Modeling methods for wind turbine power curves that consider random forests and improved Gaussian processes

Abstract

This invention discloses a method for modeling the power curve of wind turbines that incorporates random forests and improved Gaussian processes. It includes the following steps: S1: Using a random forest algorithm, select m variables that significantly affect the power from n variables that may influence the wind turbine's power; S2: Input the m variables that significantly affect the power into an improved Gaussian process; S3: Apply four prediction goodness-of-prediction metrics: MAPE, RMSE, 1-R², and 1-R². 2 The prediction performance of the wind turbine power curve model is evaluated using the MAE method; S4: The entropy weight method is applied to assign different weights to the above four types of indicators to obtain a comprehensive index; This invention overcomes the subjectivity problem in previous studies by combining the variable selection process with the improved Gaussian process, thereby improving the prediction efficiency of the Gaussian process model, and applying the entropy weight method to obtain a comprehensive index to fully evaluate the model performance.

Description

Technical Field

[0001] This invention relates to the field of optimal operation technology for wind turbines, and in particular to a method for modeling the power curve of wind turbines that takes into account random forests and improved Gaussian processes. Background Technology

[0002] By the end of 2022, global installed wind power capacity had reached 940 gigawatts, demonstrating the enormous potential of wind energy as a renewable resource and its increasing market acceptance. Against this backdrop, studying wind turbine power curves is particularly important. These curves not only reveal the complex nonlinear relationship between wind speed and wind turbine output power but also provide crucial technical support for the design, operation, and maintenance of wind farms. Wind turbine power curves are key to understanding and optimizing wind power system performance, playing a vital role in improving the accuracy of wind turbine power estimation, turbine condition monitoring, and overall wind farm efficiency.

[0003] Despite progress in research on wind turbine power curves, many scholars still exhibit a degree of subjectivity in selecting model variables. They often arbitrarily choose variables that influence wind turbine power. Furthermore, existing research neglects the limitations of Cholesky decomposition in Gaussian process regression when finding symmetric positive definite matrices and relies solely on a single predictive goodness index to evaluate model performance. These factors limit the model's predictive accuracy, impacting the effective utilization of wind energy resources and the economic benefits of wind farms. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a method for modeling the power curve of wind turbines that takes into account random forests and improved Gaussian processes. This method overcomes the subjectivity problem in previous studies, improves the prediction efficiency of Gaussian process models by combining variable selection processes with improved Gaussian processes, and obtains comprehensive indicators by applying the entropy weight method to comprehensively evaluate model performance.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for modeling the power curve of wind turbines that considers random forests and improved Gaussian processes, which includes the following steps:

[0006] S1: Use the random forest algorithm to select m variables that have a significant impact on power from n variables that may affect the power of wind turbine units;

[0007] S2: Input m variables that have a significant impact on power into the improved Gaussian process;

[0008] S3: Apply four predictive goodness metrics: MAPE, RMSE, 1-R 2 The predictive performance of the wind turbine power curve model was evaluated by MAE.

[0009] S4: Apply the entropy weight method to assign different weights to the above four types of indicators, so as to obtain a comprehensive indicator.

[0010] Further, the specific steps of S1 include:

[0011] S11: Collect n input variables of a wind farm's SCADA system over a period of time, and the output variable is power;

[0012] S12: Input the above variables into the random forest algorithm to evaluate the importance of variables to the output power, so as to obtain the importance score of each variable; then, select the top m variables with the highest scores for further analysis.

[0013] Further, the specific steps of S12 are as follows:

[0014] Randomly and with replacement, draw z (z < N) samples from N samples and n variables, and perform G repeated samplings to obtain G sub-training sets; among them, the data not selected constitutes out-of-bag (OBB) data; for the g-th (g = 1, 2,..., G) sub-training set, independently construct a decision tree and train it; each decision tree calculates its voting result L on the corresponding OBB g ; Randomly perturb the variable A i (i = 1, 2,..., n) in the OBB, and recalculate the voting result L obtained by the decision tree in the corresponding OBB g,i ; By calculating the importance score P of each variable i and arranging them in descending order to determine the most important variables to construct an optimal variable combination, where the larger P i the more important the variable; the corresponding formula is as follows:

[0015]

[0016] In the formula: G is the total number of decision trees; P i is the variable importance score;

[0017] After obtaining the importance scores of the above variables, select the top m variables with the highest scores for analysis.

[0018] Further, the specific steps of S2 include:

[0019] S21: Input the selected m variables into the improved Gaussian process;

[0020] S22: Select LDL decomposition to perform the calculation of symmetric positive definite matrices.

[0021] Further, the improved Gaussian process in S21 is as follows:

[0022] The characteristics of a Gaussian process (GP) are determined by the mean function m(x) and the covariance function k(x,x′), and their corresponding formulas are shown below:

[0023] m(x) = E[f(x)]

[0024] k(x,x′)=E[(f(x)-m(x))(f(x′)-m(x′))]

[0025] In the formula: x, x′∈R d Let R be any random variable (R represents the set of real numbers, d represents the dimension, R...) d (representing d-dimensional real space);

[0026] Therefore, a Gaussian process can be defined as f(x)~GP(m(x),k(x,x′)), where m(x) is usually assumed to be 0;

[0027] Assuming the observed target y contains noise, denoted as ε, the relationship between the observed target y and the function output value f(x) is as follows:

[0028] y = f(x) + ε

[0029] In the formula: x is the input vector, ε is a vector with a mean of 0 and a variance of . A normally distributed random variable can be denoted as

[0030] When the input x is a matrix X, the function f(X) = [f(x1), f(x2), ..., f(x3)] is a function of any finite set of x. n The distribution follows a multivariate Gaussian distribution, i.e., f(X) ~ N(0,K(X,X)), where K(X,X) is the covariance matrix calculated from the covariance function;

[0031] Therefore, the prior distribution of the observed value y is:

[0032]

[0033] and the observed values ​​y and f(X) * The joint prior distribution of ) is:

[0034]

[0035] In the formula: K(X,X) represents all pairwise combinations (x,X) of the covariance function k on the training set X. i ,x j The B×B covariance matrix formed by the evaluation results between ) ; K(X,X * )=K(X * ,X) ΤFor test data X and training data X * B×B between * The first-order covariance matrix; I is a B×B dimensional identity matrix, K(X) * ,X * () is the test point X * B of its own * ×B * Dimension covariance matrix;

[0036] Therefore, the predicted value f(X) can be calculated. * (represented as f) * The posterior distribution of ) is:

[0037]

[0038] in:

[0039]

[0040] In the formula: and Σ * Test sample X * Corresponding predicted value f * The predicted mean and predicted variance.

[0041] Furthermore, the specific process of S22 is as follows:

[0042] Applying LDL decomposition, the inverse of a matrix can be calculated as:

[0043] K -1 =(L T ) -1 D -1 L -1

[0044]

[0045] In the formula: L is a lower triangular matrix with all diagonal elements equal to 1; K is a symmetric positive definite matrix; D is a diagonal matrix containing all diagonal elements; L T It is the transpose of L, and is an upper triangular matrix.

[0046] Further, S3 includes:

[0047] S31: First, the calculation formulas for four predictive goodness indices are given:

[0048]

[0049] In the formula: y i This is the actual power value. Here are the predicted power values, where N is the total number of samples; MAPE, R 2RMSE and MAE are the mean absolute percentage error, coefficient of determination, root mean square error, and mean absolute error, respectively.

[0050] Then, the four prediction goodness indices mentioned above were used to evaluate the performance of different combinations of variables input into the Gaussian process model.

[0051] Further, S4 includes:

[0052] S41: In view of MAPE, RMSE, 1-R 2 The four predictive goodness indices, namely MAE, have different orientations. By applying the entropy weight method, different weights are assigned to each index to obtain a comprehensive index.

[0053] S42: Multiply the four prediction goodness index values ​​by their corresponding weights and sum them to obtain the comprehensive index.

[0054] Furthermore, in S41, the specific steps of the entropy weight method are as follows:

[0055] Collect the values ​​of M samples under four prediction goodness metrics to construct a decision matrix:

[0056]

[0057] Standardize the decision matrix C;

[0058]

[0059] Calculate the information entropy of the predictive excellence index (MAE):

[0060]

[0061] In the formula: when Q i,MAE When = 0, let Q i,MAE lnQ i,MAE =0;

[0062] Calculate the weights of the predictive goodness index (MAE):

[0063]

[0064] In the formula: w MAE The larger the value, the higher the weight of the predictive excellence index (MAE) in the overall evaluation.

[0065] Further, step S42 specifically involves multiplying the prediction goodness index value by its corresponding weight and then summing the results to obtain the expression for the comprehensive index T, as shown below:

[0066]

[0067] In the formula: s MAE sRMSE , and s MAPE These are the MAE, RMSE, and 1-R values ​​for the wind turbine power curve model. 2 The values ​​of MAPE.

[0068] Beneficial effects of this invention:

[0069] 1. This invention first applies the Random Forest algorithm to objectively select key variables, and then inputs the key variables determined by the Random Forest into an improved Gaussian process; then, it utilizes MAPE, RMSE, and 1-R... 2 The model performance is evaluated using multiple prediction goodness indices such as MAE, and the comprehensive index is obtained by weighting each index using the entropy weight method to evaluate the prediction accuracy of the model. The method of this invention not only improves the prediction accuracy of the wind turbine power curve model, but also provides an important reference for accurately representing the performance of wind turbines. This model provides a scientific and accurate basis for the optimal operation and economic construction of wind farms.

[0070] 2. This invention addresses the issues of subjectivity in selecting model variables, neglecting the computational efficiency of Gaussian process regression, and using only a single evaluation index to assess model performance in existing studies. The model involved in this invention uses the random forest algorithm for variable selection, achieving objective evaluation and selection of variables, thereby overcoming the subjectivity problem in previous studies. By combining the variable selection process with the improved Gaussian process, the predictive efficiency of the Gaussian process model is improved. The entropy weight method is used to obtain a comprehensive index, which can comprehensively evaluate the model performance. Attached Figure Description

[0071] Figure 1 This is a flowchart of the wind turbine power curve model based on random forest and improved Gaussian process in this invention;

[0072] Figure 2 The curves showing the predicted and actual power values ​​of wind turbine units;

[0073] Figure 3 The power prediction residual curve of the wind turbine unit;

[0074] Figure 4 This is a scatter plot showing the actual power of the wind turbine and the predicted power of the model in this invention.

[0075] Figure 5 Comparison results of comprehensive indicators of different models;

[0076] Figure 6 The predicted residual distribution of three power curve models for the second wind turbine in the same wind farm;

[0077] Figure 7It is the prediction residual distribution of three power curve models of the third wind turbine in the same wind farm. Specific implementation mode

[0078] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] Embodiment 1: As Figure 1 shown, a power curve modeling method for a wind turbine considering random forest and improved Gaussian process includes the following steps:

[0080] S1: Apply the random forest algorithm to screen out m variables that have a significant impact on power from n variables that may affect the power of the wind turbine.

[0081] S11: Collect n variables of the SCADA operation data variables every 10 minutes in a certain wind farm. Specifically, in this embodiment, it includes 15 variables such as density-adjusted wind speed, wind speed, turbulence intensity, rotor speed, tip speed ratio, pitch angle, transformer temperature, wind direction, stator temperature, ambient temperature, nacelle temperature, blade position, rotor bearing temperature, yaw error, and gearbox oil temperature. The output variable is power. That is, in this embodiment, n is 15.

[0082] S12: Input the above variables into the random forest algorithm to evaluate the importance of the variables to the output power, so as to obtain the importance score of each variable; then, select the top m variables with the highest scores for further analysis. In this embodiment, m is 6.

[0083] Further, the S12 is specifically:

[0084] Randomly and with replacement, z (z < N) samples are drawn from N samples and n variables, and G repeated samplings are performed to obtain G sub-training sets; among them, the data not selected constitutes out-of-bag data (OBB); for the g (g = 1, 2,..., G) sub-training sets, decision trees are independently constructed and trained; each decision tree calculates its voting result L on the corresponding OBB g ; randomly perturb the variable A i (i = 1, 2,... n) in the OBB, and recalculate the voting result L obtained by the decision tree in the corresponding OBB g,i ; by calculating the importance score P of each variable i and arranging them in descending order to determine the most important variables to construct an optimal variable combination, where P i The larger it is, the more important the variable is; the corresponding formula is as follows:

[0085]

[0086] In the formula: G is the total number of decision trees; Pi Assigning importance scores to variables;

[0087] After obtaining the importance scores of the above variables, the top m variables with the highest scores are selected for analysis.

[0088] S2: Input m variables that have a significant impact on power into the improved Gaussian process;

[0089] S21: Input the selected m variables into the improved Gaussian process;

[0090] The improved Gaussian process in S21 is as follows:

[0091] The Gaussian process (GP) is a powerful nonparametric machine learning technique whose properties are determined by the mean function m(x) and the covariance function k(x,x′), as shown in the following formula:

[0092] m(x) = E[f(x)]

[0093] k(x,x′)=E[(f(x)-m(x))(f(x′)-m(x′))]

[0094] In the formula: x, x′∈R d Let R be any random variable (R represents the set of real numbers, d represents the dimension, R...) d (representing d-dimensional real space);

[0095] Therefore, a Gaussian process can be defined as f(x)~GP(m(x),k(x,x′)), where m(x) is usually assumed to be 0;

[0096] Assuming the observed target y contains noise, denoted as ε, the relationship between the observed target y and the function output value f(x) is as follows:

[0097] y = f(x) + ε

[0098] In the formula: x is the input vector, ε is a vector with a mean of 0 and a variance of . A normally distributed random variable can be denoted as

[0099] When the input x is a matrix X, the function f(X) = [f(x1), f(x2), ..., f(x3)] is a function of any finite set of x. n The distribution follows a multivariate Gaussian distribution, i.e., f(X) ~ N(0,K(X,X)), where K(X,X) is the covariance matrix calculated from the covariance function;

[0100] Therefore, the prior distribution of the observed value y is:

[0101]

[0102] and the observed values ​​y and f(X) * The joint prior distribution of ) is:

[0103]

[0104] In the formula: K(X,X) represents all pairwise combinations (x,X) of the covariance function k on the training set X. i ,x j The B×B covariance matrix formed by the evaluation results between ) ; K(X,X * )=K(X * ,X) Τ For test data X and training data X * B×B between * The first-order covariance matrix; I is a B×B dimensional identity matrix, K(X) * ,X * () is the test point X * B of its own * ×B * Dimension covariance matrix;

[0105] Therefore, the predicted value f(X) can be calculated. * (represented as f) * The posterior distribution of ) is:

[0106]

[0107] in:

[0108]

[0109] Where: and Σ * Test sample X * Corresponding predicted value f * The predicted mean and predicted variance.

[0110] S22: Choose LDL decomposition to calculate the symmetric positive definite matrix.

[0111] The specific process of S22 is as follows:

[0112] This invention applies the fmincon optimization algorithm to determine the optimal hyperparameters of a Gaussian process model. This process involves calculating the inverse of a large-scale covariance matrix, which is particularly computationally intensive in high-dimensional cases. Two common methods for finding symmetric positive definite matrices are Cholesky decomposition and LDL decomposition. Compared to Cholesky decomposition, LDL decomposition does not involve square root operations, thus reducing computational overhead. Furthermore, LDL decomposition produces unit lower triangular and diagonal matrices, and its structural simplicity further improves computational efficiency. Applying LDL decomposition, the matrix inverse can be calculated as follows:

[0113] K -1 =(L T ) -1 D -1 L -1

[0114]

[0115] In the formula: L is a lower triangular matrix with all diagonal elements equal to 1; K is a symmetric positive definite matrix; D is a diagonal matrix containing all diagonal elements; L T It is the transpose of L, and is an upper triangular matrix.

[0116] S3: Apply four predictive goodness metrics: MAPE, RMSE, 1-R 2 The predictive performance of the wind turbine power curve model was evaluated by MAE.

[0117] Further, S3 includes:

[0118] S31: First, the calculation formulas for four predictive goodness indices are given:

[0119]

[0120]

[0121] In the formula: y i This is the actual power value. Here are the predicted power values, where N is the total number of samples; MAPE, R 2 RMSE and MAE are the mean absolute percentage error, coefficient of determination, root mean square error, and mean absolute error, respectively.

[0122] Then, the four prediction goodness indices mentioned above were used to evaluate the performance of different combinations of variables input into the Gaussian process model.

[0123] S4: Apply the entropy weight method to assign different weights to the above four types of indicators, thereby obtaining a comprehensive indicator.

[0124] S41: In view of MAPE, RMSE, 1-R 2 The four predictive goodness indices, namely MAE, have different orientations. By applying the entropy weight method, different weights are assigned to each index to obtain a comprehensive index.

[0125] The specific steps of the entropy weight method are as follows:

[0126] Collect the values ​​of M samples under four prediction goodness metrics to construct a decision matrix:

[0127]

[0128] The decision matrix C is standardized. Here, we only list the standardization method for the predictive goodness index MAE. The standardization methods for other predictive goodness indices are the same.

[0129]

[0130] Calculate the information entropy of the predictive excellence index (MAE):

[0131]

[0132] In the formula: when Q i,MAE When = 0, let Q i,MAE lnQ i,MAE =0.

[0133] Calculate the weights of the predictive goodness index (MAE):

[0134]

[0135] In the formula: w MAE The larger the value, the higher the weight of the predictive goodness of prediction (MAE) index in the overall evaluation. RMSE , and w MAPE The calculation method is the same.

[0136] S42: Multiply the four prediction goodness index values ​​by their corresponding weights and sum them to obtain the comprehensive index.

[0137] Further, step S42 specifically involves multiplying the prediction goodness index value by its corresponding weight and then summing the results to obtain the expression for the comprehensive index T, as shown below:

[0138]

[0139] In the formula: s MAE s RMSE , and s MAPE These are the MAE, RMSE, and 1-R values ​​for the wind turbine power curve model. 2 The values ​​of MAPE.

[0140] Example 2:

[0141] This invention collects SCADA operation data every 10 minutes from January 1, 2021 to February 16, 2021 from the Penmanshiel Wind Farm in the UK for experimental analysis. The original dataset contained 6768 records; after removing outlier data points, 5538 valid data points were obtained.

[0142] The data includes 15 different variables: density-adjusting wind speed, wind speed, turbulence intensity, rotor speed, tip speed ratio, blade pitch angle, transformer temperature, wind direction, stator temperature, ambient temperature, nacelle temperature, blade position, rotor bearing temperature, yaw error, and gearbox oil temperature.

[0143] Subsequently, the importance of the 15 variables was evaluated using the random forest algorithm. The results were sorted in descending order of importance scores and are shown in Table 1.

[0144] Table 1 Importance scores of 15 variables

[0145]

[0146] This invention selects the following six variables as model inputs: density adjustment wind speed, rotor speed, turbulence intensity, blade pitch angle, tip velocity ratio, and transformer temperature. (Wind speed was not selected because density adjustment wind speed and wind speed have a strong correlation.)

[0147] Figure 2 and 3 The verification results obtained by substituting the above variables into the improved Gaussian process model are presented. From Figure 2 As can be seen, the predicted value is very close to the actual value. Figure 3 As can be seen, most of the normalized residuals are concentrated between -0.1 and 0.1. This observation indicates that the model has high predictive accuracy.

[0148] Figure 4 The diagram shows a scatter plot of the actual power of the wind turbine and the predicted power of the model of this invention, which is obtained by converting the normalized values ​​of the actual power and the predicted power back to the original power measurement range and redrawing them in the coordinate system of wind speed and power.

[0149] pass Figure 4 A thorough analysis of the results presented reveals that the model proposed in this invention performs exceptionally well in predicting wind turbine power, closely matching the actual measured power data. This result not only demonstrates the accuracy of the model's predictive capabilities but also highlights its practical value in wind power curve prediction.

[0150] To evaluate the effectiveness of the power curve model proposed in this invention, six different methods were compared: k-nearest neighbor (KNN) algorithm, Bean's method (BM), artificial neural network (ANN) algorithm, XGBoost algorithm, a 15-variable Gaussian process model (GP-15), and the original Gaussian process model (GP-O). It is worth noting that, except for the Bean's method which uses only wind speed as a single input variable and the original Gaussian process model which uses subjectively selected multivariate inputs, all other models employ the same multivariate input strategy as the model in this invention.

[0151] This invention applies the aforementioned MAPE, MAE, RMSE, and 1-R. 2 The prediction accuracy of six different power curve model methods was calculated using four prediction goodness indices, and the results are shown in Table 2.

[0152] Table 2. Four types of prediction goodness indices for different power curve models.

[0153]

[0154] The data in Table 2 show that the model proposed in this invention performs well in three key indicators: MAPE, MAE, and 1-R. 2 The results show that the proposed model outperforms the comparison model in all aspects, indicating that it has certain advantages in prediction accuracy and applicability. However, in terms of the RMSE metric, the proposed model is slightly inferior to the XGBoost algorithm. This phenomenon may stem from the fact that XGBoost is more efficient when handling certain types of data structures. Furthermore, although the BM model performs better in RMSE and 1-R... 2 The performance index is lower than that of the KNN model, but its MAPE and MAE are higher. This result reveals the limitations of relying on a single performance index. To address this issue, this invention applies the entropy weight method to comprehensively consider various performance indices and calculates the comprehensive index T for each model, such as... Figure 5 As shown.

[0155] This invention further verifies the accuracy of the model by introducing data from two other wind turbines of the same model from the Penmanshiel wind farm, and plots the corresponding power prediction residual distribution diagram. Figure 6 and Figure 7 The two wind turbine units are designated as WT1 and WT2, respectively.

[0156] This invention proposes a wind turbine power curve model based on random forest and improved Gaussian process, and demonstrates the model's effectiveness through empirical analysis of operating data from a 2.05MW experimental turbine at the Penmanshiel Wind Farm in the UK. Compared to existing models, the original contributions of this invention are as follows:

[0157] (1) This invention uses the random forest algorithm to identify key variables that affect power, effectively improving the prediction accuracy of the power curve model of the 2.05MW test unit of the Penmanshiel wind farm.

[0158] (2) Introducing LDL decomposition to calculate the inverse matrix in the Gaussian process effectively shortens the calculation time for finding the inverse matrix.

[0159] (3) The entropy weight method is used to generate comprehensive indicators, which effectively resolves the conflict between the four types of indicators in terms of prediction accuracy.

[0160] (4) The prediction residual distribution of the other two wind turbines in the Penmanshiel wind farm was analyzed to further confirm the effectiveness of the model.

[0161] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for modeling the power curve of wind turbines that considers random forests and improved Gaussian processes, characterized in that: It includes the following steps: S1: Use the random forest algorithm to select m variables that have a significant impact on power from n variables that may affect the power of wind turbine units; S2: Input m variables that have a significant impact on power into the improved Gaussian process; S3: Apply four predictive goodness metrics: MAPE, RMSE, 1-R 2 The predictive performance of the wind turbine power curve model was evaluated by MAE. S4: Apply the entropy weight method to assign different weights to the above four types of prediction goodness indicators, thereby obtaining a comprehensive index; S2 specifically includes: S21: Input the selected m variables into the improved Gaussian process; S22: Choose LDL decomposition to calculate the symmetric positive definite matrix; The improved Gaussian process in S21 is as follows: The characteristics of a Gaussian process (GP) are determined by the mean function m(x) and the covariance function k(x,x′), and their corresponding formulas are shown below: m(x) = E[f(x)] k(x,x′)=E[(f(x)-m(x))(f(x′)-m(x′))] In the formula: x, x′∈R d Let R be any random variable, d represent the set of real numbers, and d represent the dimension. d Represents the d-dimensional real space; Therefore, a Gaussian process can be defined as f(x)~GP(m(x),k(x,x′)), where m(x) is usually assumed to be 0; Assuming the observed target y contains noise, denoted as ε, the relationship between the observed target y and the function output value f(x) is as follows: y = f(x) + ε In the formula: x is the input vector, ε is a vector with a mean of 0 and a variance of . A normally distributed random variable can be denoted as When the input x is a matrix X, the function f(X) = [f(x1), f(x2), ..., f(x3)] is a function of any finite set of x. n The distribution follows a multivariate Gaussian distribution, i.e., f(X) ~ N(0,K(X,X)), where K(X,X) is the covariance matrix calculated from the covariance function; Therefore, the prior distribution of the observed value y is: and the observed values ​​y and f(X) * The joint prior distribution of ) is: In the formula: K(X,X) represents all pairwise combinations (x,X) of the covariance function k on the training set X. i ,x j The B×B covariance matrix formed by the evaluation results between ) ; K(X,X * )=K(X * ,X) Τ For test data X and training data X * The covariance matrix between them is a B×B* order matrix; I is a B×B dimensional identity matrix, K(X) * ,X * () is the test point X * Its own B*×B* dimension covariance matrix; Therefore, the predicted value f(X) can be calculated. * ), represented as f * Its posterior distribution is: in: In the formula: and Σ * Test sample X * Corresponding predicted value f * The predicted mean and predicted variance; The specific process of S22 is as follows: Applying LDL decomposition, the inverse of a matrix can be calculated as: K -1 =(L T ) -1 D -1 L -1 In the formula: L is a lower triangular matrix with all diagonal elements equal to 1; K is a symmetric positive definite matrix; D is a diagonal matrix containing all diagonal elements; L T It is the transpose of L, and is an upper triangular matrix.

2. The method for modeling wind turbine power curves considering random forests and improved Gaussian processes according to claim 1, characterized in that: S1 specifically includes: S11: Collect n input variables of a wind farm's SCADA system over a period of time, with power as the output variable; S12: Input the above variables into the random forest algorithm to evaluate the importance of the variables to the output power, thereby obtaining the importance score of each variable; then, select the top m variables with the highest scores for further analysis.

3. The method for modeling wind turbine power curves considering random forests and improved Gaussian processes according to claim 2, characterized in that: Specifically, S12 is: Randomly draw z samples with replacement from N samples and n variables, where z < N, and perform G repeated samplings to obtain G sub-training sets; among them, the data not selected constitutes out-of-bag (OBB) data; for the g-th sub-training set, independently construct a decision tree and train it, where g = 1, 2, …, G; each decision tree calculates its voting result L on the corresponding OBB g ; randomly perturb the variable A in the OBB i , where i = 1, 2, …, n, and recalculate the voting result L obtained by the decision tree in the corresponding OBB g,i ; determine the importance score P of each variable i and sort them in descending order to identify the most important variables for constructing the optimal variable combination, where the larger P i indicates that the variable is more important; the corresponding formula is shown below: In the formula: G is the total number of decision trees; P i Assigning importance scores to variables; After obtaining the importance scores of the above variables, the top m variables with the highest scores are selected for analysis.

4. The method for modeling wind turbine power curves considering random forests and improved Gaussian processes according to claim 1, characterized in that: S3 includes: S31: First, the calculation formulas for four predictive goodness indices are given: In the formula: y i This is the actual power value. Here are the predicted power values, where N is the total number of samples; MAPE, R 2 RMSE and MAE are the mean absolute percentage error, coefficient of determination, root mean square error, and mean absolute error, respectively. Then, the performance of the variables input into the Gaussian process model is evaluated using the four prediction goodness indices mentioned above.

5. The method for modeling wind turbine power curves considering random forests and improved Gaussian processes according to claim 1, characterized in that: S4 includes: S41: In view of MAPE, RMSE, 1-R 2 The four predictive goodness indices, namely MAE, have different orientations. By applying the entropy weight method, different weights are assigned to each index to obtain a comprehensive index. S42: Multiply the four prediction goodness index values ​​by their corresponding weights and sum them to obtain the comprehensive index.

6. The method for modeling wind turbine power curves considering random forests and improved Gaussian processes according to claim 5, characterized in that: In step S41, the specific steps of the entropy weight method are as follows: Collect the values ​​of M samples under four prediction goodness metrics to construct a decision matrix: Standardize the decision matrix C; Calculate the information entropy of the predictive excellence index (MAE): In the formula: when Q i,MAE When = 0, let Q i,MAE lnQ i,MAE =0; Calculate the weights of the predictive goodness index (MAE): In the formula: w MAE The larger the value, the higher the weight of the predictive goodness index (MAE) in the overall evaluation; the same method is used to calculate the predictive goodness indices RMSE and 1-R. 2 The weights of MAPE.

7. The method for modeling wind turbine power curves considering random forests and improved Gaussian processes according to claim 5, characterized in that: Specifically, S42 involves multiplying the prediction goodness index value by its corresponding weight and then summing the results to obtain the expression for the comprehensive index T, as shown below: In the formula: s MAE s RMSE , and s MAPE These are the MAE, RMSE, and 1-R values ​​for the wind turbine power curve model. 2 The values ​​of MAPE.

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