A data-driven modeling method for three-dimensional aerodynamic effects of wind turbine blades

By constructing axial and radial velocity factor models using data-driven symbolic regression and population evolution algorithms, the problem of insufficient prediction accuracy of blade element theory in the correction of three-dimensional geometric effects is solved, and efficient and high-precision prediction of three-dimensional aerodynamic forces of wind turbine blades is achieved.

CN122047015BActive Publication Date: 2026-06-19NORTHWESTERN POLYTECHNICAL UNIV

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
NORTHWESTERN POLYTECHNICAL UNIV
Filing Date
2026-04-17
Publication Date
2026-06-19

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Abstract

This invention discloses a data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades, relating to the field of wind turbine blade aerodynamic prediction technology. The method includes: collecting aerodynamic data of the three-dimensional wind turbine blade and load data of each two-dimensional section, dividing the data into training and testing sets; constructing physical models for the downwash effect and tip loss effect in the three-dimensional geometric effects; selecting axial velocity factors and radial velocity factors as modeling objects for symbolic regression, and establishing an axial velocity factor model using a population evolution-based symbolic regression algorithm; calculating the equivalent angle of attack for each section based on the axial velocity factor model, and establishing a radial velocity factor model; and combining the axial velocity factor model, radial velocity factor model, and blade element theory to correct the geometric effects of the three-dimensional blade. This invention requires only a small amount of high-precision data to efficiently and accurately predict the three-dimensional aerodynamic forces of different models, shapes, and locations.
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Description

Technical Field

[0001] This invention relates to the field of wind turbine blade aerodynamic prediction technology, and in particular to a data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades. Background Technology

[0002] With the rapid development of horizontal axis wind turbines, the accurate assessment of their complex aerodynamic effects directly impacts blade load, power generation efficiency, and structural stability. Theoretical models, represented by momentum element theory, have gradually become the mainstream engineering method in the wind turbine and rotor fields due to their high physical interpretability and solution efficiency. However, when the incoming flow conditions are not perfectly perpendicular or symmetrical to the rotor plane, or when the blades are in a high angle-of-attack stall state, complex nonlinear unsteady flow effects are induced, causing the classical one-dimensional momentum theory to fail. Furthermore, the two-dimensional assumptions of the blade element theory neglect the three-dimensional effects of real blades.

[0003] The blade element theory widely used in wind turbine industrial design relies on airfoil databases. Airfoil characteristics are typically based on two-dimensional airfoil wind tunnel measurements or high-precision simulation calculations. Therefore, the momentum blade element method cannot calculate the spanwise flow of a real blade and the aerodynamic changes caused by its three-dimensional effects. Furthermore, the failure to predict three-dimensional aerodynamic forces induced by geometric effects is also a significant reason for the significant discrepancies observed in classical momentum blade element theory under shutdown conditions. However, classical theoretical models are difficult to directly apply to the correction of the momentum blade element method, mainly because the empirical parameters of the Oswald factor (a parameter describing the geometry) of the wind turbine blade geometry are difficult to determine, and the aspect ratio of different blade elements is difficult to quantify effectively. Moreover, the correction of three-dimensional geometric effects affects the prediction accuracy of aerodynamic forces under shutdown and rotation conditions. Therefore, further research is needed on the three-dimensional geometric effect correction model for the momentum blade element theory BEM method. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades. For three-dimensional blades, based on symbolic regression and classical aerodynamic theory, a three-dimensional aerodynamic modeling framework is proposed. It requires only a small amount of high-precision data to achieve efficient and high-precision prediction of the three-dimensional aerodynamic effects of different models, shapes, and locations.

[0005] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades, comprising the following steps:

[0006] S1: Collect aerodynamic data of the three-dimensional blades of the wind turbine and load data of each two-dimensional section, and divide the data into training set and test set;

[0007] S2: Based on the differences between two-dimensional and three-dimensional loads in the training set, physical models of the underwash effect and the tip loss effect in the three-dimensional geometric effect are constructed respectively.

[0008] S3: Select the axial velocity factor and radial velocity factor as the modeling objects of symbolic regression, and use the symbolic regression algorithm of population evolution to establish the axial velocity factor model.

[0009] S4: Calculate the equivalent angle of attack for each section based on the axial velocity factor model, and establish the radial velocity factor model using the symbolic regression algorithm of population evolution;

[0010] S5: Combining the axial velocity factor model, radial velocity factor model and blade element theory, the geometric effect of the three-dimensional blade is corrected to realize the three-dimensional aerodynamic effect modeling of the wind turbine blade.

[0011] Furthermore, the construction of the physical model of the downwash effect includes the following steps:

[0012] A1: Reducing the slope of the lift line induced by the downwash effect of finite-span blades is equivalent to a decrease in axial velocity. The resulting change in angle of attack;

[0013] A2: Define the free flow velocity The velocity projections in the x and y directions are respectively and ;

[0014] A3: Express the reduction in axial velocity caused by the downwash effect as... The physical model of the downwash effect is then expressed as:

[0015]

[0016] in, This is the equivalent angle of attack induced by the downwash effect. It is a two-dimensional angle of attack.

[0017] Furthermore, the construction of the physical model for the tip loss effect includes the following steps:

[0018] B1: For the same free-flow velocity Based on the characteristic of uniform total pressure under incompressible flow, Bernoulli's law is used to establish the velocity on the three-dimensional blade surface. ,pressure With the velocity of the corresponding two-dimensional airfoil ,pressure Relationship:

[0019]

[0020] in, For free flow density;

[0021] B2: Introducing radial velocity loss The velocity of the three-dimensional blade surface If the velocity and radial velocity losses are represented as the superposition of the two-dimensional airfoil's velocity, then the load relationship between the two-dimensional and three-dimensional airfoils is expressed as follows:

[0022]

[0023] in, This represents the three-dimensional lift of the three-dimensional blade at different angles of attack. This represents the lift at the airfoil's angle of attack. Let be the chord length of the blade cross section;

[0024] B3: Assuming the velocity distribution on the upper surface is simplified as follows Introducing error characterization parameters to quantify equation error and :

[0025]

[0026]

[0027] Radial velocity was derived The expression:

[0028]

[0029] in, Let be the lift coefficient of the three-dimensional blade section. Let be the two-dimensional lift coefficient of the blade cross section with respect to the airfoil.

[0030] Furthermore, the establishment of the axial velocity factor model includes the following steps:

[0031] S31: Determine the symbol input parameters, including the chord length of the blade section. The position of the blade cross section from the leaf root Total blade length Two-dimensional angle of attack ,in , For the local section angle of attack, For airfoil zero-lift angle of attack;

[0032] S32: Select symbolic expressions, including addition, subtraction, multiplication, division, quadratic, cubic, sine, and exponential functions;

[0033] S33: Optimize the relevant tree structure to obtain the symbolic expression. ,in, For axial velocity factor, It is a functional expression of the axial velocity factor;

[0034] S34: Calculate the loss function between the prediction model and the training data. Evaluate the accuracy of the modeling results:

[0035]

[0036] in, For the first Functional expression of the axial velocity factor in the next iteration;

[0037] S35: If the loss function continues to decrease, perform genetic, mutation, and crossover operations on the expressions in the population to adjust them. The mathematical expression of;

[0038] S36: When the loss function no longer decreases or reaches the maximum number of iterations, the output accuracy and complexity are balanced. ;

[0039] S37: Inspection The physical interpretability and prediction accuracy are considered. If non-physical mathematical forms exist, return to step S31 to modify the input and settings; if physical interpretability is satisfied and a balance between accuracy and complexity is achieved, then output... .

[0040] Furthermore, the establishment of the radial velocity factor model includes the following steps:

[0041] S41: Determine the symbol input parameters, including the chord length of the blade section. The position of the blade cross section from the leaf root Total blade length Equivalent angle of attack ;

[0042] S42: Select symbolic expressions, including addition, subtraction, multiplication, division, quadratic, cubic, sine, and exponential functions;

[0043] S43: Optimize the tree structure to obtain the symbolic expression. ,in, Radial velocity factor, This is a functional expression of the radial velocity factor;

[0044] S44: Calculate the loss function between the prediction model and the training data, and evaluate the accuracy of the modeling results;

[0045] S45: If the loss function continues to decrease, perform genetic, mutation, and crossover operations on the expressions in the population to adjust them. The mathematical expression of;

[0046] S46: When the loss function no longer decreases or reaches the maximum number of iterations, the output accuracy and complexity are balanced. ;

[0047] S47: Inspection The physical interpretability and prediction accuracy are considered. If non-physical mathematical forms exist, return to step S41 to modify the input and settings; if physical interpretability is satisfied and a balance between accuracy and complexity is achieved, then output... .

[0048] Furthermore, the geometric effect correction of the three-dimensional blade, which combines the axial velocity factor model, the radial velocity factor model, and the blade element theory, specifically includes:

[0049] For shutdown conditions, the axial velocity factor is used. The angle of attack corresponding to the two-dimensional airfoil load data in the test set is corrected to obtain the load on the three-dimensional cross-section; the radial velocity factor is then used. The loads on the obtained three-dimensional cross-sections are corrected to finally obtain the blade cross-section loads that take into account three-dimensional geometric effects.

[0050] The beneficial effects of this invention are:

[0051] (1) The present invention constructs a modeling method for describing the three-dimensional geometric effect of the blade, realizes the correction of the aerodynamic force induced by the three-dimensional geometric effect of the blade element theory, and improves the prediction accuracy of the three-dimensional aerodynamic force.

[0052] (2) This invention constructs a knowledge- and data-driven three-dimensional effect modeling process. Traditional methods rely on function fitting and have poor generalization. Based on the physical understanding of three-dimensional geometric effects, this invention deconstructs two dimensionless parameters and automatically identifies the parameter expressions based on the data-driven symbolic regression method. That is, it reduces the modeling difficulty and guides the modeling direction based on physical knowledge, and also realizes the mining of physical knowledge and prediction model from data based on data-driven methods.

[0053] (3) The three-dimensional geometric effect modeling process constructed by the present invention has strong generalization extrapolation ability. Based on a small amount of high-precision training data, it can effectively predict three-dimensional aerodynamic forces of different shapes, different models, and different positions. Attached Figure Description

[0054] Figure 1 Flowchart of a data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades.

[0055] Figure 2 A schematic diagram of the physical model for modeling the downwash effect.

[0056] Figure 3A schematic diagram of the physical model for modeling the tip loss effect.

[0057] Figure 4 This is a comparison chart of the aerodynamic prediction results at 47% of the NREL Phase VI blade positions with the original method.

[0058] Figure 5 This is a comparison chart of the aerodynamic prediction results at 80% of the NREL Phase VI blade locations with the original method.

[0059] Figure 6 This is a comparison chart of the aerodynamic prediction results at the 25% station position of the MEXICO blade with the original method.

[0060] Figure 7 This is a comparison chart of the aerodynamic prediction results at the 35% station position of the MEXICO blade with the original method.

[0061] Figure 8 This is a comparison chart of the aerodynamic prediction results at 60% of the MEXICO blade positions with the original method.

[0062] Figure 9 This is a comparison chart of the aerodynamic prediction results at 82% of the MEXICO blade locations with the original method. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0064] like Figure 1 As shown, a data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades includes the following steps:

[0065] S1: Collect aerodynamic data of the three-dimensional blades of the wind turbine and load data of each two-dimensional section, and divide the data into training set and test set;

[0066] The data includes three-dimensional blades at different stations. Different cross sections and different angles of attack The corresponding three-dimensional lift ,resistance Data, and corresponding airfoil angle of attack The corresponding lift ,resistance The data in this embodiment includes three-dimensional aerodynamic data of the blade from the blade root position to the blade tip position;

[0067] The dataset is divided into a training set and a prediction set. The prediction set includes data for different cross-sectional positions and different shapes to enable training and generalization testing of the model. In this embodiment, three typical cross-sectional data containing relatively comprehensive physical information—leaf root, leaf middle, and leaf tip—are selected as training data.

[0068] S2: Based on the differences between two-dimensional and three-dimensional loads in the training set, physical models of the underwash effect and the tip loss effect in the three-dimensional geometric effect are constructed respectively.

[0069] The construction of the physical model of the downwash effect includes the following steps:

[0070] A1: Reducing the slope of the lift line induced by the downwash effect of finite-span blades is equivalent to a decrease in axial velocity. The resulting change in angle of attack;

[0071] A2: Define the free flow velocity The velocity projections in the x and y directions are respectively and ;

[0072] A3: Express the reduction in axial velocity caused by the downwash effect as... The physical model of the downwash effect is then expressed as:

[0073]

[0074] in, This is the equivalent angle of attack induced by the downwash effect. It is a two-dimensional angle of attack.

[0075] The construction of the physical model for the tip loss effect includes the following steps:

[0076] B1: For the same free-flow velocity Based on the characteristic of uniform total pressure under incompressible flow, Bernoulli's law is used to establish the velocity on the three-dimensional blade surface. ,pressure With the velocity of the corresponding two-dimensional airfoil ,pressure Relationship:

[0077]

[0078] in, For free flow density;

[0079] B2: Introducing radial velocity loss The velocity of the three-dimensional blade surface If the velocity and radial velocity losses are represented as the superposition of the two-dimensional airfoil's velocity, then the load relationship between the two-dimensional and three-dimensional airfoils is expressed as follows:

[0080]

[0081] in, This represents the three-dimensional lift of the three-dimensional blade at different angles of attack. This represents the lift at the airfoil's angle of attack. Let be the chord length of the blade cross section;

[0082] B3: Assuming the velocity distribution on the upper surface is simplified as follows Introducing error characterization parameters ( ) to quantify the equation error and :

[0083]

[0084]

[0085] Radial velocity was derived The expression:

[0086]

[0087] in, Let be the lift coefficient of the three-dimensional blade section. Let be the two-dimensional lift coefficient of the blade cross section with respect to the airfoil.

[0088] S3: Select the axial velocity factor and radial velocity factor as the modeling objects of symbolic regression, and use the symbolic regression algorithm of population evolution to establish the axial velocity factor model.

[0089] To reduce the difficulty of data-driven modeling, dimensionless variables were extracted as the modeling objects for symbolic regression, including the axial velocity factor. radial velocity factor ;

[0090] The establishment of the axial velocity factor model includes the following steps:

[0091] S31: Based on the aspect ratio theory, considering the aerodynamic and geometric torsion distributed along the blade, determine the symbolic input parameters, including the chord length of the blade section. The position of the blade cross section from the leaf root Total blade length Two-dimensional angle of attack The two-dimensional angle of attack takes into account aerodynamic torsion and camber effects, that is, the difference between the angle of attack at the local section and the zero-lift angle of attack of the airfoil: , For the local section angle of attack, For airfoil zero-lift angle of attack;

[0092] S32: Select symbolic expressions, including addition, subtraction, multiplication, division, quadratic, cubic, sine, and exponential functions;

[0093] S33: Optimize the relevant tree structure to obtain the symbolic expression. ,in, For axial velocity factor, It is a functional expression of the axial velocity factor;

[0094] S34: Calculate the loss function between the prediction model and the training data. Evaluate the accuracy of the modeling results:

[0095]

[0096] in, For the first Functional expression of the axial velocity factor in the next iteration;

[0097] S35: If the loss function continues to decrease, perform genetic, mutation, and crossover operations on the expressions in the population to adjust them. The mathematical expression of;

[0098] S36: When the loss function no longer decreases or reaches the maximum number of iterations, the output accuracy and complexity are balanced. In this embodiment, the maximum number of iterations is set to 600.

[0099] S37: Inspection The physical interpretability and prediction accuracy are considered. If non-physical mathematical forms exist, return to step S31 to modify the input and settings; if physical interpretability is satisfied and a balance between accuracy and complexity is achieved, then output... .

[0100] S4: Calculate the equivalent angle of attack for each section based on the axial velocity factor model, and establish the radial velocity factor model using the symbolic regression algorithm of population evolution;

[0101] The establishment of the radial velocity factor model includes the following steps:

[0102] S41: Determine the symbol input parameters, including the chord length of the blade section. The position of the blade cross section from the leaf root Total blade length Equivalent angle of attack ;

[0103] S42: Select symbolic expressions, including addition, subtraction, multiplication, division, quadratic, cubic, sine, and exponential functions;

[0104] S43: Optimize the tree structure to obtain the symbolic expression. ,in, Radial velocity factor, This is a functional expression of the radial velocity factor;

[0105] S44: Calculate the loss function between the prediction model and the training data, and evaluate the accuracy of the modeling results;

[0106] S45: If the loss function continues to decrease, perform genetic, mutation, and crossover operations on the expressions in the population to adjust them. The mathematical expression of;

[0107] S46: When the loss function no longer decreases or reaches the maximum number of iterations, the output accuracy and complexity are balanced. ;

[0108] S47: Inspection The physical interpretability and prediction accuracy are considered. If non-physical mathematical forms exist, return to step S41 to modify the input and settings; if physical interpretability is satisfied and a balance between accuracy and complexity is achieved, then output... .

[0109] S5: Combining the axial velocity factor model, radial velocity factor model and blade element theory, the geometric effect of the three-dimensional blade is corrected to realize the three-dimensional aerodynamic effect modeling of the wind turbine blade.

[0110] In this embodiment, for the shutdown condition, the axial velocity factor is... This is used to correct the angle of attack corresponding to the two-dimensional airfoil load data in the test set, thus obtaining the two-dimensional load at the equivalent angle of attack, which is the load of the three-dimensional cross-section. Additionally, a radial velocity factor is used. The obtained three-dimensional load is corrected, that is, the load loss at the blade tip is corrected, and finally the blade section load considering the three-dimensional geometric effects is obtained.

[0111] In one embodiment of the present invention, Table 1 shows the training and generalization data used for modeling in the embodiment. Based on the physical understanding of three-dimensional geometric effects, only a small amount of high-cost, high-precision wind tunnel test data is used during the training process. Only load data at the 30%, 63%, and 95% spanwise positions of the airfoil are used to train the three-dimensional geometric effect model. Furthermore, aerodynamic data from other positions of the NRELPhase VI rotor and the MEXICO rotor are used as the prediction dataset. And since the blades of the MEXICO rotor are used for three completely different airfoil shapes from the training data, these operating conditions also represent the generalization capability of the modeling method of the present invention for geometric shapes.

[0112] Table 1 Training Data and Generalization Data

[0113]

[0114] Figure 2 A schematic diagram of the physical model of the downwash effect developed in this invention is shown, which uses the axial velocity deficit to represent the influence of the downwash flow on the slope of the lift line. Figure 3 This diagram illustrates the physical model of the tip loss effect developed in this invention, using radial velocity transport to represent the tip loss effect. Due to the presence of radial velocity, the three-dimensional pressure coefficient of the upper surface is significantly reduced compared to the two-dimensional coefficient. This is reflected in a reduction in lift.

[0115] Specifically Figures 4-9 The results demonstrate the predictive performance of the geometric effect correction model for lift coefficients at different spanwise cross-sections. The proposed geometric effect correction method (solid black line) shows good agreement with high-precision experimental data (boxes). In blade element theory, blade loads under shutdown conditions are often predicted using two-dimensional aerodynamic data. Therefore, the original prediction results (dashed line) shown in the figure exhibit significant errors compared to the experimental data. The prediction accuracy is improved by more than 50%.

[0116] In summary, guided by physical principles and using only a small amount of high-precision experimental data, the three-dimensional aerodynamic modeling method of this invention achieves efficient prediction of three-dimensional aerodynamic forces for different aircraft types, shapes, and positions. Compared with the prediction results of classical blade element theory, the accuracy is improved by more than 50%. Due to the guidance of physical principles and the rationality of the theoretical framework proposed in this invention, the method demonstrates strong generalization ability, still providing accurate prediction results for operating conditions outside the training dataset.

[0117] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A data-driven method for modeling the three-dimensional aerodynamic effects of wind turbine blades, characterized in that, Includes the following steps: S1: Collect aerodynamic data of the three-dimensional blades of the wind turbine and load data of each two-dimensional section, and divide the data into training set and test set; S2: Based on the differences between two-dimensional and three-dimensional loads in the training set, physical models of the underwash effect and the tip loss effect in the three-dimensional geometric effect are constructed respectively. The construction of the physical model of the downwash effect includes the following steps: A1: Reducing the slope of the lift line induced by the downwash effect of finite-span blades is equivalent to a decrease in axial velocity. The resulting change in angle of attack; A2: Define the free flow velocity The velocity projections in the x and y directions are respectively and ; A3: Express the reduction in axial velocity caused by the downwash effect as... The physical model of the downwash effect is then expressed as: ; in, This is the equivalent angle of attack induced by the downwash effect. Angle of attack in two dimensions; The construction of the physical model for the tip loss effect includes the following steps: B1: For the same free-flow velocity Based on the characteristic of uniform total pressure under incompressible flow, Bernoulli's law is used to establish the velocity on the three-dimensional blade surface. ,pressure With the velocity of the corresponding two-dimensional airfoil ,pressure Relationship: ; in, For free flow density; B2: Introducing radial velocity loss The velocity of the three-dimensional blade surface If the velocity and radial velocity losses are represented as the superposition of the two-dimensional airfoil's velocity, then the load relationship between the two-dimensional and three-dimensional airfoils is expressed as follows: ; in, This represents the three-dimensional lift of the three-dimensional blade at different angles of attack. This represents the lift at the airfoil's angle of attack. Let be the chord length of the blade cross section; B3: Assuming the velocity distribution on the upper surface is simplified as follows Introducing error characterization parameters to quantify equation error and : ; ; Radial velocity was derived The expression: ; in, The lift coefficient of the three-dimensional blade section is denoted as . Let be the two-dimensional lift coefficient of the blade cross section with respect to the airfoil; S3: Select the axial velocity factor and radial velocity factor as the modeling objects of symbolic regression, and use the symbolic regression algorithm of population evolution to establish the axial velocity factor model. S4: Calculate the equivalent angle of attack for each section based on the axial velocity factor model, and establish the radial velocity factor model using the symbolic regression algorithm of population evolution; S5: Combining the axial velocity factor model, radial velocity factor model and blade element theory, the geometric effect of the three-dimensional blade is corrected to realize the three-dimensional aerodynamic effect modeling of the wind turbine blade.

2. The data-driven three-dimensional aerodynamic effect modeling method for wind turbine blades according to claim 1, characterized in that, The establishment of the axial velocity factor model includes the following steps: S31: Determine the symbol input parameters, including the chord length of the blade section. The position of the blade cross section from the blade root Total blade length Two-dimensional angle of attack ,in , For the local section angle of attack, Zero lift angle of attack for airfoil; S32: Select symbolic expressions, including addition, subtraction, multiplication, division, quadratic, cubic, sine, and exponential functions; S33: Optimize the relevant tree structure to obtain the symbolic expression. ,in, For axial velocity factor, It is a functional expression of the axial velocity factor; S34: Calculate the loss function between the prediction model and the training data. Evaluate the accuracy of the modeling results: ; in, For the first Functional expression of the axial velocity factor in the next iteration; S35: If the loss function continues to decrease, perform genetic, mutation, and crossover operations on the expressions in the population to adjust them. The mathematical expression of; S36: When the loss function no longer decreases or reaches the maximum number of iterations, the output accuracy and complexity are balanced. ; S37: Inspection The physical interpretability and prediction accuracy are considered. If non-physical mathematical forms exist, return to step S31 to modify the input and settings; if physical interpretability is satisfied and a balance between accuracy and complexity is achieved, then output... .

3. The data-driven three-dimensional aerodynamic effect modeling method for wind turbine blades according to claim 2, characterized in that, The establishment of the radial velocity factor model includes the following steps: S41: Determine the symbol input parameters, including the chord length of the blade section. The position of the blade cross section from the blade root Total blade length Equivalent angle of attack ; S42: Select symbolic expressions, including addition, subtraction, multiplication, division, quadratic, cubic, sine, and exponential functions; S43: Optimize the tree structure to obtain the symbolic expression. , in, Radial velocity factor, This is a functional expression of the radial velocity factor; S44: Calculate the loss function between the prediction model and the training data to evaluate the accuracy of the modeling results; S45: If the loss function continues to decrease, perform genetic, mutation, and crossover operations on the expressions in the population to adjust them. The mathematical expression of; S46: When the loss function no longer decreases or reaches the maximum number of iterations, the output accuracy and complexity are balanced. ; S47: Inspection The physical interpretability and prediction accuracy are considered. If non-physical mathematical forms exist, return to step S41 to modify the input and settings; if physical interpretability is satisfied and a balance between accuracy and complexity is achieved, then output... .

4. The data-driven three-dimensional aerodynamic effect modeling method for wind turbine blades according to claim 3, characterized in that, The method of combining axial velocity factor model, radial velocity factor model and blade element theory to correct the geometric effects of three-dimensional blades specifically includes: For shutdown conditions, the axial velocity factor is used. The angle of attack corresponding to the two-dimensional airfoil load data in the test set is corrected to obtain the load on the three-dimensional cross-section; the radial velocity factor is then used. The loads on the obtained three-dimensional cross-sections are corrected to finally obtain the blade cross-section loads that take into account three-dimensional geometric effects.