Neural network continuous casting billet slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyper-parameter optimization

Abstract

The invention relates to a neural network continuous casting billet slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyper-parameter optimization. The method comprises the following steps: firstly, acquiring continuous casting billet production process data, and performing oversampling processing on fault samples to solve the problem of class imbalance; thirdly, calculating mutual information values between the feature variables and the category features, removing the feature variables of which the mutual information values are lower than a set threshold value, introducing agent variables, and performing error discovery rate estimation processing through a neural network to obtain an optimal variable subset; and finally, fault diagnosis is carried out on the data after variable selection by using a neural network, hyper-parameters of the neural network are adjusted by using a Bayesian optimization algorithm, an optimal classification model is obtained, and a classification result is visualized by using a t-SNE algorithm. According to the method, by selecting the high-quality variable subset and the optimal hyper-parameter combination, accurate diagnosis of the slag inclusion quality fault of the continuous casting billet is effectively achieved, and important guidance and support are provided for the production process of the continuous casting billet.

Description

Technical Field

[0001] The invention belongs to the field of metallurgical continuous casting billet quality fault diagnosis, and in particular relates to a neural network continuous casting billet slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization. Background Art

[0002] The continuous casting process plays a vital role in steel production, and its quality is directly related to the product performance and processing cost of subsequent production links. In the continuous casting process, slag inclusion is one of the common quality defects. Slag inclusion refers to the quality defect formed when non-metallic inclusions entrained in the liquid molten steel are captured and solidified in the ingot during the continuous casting process. These inclusions not only lead to the deterioration of the mechanical properties of the ingot, but may also cause serious quality problems such as cracks in the subsequent processing. Therefore, accurately diagnosing slag inclusion defects in continuous casting ingots is of great significance to improving product quality and production efficiency.

[0003] Traditional slag inclusion fault diagnosis methods mainly rely on manual detection and empirical judgment. These methods are not only inefficient, but also have great subjectivity and uncertainty, and are difficult to meet the needs of modern metallurgical industry for efficient and accurate diagnosis. With the rapid development of intelligent manufacturing and big data technology, data-driven fault diagnosis methods have become a research hotspot. Neural networks have been widely used in continuous casting billet quality fault diagnosis due to their powerful nonlinear modeling and learning capabilities.

[0004] However, the performance of the neural network model is highly dependent on its structure and parameter selection. Traditional parameter adjustment methods, such as random search and grid search, often have high computational costs and low efficiency, and it is difficult to find the optimal solution in a complex hyperparameter space. In addition, due to the complexity of the continuous casting process, the collected slag inclusion quality data of the continuous casting billet has the characteristics of high data redundancy and high data dimension, which will affect the classification accuracy of the model. In view of the above problems, the present invention proposes a neural network classification model that combines the mutual information method and Bayesian hyperparameter optimization, aiming to achieve accurate diagnosis of slag inclusion quality failures of continuous casting billets. Summary of the invention

[0005] In order to overcome the above-mentioned problems of the prior art, the present invention proposes a neural network continuous casting billet slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization. The method can effectively process the continuous casting billet process data with high complexity and strong redundancy, and realize the accurate diagnosis of the continuous casting billet slag inclusion quality defects.

[0006] In order to achieve the above object, the neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization of the present invention is as follows:

[0007] The neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization is mainly characterized in that the method comprises the following steps:

[0008] (1) Obtain continuous casting production process data and perform oversampling on the data samples to solve the problem of class imbalance;

[0009] (2) Calculate the mutual information value between the feature variables and the quality category, eliminate the feature variables whose mutual information value is lower than the set threshold, and then introduce the proxy variable to perform false discovery rate (FDR) estimation through the neural network to obtain the optimal variable subset;

[0010] (3) A neural network is used to perform fault diagnosis on the data after variable selection, and the Bayesian optimization algorithm is used to adjust the neural network hyperparameters to obtain the optimal classification model. The t-SNE algorithm is used to visualize the classification results.

[0011] Preferably, the step (1) specifically comprises the following steps:

[0012] (1.1) Obtaining the continuous casting process data of the steel plant through sensors and data acquisition systems;

[0013] (1.2) Adaptive synthetic oversampling technology (ADASYN) is used to oversample minority class samples to achieve data equalization.

[0014] Preferably, the step (2) specifically comprises the following steps:

[0015] (2.1) Calculate the mutual information value between the characteristic variables and the quality category, eliminate the characteristic variables whose mutual information value is lower than the set threshold, and conduct preliminary screening of the characteristic variables;

[0016] (2.2) Input the data after preliminary variable screening into the neural network and train the neural network;

[0017] (2.3) Calculate the importance of each variable and sort them, and remove the m variables with lower importance after sorting;

[0018] (2.4) Perform false discovery rate (FDR) estimation and determine whether the FDR value meets the termination condition to obtain the optimal variable subset.

[0019] The mutual information value is calculated as follows:

[0020]

[0021] Among them, X represents the feature variable, Y represents the quality category label, n represents the total number of samples, p(x,y) represents the joint probability distribution function of X and Y, and p(x) and p(y) represent the marginal probability density distribution functions of X and Y respectively.

[0022] The mutual information threshold is defined as λ, and the feature variables with mutual information values ​​less than λ are deleted for preliminary variable screening.

[0023] Variable importance is calculated as follows:

[0024]

[0025] Where L represents the loss function, Represents the loss function L for the jth variable x j The partial derivative value of the i-th sample.

[0026] The m variables with low variable importance are calculated as follows:

[0027]

[0028] Among them, m represents the number of variables that need to be deleted in one iteration. represents the ceil function, which returns the smallest integer among all integers greater than or equal to ·, δ is the elimination rate, which is used to adjust the speed at which the neural network deletes variables, and γ * represents the set critical FDR value, represents the current estimated FDR value, and q0 represents the number of remaining proxy variables.

[0029] Preferably, the step (2.4) specifically includes the following steps:

[0030] (2.4.1) The FDR value is estimated by:

[0031]

[0032] Among them, q represents the number of remaining variables, a represents the number of proxy variables added in the initial state, and b represents the number of original variables under the initial conditions.

[0033] (2.4.2) Determine the estimated FDR value Is it less than the FDR critical value γ * If the condition is met, the proxy variables in the remaining variables are deleted and the high-quality variable subset is output; if the condition is not met, return to step (2.2) and repeat the process.

[0034] Preferably, the step (3) specifically comprises the following steps:

[0035] (3.1) Input the selected high-quality variable data set into the neural network classification model;

[0036] (3.2) Define the objective function of Bayesian optimization as the inverse of the neural network loss function, initialize the network parameters θ and the hyperparameter group [ξ1,ξ2,…,ξ k ] and train the neural network;

[0037] (3.3) Use Gaussian process regression to fit the target function and obtain the prior distribution and posterior distribution of the target function;

[0038] (3.4) Based on the posterior distribution and acquisition function, a new hyperparameter combination is obtained and the neural network is trained again;

[0039] (3.5) Update the hyperparameters until the preset conditions are met, obtain the optimal hyperparameter combination and its corresponding classification model, and use the t-SNE algorithm to visualize the model classification results.

[0040] The loss function of the neural network is obtained as follows:

[0041]

[0042] Among them, C represents the number of categories, y i,c Indicates that the i-th sample belongs to the true label of the c-th class, represents the probability that the model predicts that the i-th sample belongs to the c-th category, ξ k represents the kth group of hyperparameters, θ k Represent the network parameters and optimize them via back-propagation.

[0043] Optimize network parameters as follows:

[0044]

[0045] The objective function of Bayesian optimization is obtained as follows:

[0046] g(ξ k )=-L(θ k ,ξ k )

[0047] The prior distribution of the objective function is obtained as follows:

[0048]

[0049] Among them, ξ 1:k represents 1 to k sets of hyperparameter sequences, μ0(·) represents the mean function, and Σ0(·) represents the kernel function.

[0050] Assuming h = k + 1, the posterior distribution of the objective function is obtained as follows:

[0051]

[0052] μ h (ξ)=Σ0(ξ,ξ 1:h )Σ0(ξ 1:h ,ξ 1:h ) -1 (g(ξ 1:h )-μ0(ξ 1:h ))+μ0(ξ)

[0053]

[0054] Among them, ξ 1:h Represents 1 to h sets of hyperparameter sequences, μ h (ξ) represents the posterior mean, represents the posterior variance.

[0055] The acquisition function EI is obtained as follows h (ξ):

[0056]

[0057] in, represents the currently observed optimal value, represents the probability density function of the standard normal distribution, and φ(·) represents the cumulative distribution function of the standard normal distribution.

[0058] The next set of hyperparameters is obtained as follows:

[0059] ξ h+1 = argmax EI h (ξ)

[0060] When the number of optimizations reaches I, the optimal hyperparameter group ξ is output * And the network parameters θ * , and obtain the optimal classification model.

[0061] The neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization of the present invention can effectively reduce data redundancy and the complexity of the classification model by selecting high-quality variables, while improving the classification accuracy of the model. The optimal hyperparameters of the neural network can be efficiently selected through Bayesian hyperparameter optimization, reducing the calculation time, improving the robustness and generalization ability of the model, and effectively realizing the accurate diagnosis of the continuous casting slag inclusion quality fault, providing important guidance and support for the continuous casting production process. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The present invention is a flowchart for selecting high-quality variables for the neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization.

[0063] Figure 2 The figure is a ROC-AUC curve diagram for model evaluation of the neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization of the present invention.

[0064] Figure 3 It is a t-SNE visualization projection diagram of the classification results of the training set and the test set of the neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization of the present invention.

[0065] Figure 4 This is a t-SNE visualization projection diagram of the classification results of another training set and test set of the neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization of the present invention. DETAILED DESCRIPTION

[0066] In order to more clearly describe the technical content of the present invention, further description is given below in conjunction with the drawings and specific embodiments.

[0067] The present invention proposes a neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization, such as Figure 1 As shown, the specific steps of the method are as follows:

[0068] (1) Obtain continuous casting production process data and perform oversampling on the data samples to solve the problem of class imbalance;

[0069] (2) Calculate the mutual information value between the feature variables and the quality category, eliminate the feature variables whose mutual information value is lower than the set threshold, and then introduce the proxy variable to perform false discovery rate (FDR) estimation through the neural network to obtain the optimal variable subset;

[0070] (3) A neural network is used to perform fault diagnosis on the data after variable selection, and the Bayesian optimization algorithm is used to adjust the neural network hyperparameters to obtain the optimal classification model. The t-SNE algorithm is used to visualize the classification results.

[0071] The specific implementation process is as follows:

[0072] 1. Data acquisition and processing

[0073] In the embodiment, the original data is the continuous casting process data collected on-site at a steel plant. The original data contains 80 feature variables and a category label, the category label is 0 and 1, where 0 represents a normal sample and 1 represents a slag inclusion sample. Since the probability of slag inclusion defects occurring during continuous casting production is low, there is a serious problem of imbalanced category distribution in the data. According to the preferred data processing method of the present invention, the ADASYN oversampling method is used to increase the number of minority class samples to achieve data category balancing.

[0074] 2. Selection of high-quality variable subsets

[0075] The selection of high-quality variable subsets is as follows: Figure 1 shown.

[0076] First, the mutual information value between the feature variables and the quality categories is calculated to perform preliminary variable screening on the original data, and then a high-quality variable subset is screened out through a neural network combined with estimated FDR processing. The specific steps include:

[0077] (1) Input data {X n×s ,Y n×1}, where s represents the dimension of the feature variable, n is the total number of samples, X represents the feature variable, and Y is the quality category label.

[0078] (2) Set the mutual information threshold λ to 0.4, calculate the mutual information MI(X;Y) of X and Y by the following formula (1), and remove the feature variables with mutual information values ​​less than λ. After screening, the dimension of the feature variables is l.

[0079]

[0080] Where p(x,y) represents the joint probability distribution function of X and Y, and p(x) and p(y) represent the marginal probability density distribution functions of X and Y, respectively.

[0081] (3) Set the hyperparameters of the neural network and set the false discovery rate (FDR) critical value γ * Set to 0.1, the elimination rate δ to 0.5, the neural network hidden layer structure to [32,16], the learning rate to 0.007, the batch size to 256, and the number of iterations to 50. Enter the data after the preliminary variable screening {X n×l ,Y n×1}, and introduce proxy variables, set the proxy variable dimension to be equal to the original variable dimension, both are l-dimensional, and the data at this time is {X n×2l ,Y n×1}, start training the neural network, calculate the variable importance of each feature variable and sort them by the following formula (2). Eliminate m variables with small variable importance, and calculate the number of variables m that need to be eliminated in one iteration by the following formula (3).

[0082]

[0083] Where L represents the loss function, Represents the loss function L for the jth variable x j The partial derivative value of the i-th sample, represents the ceil function, which returns the smallest integer among all integers greater than or equal to ·, δ is the elimination rate, which is used to adjust the speed at which the neural network deletes variables, and γ * represents the set critical FDR value, represents the current estimated FDR value, and q0 represents the number of remaining proxy variables.

[0084] (4) Estimate the current FDR value according to the following formula (4). , delete the remaining proxy variables and output the optimal variable subset; when γ>γ * Repeat the previous step. Finally, the optimal variable data set is {X n×d ,Y n×1}, where d represents the dimension of the preferred variable.

[0085]

[0086] Among them, q represents the number of remaining variables, a represents the number of proxy variables added in the initial state, and b represents the number of original variables under the initial conditions.

[0087] 3. Bayesian Hyperparameter Optimization of Neural Networks

[0088] (1) Input data into the neural network and use the Bayesian optimization algorithm to adjust the neural network hyperparameters. The neural network loss function is calculated by the following formula (5), and the network parameters based on back-propagation optimization are calculated by the following formula (6). The objective function of Bayesian optimization is defined as the inverse of the neural network loss function, and the objective function is calculated by the following formula (7).

[0089]

[0090]

[0091] g(ξ k )=-L(θ k ,ξ k ) (7)

[0092] Among them, C represents the number of categories, y i,cIndicates that the i-th sample belongs to the true label of the c-th class, represents the probability that the model predicts that the i-th sample belongs to the c-th category, ξ k represents the kth group of hyperparameters, θ k Represents network parameters.

[0093] (2) Use Gaussian process regression to fit the objective function, and calculate the prior distribution and posterior distribution of the objective function by the following equations (8) and (9). Calculate the posterior mean and posterior variance of the objective function by the following equation (10).

[0094]

[0095] Among them, ξ 1:k represents 1 to k sets of hyperparameter sequences, μ0(·) represents the mean function, ∑0(·) represents the kernel function, ξ 1:h Represents 1 to h sets of hyperparameter sequences, μ h (ξ) represents the posterior mean, represents the posterior variance.

[0096] (3) Based on the posterior distribution and the acquisition function, the next possible hyperparameter group is obtained. The difference between the posterior mean and the current optimal observation is calculated by the following formula (11), and the acquisition function is obtained by the following formula (12). The next hyperparameter group is selected by maximizing the acquisition function by the following formula (13).

[0097]

[0098] ξ h+1 = argmax EI h (ξ) (13)

[0099] in, represents the currently observed optimal value, represents the probability density function of the standard normal distribution, and Φ(·) represents the cumulative distribution function of the standard normal distribution.

[0100] (4) Update the hyperparameter group and continue to train the neural network. Set the maximum number of optimizations to I = 20. When the number of optimizations reaches I, output the optimal hyperparameter group ξ * And the network parameters θ * , and obtain the optimal classification model.

[0101] The high-quality variables selected by the preferred variable selection method of the present invention are shown in Table 1.

[0102] Table 1 Preferred variable description table

[0103]

[0104]

[0105] In this embodiment, the data samples are divided into a training set, a validation set, and a test set in a ratio of 7:2:1. The training set is used to train the neural network model, the validation set is used to adjust the model parameters, and the test set is used to independently evaluate the generalization performance of the model. In order to verify the performance of the model, it is compared with five classification models, namely, logistic regression, support vector machine SVM, LightGBM, BP neural network, and single hidden layer feedforward neural network. The performance of the model is comprehensively evaluated using accuracy, precision, recall rate, and F1 score. The specific results are shown in Table 2. Comprehensively comparing the six classification models, the neural network classification model based on mutual information and Bayesian hyperparameter optimization has higher evaluation indicators, indicating that the model has a stronger ability to distinguish data of different categories and can more accurately identify and classify slag inclusion defects in continuous casting billets. At the same time, the ROC-AUC curve is used to evaluate the performance of the six classification models. The results are as follows: Figure 2 The AUC value of the neural network classification model based on mutual information and Bayesian hyperparameter optimization is significantly higher than that of other comparison models, indicating that the overall classification performance of this model is better. In order to more intuitively display the classification effect of the model, the t-SNE algorithm is used to visualize the classification results of the model. The results are shown in the figure. Figure 3 The t-SNE visualization results show that the neural network classification model based on mutual information and Bayesian hyperparameter optimization has a good separation effect between different categories.

[0106] Table 2 Classification model evaluation results

[0107]

[0108]

[0109] In the above embodiment, the neural network continuous casting billet slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization can effectively realize the diagnosis of continuous casting billet quality defects. The mutual information method is combined with the neural network, and the estimated FDR processing is introduced to perform variable screening on the original data, reduce the data dimension and noise, and select a better variable subset, thereby reducing the complexity of the model. In addition, the Bayesian optimization algorithm is used to adjust the hyperparameters of the model, and the optimal hyperparameter combination can be found with fewer times, which greatly reduces the calculation time and improves the robustness and generalization ability of the model. In summary, the method of the present invention has higher accuracy and reliability in the diagnosis of continuous casting billet slag inclusion quality faults, and provides strong technical support for quality control in the continuous casting billet production process.

[0110] In this specification, the present invention has been described with reference to specific embodiments thereof. However, it is apparent that various modifications and variations may be made without departing from the spirit and scope of the present invention. Therefore, the specification and drawings should be regarded as illustrative rather than restrictive.

Claims

1. A neural network continuous casting slag inclusion quality fault diagnosis method based on mutual information and Bayesian hyperparameter optimization, characterized in that: The method comprises the following steps: (1) Obtain continuous casting production process data and perform oversampling on the data samples to solve the problem of class imbalance; (2) Calculate the mutual information value between the feature variables and the quality category, eliminate the feature variables whose mutual information value is lower than the set threshold, introduce the proxy variable, and perform false discovery rate estimation through the neural network to obtain the optimal variable subset; (3) A neural network is used to perform fault diagnosis on the data after variable selection, and the Bayesian optimization algorithm is used to adjust the neural network hyperparameters to obtain the optimal classification model. The t-SNE algorithm is used to visualize the classification results.

2. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 1, characterized in that: The step (1) specifically comprises the following steps: (1.1) Obtaining the continuous casting process data of the steel plant through sensors and data acquisition systems; (1.2) Adaptive synthetic oversampling technology is used to oversample minority class samples to achieve data equalization.

3. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 2, characterized in that: The step (2) specifically comprises the following steps: (2.1) Calculate the mutual information value between the characteristic variables and the quality category, eliminate the characteristic variables whose mutual information value is lower than the set threshold, and perform preliminary screening on the characteristic variables; (2.2) Inputting the data after preliminary variable screening into the neural network and training the neural network; (2.3) Calculate the importance of each variable and sort them, and remove the m variables with lower importance after sorting; (2.4) Perform false discovery rate estimation and determine whether the obtained false discovery rate value meets the termination condition, so as to obtain the optimal variable subset.

4. The continuous casting slag inclusion quality fault diagnosis method based on mutual information method and Bayesian hyperparameter optimization according to claim 3 is characterized in that: The mutual information value is calculated as follows: Among them, X represents the feature variable, Y represents the quality category label, p(x,y) represents the joint probability distribution function of X and Y, n represents the total number of samples, p(x) and p(y) represent the marginal probability density distribution functions of X and Y respectively; The mutual information threshold is defined as λ, and the feature variables with mutual information values ​​less than λ are deleted for preliminary variable screening.

5. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 4, characterized in that: Variable importance is calculated as follows: Among them, L represents the loss function, Represents the loss function L for the jth variable x j The partial derivative value of the o-th sample; The m variables with low variable importance are calculated as follows: Among them, m represents the number of variables that need to be deleted in one iteration. represents the ceil function, which returns the smallest integer among all integers greater than or equal to ·, δ is the elimination rate, which is used to adjust the speed at which the neural network deletes variables, and γ * represents the set critical FDR value, represents the currently estimated false discovery rate value, and q0 represents the number of proxy variables currently remaining.

6. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 5, characterized in that: The step (2.4) specifically includes the following two steps: (2.4.1) The false discovery rate is estimated by: Among them, q represents the number of remaining variables, a represents the number of proxy variables added in the initial state, and b represents the number of original variables under the initial conditions; (2.4.2) Determine and estimate the false discovery rate value Is it less than the FDR critical value γ * If the condition is met, the proxy variables in the remaining variables are deleted and the high-quality variable subset is output; if the condition is not met, return to step (2.2) and repeat the process.

7. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 6, characterized in that: The step (3) specifically comprises the following steps: (3.1) Input the screened high-quality variable data set into the neural network classification model; (3.2) Define the objective function of Bayesian optimization as the inverse of the neural network loss function, initialize the network parameters θ and the hyperparameter group [ξ1,ξ2,…,ξ k ] and train the neural network; (3.3) Use Gaussian process regression to fit the target function and obtain the prior distribution and posterior distribution of the target function; (3.4) obtaining a new hyperparameter combination based on the posterior distribution and the acquisition function, and training the neural network again; (3.5) Update the hyperparameters until the preset conditions are met, obtain the optimal hyperparameter combination and its corresponding fault diagnosis model, and use the t-SNE algorithm to visualize the model classification results.

8. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 7, characterized in that: The loss function of the neural network is obtained as follows: Among them, C represents the number of categories, y i,c Indicates that the i-th sample belongs to the true label of the c-th class, represents the probability that the model predicts that the i-th sample belongs to the c-th category, ξ k represents the kth group of hyperparameters, θ k Represent network parameters and optimize them through back-propagation; Optimize network parameters as follows: The objective function of Bayesian optimization is obtained as follows: g(ξ k )=-L(θ k ,x k )。 9. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 7, characterized in that: The prior distribution of the objective function is obtained as follows: Among them, ξ 1:k represents 1 to k sets of hyperparameter sequences, μ0(·) represents the mean function, and ∑0(·) represents the kernel function; Assuming h = k + 1, the posterior distribution of the objective function is obtained as follows: m h (ξ)=Σ0(ξ,ξ 1:h )Σ0(ξ 1:h ,x 1:h ) -1 (g(ξ 1:h )-μ0(ξ 1:h ))+μ0(ξ) s h 2 (ξ)=Σ0(ξ,ξ)-Σ0(ξ,ξ 1:h )Σ0(ξ 1:h ,x 1:h ) -1 Σ0(ξ 1:h ,x) Among them, ξ 1:h Represents 1 to h sets of hyperparameter sequences, μ h (ξ) represents the posterior mean, represents the posterior variance.

10. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 9, characterized in that: The acquisition function EI is obtained as follows h (ξ): in, represents the currently observed optimal value, represents the probability density function of the standard normal distribution, Φ(·) represents the cumulative distribution function of the standard normal distribution; The next hyperparameter group ξ is obtained as follows h+1 : x h+1 =argmax EI h (x)。 11. The method for diagnosing slag inclusion quality faults of continuous casting billets based on mutual information and Bayesian hyperparameter optimization using a neural network according to claim 10, characterized in that: When the number of optimizations reaches I, the optimal hyperparameter group ξ is output * And the network parameters θ * , and obtain the optimal classification model.

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