Power system inertia estimation method based on feature extraction and regression learning separation

Abstract

The invention discloses a power system inertia estimation method based on feature extraction and regression learning separation, and the method comprises the following steps: S1, building a power system frequency response model SFR, and generating data for simulating the operation of a power system; s2, extracting characteristics of frequency deviation and power disturbance of the power system by using a convolutional neural network (CNN); s3, using an activation value extraction function to extract advanced features from a full connection layer of the convolutional neural network CNN as input of an extreme gradient boosting tree XGBoost, using a bird mating optimizer to optimize hyper-parameters of the extreme gradient boosting tree XGBoost, performing regression learning on the model, and outputting an inertia estimation value; according to the method, data features are extracted by using the powerful feature extraction capability of a convolutional neural network CNN, then the data features are processed by using the efficient regression learning capability of an optimized extreme gradient boosting tree XGBoost, and based on time sequence data of frequency deviation and power disturbance, through a mode of feature extraction and regression learning separation, the frequency deviation and the power disturbance are calculated. The inertia of the system can be accurately estimated.

Description

Technical Field

[0001] The invention relates to the field of power systems, and in particular to a method for estimating inertia of a power system based on separation of feature extraction and regression learning. Background Art

[0002] The inertia of the power system is an important indicator that reflects the stability of the system operation. When a power disturbance occurs in the system, the inertia can reduce the frequency change rate through energy conversion, providing reaction time for the adjustment measures. Therefore, accurate estimation of the system inertia is very important to ensure the safety and stability of the power grid. There are some shortcomings in the existing inertia estimation methods: for example, the traditional physical model method is difficult to accurately describe the nonlinear characteristics and dynamic behavior of the system, most methods rely on large disturbance events and cannot continuously estimate the inertia under normal operating conditions, and the estimation accuracy is insufficient. To this end, the present invention proposes a power system inertia estimation method based on the separation of feature extraction and regression learning. Summary of the invention

[0003] To achieve the above purpose, the technical solution provided by the present invention is:

[0004] The power system inertia estimation method based on feature extraction and regression learning separation includes the following steps:

[0005] S1: Establish the power system frequency response model SFR to generate data simulating the operation of the power system;

[0006] S2: Use convolutional neural network (CNN) to extract the characteristics of frequency deviation and power disturbance of power system;

[0007] S3: The activation value extraction function extracts high-level features from the fully connected layer of the convolutional neural network CNN as the input of the extreme gradient boosting tree XGBoost, and the bird mating optimizer is used to optimize the hyperparameters of the extreme gradient boosting tree XGBoost. The model performs regression learning and outputs the inertia estimation value.

[0008] Furthermore, the specific steps of step S1 are as follows:

[0009] S1-1: Swing equation of synchronous generator:

[0010]

[0011] In formula (1), H is the inertia constant, Δf is the frequency deviation of the synchronous generator rotor (pu), and Δp m is the change in mechanical power (pu), Δp e is the change in electromagnetic power (pu), D is the damping coefficient;

[0012] Assume that in the very short time when the system is disturbed, the change in electromagnetic power Δp m ≈0, the simplified equation becomes:

[0013]

[0014] It is considered that the change of electromagnetic power is caused by the input power disturbance p d Caused by, Laplace transform is performed on equation (2) to obtain the response function G of the system frequency deviation to power disturbance:

[0015]

[0016] In formula (3), ΔF(s) is the frequency deviation in the Laplace domain, ΔP(s) is the power disturbance in the Laplace domain, and s is the complex frequency variable in the Laplace transform;

[0017] S1-2: Transfer function of turbine speed governor:

[0018] Consider the dynamic characteristics of the turbine governor, that is, the mechanical power p m The influence of the turbine speed regulator is added as follows:

[0019]

[0020] In formula (4), K m is the mechanical power gain factor, F H is the high pressure turbine power ratio, T R is the reheat time constant, R is the turbine governor droop constant;

[0021] S1-3: Establish the power system frequency response model SFR:

[0022] The response function G of the system frequency deviation to power disturbance and the transfer function T of the turbine governor are connected through negative feedback to form a complete power system frequency response model SFR. By inputting small-amplitude random power disturbance data into the power system frequency response model SFR, the frequency deviation and corresponding inertia value of the simulated power system during operation can be output.

[0023] Furthermore, the specific steps of step S2 are as follows:

[0024] S2-1: Establish convolutional neural network CNN:

[0025] Set up the input layer, input the frequency deviation and power disturbance data, and standardize the data:

[0026]

[0027] In formula (5), x nis the result of standardization, x is the input data, μ is the mean of the input data, and σ is the standard deviation of the input data;

[0028] Set the convolution layer to extract the local features of the input data. The formula is as follows:

[0029] h=W*x n +b (22)

[0030] In formula (6), h is the feature map of the convolution layer, W is the weight of the convolution kernel, b is the bias term, and * is the convolution operation;

[0031] Setting the activation layer introduces nonlinearity:

[0032] y=max(0,h) (23)

[0033] In formula (7), y is the activation layer feature map after the nonlinearity is introduced, and max is to compare the elements in the convolutional layer feature map h with 0 one by one. If it is greater than 0, it is retained, otherwise it is taken as 0;

[0034] Set the normalization layer to process the activation layer feature map y:

[0035]

[0036] In formula (8), It is the result of normalizing the activation layer feature map y. E and V are the mean and variance of the activation layer feature map y, respectively. ε is a very small constant to prevent the denominator from being zero.

[0037]

[0038] In formula (9), z is the normalized layer feature map, γ and β are learnable scaling and translation parameters respectively;

[0039] Continue to set the convolution layer, activation layer and normalization layer in sequence. The normalization layer feature map z passes through these layers and the output is the total feature map z n ;

[0040] Set the global average pooling layer to pool each total feature map z n The average formula is as follows:

[0041]

[0042] In formula (10), y k is the feature vector after global average pooling, and N is the total number of elements in each total feature map;

[0043] Set the fully connected layer fc1 to map the feature vector into a high-dimensional feature vector:

[0044] y'=W k zn +b k (27)

[0045] In formula (11), y' is the high-dimensional feature vector output by the fully connected layer, W k is the weight matrix, b k is the bias vector;

[0046] Set up the activation layer and the fully connected layer fc2. The fully connected layer fc2 maps all features into a scalar output of an inertia value. Finally, connect a regression layer to calculate the error, backpropagate for feedback, and update the parameters of the convolutional layer and the fully connected layer.

[0047] S2-2: Determine the parameters of the fully connected layer of the convolutional neural network CNN:

[0048] The data is divided into a training set and a test set. The data of the training set is input into the established convolutional neural network CNN. The convolutional neural network CNN is trained. The weight matrix W in the fully connected layer is determined through the feedback of the last regression layer. k and the bias vector b k ;

[0049] S2-3: Extract features using convolutional neural network (CNN):

[0050] Both the training set and the test set of the data are input into the convolutional neural network CNN. After the convolution layer, activation layer and global average pooling layer, the local, linear and nonlinear features of the data are integrated into high-level features in the fully connected layer fc1.

[0051] Furthermore, the specific steps of step S3 are as follows:

[0052] S3-1: Building Extreme Gradient Boosting Tree XGBoost:

[0053] The objective function L of the model is determined by measuring the error size and model complexity, and regression learning is performed in the direction of reducing the objective function value:

[0054]

[0055] In formula (12), y i is the true value of inertia, is the estimated value of inertia, Ω is the regularization term that controls the complexity of the model, and A is the loss function, which is formulated as follows:

[0056]

[0057] Determine the update iteration formula:

[0058]

[0059] In formula (14), is the estimated inertia after the tth iteration, is the estimated inertia after the t-1th iteration, η is the learning rate, and f t (y') is the newly constructed decision tree in round t;

[0060] At each iteration, the loss function is approximated using the first-order gradient and the second-order gradient:

[0061]

[0062] In formula (15), g i is the loss function A for the inertia estimate The first-order gradient, h i is the loss function A for the estimated inertia The second-order gradient of

[0063] When building a decision tree, the information gain Gain is calculated to determine the effect of each node splitting, so as to select the optimal splitting point. The formula is as follows:

[0064]

[0065] In formula (16), I represents the dataset index of the current node, I L and I R Represents the dataset index of the left child node and the right child node respectively, λ is the regularization parameter, γ n is the penalty parameter for splitting a node;

[0066] S3-2: Optimizing the Hyperparameters of Extreme Gradient Boosting Tree XGBoost with Birds Mating Optimizer:

[0067] Use the activation value extraction function activations to extract high-level features from the fully connected layer fc1, which includes the training set and the test set, and input the training set into the extreme gradient boosting tree XGBoost;

[0068] Initialize the bird flock of the bird mating optimizer and set the hyperparameters of the extreme gradient boosting tree XGBoost: maximum depth, learning rate, sample sampling ratio, feature sampling ratio and regularization parameter. One bird corresponds to a set of hyperparameter combinations.

[0069] Calculate the root mean square error of each bird on the training set and use it as the evaluation criterion;

[0070] Select birds with small root mean square error for mating to generate new hyperparameter combinations;

[0071] Perform mutation operations on the new hyperparameter combination and iterate the optimization until the maximum number of iterations is reached to obtain the optimal hyperparameter combination;

[0072] S3-3: Estimating inertia values ​​using extreme gradient boosting tree XGBoost:

[0073] Use the optimal hyperparameter combination to set the hyperparameters of the extreme gradient boosting tree XGBoost, perform regression learning on the extreme gradient boosting tree XGBoost, and then input the test set of high-level features into the extreme gradient boosting tree XGBoost to output the estimated value of inertia.

[0074] Compared with the existing technology, the principles and advantages of this solution are as follows:

[0075] This scheme first establishes the power system frequency response model SFR and generates data simulating the operation of the power system. Secondly, the convolutional neural network CNN is used to extract the characteristics of the frequency deviation and power disturbance of the power system. Then the activation value extraction function extracts high-level features from the fully connected layer of the convolutional neural network CNN as the input of the extreme gradient boosting tree XGBoost. The bird mating optimizer is used to optimize the hyperparameters of the extreme gradient boosting tree XGBoost. The model performs regression learning and outputs the inertia estimation value.

[0076] This solution uses the powerful feature extraction capability of convolutional neural network (CNN) to extract data features, and then uses the efficient regression learning capability of tuned extreme gradient boosting tree XGBoost to process data features. Based on the time series data of frequency deviation and power disturbance, the inertia of the system can be accurately estimated through the separation of feature extraction and regression learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a flowchart of the steps of the method for estimating inertia of a power system based on separation of feature extraction and regression learning in an embodiment of the present invention;

[0078] Figure 2 A control block diagram of a power system frequency response model SFR in an embodiment of the present invention;

[0079] Figure 3 A comparison diagram of the actual value and the estimated value of inertia in an embodiment of the present invention;

[0080] Figure 4 4 is a comparison chart of the error results of the model in the embodiment of the present invention. DETAILED DESCRIPTION

[0081] The present invention will be further described below in conjunction with specific embodiments:

[0082] Figure 1 The figure shows a flow chart of the steps of the power system inertia estimation method based on feature extraction and regression learning separation. Figure 2The control block diagram of the power system frequency response model SFR is shown. The power system inertia estimation method based on feature extraction and regression learning separation described in this embodiment includes the following steps:

[0083] S1: Establish the power system frequency response model SFR and generate data simulating the operation of the power system; the specific process is as follows:

[0084] S1-1: Swing equation of synchronous generator:

[0085]

[0086] In formula (17), H is the inertia constant, Δf is the frequency deviation of the synchronous generator rotor (pu), and Δp m is the change in mechanical power (pu), Δp e is the change in electromagnetic power (pu), D is the damping coefficient;

[0087] Assume that in the very short time when the system is disturbed, the change in electromagnetic power Δp m ≈0, the simplified equation becomes:

[0088]

[0089] It is considered that the change of electromagnetic power is caused by the input power disturbance p d Caused by, Laplace transform is performed on equation (18) to obtain the response function G of the system frequency deviation to power disturbance:

[0090]

[0091] In formula (19), ΔF(s) is the frequency deviation in the Laplace domain, ΔP(s) is the power disturbance in the Laplace domain, and s is the complex frequency variable in the Laplace transform;

[0092] S1-2: Transfer function of turbine speed governor:

[0093] Consider the dynamic characteristics of the turbine governor, that is, the mechanical power p m The influence of the turbine speed regulator is added as follows:

[0094]

[0095] In formula (20), K m is the mechanical power gain factor, F H is the high pressure turbine power ratio, T R is the reheat time constant, R is the turbine governor droop constant;

[0096] S1-3: Establish the power system frequency response model SFR:

[0097] The response function G of the system frequency deviation to power disturbance and the transfer function T of the turbine governor are connected through negative feedback to form a complete power system frequency response model SFR. By inputting small-amplitude random power disturbance data into the power system frequency response model SFR, the frequency deviation and corresponding inertia value of the simulated power system during operation can be output.

[0098] The following step S2 uses the convolutional neural network CNN to extract the characteristics of the frequency deviation and power disturbance of the power system. The specific process is as follows:

[0099] S2-1: Establish convolutional neural network CNN:

[0100] Set up the input layer, input the frequency deviation and power disturbance data, and standardize the data:

[0101]

[0102] In formula (21), x n is the result of standardization, x is the input data, μ is the mean of the input data, and σ is the standard deviation of the input data;

[0103] Set the convolution layer to extract the local features of the input data. The formula is as follows:

[0104] h=W*x n +b (22)

[0105] In formula (22), h is the feature map of the convolution layer, W is the weight of the convolution kernel, b is the bias term, and * is the convolution operation;

[0106] Setting the activation layer introduces nonlinearity:

[0107] y=max(0,h) (23)

[0108] In formula (23), y is the activation layer feature map after the nonlinearity is introduced, and max is to compare the elements in the convolutional layer feature map h with 0 one by one. If it is greater than 0, it is retained, otherwise it is taken as 0;

[0109] Set the normalization layer to process the activation layer feature map y:

[0110]

[0111] In formula (24), It is the result of normalizing the activation layer feature map y. E and V are the mean and variance of the activation layer feature map y, respectively. ε is a very small constant to prevent the denominator from being zero.

[0112]

[0113] In formula (25), z is the normalized layer feature map, γ and β are learnable scaling and translation parameters respectively;

[0114] Continue to set the convolution layer, activation layer and normalization layer in sequence. The normalization layer feature map z passes through these layers and the output is the total feature map z n ;

[0115] Set the global average pooling layer to pool each total feature map z n The average formula is as follows:

[0116]

[0117] In formula (26), y k is the feature vector after global average pooling, and N is the total number of elements in each total feature map;

[0118] Set the fully connected layer fc1 to map the feature vector into a high-dimensional feature vector:

[0119] y'=W k z n +b k (27)

[0120] In formula (27), y' is the high-dimensional feature vector output by the fully connected layer, W k is the weight matrix, b k is the bias vector;

[0121] Set up the activation layer and the fully connected layer fc2. The fully connected layer fc2 maps all features into a scalar output of an inertia value. Finally, connect a regression layer to calculate the error, backpropagate for feedback, and update the parameters of the convolutional layer and the fully connected layer.

[0122] S2-2: Determine the parameters of the fully connected layer of the convolutional neural network CNN:

[0123] The data is divided into a training set and a test set. The data of the training set is input into the established convolutional neural network CNN. The convolutional neural network CNN is trained. The weight matrix W in the fully connected layer is determined through the feedback of the last regression layer. k and the bias vector b k ;

[0124] S2-3: Extract features using convolutional neural network (CNN):

[0125] Both the training set and the test set of the data are input into the convolutional neural network CNN. After the convolution layer, activation layer and global average pooling layer, the local, linear and nonlinear features of the data are integrated into high-level features in the fully connected layer fc1.

[0126] The following step S3 is to extract high-level features from the fully connected layer of the convolutional neural network CNN using the activation value extraction function as the input of the extreme gradient boosting tree XGBoost, optimize the hyperparameters of the extreme gradient boosting tree XGBoost using the bird mating optimizer, perform regression learning on the model, and output the inertia estimation value. The specific process is as follows:

[0127] S3-1: Building Extreme Gradient Boosting Tree XGBoost:

[0128] The objective function L of the model is determined by measuring the error size and model complexity, and regression learning is performed in the direction of reducing the objective function value:

[0129]

[0130] In formula (28), y i is the true value of inertia, is the estimated value of inertia, Ω is the regularization term that controls the complexity of the model, and A is the loss function, which is formulated as follows:

[0131]

[0132] Determine the update iteration formula:

[0133]

[0134] In formula (30), is the estimated inertia after the tth iteration, is the estimated inertia after the t-1th iteration, η is the learning rate, and f t (y') is the newly constructed decision tree in round t;

[0135] At each iteration, the loss function is approximated using the first-order gradient and the second-order gradient:

[0136]

[0137] In formula (31), g i is the loss function A for the estimated inertia The first-order gradient, h i is the loss function A for the estimated inertia The second-order gradient of

[0138] When building a decision tree, the information gain Gain is calculated to determine the effect of each node splitting, so as to select the optimal splitting point. The formula is as follows:

[0139]

[0140] In formula (32), I represents the dataset index of the current node, I L and IR Represents the dataset index of the left child node and the right child node respectively, λ is the regularization parameter, γ n is the penalty parameter for splitting a node;

[0141] S3-2: Optimizing the Hyperparameters of Extreme Gradient Boosting Tree XGBoost with Birds Mating Optimizer:

[0142] Use the activation value extraction function activations to extract high-level features from the fully connected layer fc1, which includes the training set and the test set, and input the training set into the extreme gradient boosting tree XGBoost;

[0143] Initialize the bird flock of the bird mating optimizer and set the hyperparameters of the extreme gradient boosting tree XGBoost: maximum depth, learning rate, sample sampling ratio, feature sampling ratio and regularization parameter. One bird corresponds to a set of hyperparameter combinations.

[0144] Calculate the root mean square error of each bird on the training set and use it as the evaluation criterion;

[0145] Select birds with small root mean square error for mating to generate new hyperparameter combinations;

[0146] Perform mutation operations on the new hyperparameter combination and iterate the optimization until the maximum number of iterations is reached to obtain the optimal hyperparameter combination;

[0147] S3-3: Estimating inertia values ​​using extreme gradient boosting tree XGBoost:

[0148] Use the optimal hyperparameter combination to set the hyperparameters of the extreme gradient boosting tree XGBoost, perform regression learning on the extreme gradient boosting tree XGBoost, and then input the test set of high-level features into the extreme gradient boosting tree XGBoost to output the estimated value of inertia.

[0149] In order to verify the effectiveness of the power system inertia estimation method, the integrated model was built on the MATLAB platform. The convolutional neural network CNN parameter settings are: the number of iterations is 400 times, and the batch size is 15. The extreme gradient boosting tree XGBoost hyperparameter range settings are: maximum depth [3,10], learning rate [0.01,0.1], sample sampling ratio [0.3,1.0], feature sampling ratio [0.3,1.0], regularization parameter [0.1,1.0], and the number of iterations is 80 times. The bird mating optimizer parameter settings are: the flock size is 15, the maximum number of iterations is 15, the reproduction coefficient is 0.5, and the mutation rate is 0.1. The comparison between the true value and the estimated value of inertia is plotted on Figure 3 , the error results of the model are compared and plotted on Figure 4 .

[0150] Combination Figures 3-4It can be seen that the estimated inertia value can better track the changing trend of the true inertia value. Compared with the use of convolutional neural network CNN alone, the determination coefficient of the power system inertia estimation method based on feature extraction and regression learning separation is increased from 0.8721 to 0.9861, the root mean square error is reduced from 0.2991 to 0.0986, and the mean absolute percentage error is reduced from 5.88% to 2.00%. The fitting effect and estimation accuracy have been significantly improved. This shows that this method can accurately estimate the inertia of the power system.

[0151] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A power system inertia estimation method based on feature extraction and regression learning separation, characterized in that: The following steps are involved: S1: Establish a power system frequency response model SFR to generate data simulating the operation of the power system; S2: Use convolutional neural network (CNN) to extract the characteristics of frequency deviation and power disturbance of power system; S3: The activation value extraction function extracts high-level features from the fully connected layer of the convolutional neural network CNN as the input of the extreme gradient boosting tree XGBoost, and the bird mating optimizer is used to optimize the hyperparameters of the extreme gradient boosting tree XGBoost. The model performs regression learning and outputs the inertia estimation value.

2. The method for estimating inertia of a power system based on separation of feature extraction and regression learning according to claim 1, characterized in that: The step S1 comprises: S1-1: Swing equation of synchronous generator: In formula (1), H is the inertia constant, Δf is the frequency deviation of the synchronous generator rotor (pu), and Δp m is the change in mechanical power (pu), Δp e is the change in electromagnetic power (pu), D is the damping coefficient; Assume that in the very short time when the system is disturbed, the change in electromagnetic power Δp m ≈0, the simplified equation becomes: It is considered that the change of electromagnetic power is caused by the input power disturbance p d Caused by, Laplace transform is performed on equation (2) to obtain the response function G of the system frequency deviation to power disturbance: In formula (3), ΔF(s) is the frequency deviation in the Laplace domain, ΔP(s) is the power disturbance in the Laplace domain, and s is the complex frequency variable in the Laplace transform; S1-2: Transfer function of turbine speed governor: Consider the dynamic characteristics of the turbine governor, that is, the mechanical power p m The influence of the turbine speed regulator is added as follows: In formula (4), K m is the mechanical power gain factor, F H is the high pressure turbine power ratio, T R is the reheat time constant, R is the turbine governor droop constant; S1-3: Establish the power system frequency response model SFR: The response function G of the system frequency deviation to power disturbance and the transfer function T of the turbine governor are connected through negative feedback to form a complete power system frequency response model SFR. By inputting small-amplitude random power disturbance data into the power system frequency response model SFR, the frequency deviation and corresponding inertia value of the simulated power system during operation can be output.

3. The method for estimating inertia of a power system based on separation of feature extraction and regression learning according to claim 2 is characterized in that: The step S2 comprises: S2-1: Establish convolutional neural network CNN: Set up the input layer, input the frequency deviation and power disturbance data, and standardize the data: In formula (5), x n is the result of standardization, x is the input data, μ is the mean of the input data, and σ is the standard deviation of the input data; Set the convolution layer to extract the local features of the input data. The formula is as follows: h=W*x n +b (6) In formula (6), h is the feature map of the convolution layer, W is the weight of the convolution kernel, b is the bias term, and * is the convolution operation; Setting the activation layer introduces nonlinearity: y=max(0,h) (7) In formula (7), y is the activation layer feature map after the nonlinearity is introduced, and max is to compare the elements in the convolutional layer feature map h with 0 one by one. If it is greater than 0, it is retained, otherwise it is taken as 0; Set the normalization layer to process the activation layer feature map y: In formula (8), It is the result of normalizing the activation layer feature map y. E and V are the mean and variance of the activation layer feature map y, respectively. ε is a very small constant to prevent the denominator from being zero. In formula (9), z is the normalized layer feature map, γ and β are learnable scaling and translation parameters respectively; Continue to set the convolution layer, activation layer and normalization layer in sequence. The normalization layer feature map z passes through these layers and the output is the total feature map z n ; Set the global average pooling layer to pool each total feature map z n The average formula is as follows: In formula (10), y k is the feature vector after global average pooling, and N is the total number of elements in each total feature map; Set the fully connected layer fc1 to map the feature vector into a high-dimensional feature vector: y'=W k z n +b k (11) In formula (11), y' is the high-dimensional feature vector output by the fully connected layer, W k is the weight matrix, b k is the bias vector; Set up the activation layer and the fully connected layer fc2. The fully connected layer fc2 maps all features into a scalar output of an inertia value. Finally, connect a regression layer to calculate the error, backpropagate for feedback, and update the parameters of the convolutional layer and the fully connected layer. S2-2: Determine the parameters of the fully connected layer of the convolutional neural network CNN: The data is divided into a training set and a test set. The data of the training set is input into the established convolutional neural network CNN. The convolutional neural network CNN is trained. The weight matrix W in the fully connected layer is determined through the feedback of the last regression layer. k and the bias vector b k ; S2-3: Extract features using convolutional neural network (CNN): Both the training set and the test set of the data are input into the convolutional neural network CNN. After the convolution layer, activation layer and global average pooling layer, the local, linear and nonlinear features of the data are integrated into high-level features in the fully connected layer fc1.

4. The method for estimating inertia of a power system based on separation of feature extraction and regression learning according to claim 3 is characterized in that: The step S3 comprises: S3-1: Building Extreme Gradient Boosting Tree XGBoost: The objective function L of the model is determined by measuring the error size and model complexity, and regression learning is performed in the direction of reducing the objective function value: In formula (12), y i is the true value of inertia, is the estimated value of inertia, Ω is the regularization term that controls the complexity of the model, and A is the loss function, which is formulated as follows: Determine the update iteration formula: In formula (14), is the estimated inertia after the tth iteration, is the estimated inertia after the t-1th iteration, η is the learning rate, and f t (y') is the newly constructed decision tree in round t; At each iteration, the loss function is approximated using the first-order gradient and the second-order gradient: In formula (15), g i is the loss function A for the estimated inertia The first-order gradient, h i is the loss function A for the estimated inertia The second-order gradient of When building a decision tree, the information gain Gain is calculated to determine the effect of each node splitting, so as to select the optimal splitting point. The formula is as follows: In formula (16), I represents the dataset index of the current node, I L and I R Represents the dataset index of the left child node and the right child node respectively, λ is the regularization parameter, γ n is the penalty parameter for splitting a node; S3-2: Optimizing the Hyperparameters of Extreme Gradient Boosting Tree XGBoost with Birds Mating Optimizer: Use the activation value extraction function activations to extract high-level features from the fully connected layer fc1, which includes the training set and the test set, and input the training set into the extreme gradient boosting tree XGBoost; Initialize the bird flock of the bird mating optimizer and set the hyperparameters of the extreme gradient boosting tree XGBoost: maximum depth, learning rate, sample sampling ratio, feature sampling ratio and regularization parameter. One bird corresponds to a set of hyperparameter combinations. Calculate the root mean square error of each bird on the training set and use it as the evaluation criterion; Select birds with small root mean square error for mating to generate new hyperparameter combinations; Perform mutation operations on the new hyperparameter combination and iterate the optimization until the maximum number of iterations is reached to obtain the optimal hyperparameter combination; S3-3: Estimating inertia values ​​using extreme gradient boosting tree XGBoost: Use the optimal hyperparameter combination to set the hyperparameters of the extreme gradient boosting tree XGBoost, perform regression learning on the extreme gradient boosting tree XGBoost, and then input the test set of high-level features into the extreme gradient boosting tree XGBoost to output the estimated value of inertia.

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