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

Abstract

The present invention discloses a method for estimating inertia of a power system based on separation of feature extraction and regression learning, comprising the following steps: S1: establishing a power system frequency response model SFR to generate data simulating the operation of the power system; S2: using a convolutional neural network (CNN) to extract features of frequency deviation and power disturbance of the power system; S3: using an activation value extraction function to extract high-level features from a fully connected layer of the convolutional neural network (CNN) as input to an extreme gradient boosting tree (XGBoost), optimizing hyperparameters of the extreme gradient boosting tree (XGBoost) using a bird mating optimizer, performing regression learning on the model, and outputting an inertia estimation value; the present invention utilizes the powerful feature extraction capability of the convolutional neural network (CNN) to extract data features, and then utilizes the efficient regression learning capability of the tuned extreme gradient boosting tree (XGBoost) to process the data features. Based on time series data of frequency deviation and power disturbance, the method can accurately estimate the inertia of the system through a mode of separation of feature extraction and regression learning.

Description

Technical Field

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

[0002] The inertia of the power system is an important indicator reflecting 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, accurately estimating 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 objectives, the technical solutions provided by the present invention are:

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

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

[0006] S2: Use convolutional neural networks (CNNs) to extract the characteristics of frequency deviation and power disturbance in power systems;

[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). The bird mating optimizer is used to optimize the hyperparameters of the extreme gradient boosting tree (XGBoost). The model performs regression learning and outputs an inertia estimate.

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

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

[0010] (1)

[0011] In formula (1), H is the inertia constant, is the frequency deviation of the synchronous generator rotor (pu), is the change in mechanical power (pu), 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 , the simplified equation becomes:

[0013] (2)

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

[0015] (3)

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

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

[0018] Considering the dynamic characteristics of the turbine governor, that is, the mechanical power p m The effect of adding the transfer function of the turbine governor T :

[0019] (4)

[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 of system frequency deviation to power disturbance is G and the transfer function of the turbine governor T Through negative feedback connection, a complete power system frequency response model SFR is formed. 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 frequency deviation and power disturbance data, and standardize the data:

[0026] (5)

[0027] In formula (5), x n It is the result of standardization. x is the input data, is the mean of the input data, 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] (6)

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

[0031] Setting the activation layer to introduce nonlinearity:

[0032] (7)

[0033] In formula (7), y It is the activation layer feature map after the introduction of nonlinearity, and max is the convolution layer feature map h The elements in are compared with 0 one by one. If they are greater than 0, they are retained, otherwise they are taken as 0.

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

[0035] (8)

[0036] In formula (8), is the activation layer feature map y The normalized result is E and V They are activation layer feature maps y The mean and variance of is a small constant that prevents the denominator from being zero;

[0037] (9)

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

[0039] Continue to set the convolution layer, activation layer and normalization layer in sequence, normalization layer feature map z After these layers, 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] (10)

[0042] In formula (10), y k is the feature vector after global average pooling, 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] (11)

[0045] In formula (11), 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, perform backpropagation 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 training set and test set. The data of the training set is input into the established convolutional neural network CNN. The convolutional neural network CNN is trained and the weight matrix in the fully connected layer is determined through the feedback of the last regression layer. W 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] Determine the objective function of the model by measuring the error size and model complexity L , regression learning is performed in the direction of reducing the objective function value:

[0054] (12)

[0055] In formula (12), is the true value of inertia, is an estimate of the inertia, is a regularization term that controls the complexity of the model, A is the loss function, which is formulated as follows:

[0056] (13)

[0057] Determine the update iteration formula:

[0058] (14)

[0059] In formula (14), It is t The estimated inertia after rounds of iterations, It is t -The estimated inertia after 1 round of iteration, is the learning rate, In the t A new decision tree is constructed;

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

[0061] (15)

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

[0063] When building a decision tree, calculate the information gain Gain To judge the effect of each node splitting, and thus select the optimal splitting point, the formula is as follows:

[0064] (16)

[0065] In formula (16), I Indicates 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, is the regularization parameter, is the penalty parameter for splitting the node;

[0066] S3-2: Optimizing the hyperparameters of extreme gradient boosting tree XGBoost using bird 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. Each 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 iteratively optimize until the maximum number of iterations is reached to obtain the optimal hyperparameter combination;

[0072] S3-3: Estimating inertia 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 to generate data simulating the power system operation. Secondly, the convolutional neural network (CNN) is used to extract the characteristics of the power system frequency deviation and power disturbance. 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.

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

[0077] Figure 1 Flowchart of the steps of a 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 This is a control block diagram of the power system frequency response model SFR in an embodiment of the present invention;

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

[0080] Figure 4 2 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 2 FIG. 1 is a control block diagram of a power system frequency response model SFR. The power system inertia estimation method based on separation of feature extraction and regression learning described in this embodiment includes the following steps:

[0083] S1: Establish a power system frequency response model SFR to generate data simulating the operation of the power system. The specific process is as follows:

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

[0085] (17)

[0086] In formula (17), His the inertia constant, is the frequency deviation of the synchronous generator rotor (pu), is the change in mechanical power (pu), 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 , the simplified equation becomes:

[0088] (18)

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

[0090] (19)

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

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

[0093] Considering the dynamic characteristics of the turbine governor, that is, the mechanical power p m The effect of adding the transfer function of the turbine governor T :

[0094] (20)

[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 of system frequency deviation to power disturbance is G and the transfer function of the turbine governor TThrough negative feedback connection, a complete power system frequency response model SFR is formed. 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 frequency deviation and power disturbance data, and standardize the data:

[0101] (twenty one)

[0102] In formula (21), x n It is the result of standardization. x is the input data, is the mean of the input data, 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] (twenty two)

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

[0106] Setting the activation layer to introduce nonlinearity:

[0107] (twenty three)

[0108] In formula (23), y It is the activation layer feature map after the introduction of nonlinearity, and max is the convolution layer feature map h The elements in are compared with 0 one by one. If they are greater than 0, they are retained, otherwise they are taken as 0.

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

[0110] (twenty four)

[0111] In formula (24), is the activation layer feature map y The normalized result isE and V They are activation layer feature maps y The mean and variance of is a small constant that prevents the denominator from being zero;

[0112] (25)

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

[0114] Continue to set the convolution layer, activation layer and normalization layer in sequence, normalization layer feature map z After these layers, 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] (26)

[0117] In formula (26), y k is the feature vector after global average pooling, 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] (27)

[0120] In formula (27), 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, perform backpropagation 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 training set and test set. The data of the training set is input into the established convolutional neural network CNN. The convolutional neural network CNN is trained and the weight matrix in the fully connected layer is determined through the feedback of the last regression layer. W 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 use the activation value extraction function to extract 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 estimate. The specific process is as follows:

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

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

[0129] (28)

[0130] In formula (28), is the true value of inertia, is an estimate of the inertia, is a regularization term that controls the complexity of the model, A is the loss function, which is formulated as follows:

[0131] (29)

[0132] Determine the update iteration formula:

[0133] (30)

[0134] In formula (30), It is t The estimated inertia after rounds of iterations, It is t -The estimated inertia after 1 round of iteration, is the learning rate, In the tA new decision tree is constructed;

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

[0136] (31)

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

[0138] When building a decision tree, calculate the information gain Gain To judge the effect of each node splitting, and thus select the optimal splitting point, the formula is as follows:

[0139] (32)

[0140] In formula (32), I Indicates 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, is the regularization parameter, is the penalty parameter for splitting the node;

[0141] S3-2: Optimizing the hyperparameters of extreme gradient boosting tree XGBoost using bird 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. Each 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 iteratively optimize until the maximum number of iterations is reached to obtain the optimal hyperparameter combination;

[0147] S3-3: Estimating inertia 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] 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 were: 400 iterations and a batch size of 15. The extreme gradient boosting tree (XGBoost) hyperparameter range settings were: 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 80 iterations. The bird mating optimizer parameter settings were: flock size 15, maximum number of iterations 15, reproduction coefficient 0.5, and mutation rate 0.1. The comparison between the true and estimated values ​​of inertia is plotted on Figure 3 , the error results of the model are compared and plotted on Figure 4 .

[0150] Combine Figures 3 and 4 It can be seen that the inertia estimate can well track the changing trend of the true inertia value. Compared with using the convolutional neural network (CNN) alone, the power system inertia estimation method based on feature extraction and regression learning separation increases the determination coefficient from 0.8721 to 0.9861, reduces the root mean square error from 0.2991 to 0.0986, and reduces the mean absolute percentage error from 5.88% to 2.00%. Both the fitting effect and estimation accuracy are 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, any changes made based on the shape and principle of the present invention should be included in the scope of protection 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 power system operation; S2: Use convolutional neural networks (CNNs) to extract the characteristics of frequency deviation and power disturbance in power systems; S3: The activation value extraction function extracts high-level features from the fully connected layer of the convolutional neural network (CNN) as the input to 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 an inertia estimate. The step S1 comprises: S1-1: Swing equation of synchronous generator: (1) In formula (1), H is the inertia constant, is the frequency deviation of the synchronous generator rotor (pu), is the change in mechanical power (pu), 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 , the simplified equation becomes: (2) It is believed that the change of electromagnetic power is caused by the input power disturbance p d Caused by, perform Laplace transform on Equation (2) to obtain the response function of system frequency deviation to power disturbance G : (3) In formula (3), is the frequency deviation in the Laplace domain, is the power perturbation in the Laplace domain, s is the complex frequency variable in the Laplace transform; S1-2: Transfer function of turbine governor: Considering the dynamic characteristics of the turbine governor, that is, the mechanical power p m The effect of adding the transfer function of the turbine governor T : (4) 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 of system frequency deviation to power disturbance is G and the transfer function of the turbine governor T Through negative feedback connection, a complete power system frequency response model SFR is formed. 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.

2. The power system inertia estimation method based on feature extraction and regression learning separation according to claim 1 is characterized in that: The step S2 comprises: S2-1: Establish convolutional neural network CNN: Set up the input layer, input frequency deviation and power disturbance data, and standardize the data: (5) In formula (5), x n It is the result of standardization. x is the input data, is the mean of the input data, 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: (6) In formula (6), h is the convolutional layer feature map, W is the weight of the convolution kernel, b is the bias term, is the convolution operation; Setting the activation layer to introduce nonlinearity: (7) In formula (7), y It is the activation layer feature map after the introduction of nonlinearity, and max is the convolution layer feature map h The elements in are compared with 0 one by one. If they are greater than 0, they are retained, otherwise they are taken as 0. Set the normalization layer to the activation layer feature map y Processing: (8) In formula (8), is the activation layer feature map y The normalized result is E and V They are activation layer feature maps y The mean and variance of is a small constant that prevents the denominator from being zero; (9) In formula (9), z is the normalized layer feature map, and are learnable scaling and translation parameters; Continue to set the convolution layer, activation layer and normalization layer in sequence, normalization layer feature map z After these layers, 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: (10) In formula (10), y k is the feature vector after global average pooling, 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: (11) In formula (11), 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, perform backpropagation 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 training set and test set. The data of the training set is input into the established convolutional neural network CNN. The convolutional neural network CNN is trained and the weight matrix in the fully connected layer is determined through the feedback of the last regression layer. W 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.

3. The power system inertia estimation method based on feature extraction and regression learning separation according to claim 2 is characterized in that: The step S3 comprises: S3-1: Building Extreme Gradient Boosting Tree XGBoost: Determine the objective function of the model by measuring the error size and model complexity L , regression learning is performed in the direction of reducing the objective function value: (12) In formula (12), is the true value of inertia, is an estimate of the inertia, is a regularization term that controls the complexity of the model, A is the loss function, which is formulated as follows: (13) Determine the update iteration formula: (14) In formula (14), It is t The estimated inertia after rounds of iterations, It is t -The estimated inertia after 1 round of iteration, is the learning rate, In the t A new decision tree is constructed; At each iteration, the loss function is approximated using the first-order gradient and the second-order gradient: (15) In formula (15), g i is the loss function A Estimated inertia The first-order gradient of h i is the loss function A Estimated inertia The second-order gradient of When building a decision tree, calculate the information gain Gain To judge the effect of each node splitting, and thus select the optimal splitting point, the formula is as follows: (16) In formula (16), I Indicates 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, is the regularization parameter, is the penalty parameter for splitting the node; S3-2: Optimizing the hyperparameters of extreme gradient boosting tree XGBoost using bird 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. Each 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 iteratively optimize until the maximum number of iterations is reached to obtain the optimal hyperparameter combination; S3-3: Estimating inertia 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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