Compressor blade high-dimensional optimization method based on multi-model dimension reduction and sensitivity guidance

Abstract

This invention discloses a high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance, belonging to the field of compressor blade design. The method includes dimensionality reduction of the compressor blade design variables, generating samples based on the key variables of the dimensionality reduction, training a surrogate model, and calculating the total effect Sobol exponent of the isentropic efficiency and pressure ratio for each key variable based on the output of the surrogate model. Based on the total effect Sobol exponent, a population and individual crossover mutations are generated. Then, it is determined whether to update the surrogate model. If not updated, or if updated, a non-dominated sorting is performed based on the objective function values ​​of individuals in the new population to obtain a frontier set. A new generation population P is then constructed from the frontier set. g Determine if g equals T; if so, then in P... g Candidate solutions are selected from the non-dominated solution set and input into the CFD solver. Samples that meet the design requirements in terms of isentropic efficiency and pressure ratio calculated by the CFD solver are selected as the final sample set; otherwise, the process returns to the crossover and mutation step.

Description

Technical Field

[0001] This invention relates to the field of compressor blade design technology, specifically to a high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance. Background Technology

[0002] As compressor blade aerodynamic design evolves towards high-degree-of-freedom parameterization and high-fidelity CFD numerical simulation, the number of design variables is constantly increasing. Significant nonlinear coupling relationships also exist between performance indicators such as isentropic efficiency and pressure ratio, making the compressor blade optimization problem exhibit high-dimensionality, high cost, black-box nature, and multi-objective characteristics. To reduce the complexity of high-dimensional surrogate modeling and optimization search, existing techniques typically employ dimensionality reduction, variable selection, or low-dimensional surrogate modeling methods to transform the original high-dimensional design space into a low-dimensional representation, and then conduct surrogate modeling and optimization search within the low-dimensional subspace.

[0003] However, existing dimensionality reduction and variable selection methods still suffer from insufficient stability when the number of high-fidelity samples is limited. Because the number of CFD samples available for modeling is small in the early stages of optimization, single surrogate models or single variable importance evaluation methods are easily affected by sampling distribution, model errors, and variable coupling relationships, leading to significant fluctuations in variable importance ranking. This can result in problems such as the omission of key variables, the incorrect retention of non-key variables, or inaccurate low-dimensional subspace construction. For strongly coupled systems like compressor blades, some design variables may affect isentropic efficiency or pressure ratio through interactions; if they are incorrectly removed early on, their effects are difficult to recover in subsequent optimizations.

[0004] Furthermore, the biases generated during the dimensionality reduction stage will be directly transmitted to subsequent surrogate modeling and multi-objective optimization processes. When the low-dimensional subspace cannot accurately reflect the key structural information in the real high-dimensional design space, the subsequently established surrogate model will approximate the true response in a biased sample space. The initialization, crossover, mutation, and Pareto front search of the evolutionary algorithm will also be guided by error sensitivity information, which may ultimately lead to a shift in the convergence direction of the Pareto front, distortion of the trade-off between efficiency and pressure ratio, or obtaining candidate solutions that deviate from the true optimal region under a limited sample budget.

[0005] Therefore, existing technologies still need to address the following issues: 1. How to more stably identify key variables under small sample conditions and reduce the ranking bias caused by single model variable selection; 2. After dimensionality reduction, how to use more reliable global sensitivity information to guide multi-objective evolutionary search and reduce the impact of dimensionality reduction error on Pareto optimization results; 3. How to balance surrogate model accuracy, search efficiency and optimization result robustness under a limited high-fidelity evaluation budget. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, the high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance provided by this invention solves the problem of unstable extraction and effective utilization of structural information under small sample conditions in high-dimensional compressor aerodynamic optimization.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: A method for high-dimensional optimization of compressor blades based on multi-model dimensionality reduction and sensitivity guidance is provided, which includes the following steps: S1. Obtain several design variables for the compressor blades, and use multiple models to reduce the dimensionality of the compressor blade design variables, and select several key variables related to isentropic efficiency and pressure ratio. S2. Generate several samples within the design space of the key variables, use the CDF solver to calculate the isentropic efficiency and pressure ratio of the samples, and use the samples and their corresponding isentropic efficiency and pressure ratio to form a training set. S3. Train the surrogate model using the training set, and calculate the total effect Sobol exponent of the isentropic efficiency and pressure ratio of each key variable based on the output of the surrogate model to the samples. S4. Based on the Sobol index of the total effect, guide the generation of the initial population within the design space of the key variables; S5. Generate a new population by performing individual crossover mutation based on the total effect Sobol index. Then determine whether the surrogate model needs to be updated. If so, update it and proceed to step S6; otherwise, proceed directly to step S6. S6. Use a surrogate model to determine the objective function values ​​of individuals in the new population, perform non-dominated sorting on the new population to obtain the frontier set, and construct a new generation population from the frontier set. ; S7. Determine whether the current iteration count has reached the total number of iterations. If yes, proceed to step S8; otherwise, return to step S5. S8, in A preset number of candidate solutions are selected from the non-dominated solution set and input into the CFD solver. The isentropic efficiency and pressure ratio of each candidate solution are calculated. The samples whose isentropic efficiency and pressure ratio both meet the design requirements are selected as the final sample set.

[0008] Furthermore, step S4 further includes: S41. Calculate the comprehensive weight of each key variable based on the Sobol exponent of the total effect of isentropic efficiency and pressure ratio, and then use the vector formed by normalizing all comprehensive weights as the sensitivity. S42. Generate an initial population using a sensitivity-guided Latin hypercube sampling strategy within the design space of key variables; input individuals from the population into the trained surrogate model and calculate the objective function value for each individual.

[0009] Furthermore, methods for generating new populations based on individual crossover variation using the total effect Sobol index include: S51. Select the parent generation from the previous generation population, and use the sensitivity as the crossover probability to pair the parent individuals to generate the offspring population. S52. When performing individual mutations in the offspring population, determine whether to perform a mutation operation based on the mutation probability. For the i-th key variable of the mutated individual, apply an adaptive perturbation scale for mutation. The formula for calculating the adaptive perturbation scale is: in, is the adaptive perturbation scale for the i-th key variable; and These are the lower and upper limits of the variation scale, respectively; is the normalized composite weight of the i-th key variable; d is the total number of key variables; S53. Calculate the objective function value of individuals in the offspring population after the mutation operation using a surrogate model, perform non-dominated sorting on the offspring population, and merge the previous generation population and the offspring population into a new population.

[0010] Furthermore, step S1 further includes: S11. Obtain several design variables for the compressor blades, generate initial training samples within the design space formed by the upper and lower bounds of each design variable, and use a CFD solver to calculate the isentropic efficiency and pressure ratio of each initial sample. S12. Input the initial training samples and their corresponding isentropic efficiency and pressure ratio into multiple models respectively, and obtain two importance vectors of each model for each design variable in terms of isentropic efficiency and pressure ratio. S13. Normalize all importance vectors and use multiple models to construct the isentropic efficiency importance set and the pressure ratio importance set for the same design variable under isentropic efficiency and pressure ratio. S14. Based on the model's prediction accuracy, importance ranking stability, and interpretation inconsistency, calculate the reliability coefficient of each model for each design variable under isentropic efficiency and pressure ratio. S15. Based on the isentropic efficiency importance set and the pressure ratio importance set and their corresponding reliability coefficients, calculate the comprehensive impact of each design variable on isentropic efficiency and pressure ratio. S16. Construct a consistency correction term for the design variables based on the combined influence of isentropic efficiency and pressure ratio, and calculate the comprehensive physical prior term for each design variable using the prior coefficients of the design variables. S17. Calculate the weighted fusion score for each design variable based on the comprehensive influence of the design variables on the isentropic efficiency and pressure ratio, as well as the consistency correction term and the comprehensive physical prior term. S18. Normalize all weighted fusion scores to obtain the final score, and then select the design variables that meet the set conditions as key variables.

[0011] Furthermore, the formula for calculating the reliability coefficient is as follows: in, Let be the reliability coefficient of the m-th model under the objective y, where y takes the value of . and , and These are isentropic efficiency and pressure ratio, respectively. , and These represent the prediction accuracy, importance ranking stability, and interpretation inconsistency of the m-th model under the target y, respectively. The weighting coefficients for the stability of importance ranking; Weighting coefficients to explain inconsistencies.

[0012] Furthermore, the expression for calculating the combined impact of each design variable on isentropic efficiency and pressure ratio is as follows: [ ];[ ] [ ], [ ] in, and These represent the combined impact of the i-th design variable on isentropic efficiency and pressure ratio, respectively. and These are the dynamic weights of the m-th model under isentropic efficiency and pressure ratio, respectively; and These are the normalized parameters of the importance vector of the m-th model for the i-th design variable in terms of isentropic efficiency and pressure ratio, respectively. Let m be the dynamic weights of model m for target y, where y takes the value of and , and These are isentropic efficiency and pressure ratio, respectively. Let be the reliability coefficient of model m for target y.

[0013] Furthermore, the expression for the consistency correction term of the design variables is: , in, and These are the consistency correction term and the bi-objective consistency coefficient for the i-th design variable, respectively. and These are the changes in isentropic efficiency and pressure ratio after the qth perturbation of the i-th design variable, respectively. It is a very small positive number; This represents the total number of disturbances; The expression for the comprehensive physical prior terms of the design variables is: in, For the i-th design variable, the comprehensive physical prior term is given. The prior correlation between the i-th design variable and the isoentropy efficiency-related loss mechanism; The degree of prior correlation between the i-th design variable and the pressure ratio, either the work capacity or the diffusion capacity. The target preference coefficient; The expression for the weighted fusion score is: , in, The weighted fusion score for the i-th design variable; For isentropic efficiency channel weights; For pressure ratio channel weights; This is the consistency correction coefficient for the two objectives; For physical prior correction coefficients.

[0014] Furthermore, methods for determining whether the proxy model needs to be updated include: S51. Determine the current iteration number. Does it meet the requirements? If yes, proceed to step S52; otherwise, do not update the proxy model. This represents the total number of iterations. The modulo operation represents the remainder after dividing two integers; S52. Select individuals that meet the preset conditions from the new population, calculate their isentropic efficiency and pressure ratio, add them to the training set, and execute step S3 to update the model. The method for selecting a predetermined number of candidate solutions in the non-dominated solution set is as follows: k-means clustering is used to select candidate solutions from the non-dominated solutions, and the samples with the highest entropy efficiency and the highest pressure ratio in the candidate solutions and the non-dominated solutions are taken as sample candidate solutions.

[0015] Furthermore, the setting condition is: sort the final scores of all design variables in descending order, and select the top K design variables as key variables; Alternatively, select a threshold that represents the cumulative importance percentage. The design variables are used as key variables; Alternatively, select design variables whose final scores are greater than or equal to the preset scores as key variables; Alternatively, an inflection point detection method can be used to identify the point where the rapid decline transitions to a gradual decline in the curves plotted from all the final scores, and the design variables preceding this point can be used as key variables.

[0016] Furthermore, the formula for calculating the total effect Sobol index is as follows: in, For the i-th key variable The Sobol exponent represents the total effect on target y, where y takes the value of and , and These are isentropic efficiency and pressure ratio, respectively. For proxy model samples based on target y The output; To determine the impact of the i-th key variable after fixing its influence, for the set of key variables... The variance operator calculated based on the changes in the values; Let x be the mathematical expectation operator for the sample x, representing the averaging of the surrogate model output under the design space or sample distribution; This is the variance operator, used to characterize the overall volatility of the output response of the surrogate model; To exclude the i-th key variable The set of variables consisting of all other key variables besides the one mentioned above.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) In view of the problem that traditional variable screening methods are not stable under high-dimensional, small-sample, and strongly coupled conditions, this invention proposes a weighted fusion variable screening method with multi-model integration. It can robustly identify key design variables that have a significant impact on performance indicators such as isoentropy efficiency and pressure ratio when the proxy model has not yet fully converged in the early stage of optimization, thus providing a reliable basis for subsequent dimensionality reduction modeling and optimization search.

[0018] (2) The present invention uses a surrogate model to approximate the complex nonlinear response in the high-dimensional design space, which can take into account the model accuracy, computational efficiency and numerical stability. Compared with the traditional surrogate method that relies on a large number of samples, it is more suitable for application scenarios where high-fidelity samples are costly and budget is strictly limited in the aerodynamic optimization of compressor blades.

[0019] (3) Based on the surrogate model, this invention further calculates the global sensitivity index of Sobol, especially the total effect index, and uses it to guide the initial sampling, mutation scale allocation and cross information transmission in the evolutionary optimization process. This enables the search process to focus more on the key dimensions that contribute more to the target response, while retaining the necessary global exploration capability. Therefore, it can effectively improve the search efficiency and optimization convergence performance in the high-dimensional decision space.

[0020] (4) This invention organically combines variable selection, surrogate modeling, Sobol global sensitivity analysis and non-dominated ranking to form an integrated optimization framework suitable for high-dimensional multi-objective optimization of compressor blades. This framework can obtain better Pareto front approximation results under a finite high-fidelity evaluation budget, and shows good comprehensive advantages in terms of convergence, solution set distribution and overall operating efficiency.

[0021] (5) The method of the present invention has strong engineering adaptability and scalability. It is not only applicable to the aerodynamic optimization problem of compressor blades with isentropic efficiency and pressure ratio as the target, but can also be extended to other turbomachinery optimization design tasks with high-dimensional, expensive, multi-objective and strongly coupled characteristics. Attached Figure Description

[0022] Figure 1 This is a flowchart of a high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance.

[0023] Figure 2 The final optimized Pareto front plot of the compressor rotor37 blade is shown in the comparison of the 197-point 7-dimensional 2-objective with FFD neural network + NSGA-II, sparse grid unweighted guided NSGA-II, and 1197-point FFD neural network + NSGA-II. Detailed Implementation

[0024] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0025] refer to Figure 1 , Figure 1 A flowchart of a high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance is shown; Figure 1 As shown, the method S includes steps S1 to S8.

[0026] In step S1, several design variables of the compressor blade are obtained, and multiple models are used to reduce the dimensionality of the compressor blade design variables, and select several key variables related to isentropic efficiency and pressure ratio. In one embodiment of the present invention, step S1 further includes: S11. Obtain several design variables for the compressor blades. Generate initial training samples using the Latin hypercube sampling method within the design space formed by the upper and lower bounds of each design variable. Calculate the isentropic efficiency and pressure ratio of each initial sample using a CFD solver. The design variables include local load distribution of the blade profile, leading / tailing edge parameters, sweep, thickness distribution, flow near the endwall, separation and secondary flow related variables, camber, installation angle, consistency, diffusion degree, and load distribution in the blade height direction.

[0027] For d-dimensional design variables, the initial sample size is preferably chosen to be... More preferably about 5d, so as to balance space filling and stability of subsequent variable selection model training under small sample conditions.

[0028] S12. Input the initial training samples and their corresponding isentropic efficiency and pressure ratio into various models respectively, and obtain two importance vectors for each model on each design variable in terms of isentropic efficiency and pressure ratio. This scheme preferentially selects multiple linear regression, random forest model, XGBoost model, and Permutation Importance (ranking importance). For these four models, two are set for each: one for determining the importance vector of isentropic efficiency, whose input is the initial training samples and their corresponding isentropic efficiency; and the other for determining the importance vector of pressure ratio, whose input is the initial training samples and their corresponding pressure ratio. The comparison of the four models used in this scheme is shown in Table 1.

[0029] Table 1 Comparison of the four models Importance vector is , [ ],in: When m=1 , is the absolute value of the standardized regression coefficient of the i-th variable in the multiple linear regression model established for the target y, or the non-negative importance value after VIF correction; When m=2 This represents the average decrease in impurity caused by node splitting in the random forest model. When m=3 This represents the cumulative gain value corresponding to this variable in the XGBoost model; When m=4 This is the predicted performance degradation of the model after random permutation of the i-th variable (Permutation Importance).

[0030] S13. Normalize all importance vectors: in, d is the normalization parameter for the importance vector of the i-th design variable to the target y of the m-th model; d is the total number of design variables; To prevent extremely small positive numbers with a denominator of zero.

[0031] Multiple models are used to construct the isentropic efficiency importance set and the pressure ratio importance set for the normalized parameters of the same design variable under isentropic efficiency and pressure ratio: [ ];[ ], The four models represent the isentropic efficiency of the i-th design variable. The normalization parameter of the importance vector on; The four models represent the application of the i-th design variable in pressure ratio. The normalization parameter of the importance vector on the vector.

[0032] S14. Based on the model's prediction accuracy, importance ranking, stability, and interpretation inconsistency, calculate the reliability coefficient of each model for each design variable under isentropic efficiency and pressure ratio: in, Let be the reliability coefficient of the m-th model under the objective y, where y takes the value of . and , and These are isentropic efficiency and pressure ratio, respectively. , and These represent the prediction accuracy, importance ranking stability, and interpretation inconsistency of the m-th model under the target y, respectively. The weighting coefficients for the stability of importance ranking; Weighting coefficients to explain inconsistencies.

[0033] S15. Based on the isentropic efficiency importance set and the pressure ratio importance set, and their corresponding reliability coefficients, calculate the comprehensive impact of each design variable on isentropic efficiency and pressure ratio: [ ];[ ] [ ], [ ] in, and These represent the combined impact of the i-th design variable on isentropic efficiency and pressure ratio, respectively. and These are the dynamic weights of the m-th model under isentropic efficiency and pressure ratio, respectively; and These are the normalized parameters of the importance vector of the m-th model for the i-th design variable in terms of isentropic efficiency and pressure ratio, respectively. Let m be the dynamic weights of model m for target y, where y takes the value of and , and These are isentropic efficiency and pressure ratio, respectively. Let be the reliability coefficient of model m for target y.

[0034] S16. Construct a consistency correction term for the design variables based on the combined influence of isentropic efficiency and pressure ratio: , in, and These are the consistency correction term and the bi-objective consistency coefficient for the i-th design variable, respectively. and These are the changes in isentropic efficiency and pressure ratio after the qth perturbation of the i-th design variable, respectively. It is a very small positive number; This represents the total number of disturbances.

[0035] The comprehensive physical prior term for each design variable is calculated using its prior coefficients: in, For the i-th design variable, the comprehensive physical prior term is given. The prior correlation between the i-th design variable and the isoentropy efficiency-related loss mechanism; The degree of prior correlation between the i-th design variable and the pressure ratio, either the work capacity or the diffusion capacity. The target preference coefficient; S17. Based on the combined influence of design variables on isentropic efficiency and pressure ratio, as well as the consistency correction term and the comprehensive physical prior term, calculate the weighted fusion score for each design variable: , in, The weighted fusion score for the i-th design variable; For isentropic efficiency channel weights; For pressure ratio channel weights; This is the consistency correction coefficient for the two objectives; For physical prior correction coefficients.

[0036] S18. Normalize all weighted fusion scores to obtain the final score, and then select the design variables whose final scores meet the set conditions as key variables. The set conditions are: sort the final scores of all design variables in descending order, and select the top K design variables as key variables; Alternatively, select a threshold that represents the cumulative importance percentage. The design variables are used as key variables; Alternatively, select design variables whose final scores are greater than or equal to the preset scores as key variables; Alternatively, an inflection point detection method can be used to identify the point where the rapid decline transitions to a gradual decline in the curves plotted from all the final scores, and the design variables preceding this point can be used as key variables.

[0037] In step S2, several samples are generated within the design space of the key variables. The isentropic efficiency and pressure ratio of the samples are calculated using a CDF solver, and the samples and their corresponding isentropic efficiency and pressure ratio are used to form a training set. Preferably, the initial training samples are generated using the Latin hypercube sampling method within the design space formed by the upper and lower bounds of the key variables. The training set here can be subdivided into two parts: a training set consisting of the samples and their corresponding isentropic efficiency, and a training set consisting of the samples and their corresponding pressure ratio.

[0038] In step S3, the surrogate model is trained using the training set, and the total effect Sobol exponent of the isentropic efficiency and pressure ratio of each key variable is calculated based on the output of the surrogate model to the sample. In this scheme, the surrogate model is preferably a sparse grid surrogate model, and two are set up. One is trained to predict the isentropic efficiency, and the other is trained to predict the pressure ratio.

[0039] In implementation, the preferred formula for calculating the Sobol index of the total effect in this scheme is: in, For the i-th key variable The Sobol exponent represents the total effect on target y, where y takes the value of and , and These are isentropic efficiency and pressure ratio, respectively. For proxy model samples based on target y The output; To determine the impact of the i-th key variable after fixing its influence, for the set of key variables... The variance operator calculated based on the changes in the values; Let x be the mathematical expectation operator for the sample x, representing the averaging of the surrogate model output under the design space or sample distribution; This is the variance operator, used to characterize the overall volatility of the output response of the surrogate model; To exclude the i-th key variable The set of variables consisting of all other key variables besides the one mentioned above.

[0040] In step S4, based on the total effect Sobol index, the initial population is generated within the design space of the key variables: S41. Calculate the comprehensive weight of each key variable based on the Sobol exponent of the total effect of isentropic efficiency and pressure ratio, and then use the vector formed by normalizing all comprehensive weights as the sensitivity. S42. Generate an initial population using a sensitivity-guided Latin hypercube sampling strategy within the design space of key variables; input individuals from the population into a trained surrogate model, and utilize the surrogate model... Calculate population Objective function values ​​for each individual: in, and These represent the isentropic efficiency and pressure ratio predicted by the surrogate model, respectively. For transpose; Then the population Perform a non-dominated sort and calculate the crowding distance.

[0041] In step S5, a new population is generated by individual crossover mutation based on the total effect Sobol index. Then it is determined whether the surrogate model needs to be updated. If so, the surrogate model is updated and the process proceeds to step S6; otherwise, the process proceeds directly to step S6. In one embodiment of the present invention, a method for generating a new population based on individual crossover variation using the total effect Sobol index includes: S51. Select the parent generation from the previous generation population, and use the sensitivity as the crossover probability to pair the parent individuals to generate the offspring population. S52. When performing individual mutations in the offspring population, determine whether to perform a mutation operation based on the mutation probability. For the i-th key variable of the mutated individual, apply an adaptive perturbation scale for mutation. The formula for calculating the adaptive perturbation scale is: in, is the adaptive perturbation scale for the i-th key variable; and These are the lower and upper limits of the variation scale, respectively; is the normalized composite weight of the i-th key variable; d is the total number of key variables; S53. Calculate the objective function value of individuals in the offspring population after the mutation operation using a surrogate model, perform non-dominated sorting on the offspring population, and merge the previous generation population and the offspring population into a new population.

[0042] During implementation, this solution preferentially uses the following methods to determine whether the proxy model needs to be updated: S51. Determine the current iteration number. Does it meet the requirements? If yes, proceed to step S52; otherwise, do not update the proxy model. This represents the total number of iterations. S52. Select individuals that meet the preset conditions from the new population, calculate their isentropic efficiency and pressure ratio, add them to the training set, and execute step S3 to update the model. The preset conditions preferably include excellent individuals in the current non-dominated frontier and individuals that are relatively dispersed in the target space, so as to take into account both frontier convergence and solution set diversity.

[0043] This approach improves the prediction accuracy of the surrogate model within the current search area by retraining or incrementally updating the surrogate model.

[0044] In step S6, a surrogate model is used to determine the objective function values ​​of individuals in the new population, and a non-dominated sort is performed on the new population to obtain the frontier set. A new generation of population is then constructed from the frontier set. The detailed implementation process of the latter half of step S6 is as follows: For new populations Perform a non-dominated sort to obtain the front set. Based on the NSGA-II elite retention strategy, a new generation of populations is constructed in descending order of frontier status. : initialization ,right Frontier set [ Check the front edge in sequence ; like[ ], then the entire frontier join in Otherwise, computational frontier Calculate the crowding distance of each individual and sort them in descending order of crowding distance, then select the top [number of individuals]. Individuals join until This terminates environmental selection in the current generation, resulting in a new generation of population. .

[0045] In step S7, it is determined whether the current iteration count has reached the total number of iterations. If so, proceed to step S8; otherwise, return to step S5. In step S8, A preset number of candidate solutions are selected from the non-dominated solution set and input into the CFD solver. The isentropic efficiency and pressure ratio of each candidate solution are calculated. The samples whose isentropic efficiency and pressure ratio both meet the design requirements are selected as the final sample set.

[0046] The method for selecting a predetermined number of candidate solutions in the non-dominated solution set is as follows: k-means clustering is used to select candidate solutions from the non-dominated solutions, and the samples with the highest entropy efficiency and the highest pressure ratio in the candidate solutions and the non-dominated solutions are taken as sample candidate solutions.

[0047] The effectiveness of the high-dimensional optimization method for compressor blades in this scheme is illustrated below with specific examples: First, under the condition that the 65 design variables are aimed at isentropic efficiency and pressure ratio, this scheme generates 1000 initial sample spaces through LHS sampling. Each sample contains 65 parameter values ​​and 2 target output values. The FFD surrogate model and NSGA-II optimization algorithm built into the Numeca software are compared.

[0048] Comparison Method 1: FFD surrogate model + NSGA-II surrogate model (197 samples); Comparison Method 2: FFD surrogate model + NSGA-II surrogate model (1197 samples, 100 additional iterations, 10 samples selected for addition each time); Comparison Method 3: The sparse mesh surrogate model described in this invention, but without calculating the global sensitivity of Sobol to guide NSGA-II optimization; The effectiveness of this invention is verified by comparing it with the above three methods.

[0049] After reducing the dimensionality of 65 design variables to 7 dimensions using the dimensionality reduction method proposed in this scheme (steps S11-S18), 197 initial sample spaces are generated through LHS sampling. Each sample contains 7 parameter values ​​and 2 target output values, serving as the initial spaces for comparison method 1 and comparison method 2. The actual output values ​​of the two targets are calculated using the 197 7-dimensional parameter design spaces generated by the sparse mesh proxy model, serving as the initial spaces for the method of this invention and comparison method 3.

[0050] Experimental tests were conducted using Nuemca aerodynamic simulation software. The final optimized Pareto front plot of the compressor Rotor37 blade was compared with that of the 197-point 7D 2D objective model using FFD neural network + NSGA-II, the NSGA-II model with sparse mesh unweighted guidance, and the 197-point FFD neural network + NSGA-II model. (See figure for details.) Figure 2As shown, the optimization results indicate that, without additional sample augmentation, the highest efficiency of the FCNN+NSGA-II method is 0.870203, corresponding to a compression ratio of 2.0206; the highest compression ratio is 2.0339, corresponding to an efficiency of 0.858324.

[0051] In contrast, the NSGA-II method based on the sparse mesh proxy model achieves an efficiency of 0.872421 and a pressure ratio of 2.0246 at the highest efficiency point, and a pressure ratio of 2.0337 and an efficiency of 0.858431 at the highest pressure ratio point.

[0052] After introducing the weighted guided NSGA-II strategy proposed in this invention, an efficiency of 0.872423 and a compression ratio of 2.0246 are obtained at the highest efficiency point; and a compression ratio of 2.0336 and an efficiency of 0.866145 are obtained at the highest compression ratio point. The results show that at the highest efficiency point, the sparse mesh method improves both efficiency and compression ratio compared to the FCNN method; at the highest compression ratio point, the weighted guided NSGA-II improves efficiency by approximately 0.9%, while the compression ratio changes very little, indicating that the weighted strategy can significantly improve efficiency while maintaining compression ratio performance.

[0053] To further analyze the performance of different methods under varying sample sizes, this scheme additionally conducted large-sample neural network optimization experiments. Specifically, during the FCNN optimization process, new design points were progressively selected from the Pareto front for CFD calculations and added to the sample library, resulting in a total of 1000 new sample points and ultimately forming a training dataset of 1197 samples. Compared with the optimization method of this invention with 197 samples, it can be found that at the point of highest efficiency, the performance of the large-sample FCNN model is only about 0.07%-0.08% higher than that of the 197-sample sparse grid model; while at the point of highest pressure ratio, although the pressure ratio increases by about 0.5%, the efficiency decreases by 1.7%. This indicates that while pursuing a higher pressure ratio, the neural network model may lead to a significant decrease in efficiency. From an engineering optimization perspective, this performance trade-off is not ideal.

[0054] Analysis shows that the proposed method can achieve better optimization results with the same amount of modeling space, and is no less effective than optimization methods that use more modeling space than those used in this invention.

Claims

1. A high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity-guided optimization, characterized in that, Including the following steps: S1. Obtain several design variables for the compressor blades, and use multiple models to reduce the dimensionality of the compressor blade design variables, and select several key variables related to isentropic efficiency and pressure ratio. S2. Generate several samples within the design space of the key variables, use the CDF solver to calculate the isentropic efficiency and pressure ratio of the samples, and use the samples and their corresponding isentropic efficiency and pressure ratio to form a training set. S3. Train the surrogate model using the training set, and calculate the total effect Sobol exponent of the isentropic efficiency and pressure ratio of each key variable based on the output of the surrogate model to the samples. S4. Based on the Sobol index of the total effect, guide the generation of the initial population within the design space of the key variables; S5. Generate a new population by performing individual crossover mutation based on the total effect Sobol index. Then determine whether the surrogate model needs to be updated. If so, update it and proceed to step S6; otherwise, proceed directly to step S6. S6. Use a surrogate model to determine the objective function values ​​of individuals in the new population, perform non-dominated sorting on the new population to obtain the frontier set, and construct a new generation population P from the frontier set. g ; S7. Determine whether the current iteration count has reached the total number of iterations. If yes, proceed to step S8; otherwise, return to step S5. S8, in P g A preset number of candidate solutions are selected from the non-dominated solution set and input into the CFD solver. The isentropic efficiency and pressure ratio of each candidate solution are calculated. The samples whose isentropic efficiency and pressure ratio both meet the design requirements are selected as the final sample set.

2. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 1, characterized in that, Step S4 further includes: S41. Calculate the comprehensive weight of each key variable based on the Sobol exponent of the total effect of isentropic efficiency and pressure ratio, and then use the vector formed by normalizing all comprehensive weights as the sensitivity. S42. Generate an initial population using a sensitivity-guided Latin hypercube sampling strategy within the design space of key variables; input individuals from the population into the trained surrogate model and calculate the objective function value for each individual.

3. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 2, characterized in that, Methods for generating new populations based on individual crossover variation using the total effect Sobol index include: S51. Select the parent generation from the previous generation population, and use the sensitivity as the crossover probability to pair the parent individuals to generate the offspring population. S52. When performing individual mutations in the offspring population, determine whether to perform a mutation operation based on the mutation probability. For the i-th key variable of the mutated individual, apply an adaptive perturbation scale for mutation. The formula for calculating the adaptive perturbation scale is: in, is the adaptive perturbation scale for the i-th key variable; and These are the lower and upper limits of the variation scale, respectively; is the normalized composite weight of the i-th key variable; d is the total number of key variables; S53. Calculate the objective function value of individuals in the offspring population after the mutation operation using a surrogate model, perform non-dominated sorting on the offspring population, and merge the previous generation population and the offspring population into a new population.

4. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 1, characterized in that, Step S1 further includes: S11. Obtain several design variables for the compressor blades, generate initial training samples within the design space formed by the upper and lower bounds of each design variable, and use a CFD solver to calculate the isentropic efficiency and pressure ratio of each initial sample. S12. Input the initial training samples and their corresponding isentropic efficiency and pressure ratio into multiple models respectively, and obtain two importance vectors of each model for each design variable in terms of isentropic efficiency and pressure ratio. S13. Normalize all importance vectors and use multiple models to construct the isentropic efficiency importance set and the pressure ratio importance set for the same design variable under isentropic efficiency and pressure ratio. S14. Based on the model's prediction accuracy, importance ranking stability, and interpretation inconsistency, calculate the reliability coefficient of each model for each design variable under isentropic efficiency and pressure ratio. S15. Based on the isentropic efficiency importance set and the pressure ratio importance set and their corresponding reliability coefficients, calculate the comprehensive impact of each design variable on isentropic efficiency and pressure ratio. S16. Construct a consistency correction term for the design variables based on the combined influence of isentropic efficiency and pressure ratio, and calculate the comprehensive physical prior term for each design variable using the prior coefficients of the design variables. S17. Calculate the weighted fusion score for each design variable based on the comprehensive influence of the design variables on the isentropic efficiency and pressure ratio, as well as the consistency correction term and the comprehensive physical prior term. S18. Normalize all weighted fusion scores to obtain the final score, and then select the design variables that meet the set conditions as key variables.

5. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 4, characterized in that, The formula for calculating the reliability coefficient is as follows: ； in, Let be the reliability coefficient of the m-th model under the objective y, where y takes the value of . and , and These are isentropic efficiency and pressure ratio, respectively. , and These represent the prediction accuracy, importance ranking stability, and interpretation inconsistency of the m-th model under the target y, respectively. The weighting coefficients for the stability of importance ranking; Weighting coefficients to explain inconsistencies; It is a very small positive number.

6. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 4, characterized in that, The expression for calculating the combined impact of each design variable on isentropic efficiency and pressure ratio is as follows: [ ]；[ ]； [ ]，[ ]； in, and These represent the combined impact of the i-th design variable on isentropic efficiency and pressure ratio, respectively. and These are the dynamic weights of the m-th model under isentropic efficiency and pressure ratio, respectively; and These are the normalized parameters of the importance vector of the m-th model for the i-th design variable in terms of isentropic efficiency and pressure ratio, respectively. Let m be the dynamic weights of model m for target y, where y takes the value of and , and These are isentropic efficiency and pressure ratio, respectively. Let be the reliability coefficient of model m for target y.

7. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 6, characterized in that, The expression for the consistency correction term for the design variables is: ， ； in, and These are the consistency correction term and the bi-objective consistency coefficient for the i-th design variable, respectively. and These are the changes in isentropic efficiency and pressure ratio after the qth perturbation of the i-th design variable, respectively. It is a very small positive number; This represents the total number of disturbances; The expression for the comprehensive physical prior terms of the design variables is: ； in, For the i-th design variable, the comprehensive physical prior term is given. The prior correlation between the i-th design variable and the isoentropy efficiency-related loss mechanism; The degree of prior correlation between the i-th design variable and the pressure ratio, either the work capacity or the diffusion capacity. The target preference coefficient; The expression for the weighted fusion score is: ， ； in, The weighted fusion score for the i-th design variable; For isentropic efficiency channel weights; For pressure ratio channel weights; This is the consistency correction coefficient for the two objectives; For physical prior correction coefficients.

8. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 1, characterized in that, Methods for determining whether a proxy model needs updating include: S51. Determine the current iteration number. Does it meet the requirements? If yes, proceed to step S52; otherwise, do not update the proxy model. This represents the total number of iterations. For modulo operation; S52. Select individuals that meet the preset conditions from the new population, calculate their isentropic efficiency and pressure ratio, add them to the training set, and execute step S3 to update the model. The method for selecting a predetermined number of candidate solutions in the non-dominated solution set is as follows: k-means clustering is used to select candidate solutions from the non-dominated solutions, and the samples with the highest entropy efficiency and the highest pressure ratio in the candidate solutions and non-dominated solutions are taken as sample candidate solutions.

9. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to claim 4, characterized in that, The set condition is: sort the final scores of all design variables in descending order, and select the top K design variables as key variables; Alternatively, select a threshold that represents the cumulative importance percentage. The design variables are used as key variables; Alternatively, select design variables whose final scores are greater than or equal to the preset scores as key variables; Alternatively, an inflection point detection method can be used to identify the point where the rapid decline transitions to a gradual decline in the curves plotted from all the final scores, and the design variables preceding this point can be used as key variables.

10. The high-dimensional optimization method for compressor blades based on multi-model dimensionality reduction and sensitivity guidance according to any one of claims 1-9, characterized in that, The formula for calculating the total effect Sobol index is as follows: ； in, For the i-th key variable The Sobol exponent represents the total effect on target y, where y takes the value of and , and These are isentropic efficiency and pressure ratio, respectively. For proxy model samples based on target y The output; To determine the impact of the i-th key variable after fixing its influence, for the set of key variables... The variance operator calculated based on the changes in the values; Let x be the mathematical expectation operator with respect to the sample x; For variance operators; To exclude the i-th key variable The set of variables consisting of all other key variables besides the one mentioned above.

Images