A method and system for adaptive optimization of compressor blade design variables

Abstract

The present invention discloses a method and system for adaptive optimization of compressor blade design variables, including: obtaining an initial sample of design variables based on the original blade, using an improved FFD parameterization method to obtain a deformed blade; constructing a hybrid proxy model based on a pre-screening strategy, using an improved differential evolution algorithm to perform global iterative optimization to obtain the optimal solution of this round of iteration; judging whether the conditions for exiting a large cycle are met, if so, exiting the large cycle, using the optimal blade, otherwise judging whether the conditions for adaptively expanding the boundaries of design variables are met, if not, performing the next step of judgment; otherwise, performing design variable boundary expansion to obtain a new solution, and then performing the next step of judgment: whether the conditions for adaptively increasing control vertices are met, if so, increasing control vertices, and then ending this round of large cycle, otherwise directly ending this round of large cycle. The present invention can adaptively optimize compressor blade design variables.

Description

Technical Field

[0001] The present invention relates to the technical field of compressor blade profile optimization, and in particular to a method and system for adaptively optimizing compressor blade profile design variables. Background Art

[0002] Since the optimization of compressor blades is a systematic project involving multiple technical links such as blade parameterization, optimization algorithm, optimization strategy, and optimization platform, methods to improve the optimization efficiency from each link have been developed, among which blade parameterization technology is one of the most core technical links. There are currently three main solutions to improve the efficiency of aerodynamic optimization from the perspective of parameterization: the first idea is to create a new parameterization method suitable for a specific application field, so that this parameterization has the advantages of low-dimensional characteristics and flexibility; the second idea is to adopt the "man in the loop" method, in which the designer grasps each link of the optimization process and tries to reduce the design space by means of variable screening, visualization, and manual definition of variable range; the third idea is to use machine learning and deep learning methods for dimensionality reduction. These three methods have their own characteristics. The first method can well describe the characteristics of a certain type of blade, but its adaptability is not wide; the second method enhances the flexibility of parameterization, but relies too much on the intervention and operation of the designer during the optimization process; the third method can automatically learn the dimensionality reduction law through data-driven methods, but the disadvantage is that it requires a large amount of data for training and is difficult to apply to small sample situations. Summary of the invention

[0003] The present invention provides a method and system for adaptively optimizing compressor blade design variables to solve the problems existing in the above-mentioned prior art. The technical solution is as follows:

[0004] On the one hand, a method for adaptive optimization of compressor blade design variables is provided, comprising:

[0005] S1. Based on the original blade profile, initial samples of several design variables are obtained, the deformed blade profile is obtained using the improved FFD parameterization method, and the actual aerodynamic performance of the deformed blade profile is calculated. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library;

[0006] S2. Determine the design variable boundaries based on all samples in the sample library, and build a hybrid agent model based on the pre-screening strategy based on the sample library, use the improved differential evolution algorithm to perform global iterative optimization, determine whether the iteration termination condition is met, and terminate the iteration if it is met, and obtain the optimal solution of the design variable in this round of iteration and the corresponding real aerodynamic performance;

[0007] S3: Determine whether the conditions for exiting the large loop are met. If so, exit the large loop and use the optimal solution. Get the optimal blade shape, otherwise determine the optimal solution Whether the conditions for adaptively expanding the design variable boundary are met, if not, proceed to the next step; otherwise, expand the design variable boundary and calculate the new solution after the design variable boundary expansion The real aerodynamic performance of the new solution and the corresponding real aerodynamic performance are added to the sample library as new samples, and then the next step of judgment is performed;

[0008] S4, making the next step of judging: whether the condition of adaptively adding control vertices is met, if so, adding control vertices, and then ending this round of large cycle and proceeding to the next round of large cycle, otherwise, directly ending this round of large cycle and proceeding to the next round of large cycle.

[0009] On the other hand, a compressor blade profile design variable adaptive optimization system is provided, the system comprising:

[0010] An initial sample acquisition module is used to obtain initial samples of several design variables based on the original blade profile, obtain the deformed blade profile using the improved FFD parameterization method, and calculate the actual aerodynamic performance of the deformed blade profile. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library;

[0011] The optimal solution acquisition module is used to determine the design variable boundaries based on all samples in the sample library, and to build a hybrid agent model based on the pre-screening strategy based on the sample library, and to use the improved differential evolution algorithm to perform global iterative optimization, to determine whether the iteration termination condition is met, and to terminate the iteration if it is met, to obtain the optimal solution of the design variable in this round of iteration. and the corresponding real aerodynamic performance;

[0012] The adaptive expansion design variable boundary module is used to determine whether the exit condition of the large cycle is met. If it is met, the large cycle is exited and the optimal solution is used. Get the optimal blade shape, otherwise determine the optimal solution Whether the conditions for adaptively expanding the design variable boundary are met, if not, proceed to the next step; otherwise, expand the design variable boundary and calculate the new solution after the design variable boundary expansion The real aerodynamic performance of the new solution and the corresponding real aerodynamic performance are added to the sample library as new samples, and then the next step of judgment is performed;

[0013] The module for adaptively adding control vertices is used to make the next step of judging whether the conditions for adaptively adding control vertices are met. If so, the control vertices are added, and then this round of large cycle is ended and the next round of large cycle is started. Otherwise, this round of large cycle is directly ended and the next round of large cycle is started.

[0014] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the above-mentioned compressor blade profile design variable adaptive optimization method.

[0015] On the other hand, 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 compressor blade profile design variable adaptive optimization method.

[0016] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0017] The present invention uses the control vertex normal offset, the control frame rotation angle and the control vertex density distribution coefficient of the FFD parameterized control frame as basic design variables, which are always involved in the optimization process. In the process of optimizing, the boundaries of the design variables are adaptively expanded and the control vertices are added, thus achieving good optimization effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0019] Figure 1 It is a flow chart of a method for adaptive optimization of compressor blade profile design variables provided by an embodiment of the present invention;

[0020] Figure 2 is a schematic diagram of an absolute coordinate system and a local coordinate system provided by an embodiment of the present invention;

[0021] Figure 3 It is a schematic diagram of updating the layout of design variables of the improved FFD parameterization method provided by an embodiment of the present invention;

[0022] Figure 4 It is a schematic diagram of controlling the normal movement of a vertex and the rotation angle of a control frame provided by an embodiment of the present invention;

[0023] Figure 5 This is a schematic diagram of achieving density control using an arithmetic coefficient method provided by an embodiment of the present invention;

[0024] Figure 6 This is a schematic diagram of achieving density control using a geometric coefficient method provided by an embodiment of the present invention;

[0025] Figure 7 is a schematic diagram of a proxy model-assisted evolutionary algorithm based on a pre-screening strategy provided by an embodiment of the present invention;

[0026] Figure 8 is a schematic diagram of a RBNN proxy model provided by an embodiment of the present invention;

[0027] Fig. 9 It is a full flow chart of adaptive optimization based on improved FFD parameterization method provided by an embodiment of the present invention;

[0028] Fig.10 This is a schematic diagram of a 5*4 control framework provided by an embodiment of the present invention;

[0029] Fig.11 It is a comparison diagram of the initial frame and the changed control frame orientation provided by an embodiment of the present invention;

[0030] Fig.12 This is a schematic diagram of an 8*3 control framework provided by an embodiment of the present invention;

[0031] Fig.13 This is a schematic diagram of a 4*3 control framework provided by an embodiment of the present invention;

[0032] Fig.14 It is a block diagram of a compressor blade profile design variable adaptive optimization system provided by an embodiment of the present invention;

[0033] Fig.15 It is a structural schematic diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0035] The embodiment of the present invention provides a method for adaptively optimizing compressor blade design variables, which can be implemented by an electronic device, which can be a terminal or a server. Figure 1 A flow chart of a compressor blade profile design variable adaptive optimization method is shown, and the processing flow of the method may include the following steps:

[0036] S1. Based on the original blade profile, initial samples of several design variables are obtained, the deformed blade profile is obtained using the improved FFD parameterization method, and the actual aerodynamic performance of the deformed blade profile is calculated. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library;

[0037] Optionally, the S1 specifically includes:

[0038] S11, using Latin hypercube sampling LHS to sample design variables, and obtaining initial samples of several design variables, each initial sample of design variables includes a set of design variables: control vertex normal offset of FFD parameterized control frame, control frame rotation inclination angle and control vertex density distribution coefficient, these three parts are basic design variables, and are always involved in the optimization process;

[0039] The basic idea of ​​the FFD parameterization method is to establish a control framework, put the object (the blade in the embodiment of the present invention) into the control framework, and establish a mapping relationship from the object to the control framework, such as Figure 2 As shown, the basic principle is to construct a local coordinate system in the control frame. , take a little As the origin of the local coordinate system, any point in the absolute coordinate system The coordinates in can be written as:

[0040]

[0041] In the formula , its value is as follows:

[0042]

[0043] Will The cross section in both directions is divided into l and m intervals, then the control vertices of the control frame It can be expressed as:

[0044]

[0045] Where i and j are natural numbers, so the absolute coordinates of any point on the blade surface are It can be expressed as:

[0046]

[0047] In the formula is the Bernstein polynomial basis function;

[0048] New control vertices can be created by changing The absolute coordinates of any point (s, t) on the blade surface can be determined by the following formula:

[0049]

[0050] In the formula is the new control vertex.

[0051] like Figure 3 As shown, the improved FFD parameterization method of the embodiment of the present invention is to use the control vertex normal offset of the FFD parameterized control frame, the control frame rotation inclination angle and the control vertex density distribution coefficient as basic design variables, which are always involved in the optimization process (including: control vertex normal offset, control frame rotation, control vertex density distribution control), and adaptively expand the design variable boundary and increase the control vertices in the optimization process (the embodiment of the present invention is to separately study the influence of the number of control vertices, control frame orientation, design variable range and density distribution on the optimization performance of the FFD parameterization method, and these studies are introduced in detail later, and then propose an improved FFD parameterization method that uses the control vertex normal offset, control frame rotation inclination angle and control vertex density distribution coefficient of the FFD parameterized control frame as basic design variables, which are always involved in the optimization process, and adaptively expand the design variable boundary and increase the control vertices in the optimization process). For example, for a 4 For the control framework of 3, the number of control vertices is 12. According to the existing FFD parameterization method, each control vertex has an offset in the x and y directions, and the number of design variables is 1. 22=24, that is, each group of design variables is 24-dimensional, and according to the improved FFD parameterization method of the embodiment of the present invention: each control vertex has a normal offset, 12 control vertices have 12 normal offsets, plus the control frame rotation angle and the control vertex density distribution coefficient, there are 14 design variables in total, that is, each group of design variables is 14-dimensional, which can effectively reduce the number of design variables, reduce the design space, and improve the optimization efficiency under the premise of ensuring that the design space structure is not degraded. Assume that the embodiment of the present invention uses the LHS method to sample 100 samples, that is, to generate 100 initial sample arrays (vectors) of 14-dimensional design variables, and further apply the improved FFD parameterization method, grid generation and flow field calculation program to obtain the corresponding 100 real aerodynamic performances. Each initial sample of the 14-dimensional design variable is combined with the corresponding real aerodynamic performance to form a 15-dimensional array, that is, a complete sample, and a total of 100 15-dimensional complete samples can be obtained.

[0052] S12, using the FFD parameterization method to control the specific layout update of the design variables consisting of the three parts, and obtaining several deformed blade profiles;

[0053] S13, according to the several deformed blades, distributed and parallel grid generation and CFD aerodynamic performance calculation are performed to obtain the actual aerodynamic performance of the several deformed blades, the initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library, the complete sample includes dimensional vector, =Number of control vertices + 2, the actual aerodynamic performance uses the loss coefficient after the airflow passes through the moving blades To characterize, define the following formula:

[0054] (1)

[0055] In the formula represents the relative static pressure at the moving blade inlet, , They represent the relative total pressure at the inlet and outlet of the moving blade respectively.

[0056] Alternatively, if Figure 4 As shown, the normal direction of the control vertex normal offset refers to the direction orthogonal to the long side of the control frame (the direction of the arrow in the figure);

[0057] The embodiment of the present invention limits the change of the control vertex in the direction parallel to the long side of the control frame, which can effectively reduce invalid space exploration and greatly improve the optimization efficiency; and the control frame rotation, density control and design variable boundary expansion can just make up for the loss of effective space caused by the lack of freedom of movement of the control vertex parallel to the long side of the control frame.

[0058] Since each design variable changes independently, in order to prevent the large normal offset of each control vertex from causing the control frame to cross, which makes it impossible to calculate the result during the flow field calculation, the embodiment of the present invention sets the normal offset of the control vertex to be within the range of -3.0~3.0mm. However, since the size of the control frame is constant, as the frame equal fraction increases, the distance between two adjacent control vertices becomes smaller and smaller, and the control frame will still cross in the range of -3.0~3.0mm, and the blade will not converge during the optimization process, affecting the direction of optimization. The embodiment of the present invention studies the inlet and outlet flow rates obtained after flow field calculation and finds that the inlet and outlet flow rates of the convergent blade type are very small, while the inlet and outlet flow rates of the non-convergent blade type are relatively large. For this reason, the embodiment of the present invention designs a blade convergence judgment program DECIDE to calculate and judge the inlet and outlet flow rates obtained by flow field calculation. If the absolute value of the difference between the two is less than 0.1, the original loss coefficient is retained. If the absolute value of the difference between the two is greater than 0.1, the loss coefficient is taken as 100 (that is, the loss coefficient is assigned a larger value to make the direction of the optimization search away from the non-convergence direction) to reduce the number of non-convergence results, so that the optimization can be better carried out in the right direction.

[0059] As the control frame rotates the inclination As the normal movement direction of the control vertex changes, the relationship between the two is as follows:

[0060] (2)

[0061] in, Refers to the control vertex exist Directional deviation, Refers to the control vertex exist Directional deviation, It is the control vertex The normal offset of Direction and The offset in the direction is taken as the basic design variable, and the rotation angle of the control frame and the density distribution coefficient of the control vertex are added as basic design variables (this can effectively reduce the number of design variables, narrow the design space, and improve the optimization efficiency while ensuring that the design space structure is not degraded);

[0062] Prior knowledge is incorporated into the control of the vertex density distribution coefficient: the curvature of the leading and trailing edges of the blade is large, while the curvature of the middle part of the leaf is small. Therefore, the density control adopts a method of dense at both ends and sparse in the middle in the horizontal direction of the control frame, and a uniform distribution method in the vertical direction of the control frame. The quantitative control of the vertex density distribution coefficient adopts two methods: arithmetic coefficients or geometric coefficients, and the distance from the two ends to the middle increases in arithmetic or geometric increments.

[0063] The arithmetic coefficient method is used to achieve density control, such as Figure 5 As shown in the figure, there are eight control vertices in the x direction, and the distances from the two ends to the middle are increased by the same distance in sequence to obtain an 8*3 control frame with dense control vertices at both ends and sparse in the middle in the x direction. The increased distance (i.e., the arithmetic coefficient) is set to p, and the distances of the 7 segments from the front to the back are a, a+p, a+2p, a+3p, a+2p, a+p, a. The coordinates of each point can be calculated according to the arithmetic coefficient and the number of points in the long side direction. By changing the size of the arithmetic coefficient, the density of the frame in the long side direction can be controlled.

[0064] The geometric coefficient method is used to achieve density control, such as Figure 6 As shown in the figure, the control vertices of the long side direction of the 7*3 control frame are distributed in geometric proportion. Since the size of the control frame is fixed, a geometric coefficient k can be set, which represents the increase multiple of the distance from the two ends to the middle of the two adjacent sections, so that the intervals are a, ka, k respectively. 2 a.k 2 a, ka, a, the coordinates of each point can be calculated according to the geometric coefficient and the number of points in the long side direction. By changing the size of the geometric coefficient, the density of the frame in the long side direction can be controlled.

[0065] S2. Determine the design variable boundaries based on all samples in the sample library, and build a hybrid agent model based on the pre-screening strategy based on the sample library, use the improved differential evolution algorithm to perform global iterative optimization, determine whether the iteration termination condition is met, and terminate the iteration if it is met, and obtain the optimal solution of the design variable in this round of iteration and the corresponding real aerodynamic performance;

[0066] Optionally, determining the design variable boundaries according to all samples in the sample library in S2 specifically includes:

[0067] The lower and upper bounds of each design variable are given by and Determine, among which and For all samples The minimum and maximum values ​​of the dimension elements are as follows:

[0068] (3)

[0069] in, Refers to all samples The minimum value of the dimension element, Refers to all samples The maximum value of the dimension element, It refers to the first sample Dimensional elements, The second sample Dimensional elements, The third sample Dimensional elements, It refers to the n-1th sample Dimensional elements, It refers to the nth sample. Dimensional elements, refers to a dimension of each sample, is the dimension of each sample, and n is the number of samples in the sample library.

[0070] Optionally, the hybrid proxy model based on the pre-screening strategy is constructed based on the sample library in S2 (the hybrid proxy model based on the pre-screening strategy of the embodiment of the present invention uses a proxy model assisted evolution algorithm based on the pre-screening strategy (Pre-screen Surrogate Model Assistant Differential Evolution, Pre-SADE), Pre-SADE is based on the differential evolution algorithm, and uses a pre-screening strategy to reduce the number of real evaluations of each generation. After obtaining a new generation of populations, the hybrid proxy model is first used for evaluation, and the population is sorted according to the evaluation results, and some samples of real evaluation are selected to update the hybrid proxy model. The proportion of real evaluation Refers to the proportion of real evaluation samples to the total number of samples in each iteration. Sample calculation uses a distributed parallel computing module. After screening out the samples to be calculated, the candidate samples are placed in the task pool, and the management program automatically allocates computing resources for parallel calculation. Each local parallel node independently calculates 1 candidate sample in the task pool. After the calculation is completed, the result is placed in the result pool until the task pool is empty. Each node contains multiple parallel cores). The improved differential evolution algorithm is used for global optimization to determine whether the iteration termination condition is met. If it is met, the iteration is exited to obtain the optimal solution of the design variables in this round of iteration. And the corresponding real aerodynamic performance, including:

[0071] S21, using the initial sample of the design variables as the first generation population of the improved differential evolution algorithm, and using the loss coefficient representing the actual aerodynamic performance As the objective function, the hybrid agent model based on the pre-screening strategy is trained. The hybrid agent model is a hybrid agent model composed of a polynomial regression model, a Kriging model, and a radial basis neural network model. After the training is completed, the first generation population and the value of its corresponding objective function are returned to the differential evolution algorithm. After mutation, crossover, and selection, a new generation of population to be evaluated is obtained, such as Figure 7 As shown;

[0072] Polynomial Regression (PR) model of the embodiment of the present invention:

[0073] According to Taylor's formula, any function can be expanded into a A polynomial can be used to fit any nonlinear function. When the distribution law within the data set meets certain characteristics, a functional relationship between a single dependent variable and a single or multiple independent variables can be established. When the data set to be fitted is nonlinear, linear regression cannot meet the accuracy requirements, so a polynomial regression model is required. Its mathematical expression is as follows:

[0074]

[0075] in are the polynomial coefficients, The degree of the polynomial is expressed as the total error of the polynomial regression using the mean square error:

[0076]

[0077] in, is the fitting value of the current point, Represents the true value of the current point. The calculation of polynomial regression is to solve a set of polynomial coefficients Make At least, a quadratic polynomial model is selected in the embodiment of the present invention.

[0078] Kriging Model (KR) of the embodiment of the present invention:

[0079] The Kriging model can be viewed as the sum of a global model and local deviations:

[0080]

[0081] in, As a known function, is the global model of the original function, is a Gaussian random function with zero mean and non-zero covariance, representing the local deviation from the global model,

[0082] The covariance of is expressed as:

[0083]

[0084] in is the correlation function between any two samples, The scale is The relationship matrix of , usually using Gaussian correlation function, is in the form of:

[0085]

[0086] in is the unknown correlation coefficient, and is the sample point and No. components, therefore, is an unknown parameter and Function:

[0087]

[0088] in Is untested and sampling data The correlation vector between them is in the following form:

[0089]

[0090] It is estimated by the following formula:

[0091]

[0092] variance The form is:

[0093]

[0094] For fitting the Kriging model, maximum likelihood estimation can be used:

[0095]

[0096] in and Both The function is calculated After that, the establishment of the Kriging model is completed. The Kriging model can obtain the estimated confidence interval at a relatively low computational cost. When calculating the model output, the inverse matrix needs to be solved. When the dimension becomes higher, the computational cost will increase significantly. The embodiment of the present invention selects the Kriging model based on the Gaussian process.

[0097] The radial basis neural network model (RBNN) of the embodiment of the present invention:

[0098] The radial basis neural network (RBNN) has the same structure as the BP neural network (Back Propagation Neural Network, BPNN) and is a common alternative to BPNN, requiring less computational cost and converging faster. RBNN consists of an input layer, a hidden layer, and an output layer, all of which are fully connected layers. That is, each input variable is assigned to a node in the input layer and is passed directly to the hidden layer without weight. The activation function of the hidden node is the radial basis function (RBF). The RBNN hidden layer can be multi-layer, with a single layer having multiple hidden nodes, and each hidden layer is connected in a feedforward parallel architecture. The output layer is a simple weighted addition of the upper layer nodes. Figure 8 The basic framework of RBNN is given.

[0099] Optimize RBF parameters during network training. RBNN training speed is faster than BPNN. Since the network structure is simple, the only parameter that can be modified is the number of neurons in the hidden layer. Therefore, RBF is easy to optimize the network structure. The embodiment of the present invention selects an RBF network with 1 hidden layer.

[0100] Hybrid agent model of the embodiment of the present invention The model consists of 3 sub-agent models , , The weighted sum is of the form:

[0101]

[0102] in, It is (1 ≤ ≤ 3) The weight of the proxy model is defined as:

[0103]

[0104] in Indicates The root mean square error of the (1≤i≤3) proxy models is calculated. In view of the low accuracy and easy overfitting of a single proxy model, the embodiment of the present invention uses a hybrid proxy model to ensure the accuracy of the prediction results. At the same time, the hybrid proxy model is only used for pre-screening and does not directly participate in the calculation of the fitness value (objective function) during the optimization process, so as to ensure the authenticity of the optimization results.

[0105] S22, using the hybrid proxy model, pre-evaluating the new generation population to reduce the number of real evaluations of each generation, sorting the new generation population according to the pre-evaluated objective function value, and screening the previous The individuals are evaluated for real CFD aerodynamic performance, and the real CFD aerodynamic performance evaluation results are used as the objective function values. The remaining individuals still use the results of the hybrid proxy model pre-evaluation as the objective function values. After all the objective function values ​​of the current generation population are obtained, the differential evolution algorithm is returned;

[0106] S23, the current generation of real evaluation The individuals and their objective function values ​​are added as new samples to the sample library to update the sample library. Based on the updated sample library, the hybrid proxy model is retrained to update the hybrid proxy model to achieve higher prediction accuracy. As the sample library size increases, the computing resources required to train the hybrid proxy model increase rapidly. Therefore, the total number of sample libraries is limited to After the sample library reaches the upper limit, the newly added samples will randomly replace the initial samples to ensure the continuous updating of the sample library and the hybrid agent model. After updating the hybrid agent model, the new generation of population and the value of its corresponding objective function are returned to the differential evolution algorithm. After mutation, crossover and selection, the new generation of population to be evaluated is obtained.

[0107] S24: Determine whether the iteration termination condition is met. If not, enter the next generation iteration. If it is met, terminate the iteration and export the sample library. The samples in the sample library are all real evaluation samples. The optimal solution is obtained in the sample library. And the corresponding actual aerodynamic performance, that is, the optimal objective function value, such as Fig. 9 shown.

[0108] S3: Determine whether the conditions for exiting the large loop are met. If so, exit the large loop and use the optimal solution. Get the optimal blade shape, otherwise determine the optimal solution Whether the conditions for adaptively expanding the design variable boundary are met, if not, proceed to the next step; otherwise, expand the design variable boundary and calculate the new solution after the design variable boundary expansion The real aerodynamic performance of the new solution and the corresponding real aerodynamic performance are added to the sample library as new samples, and then the next step of judgment is performed;

[0109] Optionally, the optimal solution is determined in S3 Whether the boundary conditions of the adaptive expansion design variables are met, including:

[0110] The conditions for adaptively expanding the design variable boundaries are Some dimension elements of reach the upper or lower boundary, and the expansion is as follows:

[0111] (4)

[0112] in, is the design variable Reform elements, yes No. The minimum value of the dimension element, yes No. The maximum value of the dimension element, is the design variable Reform elements, yes No. The maximum value of the dimension element, yes No. The minimum value of the dimension element. Coef is determined by the degree of improvement of the performance of the optimal solution in each iteration. When the degree of improvement in this iteration is large, coef takes a larger value, otherwise it takes a smaller value. If the performance fails to improve, the boundary expansion is not performed. The formula of coef is as follows:

[0113] (5)

[0114] in, and is the performance of the optimal solution of this iteration and the previous iteration, refers to the optimal performance of the first iteration, It refers to the performance of the optimal solution in the initial sample of design variables.

[0115] S4, making the next step of judging: whether the condition of adaptively adding control vertices is met, if so, adding control vertices, and then ending this round of large cycle and proceeding to the next round of large cycle, otherwise, directly ending this round of large cycle and proceeding to the next round of large cycle.

[0116] Optionally, the next step of judging in S4: whether the condition for adaptively adding control vertices is met, and if so, adding control vertices, specifically includes:

[0117] The judgment conditions for adaptively adding control vertices are as follows:

[0118] (6)

[0119] in, is a given threshold, is the improvement efficiency of optimal performance, and the calculation formula is as follows:

[0120] - (7)

[0121] in, and is the optimal solution performance before this iteration and t iterations;

[0122] Control vertices cannot be added frequently, otherwise the design space will become too large and it will be difficult to find the optimal solution. Therefore, in the embodiment of the present invention, control vertices are added every several generations (here, t generations).

[0123] If the conditions are met, the procedure of adding control vertices parametrically is started: one point is added to each row in the horizontal direction of the control frame each time, and the added points are added according to the density distribution coefficient of the control vertices.

[0124] Increasing the number of control vertices will not change the shape of the blade, nor will it require a new calculation of the corresponding actual aerodynamic performance, but it will change the number of design variables in the next large cycle.

[0125] The following is a detailed introduction to the separate studies conducted by the embodiments of the present invention on the influence of the number of control vertices, the orientation of the control framework, the range of design variables and the density distribution on the optimization performance of the FFD parameterization method:

[0126] 1) The impact of FFD control vertex number on optimization performance

[0127] The embodiment of the present invention studies the influence of the number of control vertices on the aerodynamic performance of a two-dimensional compressor blade. The change of the number of control vertices can be changed by changing the equal fractions of the control frame in the x and y directions. For a control frame with 20 control vertices, such as Fig.10 As shown, the control frame is divided into 4 equal parts in the x direction and 3 equal parts in the y direction, thus forming a 5*4 control frame. The embodiment of the present invention starts with the optimization of the 4*3 control frame with 12 control vertices, the design variable range is set to -3.0~3.0mm, and the number of control vertices is continuously increased. The influence of the number of control vertices on the aerodynamic performance is analyzed through the obtained results, and the loss coefficient obtained by optimization is shown in Table 1:

[0128] Table 1. Comparison of control vertex number optimization loss coefficients

[0129]

[0130] Comparing the loss coefficients of Opt1, Opt2, Opt3 and Opt4 in Table 1, the loss coefficient of Opt2 is reduced by 4.3% compared with the loss coefficient of Opt1, the loss coefficient of Opt3 is reduced by 3.0% compared with Opt2, and the loss coefficient of Opt4 is reduced by 4.3% compared with Opt3. It can be seen that as the number of control vertices of the design variable increases, the optimized blade loss coefficient gradually decreases, and the optimization effect is better.

[0131] 2) The influence of FFD control frame orientation on optimization performance

[0132] The change of the control vertex in the chord direction and the direction perpendicular to the chord direction has a great influence on the deformation of the two-dimensional blade profile. In the embodiment of the present invention, the initial orientation of the control frame is changed so that the rectangular frame is parallel to the chord of the two-dimensional blade profile, such as Fig.11 As shown in Figure 2, the influence of the control frame orientation on the aerodynamic performance of the compressor blade is studied. Fig.11As shown in the figure, a new control framework is constructed, the maximum and minimum values ​​of the framework are determined by the maximum and minimum values ​​of the initial two-dimensional blade profile x and y, and the specific coordinates of each equally divided point are calculated according to the slope of the initial two-dimensional blade profile chord. The embodiment of the present invention starts with the optimization of the control framework of 12 control vertices of 4*3, and the design variable range is set to -3.0~3.0mm. The number of control vertices is continuously increased, and the obtained results are compared and analyzed with the optimization results of different control vertices of the original framework (Table 1), and the optimized loss coefficient comparison is shown in Table 2:

[0133] Table 2. Comparison of frame orientation optimization loss coefficients

[0134] (a) Initial framework

[0135]

[0136] (b) Chordal frame

[0137]

[0138] The two-dimensional blade profiles obtained by optimizing the same control vertices of the two frames were calculated and compared. With the increase of the number of control vertices, the loss coefficients obtained by optimizing the two control frames decreased, and the optimization performance was improved. When the number of control vertices was 12, the loss coefficient obtained by the chord-wise frame optimization increased by 10.4% compared with the loss coefficient obtained by the initial frame optimization. When the number of control vertices was 16, 20, and 25, the loss coefficient obtained by the chord-wise frame optimization decreased by 6.4%, 6.9%, and 6.1%, respectively. Compared with the Opt1 blade profile, the geometric thinning of the leading edge of the Opt2, Opt3, and Opt4 blade profiles reduced the shock wave intensity on the suction surface, and the shock wave position was slightly pushed back. The supersonic area on the pressure surface increased, the shock wave position was significantly retreated, and the shock wave intensity was significantly reduced, thereby reducing the blade loss coefficient. In general, changing the initial frame to the chord-wise frame for optimization can improve the optimization effect, obtain a better two-dimensional blade profile, and improve the aerodynamic performance of the blade profile.

[0139] 3) The impact of FFD control vertex density distribution on optimization performance

[0140] Since the deformation of the leading and trailing edges of the two-dimensional blade has a greater impact on the aerodynamic performance of the blade than the middle, the distribution of the framework points is changed to make the control vertices dense at the ends and sparse in the middle in the x direction, so as to optimize and analyze the influence of the density of the control vertices on the aerodynamic performance of the compressor blade. The embodiment of the present invention achieves the change of density by using an arithmetic distribution method, such as Fig.12As shown in the figure, there are eight control vertices in the x direction, and the distance from the two ends to the middle is increased by the same distance in sequence, so as to obtain an 8*3 control frame with dense control vertices at both ends and sparse control vertices in the x direction, and the increased distance (i.e., the arithmetic coefficient) is set to 1, 2, and 3 respectively, and the design variable range is set to -3.0~3.0mm. The optimization is carried out, and the loss coefficient after comparison and analysis of the optimization is shown in Table 3:

[0141] Table 3 Comparison of loss coefficients of density optimization

[0142]

[0143] Comparing the loss coefficients of Opt1, Opt2 and Opt3 in Table 3, the loss coefficient of Opt2 is reduced by 4.6% compared with that of Opt1, and the loss coefficient of Opt3 is reduced by 16.5% compared with that of Opt2. As the arithmetic coefficient increases, the control vertices at both ends of the two-dimensional blade become denser, and the optimized blade loss coefficient gradually decreases, and the optimization effect is better. It can be concluded that the shape change at both ends of the two-dimensional blade has a greater impact on the aerodynamic performance of the blade.

[0144] 4) Impact of FFD control vertex design variable range on optimization performance

[0145] The first thing to consider is to study the influence of the variation range of the control vertex on the aerodynamic design performance of the compressor blade. The main research method is to gradually increase the variation range of the control vertex to study the relationship between the variation range and the loss coefficient. The embodiment of the present invention uses Fig.13 The 4*3 control framework shown in the figure is used for research, and the transformation ranges are set to -3.0~3.0mm, -5.0~5.0mm, and -7.0~7.0mm for optimization. The comparison of the loss coefficient between the initial blade shape and the optimized blade shape and the comparison of the two-dimensional blade shape are shown in Table 4:

[0146] Table 4 Comparison of loss coefficients before and after optimization

[0147]

[0148] Comparing the loss coefficients of Ori, Opt1 and Opt2 in Table 4, the loss coefficients of Opt1 and Opt2 are reduced by 27% and 32.5% respectively compared with the loss coefficient of the initial blade, and the loss coefficient of Opt2 is reduced by 3.5% compared with Opt1. It can be concluded that the optimization reduces the loss coefficient of the two-dimensional blade compared with the initial blade, and as the control range increases, the loss coefficient is also reduced. As the range of change increases, the blade will change significantly, resulting in a situation where convergence cannot occur (Opt3), affecting normal optimization. Therefore, choosing the appropriate range of control variable changes plays an extremely important role in the optimization process.

[0149] Based on the above research, an embodiment of the present invention proposes an improved FFD parameterization method that uses the control vertex normal offset of the FFD parameterized control frame, the control frame rotation inclination angle, and the control vertex density distribution coefficient as basic design variables, which are always involved in the optimization process, and adaptively expands the design variable boundaries and increases control vertices during the optimization process, achieving good optimization results.

[0150] like Fig.14 As shown, an embodiment of the present invention further provides a compressor blade profile design variable adaptive optimization system, the system comprising:

[0151] The initial sample acquisition module 1410 is used to obtain initial samples of several design variables based on the original blade profile, use the improved FFD parameterization method to control the specific layout update of the design variables, obtain the deformed blade profile, and calculate the actual aerodynamic performance of the deformed blade profile. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library;

[0152] The optimal solution obtaining module 1420 is used to determine the design variable boundary according to all samples in the sample library, and to construct a hybrid agent model based on the pre-screening strategy based on the sample library, and to use the improved differential evolution algorithm to perform global iterative optimization, to determine whether the iteration termination condition is met, and to terminate the iteration if it is met, to obtain the optimal solution of the design variable in this round of iteration and the corresponding real aerodynamic performance;

[0153] The adaptive extended design variable boundary module 1430 is used to determine whether the exit condition of the large loop is met. If the condition is met, the large loop is exited and the optimal solution is used. Get the optimal blade shape, otherwise determine the optimal solution Whether the adaptive expansion design variable boundary conditions are met, if not, proceed to the next step; otherwise, expand the design variable boundary and calculate the new solution after the design variable boundary expansion The real aerodynamic performance of the new solution and the corresponding real aerodynamic performance are added to the sample library as new samples, and then the next step of judgment is performed;

[0154] The module 1440 for adaptively adding control vertices is used to make the next step of judging whether the condition for adaptively adding control vertices is met. If so, control vertices are added, and then this round of large cycle is ended and the next round of large cycle is started. Otherwise, this round of large cycle is directly ended and the next round of large cycle is started.

[0155] An embodiment of the present invention provides a compressor blade profile design variable adaptive optimization system, whose functional structure corresponds to a compressor blade profile design variable adaptive optimization method provided by an embodiment of the present invention, and will not be repeated here.

[0156] Fig.15 It is a structural schematic diagram of an electronic device 1500 provided in an embodiment of the present invention. The electronic device 1500 may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) 1501 and one or more memories 1502, wherein at least one instruction is stored in the memory 1502, and the at least one instruction is loaded and executed by the processor 1501 to implement the steps of the above-mentioned compressor blade design variable adaptive optimization method.

[0157] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions, which can be executed by a processor in a terminal to complete the above-mentioned compressor blade profile design variable adaptive optimization method. For example, the computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0158] A person skilled in the art will understand that all or part of the steps to implement the above embodiments may be accomplished by hardware or by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc.

[0159] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for adaptive optimization of compressor blade design variables, characterized in that: The method comprises: S1. Based on the original blade profile, initial samples of several design variables are obtained, the deformed blade profile is obtained using the improved FFD parameterization method, and the actual aerodynamic performance of the deformed blade profile is calculated. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library; S2. Determine the design variable boundaries based on all samples in the sample library, and build a hybrid agent model based on the pre-screening strategy based on the sample library, use the improved differential evolution algorithm to perform global iterative optimization, and determine whether the iteration termination condition is met. If so, terminate the iteration to obtain the optimal solution X of the design variable in this round of iteration. best and the corresponding real aerodynamic performance; S3, determine whether the exit condition of the large loop is met, if it is met, exit the large loop, and use the optimal solution X best Get the optimal blade shape, otherwise determine the optimal solution X best Whether the conditions for adaptively expanding the design variable boundary are met, if not, proceed to the next step; otherwise, expand the design variable boundary and calculate the new solution X after the design variable boundary expansion ada The real aerodynamic performance of the new X ada and the corresponding real aerodynamic performance are added to the sample library as new samples, and then the next step of judgment is performed; S4, performing the next step of judging: whether the condition of adaptively increasing the control vertex is satisfied, if satisfied, then increasing the control vertex, and then ending this round of large cycle and proceeding to the next round of large cycle, otherwise, directly ending this round of large cycle and proceeding to the next round of large cycle; The S1 specifically includes: S11, using Latin hypercube sampling LHS to sample design variables, and obtaining initial samples of several design variables, each initial sample of design variables includes a set of design variables: control vertex normal offset of FFD parameterized control frame, control frame rotation inclination angle and control vertex density distribution coefficient, these three parts are basic design variables, and are always involved in the optimization process; S12, using the FFD parameterization method to control the specific layout update of the design variables consisting of the three parts, and obtaining several deformed blade profiles; S13. According to the several deformed blades, distributed parallel grid generation and CFD aerodynamic performance calculation are performed to obtain the actual aerodynamic performance of the several deformed blades. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample. The complete sample is stored in a sample library. The complete sample includes a c-dimensional vector, where c = the number of control vertices + 2. The actual aerodynamic performance uses the loss coefficient after the airflow passes through the moving blade. To characterize, define the following formula: Where p 1r represents the relative static pressure at the moving blade inlet, They represent the relative total pressure at the inlet and outlet of the moving blade respectively; The normal direction of the control vertex normal offset refers to the direction orthogonal to the long side of the control frame; As the rotation angle α of the control frame changes, the normal movement direction of the control vertex is also constantly changing. The relationship between the two is as follows: Among them, Δx(i) refers to the offset of control vertex i in the x direction, Δy(i) refers to the offset of control vertex i in the y direction, and X(i) is the normal offset of control vertex i. The normal offset replaces the offsets in the x and y directions as the basic design variable, and the rotation angle of the control frame and the density distribution coefficient of the control vertex are added as basic design variables; Prior knowledge is incorporated into the control of the vertex density distribution coefficient: the curvature of the leading and trailing edges of the blade is large, while the curvature of the middle part of the leaf is small. Therefore, the density control adopts a method of dense at both ends and sparse in the middle in the horizontal direction of the control frame, and a uniform distribution method in the vertical direction of the control frame. The quantitative control of the vertex density distribution coefficient adopts two methods: arithmetic coefficients or geometric coefficients, and the distance from the two ends to the middle increases in arithmetic or geometric increments.

2. The method according to claim 1, characterized in that The step S2 of determining the design variable boundaries according to all samples in the sample library specifically includes: The lower and upper boundaries of each dimension of the design variable are given by L min (j) and L max (j) Determine, where L min (j) and L max (j) is the minimum and maximum value of the j-th dimension element in all samples, and the formula is as follows: Among them, L min (j) refers to the minimum value of the j-th dimension elements of all samples, L max X(j) refers to the maximum value of the j-th dimension elements of all samples, X1(j) refers to the j-th dimension element of the first sample, X2(j) refers to the j-th dimension element of the second sample, X3(j) refers to the j-th dimension element of the third sample, X n-1 (j) refers to the j-th dimension element of the n-1th sample, X n (j) refers to the j-th dimension element of the n-th sample, j refers to a certain dimension of each sample, c is the dimension of each sample, and n is the number of samples in the sample library.

3. The method according to claim 2, characterized in that In S2, a hybrid agent model based on a pre-screening strategy is constructed based on the sample library, and an improved differential evolution algorithm is used for global optimization to determine whether the iteration termination condition is met. If so, the iteration is exited to obtain the optimal solution X of the design variables in this round of iteration. best And the corresponding real aerodynamic performance, including: S21, using the initial sample of the design variables as the first generation population of the improved differential evolution algorithm, and using the loss coefficient representing the actual aerodynamic performance As the objective function, the hybrid agent model based on the pre-screening strategy is trained, and the hybrid agent model is a hybrid agent model composed of a polynomial regression model, a Kriging model, and a radial basis neural network model. After the training is completed, the first generation population and the value of its corresponding objective function are returned to the differential evolution algorithm, and after mutation, crossover, and selection, a new generation of population to be evaluated is obtained; S22, using the hybrid proxy model, pre-evaluating the new generation population to reduce the number of real evaluations of each generation, sorting the new generation population according to the pre-evaluated objective function value, screening the top r% of individuals for real CFD aerodynamic performance evaluation, using the real CFD aerodynamic performance evaluation result as the objective function value, and the remaining individuals still use the pre-evaluation result of the hybrid proxy model as the objective function value, and after obtaining all the objective function values ​​of the current generation population, return to the differential evolution algorithm; S23, adding individuals of the current generation of real evaluation r% and their objective function values ​​as new samples to the sample library to update the sample library, and retraining the hybrid proxy model based on the updated sample library to update the hybrid proxy model to achieve higher prediction accuracy. As the sample library increases in size, the computing resources required to train the hybrid proxy model increase rapidly. Therefore, the total number of sample libraries is limited to N. After the sample library reaches the upper limit, the newly added samples will randomly replace the initial N / 3 samples to ensure the continuous updating of the sample library and the hybrid proxy model. After updating the hybrid proxy model, the new generation of population and its corresponding objective function value are returned to the differential evolution algorithm. After mutation, crossover and selection, a new generation of population to be evaluated is obtained; S24, determine whether the iteration termination condition is met, if not, enter the next generation iteration, if it is met, terminate the iteration, export the sample library, the samples in the sample library are all real evaluation samples, and obtain the optimal solution X in the sample library best And the corresponding actual aerodynamic performance, that is, the optimal objective function value.

4. The method according to claim 3, characterized in that In S3, the optimal solution X is determined best Whether the conditions for adaptively expanding the design variable boundaries are met, including: The condition for adaptive expansion of the design variable boundary is X best Some dimension elements of reach the upper or lower boundary, and the expansion is as follows: Among them, X ada (i) is the i-th dimension new element of the design variable, X min (i) is X best The minimum value of the i-th dimension element, X max (i) is X best The maximum value of the i-th dimension element, X ada (j) is the j-th new element of the design variable, X max (j) is X best The maximum value of the j-th dimension element of min (j) is X best The minimum value of the j-th dimension element of . coef is determined by the degree of improvement of the performance of the optimal solution of each iteration. When the degree of improvement of this iteration is large, coef takes a larger value, otherwise it takes a smaller value. If the performance fails to improve, the boundary expansion is not performed. The formula of coef is as follows: in, and is the performance of the optimal solution of this iteration and the previous iteration, refers to the optimal performance of the first iteration, It refers to the performance of the optimal solution in the initial sample of design variables.

5. The method according to claim 4, characterized in that In S4, the next step is to determine whether the condition for adaptively adding control vertices is met. If so, the control vertices are added, specifically including: The judgment conditions for adaptively adding control vertices are as follows: D eff <e (6) Among them, ε is a given threshold, Δ eff is the improvement efficiency of optimal performance, and the calculation formula is as follows: in, and is the optimal solution performance before this iteration and t iterations; If the conditions are met, the procedure of adding control vertices parametrically is started: one point is added to each row in the horizontal direction of the control frame each time, and the added points are added according to the density distribution coefficient of the control vertices.

6. A compressor blade design variable adaptive optimization system, characterized in that: The system comprises: An initial sample acquisition module is used to obtain initial samples of several design variables based on the original blade profile, obtain the deformed blade profile using the improved FFD parameterization method, and calculate the actual aerodynamic performance of the deformed blade profile. The initial sample of each design variable and the corresponding actual aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library; The optimal solution acquisition module is used to determine the design variable boundaries according to all samples in the sample library, and to build a hybrid agent model based on the pre-screening strategy based on the sample library, and to use the improved differential evolution algorithm to perform global iterative optimization, to determine whether the iteration termination condition is met, and to terminate the iteration if it is met, and to obtain the optimal solution X of the design variable in this round of iteration. best and the corresponding real aerodynamic performance; The adaptive expansion design variable boundary module is used to determine whether the exit condition of the large cycle is met. If it is met, the large cycle is exited and the optimal solution X is used. best Get the optimal blade shape, otherwise determine the optimal solution X best Whether the conditions for adaptively expanding the design variable boundary are met, if not, proceed to the next step; otherwise, expand the design variable boundary and calculate the new solution X after the design variable boundary expansion ada The real aerodynamic performance of the new X ada and the corresponding real aerodynamic performance are added to the sample library as new samples, and then the next step of judgment is performed; The module for adaptively adding control vertices is used to perform the next step of judging whether the condition for adaptively adding control vertices is met. If so, the control vertices are added, and then the current large cycle is ended and the next large cycle is started. Otherwise, the current large cycle is directly ended and the next large cycle is started. The initial sample acquisition module is specifically used for: Latin hypercube sampling LHS is used to sample the design variables to obtain the initial samples of several design variables. The initial samples of each design variable include a set of design variables: the control vertex normal offset of the FFD parameterized control frame, the control frame rotation angle, and the control vertex density distribution coefficient. These three parts are basic design variables and have been involved in the optimization process. The FFD parameterization method is used to control the specific layout update of the design variables composed of these three parts, and several deformed blade profiles are obtained; According to the several deformed blades, distributed parallel grid generation and CFD aerodynamic performance calculation, the real aerodynamic performance of the several deformed blades is obtained, the initial sample of each design variable and the corresponding real aerodynamic performance constitute a complete sample, and the complete sample is stored in a sample library, the complete sample includes a c-dimensional vector, c=the number of control vertices+2, and the real aerodynamic performance uses the loss coefficient after the airflow passes through the moving blade To characterize, define the following formula: Where p 1r represents the relative static pressure at the moving blade inlet, They represent the relative total pressure at the inlet and outlet of the moving blade respectively; The normal direction of the control vertex normal offset refers to the direction orthogonal to the long side of the control frame; As the rotation angle α of the control frame changes, the normal movement direction of the control vertex is also constantly changing. The relationship between the two is as follows: Among them, Δx(i) refers to the offset of control vertex i in the x direction, Δy(i) refers to the offset of control vertex i in the y direction, and X(i) is the normal offset of control vertex i. The normal offset replaces the offsets in the x and y directions as the basic design variable, and the rotation angle of the control frame and the density distribution coefficient of the control vertex are added as basic design variables; Prior knowledge is incorporated into the control of the vertex density distribution coefficient: the curvature of the leading and trailing edges of the blade is large, while the curvature of the middle part of the leaf is small. Therefore, the density control adopts a method of dense at both ends and sparse in the middle in the horizontal direction of the control frame, and a uniform distribution method in the vertical direction of the control frame. The quantitative control of the vertex density distribution coefficient adopts two methods: arithmetic coefficients or geometric coefficients, and the distance from the two ends to the middle increases in arithmetic or geometric increments.

7. An electronic device, comprising a processor and a memory, wherein at least one instruction is stored in the memory, wherein: The at least one instruction is loaded and executed by the processor to implement the adaptive optimization method for compressor blade design variables as described in any one of claims 1-5.

8. A computer-readable storage medium, wherein at least one instruction is stored in the storage medium, characterized in that: The at least one instruction is loaded and executed by the processor to implement the adaptive optimization method for compressor blade design variables as described in any one of claims 1-5.

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