contribution in step S5 specifically includes: constructing a residual prediction model in the original high-dimensional space to learn the systematic bias between the predicted values ​​of the manifold Gaussian process surrogate model and the actual CFD evaluation values; correcting the predicted values ​​of high-dimensional candidate solutions using the residual prediction model; performing non-dominated sorting on the corrected high-dimensional candidate solutions to select a candidate solution pool; and selecting the most promising individual from the candidate solution pool based on the hypervolume contribution index for actual evaluation.

8. A learning-based compressor airfoil proxy-assisted optimization system, comprising: include: The initialization module is used to generate several initial airfoil samples through experimental design methods, and to perform real CFD aerodynamic performance evaluation on each initial airfoil sample to obtain an initial sample library containing design variables and their corresponding aerodynamic performance. The subspace learning module is used to learn the discriminative subspace based on the initial sample library using the Riemann manifold optimization method, so as to obtain a low-dimensional discriminative subspace that can preserve the Pareto front topology and its corresponding optimal mapping matrix. The surrogate modeling module is used to construct a manifold Gaussian process surrogate model for each aerodynamic performance target using data from the sample library in the low-dimensional discriminant subspace; during the training process of the manifold Gaussian process surrogate model, a Riemannian geometric regularization term is introduced to enhance the smoothness and generalization ability of the model. An evolutionary search module is used to execute a manifold-constrained multi-objective evolutionary algorithm to generate a candidate solution set in the low-dimensional discriminant subspace; wherein the evolutionary algorithm employs a geodesic-based crossover operator and a Riemann gradient-guided mutation operator; The filling solution selection module is used to map the candidate solution set back to the original high-dimensional space through the inverse of the optimal mapping matrix to obtain high-dimensional candidate solutions; based on the filling solution selection strategy of hypervolume contribution, the most promising individuals are selected from the high-dimensional candidate solutions for real CFD aerodynamic performance evaluation, and the newly evaluated samples are added to the sample library to update the sample library. The loop control module is used to repeatedly execute the subspace learning module, surrogate modeling module, evolutionary search module, and fill solution selection module until the preset maximum number of real evaluations is reached, and outputs the Pareto optimal solution set in the sample library as the optimized compressor blade profile.

9. An electronic device, comprising: The electronic device includes a processor and a memory, the memory storing at least one instruction, which is loaded and executed by the processor to implement the learning-based compressor blade profile proxy-assisted optimization method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, which is loaded and executed by a processor to implement the learning-based compressor blade profile proxy-assisted optimization method according to any one of claims 1-7.

Images