Turbine cooling blade design space dimension reduction method

Abstract

The application discloses a turbine cooling blade design space dimension reduction method, in the method, the geometric shape of the turbine cooling blade is described through control points of N1 Bezier curves; a database with q airfoils is obtained by Latin hypercube sampling on the N1 control points, the database obtains a group of orthogonal basis modes to describe the geometric change of the airfoil through eigenvalue orthogonal decomposition dimension reduction; the main basis mode is modeled according to the initial sample in the proxy model optimization, and an integrated proxy model is used to model each design target; variance analysis is performed on each design target; the design variables irrelevant to the target are removed; after the corresponding design variables are removed, the integrated proxy model is used to model each design target based on the existing design variables; if the correlation coefficient does not improve or decrease, it is considered that the variable removal is invalid, and the statistical variable is used as the final design variable.

Description

Technical Field

[0001] This invention belongs to the field of turbine cooling blade design technology, and in particular, a method for reducing the spatial dimension of turbine cooling blade design. Background Technology

[0002] Due to the complex structure and numerous design variables of modern gas turbine turbine cooling blades, turbine design optimization is a typical high-dimensional, computationally intensive, and black-box (HEB) design optimization problem. Employing dimensionality reduction techniques to reduce the dimensionality of the design space is an effective approach to solving these HEB problems. Currently, there are two main types of dimensionality reduction techniques for HEB optimization problems: one is based on unsupervised learning methods to capture the main modes of the shape, and the other is based on supervised learning methods to select design variables that influence the design objective from a series of design variables. The former avoids the additional computational cost in the dimensionality reduction process, allowing designers to define the design space dimension based on the trade-off between the expected geometric variance of the design space and the acceptable computational cost of optimization. However, this method is only applicable to the dimensionality reduction of two-dimensional blade design variables and cannot be used to reduce the dimensionality of turbine blade cooling system design variables. The latter theoretically overcomes the limitation of the former, which is only applicable to blade dimensionality reduction, but still has many shortcomings in practical applications. For example, while local sensitivity analysis can select the design variables most relevant to the design objective, it is not suitable for highly nonlinear problems because it fails to consider the correlation between design variables; while global sensitivity analysis can consider the correlation between design variables, it requires sufficient numerical simulation to calculate the main effects and interactions of each variable, which leads to high computational costs.

[0003] The information disclosed in the background section is only intended to enhance the understanding of the background of the present invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a method for reducing the spatial dimension of turbine cooling blade design. The objective of this invention is achieved through the following technical solution: a method for reducing the spatial dimension of turbine cooling blade design, comprising the following steps...

[0005] Step 1: Determine all design variables for the turbine cooling blades, including: turbine cooling system variables and blade shape-related variables, among which,

[0006] The cooling system variables for turbine blades are determined by the type of cooling unit, resulting in N1 variables controlling the cooling system.

[0007] For the variables related to the shape of the blade, the method that can describe the geometry of the blade is used to obtain N2 variables that control the change of the blade geometry, and the blade shape is discretized into N3 points;

[0008] Therefore, all design variables are represented as D1, and the number of design variables in D1 is denoted as N4, where N4 = N1 + N2;

[0009] Step 2: Following the first sampling method, sample N² variables to obtain q different types of leaf shapes; and establish a matrix containing q leaf shapes, where...

[0010] Each row of the matrix represents N3 discrete points for each leaf shape, and different rows of the matrix represent different leaf shapes represented by different samples;

[0011] The first sampling method refers to a sampling method that can generate uniformly distributed samples in a high-dimensional design space;

[0012] Step 3: For the matrix containing q leaf shapes, obtain q orthogonal basis modes through unsupervised dimensionality reduction to describe the geometric changes of the leaf shapes;

[0013] Step 4: Select N5 orthogonal basis modes from q orthogonal basis modes, and ensure that the generalized energy contained in the N5 orthogonal basis modes is greater than or equal to the energy of all modes in the first percentage. At this time, the design variable is represented as D2, and the number of design variables in D2 is denoted as N6, where N6 = N1 + N5.

[0014] Step 5: Use a surrogate model to model each design objective of design variable D2, and record the model accuracy for each objective; where the design objective is the design performance index; the model accuracy refers to the degree of agreement between the actual performance index value of the sample and the performance index predicted by the model.

[0015] Step Six: Perform an analysis of variance for each design objective to obtain the main effects and total effects of the design variables for each design objective;

[0016] Step 7: Remove design variables irrelevant to the design objective from design variable D2. The criteria for determining whether a design variable can be removed for a given design objective are as follows: the main effects and total effects in the ANOVA are less than the first and second quantities, respectively.

[0017] The first quantity should be between 1% and 3%. If it is less than 1%, it will be difficult to reduce the variable. If it is greater than 3%, too many design variables will be reduced, thus reducing the optimization effect.

[0018] The second quantity should be between 2% and 5%, and greater than the first quantity. If it is less than 2%, it will be difficult to reduce the variable. If it is greater than 5%, too many design variables will be reduced, thus reducing the optimization effect.

[0019] Step 8: The remaining design variables are denoted as D3. For each design objective, model it again based on the remaining design variables D3 and record the model accuracy of each design objective.

[0020] Step 9: Determine whether the accuracy of the model after remodeling is improved compared to the accuracy of the model in Step 5: The accuracy of the model is reflected by the root mean square error of the corresponding design objective, the coefficient of determination, and other indicators of the model fitting accuracy.

[0021] 1) If there is an improvement, the variable removal is considered effective. Then, step five is executed again as follows: assign the design variable D3 from step eight to the design variable D2 from step five, and execute steps five to eight again.

[0022] 2) If there is no improvement, the variable removal is considered invalid. Output the design variable D2 from the last execution of step five and terminate the dimensionality reduction.

[0023] Preferred,

[0024] The unsupervised dimensionality reduction method utilizes intrinsic orthogonal decomposition.

[0025] Preferred,

[0026] The design objectives include the following five objectives, which are defined as follows:

[0027] Objective function 1: Cooling volume;

[0028] Objective function 2: Total pressure recovery coefficient;

[0029] For the total pressure recovery coefficient C p1 The definition is as follows:

[0030]

[0031]

[0032] In the formula: P out Total outlet pressure; P in Total inlet pressure; p in Inlet static pressure.

[0033] Objective function 3: Average temperature of the blades;

[0034] Objective function 4: Maximum mean temperature of the blade, defined as follows:

[0035]

[0036] In the formula:

[0037] T high This indicates a temperature exceeding 95% of the maximum blade temperature.

[0038] v tem This indicates the leaf volume corresponding to the area exceeding 95% of the maximum leaf temperature.

[0039] V blade Indicates the volume of the blade;

[0040] Objective function 5: Maximum mean temperature gradient, defined as follows:

[0041]

[0042] In the formula:

[0043] T-gra high This indicates a temperature gradient exceeding 95% of the maximum value of the blade temperature gradient.

[0044] v gra This indicates the leaf volume corresponding to the region exceeding 95% of the highest temperature gradient of the leaf.

[0045] V blade This indicates the volume of the blade.

[0046] Therefore, this invention discloses a method for dimensionality reduction in turbine cooling blade design space. The method involves describing the geometry of the turbine cooling blade using N1 control points of Bézier curves; obtaining a database with q blade profiles by performing Latin hypercube sampling on the N1 control points; and obtaining a set of orthogonal basis modes from the database through intrinsic orthogonal decomposition to describe the geometric changes of the blade profiles. The main basis modes are modeled based on the initial samples in surrogate model optimization, and an integrated surrogate model is used to model each design objective. An analysis of variance is performed on each design objective; design variables irrelevant to the objective are removed; after removing the corresponding design variables, an integrated surrogate model is used to model each design objective based on the existing design variables; if the correlation coefficient does not increase or decreases, the variable removal is considered invalid, and the statistically obtained variables are used as the final design variables.

[0047] Compared with the prior art, the present invention has the following advantages: the turbine cooling blade design space dimensionality reduction method of the present invention can effectively reduce the dimensionality of the blade aerodynamic shape and cooling system design space under the background of multidisciplinary optimization without increasing the computational cost.

[0048] Specifically, the key innovations of this invention include:

[0049] 1. A hybrid dimensionality reduction strategy, combining unsupervised and supervised methods, is employed to minimize turbine cooling blade design variables while reducing numerical computation samples as much as possible. First, an unsupervised method is used to reduce the dimensionality of the blade profile parameters, enabling aerodynamic shape design space evaluation without requiring numerical computation samples. Simultaneously, turbine blade design includes not only aerodynamic shape design variables but also numerous non-shape design variables within its cooling system. Typical blade cooling system parameters include non-shape design variables such as the location and radius of cooling channels. Therefore:

[0050] When dealing with turbine blade cooling systems, supervised sensitivity analysis can overcome this shortcoming, further reducing design variables beyond dimensionality reduction of blade geometry. This method analyzes the contribution of variables to the output, identifying parameters with significant impact on design objectives, and then achieves dimensionality reduction by filtering design variables.

[0051] Sensitivity analysis can be divided into two methods: global and local analysis. Due to the complex relationship between output and input in turbine blades, and the interactions between inputs, different input combinations have varying effects on the output; therefore, local sensitivity analysis is not applicable. Thus, this patent exemplarily proposes a global sensitivity method based on variance decomposition.

[0052] 2. In high-dimensional design spaces, global sensitivity analysis methods require sufficient samples to calculate the main effects and interactions of each variable, resulting in excessively high computational costs. The iterative global sensitivity method proposed in this invention aims to address this problem. In this method, a model is built using a certain number of samples and applied to global sensitivity analysis. Effective design variables for each objective are obtained through screening using total effects and main effects indices.

[0053] Since surrogate models built on finite sample sets often lack accuracy, the total effect and main effect indices obtained from model-based analysis of variance are unreliable. Therefore, during iteration, as model accuracy improves, the effectiveness of the indices obtained from global sensitivity analysis is assessed by observing whether the model accuracy has increased. The reason for the improved model performance is that when there are too many irrelevant features in the input design variables that have no impact on the objective function, the accuracy of model construction will be greatly affected. At the same time, after eliminating irrelevant parameters, the design variables are closely related to the objective function, reducing the difficulty of modeling and greatly improving the accuracy of model construction. Attached Figure Description

[0054] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0055] In the attached diagram:

[0056] Figure 1A , Figure 1B This is a schematic diagram of the discrete relationship between the control points of N2 Bezier splines and the blade shape, and a schematic diagram of the resulting modes, in one embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram illustrating the determination of the number of basic modes of the NASA-C3X blade based on intrinsic orthogonal decomposition in one embodiment of the present invention.

[0058] Figures 3(a) to 3(b) This is a schematic diagram of the effect of reconstruction error on gas-thermal coupling numerical simulation in one embodiment of the present invention, wherein Figure 3(a) shows the dimensionless pressure at the height of the middle blade and Figure 3(b) shows the dimensionless temperature at the height of the middle blade.

[0059] Figure 4 This is a schematic flowchart of a global sensitivity analysis of a turbine cooling blade based on an iterative mechanism according to an embodiment of the present invention, wherein analysis of variance is employed.

[0060] Figures 5(a) to 5(b) This is a schematic diagram illustrating the dimensionality reduction effect of a turbine cooling blade design space dimensionality reduction method according to an embodiment of the present invention. Specifically, it illustrates the variance analysis effect based on the iterative mechanism. Figure 5(a) shows the number of design variables for each objective, and Figure 5(b) shows the R-squared value of the optimal model in the ensemble model. 2 .

[0061] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0062] The following will refer to the appendix. Figures 1A to 5(b) Specific embodiments of the invention will be described in more detail below. While specific embodiments of the invention are shown in the accompanying drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0063] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0064] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0065] To better understand, combine Figures 1A to 5(b) As shown in one embodiment, this disclosure discloses a method for reducing the design space of turbine cooling blades, including the following steps:

[0066] Step 1: Determine all design variables for the turbine cooling blades, including: turbine cooling system variables and blade shape-related variables, among which,

[0067] The cooling system variables for turbine blades are determined by the type of cooling unit, resulting in N1 variables controlling the cooling system.

[0068] For the variables related to the shape of the blade, the method that can describe the geometry of the blade is used to obtain N2 variables that control the change of the blade geometry, and the blade shape is discretized into N3 points;

[0069] Therefore, all design variables are represented as D1, and the number of design variables in D1 is denoted as N4, where N4 = N1 + N2;

[0070] Step 2: Following the first sampling method, sample N² variables to obtain q different types of leaf shapes; and establish a matrix containing q leaf shapes, where...

[0071] Each row of the matrix represents N3 discrete points for each leaf shape, and different rows of the matrix represent different leaf shapes represented by different samples;

[0072] The first sampling method refers to a sampling method that can generate uniformly distributed samples in a high-dimensional design space;

[0073] Step 3: For the matrix containing q leaf shapes, obtain q orthogonal basis modes through unsupervised dimensionality reduction to describe the geometric changes of the leaf shapes;

[0074] Step 4: Select N5 orthogonal basis modes from q orthogonal basis modes, and ensure that the generalized energy contained in the N5 orthogonal basis modes is greater than or equal to the first percentage (e.g., 99%) of all mode energies. At this time, the design variable is represented as D2, and the number of design variables in D2 is denoted as N6, where N6 = N1 + N5.

[0075] Step 5: Use a surrogate model to model each design objective of design variable D2, where the design objective is a design performance indicator;

[0076] Step Six: Perform an analysis of variance for each design objective to obtain the main effects and total effects of the design variables for each design objective;

[0077] Step 7: Remove design variables irrelevant to the design objective from design variable D2. The criteria for determining whether a design variable can be removed for a given design objective are as follows: the main effects and total effects in the ANOVA are less than the first and second quantities, respectively.

[0078] The first quantity should be between 1% and 3%. If it is less than 1%, it will be difficult to reduce the variable. If it is greater than 3%, too many design variables will be reduced, thus reducing the optimization effect.

[0079] The second quantity should be between 2% and 5%, and greater than the first quantity. If it is less than 2%, it will be difficult to reduce the variable. If it is greater than 5%, too many design variables will be reduced, thus reducing the optimization effect.

[0080] Step 8: The remaining design variables are denoted as D3. Model each design objective again based on the remaining design variables D3.

[0081] Step Nine: Determine whether the accuracy of the model after remodeling is improved compared to the model in Step Five:

[0082] 1) If there is an improvement, the variable removal is considered effective. Then, step five is executed again as follows: assign the design variable D3 from step eight to the design variable D2 from step five, and execute steps five to eight again.

[0083] 2) If there is no improvement, the variable removal is considered invalid. Output the design variable D2 from the last execution of step five and terminate the dimensionality reduction.

[0084] In one embodiment,

[0085] Common types of cooling units in turbine cooling systems include film cooling holes, serpentine channels, and trailing edge spoilers.

[0086] When the cooling unit is a film cooling hole, the N1 variables can be the radius and position of the film cooling hole, etc.

[0087] When the cooling unit is a serpentine cooling unit, the N1 variables can be the width of the serpentine channel, etc.

[0088] When the cooling unit is a trailing edge spoiler column, the N1 variables can be the radius and distance of the spoiler column, etc.

[0089] In one embodiment,

[0090] The cooling system can be a single cooling unit or a combination of multiple cooling units.

[0091] In one embodiment,

[0092] Regarding the blade geometry, Bezier splines can be used to describe the turbine blade geometry, where N2 variables can be the control points of the Bezier splines.

[0093] To further simplify the optimization problem, the N2 variables can be the Y-axis coordinates of N2 control points (it should be noted that they can also be the X-axis coordinates, or X and Y axis coordinates, the only difference being the coordinate transformation).

[0094] In one embodiment,

[0095] For example, the first sampling method can be Latin hypercube sampling;

[0096] See appendix Figure 1A , which represents the discrete result of the control points of N2 Bezier splines on the blade shape.

[0097] In one embodiment,

[0098] Specific steps for reducing the aerodynamic shape of blades:

[0099] Bezier splines are used to form multiple control points (e.g., 13 control points) to describe the aerodynamic shape of the turbine blades. A matrix with 1000 airfoils is obtained by Latin hypercube sampling of the Y-axis coordinates of the 13 control points; each airfoil includes 200 discrete points, and each airfoil has M... i (x j y j ) can be represented as M i (x j y j ), i=1,...1000; j=1,...200;

[0100] Each row of the above matrix can be represented as: S i =Y i = [y1, y2, ... y n ](i=1,...1000,n=1,2,...200);

[0101] The extraction of the fundamental modes is performed as follows, and finally, a set of orthogonal fundamental modes describing the changes in the blade geometry is obtained through dimensionality reduction by intrinsic orthogonal decomposition:

[0102] a) Perform the following operation on each row of the matrix:

[0103]

[0104]

[0105] Wherein: S i ′ represents the difference between the discrete coordinates of the i-th leaf shape in the sample and the mean of the discrete coordinates of all leaf shapes; S i This represents the discrete point of the i-th leaf shape in the sample; This represents the mean of all discrete points of the leaf shape;

[0106] b) Orthogonal basis functions are calculated by the following formula:

[0107] CV = ΛV

[0108] C = S T S

[0109] Φ=SV

[0110] Where: C is the squared symmetric correlation matrix; V is the orthogonal basis mode; Λ is the vector composed of eigenvalues; Φ is the projection coefficient of the leaf shape matrix onto the orthogonal basis mode; S is composed of all S i Composition, for example, [S1′, S2′, S3′......S 1000 ′).

[0111] In one embodiment,

[0112] The design goal can be one of the following five design goals, which are defined as follows:

[0113] Objective function 1: Cooling volume (for economic reasons);

[0114] Objective function 2: Total pressure recovery coefficient (considering blade aerodynamic performance);

[0115] For the total pressure recovery coefficient C p1 The definition is as follows:

[0116]

[0117]

[0118] In the formula: P out Total outlet pressure; P in Total inlet pressure; p inInlet static pressure.

[0119] Objective function 4: Maximum mean temperature of the blade, defined as follows:

[0120]

[0121] In the formula: T high This indicates a temperature exceeding 95% of the maximum blade temperature; V blade Indicates the volume of the blade; v tem This indicates the leaf volume corresponding to the area exceeding 95% of the maximum leaf temperature.

[0122] For example, the blade could be a NASA-C3X blade;

[0123] Objective function 5: Maximum mean temperature gradient, defined as follows:

[0124]

[0125] In the formula: T-gra high This indicates a temperature gradient exceeding 95% of the maximum value of the blade temperature gradient; V blade Indicates the volume of the blade; v gra This indicates the leaf volume corresponding to the region exceeding 95% of the highest temperature gradient of the leaf.

[0126] For example, the blade could be a NASA-C3X blade;

[0127] In one embodiment,

[0128] For step five, an ensemble surrogate model is used to model the five design objectives based on existing design variables. For example, an ensemble surrogate model incorporating RBF neural networks, Gaussian processes, and support vector machines is used to model each design objective. The model with the highest coefficient of determination is selected as the surrogate model for the design objective, where the coefficient of determination R0 is... 2 The definition is as follows:

[0129]

[0130] Where: y i This is the actual value of the design target for each sample; It is the predicted value of the surrogate model for the design objective of each sample; It is the average of the design objectives for all samples;

[0131] In one embodiment,

[0132] In step six, the analysis of variance uses the Sobol-based analysis of variance calculation method, and the specific calculation is as follows:

[0133] The total variance V is defined as follows:

[0134]

[0135] Where: V(Y) is the total variance; f is the function of the above model; f0 is the mean estimate of function f over the integration interval;

[0136] Therefore, the main effect index is defined as follows:

[0137]

[0138] In the formula: Let V(E(Y|x) be the main effect index of the i-th variable. i V(Y) represents the mean of the conditional variances, and V(Y) represents the total variance.

[0139] X i The total effect index is defined as follows:

[0140]

[0141] In the formula: Let V(E(Y|x) be the total effect index of the i-th variable. i Let V(Y) be the mean of the conditional variance of the i-th variable, and V(Y) be the total variance. In one embodiment,

[0142] The unsupervised dimensionality reduction method utilizes intrinsic orthogonal decomposition.

[0143] In one embodiment,

[0144] Analysis of variance (ANOVA) is a specific choice of the Sobol method, an iterative global sensitivity analysis method.

[0145] Analysis of variance (ANOVA) can be replaced by other global sensitivity analysis methods. The advantages of global sensitivity analysis are mainly reflected in: ① it can capture the interactions between parameters; ② the results are closer to reality; and ③ it can be used for nonlinear models. Due to these advantages, global sensitivity analysis can be used to quantitatively assess the direct and indirect effects of various indicators in the response relationship between each indicator and vulnerability. Currently, common global sensitivity analysis methods include Morris method, FAST method, Sobol method, Extend FAST method, and GLUE method.

[0146] like Figure 1A , Figure 1B Ultimately, the 13 control points were transformed into the following 7 basic modes, named as: first mode, second mode, ..., seventh mode.

[0147] Figure 2The impact of intrinsic orthogonal decomposition (IOD) on numerical calculations before and after dimensionality reduction is presented. As can be seen from the figure, IOD has minimal impact on the gas-thermal coupling calculations in turbine blades. Therefore, the blade reparameterized by the fundamental modes can be considered equivalent to the blade parameterized by the previous design variables. Based on this, while reducing the dimensionality of the shape design variables, the optimization potential of the original parameter scheme is essentially maintained.

[0148] The flowchart of the above analysis of variance and its iterative mechanism can be found in [reference]. Figures 3(a) to 3(b) .

[0149] The final output results for the number of five target variables are as follows: Figures 5(a) to 5(b) As shown. By Figures 5(a) to 5(b) It can be seen that the proposed dimensionality reduction technique significantly improves the model's performance. Figure 5(a) shows that the number of design variables for each design objective is reduced through the proposed dimensionality reduction technique. As shown in Figure 5(b), for models with high surrogate accuracy, the proposed dimensionality reduction technique can still improve accuracy to a certain extent; for models with low surrogate accuracy, the performance improvement is more significant after dimensionality reduction.

[0150] In summary, the implementation of this invention significantly reduces design variables and improves the accuracy of the surrogate model, providing convenience for the multidisciplinary optimization design of turbine cooling blades.

[0151] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for spatial dimensionality reduction in turbine cooling blade design, characterized in that, It includes the following steps, Step 1: Determine all design variables for the turbine cooling blades, including: turbine cooling system variables and blade shape-related variables, among which, The cooling system variables for turbine blades are determined by the type of cooling unit, resulting in N1 variables controlling the cooling system. For the variables related to the shape of the blade, the method that can describe the geometry of the blade is used to obtain N2 variables that control the change of the blade geometry, and the blade shape is discretized into N3 points; Therefore, all design variables are represented as D1, and the number of design variables in D1 is denoted as N4, where N4 = N1 + N2; Step 2: Following the first sampling method, sample N² variables to obtain q different types of leaf shapes; and establish a matrix containing q leaf shapes, where... Each row of the matrix represents N3 discrete points for each leaf shape, and different rows of the matrix represent different leaf shapes represented by different samples; The first sampling method refers to a sampling method that can generate uniformly distributed samples in a high-dimensional design space; Step 3: For the matrix containing q leaf shapes, obtain q orthogonal basis modes through unsupervised dimensionality reduction to describe the geometric changes of the leaf shapes; Step 4: Select N5 orthogonal basis modes from q orthogonal basis modes, and ensure that the generalized energy contained in the N5 orthogonal basis modes is greater than or equal to the energy of all modes in the first percentage. At this time, the design variable is represented as D2, and the number of design variables in D2 is denoted as N6, where N6 = N1 + N5. Step 5: Use a surrogate model to model each design objective of design variable D2, and record the model accuracy for each objective; where the design objective is the design performance index; the model accuracy refers to the degree of agreement between the actual performance index value of the sample and the performance index predicted by the model. Step Six: Perform an analysis of variance for each design objective to obtain the main effects and total effects of the design variables for each design objective; Step 7: Remove design variables irrelevant to the design objective from design variable D2. The criteria for determining whether a design variable can be removed for a given design objective are as follows: the main effects and total effects in the ANOVA are less than the first and second quantities, respectively. The first quantity should be between 1% and 3%. If it is less than 1%, it will be difficult to reduce the variable. If it is greater than 3%, too many design variables will be reduced, thus reducing the optimization effect. The second quantity should be between 2% and 5%, and greater than the first quantity. If it is less than 2%, it will be difficult to reduce the variable. If it is greater than 5%, too many design variables will be reduced, thus reducing the optimization effect. Step 8: The remaining design variables are denoted as D3. For each design objective, model it again based on the remaining design variables D3 and record the model accuracy of each design objective. Step 9: Determine whether the accuracy of the model after remodeling is improved compared to the model in Step 5: The accuracy of the model is reflected by the root mean square error and coefficient of determination of the corresponding design target. 1) If there is an improvement, the variable removal is considered effective. Then, step five is executed again as follows: assign the design variable D3 from step eight to the design variable D2 from step five, and execute steps five to eight again. 2) If there is no improvement, the variable removal is considered invalid. Output the design variable D2 from the last execution of step five and terminate the dimensionality reduction.

2. The turbine cooling blade design space dimensionality reduction method according to claim 1, wherein, The unsupervised dimensionality reduction method utilizes intrinsic orthogonal decomposition.

3. The turbine cooling blade design space dimensionality reduction method according to claim 2, wherein, The design objectives include the following five objectives, which are defined as follows: Objective function 1: Cooling volume; Objective function 2: Total pressure recovery coefficient; For the total pressure recovery coefficient C p1 The definition is as follows: In the formula: P out Total outlet pressure; P in Total inlet pressure; p in Inlet static pressure; Objective function 3: Average temperature of the blades; Objective function 4: Maximum mean temperature of the blade, defined as follows: In the formula: T high This indicates a temperature exceeding 95% of the maximum blade temperature. v tem This indicates the leaf volume corresponding to the area exceeding 95% of the maximum leaf temperature. V blade Indicates the volume of the blade; Objective function 5: Maximum mean temperature gradient, defined as follows: In the formula: T-gra high This indicates a temperature gradient exceeding 95% of the maximum value of the blade temperature gradient. v gra This indicates the leaf volume corresponding to the region exceeding 95% of the highest temperature gradient of the leaf. V blade This indicates the volume of the blade.

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