Industrial process product quality estimation method based on stacked ensemble learning model

Abstract

The invention discloses an industrial process product quality estimation method based on a stacked ensemble learning model, and the method comprises the following steps: S1, carrying out the preprocessing and feature extraction of industrial evaporation operation data through a convolutional neural network model; s2, selecting and training a base learning device; s3, selecting a gradient boosting decision tree as a meta-learner of the stacked ensemble learning model, and estimating the concentration of the outlet sodium aluminate solution by taking a prediction result of the meta-learner and features extracted by the convolutional neural network model as input; and S4, calculating an error between the outlet solution concentration estimated value and an actual measurement value, and re-training the random forest model for error compensation to obtain a final outlet product quality estimated value. According to the industrial process product quality estimation method based on the stacked ensemble learning model, the estimation result has high accuracy, and the problem that the concentration of an outlet sodium aluminate solution in a multi-stage evaporation process in the aluminum oxide production process is difficult to estimate under the current industrial background can be solved.

Description

Technical Field

[0001] The present invention relates to the field of industrial process technology indicator estimation, and in particular to an industrial process product quality estimation method based on a stacked ensemble learning model. Background Art

[0002] my country is a major country in the world's aluminum industry production and consumption. Alumina, as a core industrial raw material, plays a key role in many fields. In 2023, China's alumina production reached 82.38 million tons, a year-on-year increase of 3.28%, accounting for 58% of global production. More than 90% of alumina is produced using the Bayer process, which has the characteristics of low energy consumption, short process and high quality. The Bayer evaporation process is a key process in alumina production. It maintains the water balance in the circulation system so that the mother liquor is evaporated and concentrated to meet the requirements of bauxite dissolution or raw material slurry configuration, as well as the discharge of impurity salts. The evaporation process consists of multi-stage evaporators, flash evaporators and other equipment. It takes about 2 hours for the stock solution to go from inlet to outlet, while the outlet sodium aluminate solution is sampled every 4 hours. The concentration detection of the outlet sodium aluminate solution is seriously delayed. According to the lagging export product concentration quality, the on-site workers make extensive adjustments, which not only reduces production efficiency, but also wastes energy resources.

[0003] Existing measurement methods, such as non-contact concentration meters and density meters, have increasingly powerful measurement capabilities, but considering the characteristics of multi-stage evaporation processes such as long processes, multiple processes, and multi-variable correlation coupling, they cannot meet the demand for testing the concentration of exported sodium aluminate solutions. Therefore, as a key indicator for the export of the evaporation process, accurately estimating the concentration of sodium aluminate solutions at the export of the industrial evaporation process is of great significance for ensuring the quality of exported products, reducing energy consumption, and stabilizing production operations. Summary of the invention

[0004] The purpose of the present invention is to provide an industrial process product quality estimation method based on a stacked ensemble learning model to solve the problem of difficulty in estimating the concentration of outlet sodium aluminate solution in a multi-stage evaporation process of an alumina production process under the current industrial background.

[0005] To achieve the above object, the present invention provides an industrial process product quality estimation method based on a stacked ensemble learning model, comprising the following steps:

[0006] S1. Use the convolutional neural network model to preprocess and extract features of industrial evaporation operation data;

[0007] S2, select and train base learners;

[0008] S3, selecting the gradient boosting decision tree as the meta-learner of the stacked ensemble learning model, taking the prediction results of the base learner and the features extracted by the convolutional neural network model as input, and estimating the outlet sodium aluminate solution concentration;

[0009] S4. Calculate the error between the estimated value of the outlet solution concentration and the actual measured value, retrain the random forest model to compensate for the error, and obtain the final estimate of the export product quality.

[0010] Preferably, in step S1, the step of facilitating feature extraction by the convolutional neural network model is:

[0011] S11. Divide the data set into a training set and a test set in a ratio of 7:3, input the divided data into the trained convolutional neural network model to extract features, convert the two-dimensional data into three-dimensional data through convolution operation, and extract local features from the data through the convolutional neural network. The convolution layer is the core part of the convolutional neural network, which is used to extract features from the input data. The formula for the convolution operation is:

[0012]

[0013] Where I is the input image, K is the convolution kernel, (x, y) is the coordinate of the output feature map, and k is the size of the convolution kernel;

[0014] S12, reduce the dimension of the feature map through the pooling layer, extract the most obvious part of the feature and input it to the lower layer, and select the maximum value from the 2×2 window;

[0015] P(x,y)=max(I(x+i,y+j))for i,j∈{1,2}

[0016] Among them, P(x,y) is the position of the feature map after pooling, and I(x+i,y+j) is the input value in the pooling window;

[0017] S13, the flattening layer flattens the multi-dimensional feature map into a one-dimensional vector fully connected layer, and maps the flattened features to the final output. Flattening operation:

[0018] Flatten(P)=Vector(P1,P2,K,Pn)

[0019] Among them, P is the feature map after pooling, and Vector is a flattening operation that converts it into a one-dimensional vector.

[0020] Preferably, in step S2, the specific steps are as follows:

[0021] S21. Select 7 machine learning and deep learning models, including K-nearest neighbor algorithm, support vector regression, random forest, convolutional neural network, extreme gradient boosting, gated recurrent unit, and recurrent neural network for training; during the training process, tune the model parameters to improve the model estimation performance;

[0022] S22. Conduct a comparative test on export product quality estimation data, input the data features extracted by the convolutional neural network model into the base learner, compare the mean absolute percentage error, mean absolute error, root mean square error and determination coefficient of the selected algorithm estimation data, and test the estimation performance of each algorithm on the features extracted by the convolutional neural network;

[0023] S23. Select the three models with the best estimation performance, namely K nearest neighbor algorithm, support vector regression and random forest as the ensemble model base learners; for each sample x in the test set test,j (j=1,2,...,m), using different base learners for estimation;

[0024] The estimation result of the base learner is expressed as:

[0025]

[0026] Among them, f k is the estimation function of the kth base learner, is the estimation result of the jth test sample obtained by the kth base learner.

[0027] Preferably, in step S3, the estimated results of the three base learner models and the features extracted by the convolutional neural network model are used as input to combine into a new feature matrix X meta,test :

[0028]

[0029] Each row represents the estimation result of a test sample, each column represents the estimation of a base learner, and the result output by the meta-classifier is the estimated value of the integrated model; use the trained gradient boosting decision tree to generate the newly generated feature matrix X meta,test To make an estimate, the expression is as follows:

[0030]

[0031] Preferably, in step S4, calculating the error between the estimated value of the outlet solution concentration and the actual measured value specifically includes the following steps:

[0032] S411. Train the meta-learner and initialize the model as a simple estimator:

[0033]

[0034] S412. Calculate the residual between the estimated value and the actual value of the current model, that is, the outlet concentration estimation error:

[0035]

[0036] S413, training a new model to train a new weak learner decision tree on the current residual, the goal of the model is to fit the residual:

[0037]

[0038] S414, Update Model The estimated results are weighted and added to the gradient boosting decision tree estimation model; the weighting factor is called the learning rate, which controls the contribution of each base learner to the final estimate:

[0039]

[0040] The estimate of the final model is the weighted sum of the model estimates from all iterations:

[0041]

[0042] S415, the stacked ensemble learning model selects the best base learner through prediction experiments, uses the base learner output as the input of the meta learner; then, the meta learner is used to perform estimation, and the estimation results generated by the learning process of the base learner are integrated;

[0043] S416. Using the estimated results of the base learner and the features extracted by the convolutional neural network model as input, a gradient boosting decision tree is trained as a meta-learner; by training the meta-learner, an estimated result of the sodium aluminate solution concentration at the industrial evaporation outlet is obtained.

[0044] Preferably, in step S4, retraining the random forest model to perform error compensation to obtain the final export product quality estimate specifically includes the following steps:

[0045] S421, calculating the error value between the outlet solution concentration estimate value initially obtained by the model and the actual measured value;

[0046] S422, using the calculated error value as the target value, using the preliminary estimation results in the training data as features, i.e., the features extracted by the base learner K nearest neighbor algorithm, the support vector machine and the random forest estimation value and the convolutional neural network model, the error between the estimated value of the outlet solution concentration and the actual measured value, input into the random forest to obtain an estimated error value;

[0047] S423, compensating the estimated error value to the estimated value output by the meta-learner to obtain the final concentration estimation result; and verifying the feasibility of the outlet sodium aluminate solution concentration estimation model through evaluation indicators.

[0048] Therefore, the beneficial effects of the industrial process product quality estimation method based on the stacked ensemble learning model adopted by the present invention are as follows:

[0049] (1) The present invention utilizes the quality estimation method of the stacked ensemble learning model to maximize the extraction of multi-dimensional features of data variables through the Convolutional Neural Network (CNN) model, thereby improving the accuracy of model estimation.

[0050] (2) The present invention utilizes the quality estimation method of the stacked ensemble learning model, and automatically integrates the advantages of the model by using the K nearest neighbor algorithm, support vector regression and random forest as base learners, thereby improving the performance of the overall estimation model. Using the gradient boosting decision tree model in the meta-learner model can reduce the risk of overfitting.

[0051] (3) The present invention utilizes a quality estimation method of a stacked ensemble learning model and applies a random forest error compensation model. The data features extracted by CNN and the concentration estimated by the base learner are used as inputs. The error is estimated by random forest and compensated to the estimated value output by the meta-learner, so that the final export sodium aluminate solution estimation result can be obtained.

[0052] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a step diagram of an embodiment of an industrial process product quality estimation method based on a stacked ensemble learning model of the present invention;

[0054] Figure 2 It is a flow chart of a stacked ensemble learning and error compensation model in an embodiment of an industrial process product quality estimation method based on a stacked ensemble learning model of the present invention;

[0055] Figure 3 It is a comparison diagram of the estimated value and actual value of the sodium aluminate solution at the outlet of different models in an embodiment of an industrial process product quality estimation method based on a stacked ensemble learning model of the present invention;

[0056] Figure 4 It is an error distribution diagram between the actual value of the outlet sodium aluminate solution and the estimated value after compensation in an industrial process product quality estimation method based on a stacked ensemble learning model in the present invention. DETAILED DESCRIPTION

[0057] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0058] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0059] Embodiment 1

[0060] like Figure 1 As shown, the present invention provides an industrial process product quality estimation method based on a stacked ensemble learning model, comprising the following steps:

[0061] S1. Using the Convolutional Neural Network (CNN) model, the industrial evaporation operation data is preprocessed and features are extracted, which specifically includes the following steps:

[0062] S11. Collect variable data of the evaporation process of alumina production, including the raw liquid flow rate entering the evaporator, new steam flow rate, secondary steam flow rate, condensed water flow rate, inlet liquid concentration, etc. CNN is used to extract the multi-dimensional features of data variables to the maximum extent, and a hierarchical representation of the data is constructed, from low-level details to high-level abstract concepts, which enhances the model's expressiveness and depth of understanding.

[0063] The data set is divided into a training set and a test set in a ratio of 7:3. The divided data is input into the trained convolutional neural network model to extract features. The two-dimensional data (number of samples × number of features) is converted into three-dimensional data (number of samples × number of features × number of channels) through convolution operation. CNN extracts local features in the data. The convolution layer is the core part of CNN and is used to extract features from the input data. The formula for the convolution operation is:

[0064]

[0065] Where I is the input image, K is the convolution kernel (filter), (x, y) is the coordinate of the output feature map, and k is the size of the convolution kernel.

[0066] S12, reduce the dimension of the feature map through the pooling layer (MaxPooling1D), extract the most obvious part of the feature and input it to the lower layer, and select the maximum value from the 2×2 window;

[0067] P(x,y)=max(I(x+i,y+j))for i,j∈{1,2}

[0068] Among them, P(x,y) is the position of the feature map after pooling, and I(x+i,y+j) is the input value in the pooling window;

[0069] S13, Flatten layer flattens the multi-dimensional feature map into a one-dimensional vector fully connected layer (Dense), maps the flattened features to the final output, flattening operation:

[0070] Flatten(P)=Vector(P1,P2,K,P n )

[0071] Among them, P is the feature map after pooling, and Vector is a flattening operation that converts it into a one-dimensional vector.

[0072] S2. Select and train a base learner, which specifically includes the following steps:

[0073] S21. Select 7 machine learning and deep learning models, including K-nearest neighbor algorithm, support vector regression, random forest, convolutional neural network, extreme gradient boosting (XGBoost), gated recurrent unit (GRU), and recurrent neural network (RNN) for training. During the training process, tune the model parameters to improve the model estimation performance.

[0074] S22. Conduct a comparative test on export product quality estimation data. Input the data features extracted by CNN into the base learner. Use the selected algorithm to estimate the mean absolute percentage error (MAPE), mean absolute error (MAE) and root mean square error (RMSE) of the data. The coefficient of determination (R 2 ) to compare and test the feature estimation performance of the above 7 models on CNN extraction. The results are shown in Table 1:

[0075] Table 1 Comparison of error indicators of the estimated values ​​of sodium aluminate solution at the outlet of different base learners

[0076]

[0077] As can be seen from Table 1, KNN, SVR and RF models perform better in terms of MSE, MAE and RMSE error indicators.

[0078] S23. Select the three models with the best estimation performance, namely K-nearest neighbor algorithm, support vector regression and random forest as the ensemble model base learners. As the components of ensemble learning, KNN, SVR and random forest are trained using the training set to estimate the outlet sodium aluminate solution concentration respectively.

[0079] The goal of SVR is to find a regression function that minimizes the error between the predicted value and the actual value of the sample point while keeping the complexity of the model as low as possible. The error of all data points from the regression line is within a preset threshold. The regression function of SVR has the following form:

[0080] f(x)=w T x+b

[0081] Where x is the input feature vector, w is the weight vector, and b is the bias term. The goal of SVM is to find the optimal values ​​of w and b to maximize the margins of the two classes in the feature space. When using kernel functions to handle nonlinear problems, the regression function of SVR is:

[0082]

[0083] Among them, α i and α i * is the Lagrange multiplier, K(x i ,x) is the kernel function, which is used to map the input data into a high-dimensional space and optimize the following objective function to the minimum:

[0084]

[0085] Subject to the following conditions:

[0086] y i -(w T +b)≤j+ξ i

[0087] (w T +b)-y i ≤j+ξ i *

[0088] ξ i ,ξ i * ≥0

[0089] ξ i and i *is a slack variable used to handle errors beyond the ε range, C is a regularization parameter that controls the trade-off between model complexity and error, and j is the allowed regression error range. By optimizing the above objective function, we can find the optimal values ​​of w and b and the Lagrange multiplier α i and α i * , the optimized SVR model was used to predict the outlet sodium aluminate solution concentration.

[0090] K-nearest neighbor algorithm is a simple and effective non-parametric classification and regression method. KNN is based on instance learning and uses distance metrics to classify or predict the category or value of new data points. KNN uses distance metrics to calculate the distance between samples. The most commonly used is Euclidean distance, as shown below:

[0091]

[0092] Random forests improve the accuracy and stability of models by building multiple decision trees and combining the estimated results. In the evaporation process of alumina production, random forests improve the accuracy of predictions by integrating multiple decision trees. Since each decision tree is built based on randomly selected features and sample subsets, the entire forest can reduce the risk of overfitting, thereby improving the generalization ability of the model.

[0093] For each sample x in the test set test,j (j=1,2,...,m), using different base learners for estimation;

[0094] The estimation result of the base learner is expressed as:

[0095]

[0096] Among them, f k is the estimation function of the kth base learner, is the estimation result of the jth test sample obtained by the kth base learner.

[0097] S3. The gradient boosting decision tree is selected as the meta-learner of the stacked ensemble learning model, and the prediction results of the base learner and the features extracted by the convolutional neural network model are used as input to estimate the outlet sodium aluminate solution concentration.

[0098] The estimated results of the three base learner models and the features extracted by the convolutional neural network model are taken as input and combined into a new feature matrix X meta,test :

[0099]

[0100] Each row represents the estimation result of a test sample, each column represents the estimation of a base learner, and the result output by the meta-classifier is the estimated value of the integrated model; use the trained gradient boosting decision tree to generate the newly generated feature matrix X meta,test To make an estimate, the expression is as follows:

[0101]

[0102] S4. Calculate the error between the estimated value of the outlet solution concentration and the actual measured value, retrain the random forest model to compensate for the error, and obtain the final estimate of the export product quality.

[0103] Calculating the error between the estimated value of the outlet solution concentration and the actual measured value specifically includes the following steps:

[0104] S411. Train the meta-learner and initialize the model as a simple estimator:

[0105]

[0106] S412. Calculate the residual between the estimated value and the actual value of the current model, that is, the outlet concentration estimation error:

[0107]

[0108] S413, training a new model to train a new weak learner decision tree on the current residual, the goal of the model is to fit the residual:

[0109]

[0110] S414, Update Model The estimated results are weighted and added to the gradient boosting decision tree estimation model; the weighting factor is called the learning rate, which controls the contribution of each base learner to the final estimate:

[0111]

[0112] The estimate of the final model is the weighted sum of the model estimates from all iterations:

[0113]

[0114] S415, the stacked ensemble learning model selects the best base learner through prediction experiments, uses the base learner output as the input of the meta-learner; then uses the meta-learner to estimate and integrate the estimated results generated by the base learner learning process.

[0115] S416. Using the estimated results of the base learner and the features extracted by the convolutional neural network model as input, a gradient boosting decision tree is trained as a meta-learner; by training the meta-learner, an estimated result of the sodium aluminate solution concentration at the industrial evaporation outlet is obtained.

[0116] Retraining the random forest model for error compensation to obtain the final export product quality estimate includes the following steps:

[0117] S421, calculating the error value between the outlet solution concentration estimate value initially obtained by the model and the actual measured value;

[0118] S422, using the calculated error value as the target value, using the preliminary estimation results in the training data as features, i.e., the features extracted by the base learner K nearest neighbor algorithm, the support vector machine and the random forest estimation value and the convolutional neural network model, the error between the estimated value of the outlet solution concentration and the actual measured value, input into the random forest to obtain an estimated error value;

[0119] S423, compensating the estimated error value to the estimated value output by the meta-learner to obtain the final concentration estimation result; and verifying the feasibility of the outlet sodium aluminate solution concentration estimation model through evaluation indicators.

[0120] In order to further illustrate the effectiveness and feasibility of this embodiment, a comparative experiment was conducted using four models: K nearest neighbor algorithm, support vector regression, random forest, and stacked ensemble learning. The flow chart is as follows: Figure 2 As shown, a total of 800 sets of data actually produced during the process operation cycle were used, the first 560 sets were selected for learning and training, and the last 240 sets were used for prediction verification.

[0121] The mean absolute percentage error (MAPE), mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R 2 ) is compared with the three estimation models, and the results are shown in Table 2.

[0122] Table 2 Comparison of prediction error indicators of four methods

[0123]

[0124] As can be seen from Table 2, the stacked ensemble learning model has good performance in RMSE, MAE, MSE, R 2The four indicators are the best among all models, with the smallest prediction error and more in line with the changing trend of the true value. For the RMSE indicator, the model proposed in this embodiment is 62.6% lower than KNN, SVR and Random Forest. In the MAE indicator, compared with KNN, SVR and RandomForest, the model proposed in this embodiment is reduced by 62.7%, 61.9% and 62.1% respectively. In the MSE indicator, the model proposed in this embodiment is reduced by 86.3%, 84.2% and 84.2% respectively than KNN, SVR and Random Forest. 2 The model proposed in this embodiment reached 0.83, which is 82.0% higher than other models, indicating that the stacked ensemble learning model has better prediction performance than a single model and can better solve the problem of estimating the concentration of sodium aluminate solution at the outlet of the multi-stage evaporation process of alumina production.

[0125] like Figure 3 As shown, the estimated values ​​and actual values ​​of the outlet sodium aluminate solution concentration obtained by the four models are compared. It can be seen from the figure that the diamond-shaped broken line of the estimation model of this embodiment is closer to the actual value represented by the circular broken line than other broken lines, indicating that the estimation error of the estimation model of this embodiment is smaller, the accuracy is higher, and it can track the changes of the circular broken line well, and has strong stability.

[0126] like Figure 4 As shown in the figure, the central tendency and dispersion of the errors are shown, and the error distribution is close to the normal distribution, which shows that the estimation error of the model is evenly distributed without obvious bias, proving that the estimation ability of the model is relatively balanced overall. In addition, there are no obvious outliers in the figure, indicating that the model is stable in most cases and is not significantly affected by individual data points. This result provides strong support for the reliability of the model and shows that it can maintain good estimation quality in practical applications.

[0127] Therefore, the present invention adopts the above-mentioned industrial process product quality estimation method based on the stacked ensemble learning model, and the estimation result has high accuracy, which can solve the problem of difficult estimation of the outlet sodium aluminate solution concentration in the multi-stage evaporation process of the alumina production process under the current industrial background.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for estimating industrial process product quality based on a stacked ensemble learning model, characterized in that: The following steps are involved: S1. Use the convolutional neural network model to preprocess and extract features of industrial evaporation operation data; S2, select and train base learners; S3, selecting the gradient boosting decision tree as the meta-learner of the stacked ensemble learning model, taking the prediction results of the base learner and the features extracted by the convolutional neural network model as input, and estimating the outlet sodium aluminate solution concentration; S4. Calculate the error between the estimated value of the outlet solution concentration and the actual measured value, retrain the random forest model to compensate for the error, and obtain the final estimate of the export product quality.

2. The method for estimating industrial process product quality based on a stacked ensemble learning model according to claim 1, characterized in that: In step S1, the steps that facilitate feature extraction by the convolutional neural network model are: S11. Divide the data set into a training set and a test set in a ratio of 7:3, input the divided data into the trained convolutional neural network model to extract features, convert the two-dimensional data into three-dimensional data through convolution operation, and extract local features from the data through the convolutional neural network. The convolution layer is the core part of the convolutional neural network, which is used to extract features from the input data. The formula for the convolution operation is: Where I is the input image, K is the convolution kernel, (x, y) is the coordinate of the output feature map, and k is the size of the convolution kernel; S12, reduce the dimension of the feature map through the pooling layer, extract the most obvious part of the feature and input it to the lower layer, and select the maximum value from the 2×2 window; P(x,y)=max(I(x+i,y+j))for i,j∈{1,2} Among them, P(x,y) is the position of the feature map after pooling, and I(x+i,y+j) is the input value in the pooling window; S13, the flattening layer flattens the multi-dimensional feature map into a one-dimensional vector fully connected layer, and maps the flattened features to the final output. Flattening operation: Flatten(P)=Vector(P1,P2,...,P n ) Among them, P is the feature map after pooling, and Vector is a flattening operation that converts it into a one-dimensional vector.

3. The method for estimating industrial process product quality based on a stacked ensemble learning model according to claim 1, characterized in that: In step S2, the specific steps are as follows: S21. Select 7 machine learning and deep learning models, including K-nearest neighbor algorithm, support vector regression, random forest, convolutional neural network, extreme gradient boosting, gated recurrent unit, and recurrent neural network for training; During the training process, the model parameters are tuned to improve the model estimation performance; S22. Conduct a comparative test on export product quality estimation data, input the data features extracted by the convolutional neural network model into the base learner, compare the mean absolute percentage error, mean absolute error, root mean square error and determination coefficient of the selected algorithm estimation data, and test the estimation performance of each algorithm on the features extracted by the convolutional neural network; S23. Select the three models with the best estimation performance, namely K nearest neighbor algorithm, support vector regression and random forest as the ensemble model base learners; for each sample x in the test set test,j (j=1,2,...,m), using different base learners for estimation; The estimation result of the base learner is expressed as: Among them, f k is the estimation function of the kth base learner, is the estimation result of the jth test sample obtained by the kth base learner.

4. The method for estimating industrial process product quality based on a stacked ensemble learning model according to claim 1, characterized in that: In step S3, the estimated results of the three base learner models and the features extracted by the convolutional neural network model are used as input to combine into a new feature matrix X meta,test : Each row represents the estimation result of a test sample, each column represents the estimation of a base learner, and the result output by the meta-classifier is the estimated value of the integrated model; use the trained gradient boosting decision tree to generate the newly generated feature matrix X meta,test To make an estimate, the expression is as follows:

5. The method for estimating industrial process product quality based on a stacked ensemble learning model according to claim 1, characterized in that: In step S4, the error between the estimated value of the outlet solution concentration and the actual measured value is calculated, which specifically includes the following steps: S411. Train the meta-learner and initialize the model as a simple estimator: S412. Calculate the residual between the estimated value and the actual value of the current model, that is, the outlet concentration estimation error: S413, train a new model to train a new weak learner decision tree on the current residual. The goal of this model is to fit the residual: S414, Update Model The estimated results are weighted and added to the gradient boosting decision tree estimation model; the weighting factor is called the learning rate, which controls the contribution of each base learner to the final estimate: The estimate of the final model is the weighted sum of the model estimates from all iterations: S415, the stacked ensemble learning model selects the best base learner through prediction experiments, uses the base learner output as the input of the meta learner; then uses the meta learner to perform estimation and integrates the estimation results generated by the base learner learning process; S416. Using the estimated results of the base learner and the features extracted by the convolutional neural network model as input, a gradient boosting decision tree is trained as a meta-learner; by training the meta-learner, an estimated result of the sodium aluminate solution concentration at the industrial evaporation outlet is obtained.

6. The method for estimating industrial process product quality based on a stacked ensemble learning model according to claim 1, characterized in that: In step S4, the random forest model is retrained to perform error compensation to obtain the final export product quality estimate, which specifically includes the following steps: S421, calculating the error value between the outlet solution concentration estimate value initially obtained by the model and the actual measured value; S422, using the calculated error value as the target value, using the preliminary estimation results in the training data as features, i.e., the features extracted by the base learner K nearest neighbor algorithm, the support vector machine and the random forest estimation value and the convolutional neural network model, the error between the estimated value of the outlet solution concentration and the actual measured value, input into the random forest to obtain an estimated error value; S423, compensating the estimated error value to the estimated value output by the meta-learner to obtain the final concentration estimation result; and verifying the feasibility of the outlet sodium aluminate solution concentration estimation model through evaluation indicators.

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