Selective ensemble learning soft measurement method based on double error metrics and game theory

Abstract

The invention discloses a selective ensemble learning soft measurement method based on double error metrics and a game theory, and belongs to the technical field of soft measurement in a chemical production process. Firstly, a plurality of training subsets are obtained from a training set through a random resampling method, and a plurality of sub-models are obtained through training; then, for a test sample, obtaining a verification set from the training set by using an instant learning thought, calculating a precision weight of each sub-model on the verification set by using a mean square error, and calculating a diversity weight between the sub-models by using double error metrics; and finally, fusing the two weights by using a game theory strategy. And the fused weight can be screened by integrating the precision and diversity of the sub-models during model selection, so that the performance of the final integrated model is improved.

Description

Technical Field

[0001] The invention relates to a selective integrated learning soft measurement method based on double error measurement and game theory, and belongs to the technical field of soft measurement modeling of industrial production processes. Background Art

[0002] In the industrial production process, accurate and real-time monitoring of dominant process variables is the key to ensuring production efficiency and product quality. Limited by actual production conditions, some key parameters (called quality variables) are difficult to measure, which brings difficulties to process control. Soft sensing technology is an effective means to achieve online estimation of quality variables. It can use easy-to-measure variables in the process (called input variables) to achieve effective estimation of variables that are difficult to measure through mathematical modeling and algorithm processing. However, in the actual industrial production process, due to the complex integration and coordination between systems, interference from environmental factors and other reasons, the collected data generally have disadvantages such as nonlinearity and many disturbances. The single data-driven model established based on these data will show problems such as low robustness and poor generalization ability, resulting in a significant decrease in the performance of the model and inability to effectively handle unknown situations in practical applications.

[0003] Therefore, in order to improve the accuracy and generalization ability of the model, the ensemble learning method with the concept of "divide and conquer" in machine learning has been applied to the field of soft sensing. The core idea is to divide a complex problem into a series of smaller, easier to manage and solve sub-problems, then solve these sub-problems separately, and finally merge the solutions to the sub-problems to solve the original problem; by building multiple base learners and combining their prediction results to improve the performance of the overall model. However, when the amount of data and the scale of integration increase to a certain extent, too many individual learners will increase the complexity of the calculation and cause the model to overfit. In this case, how to selectively select sub-models to improve the effectiveness and robustness of the overall integration has become a key issue in modeling research.

[0004] Model selection requires a trade-off between the model's prediction accuracy and diversity. Both are important concepts in machine learning. In ensemble learning, prediction accuracy and diversity complement each other. A base learner with high prediction accuracy can improve the performance of the ensemble, while diversity can help the model capture more information in the training data, reduce overfitting to obtain higher prediction accuracy, and help reduce overfitting and improve generalization. However, excessive diversity will lead to inaccurate prediction results of the ensemble model, resulting in reduced prediction accuracy; only by properly balancing these two factors can a powerful ensemble learning model be constructed.

[0005] In the paper "Selective Ensemble Method of Extreme Learning Machine Based on Double Error Measure", a selective ensemble method of ELM (Extreme Learning Machine) based on double error measure is proposed. The double error measure matrix is ​​formed by calculating the double error measure between base ELMs, and then the double error measure between each base ELM and all base ELMs is calculated according to the double error measure matrix; finally, the base ELM set with the best ensemble performance is selected by sorting and ensembling in ascending order; however, this method only considers the diversity of the model, and does not effectively consider the prediction accuracy.

[0006] In the "Selective Integration Forecasting Method for Oil Prices Based on Scale Analysis and Dynamic Error Correction", the researchers evaluated the diversity of the model by introducing the idea of ​​double error measurement, and adopted a selective integration strategy to comprehensively consider the prediction accuracy and model diversity, thereby improving the prediction accuracy and generalization ability of the model; however, this selective integration strategy has the disadvantages of lack of dynamic interaction ability, limited subset selection, weak ability to process incomplete information and more complex calculations.

[0007] In response to the above-mentioned problems, the paper "Selective ensemble modeling method based on game theory with both accuracy and diversity and its application" proposed a selective ensemble modeling method based on OSELM and game theory. The game theory principles are used to select sub-models in the model pool. The sub-models selected by game theory have achieved the optimal model accuracy and model diversity, which improves the generalization performance of the integrated model while shortening the calculation time. However, the method proposed in this paper only optimizes the fusion selection of the model. The calculation method for model accuracy and diversity has the defects of being sensitive to data order, complex model updating, and lacking a forgetting mechanism.

[0008] The present invention proposes a selective ensemble learning soft-sensing method based on double error measurement and game theory. The diversity weight of the model is calculated by the double error measurement method, and then the two are fused and selected in combination with the idea of ​​game theory to obtain the final comprehensive weight (that is, under the comprehensive weight, both are in the optimal state); the comprehensive weight is used to balance the accuracy and diversity of the model to achieve a model with high accuracy and strong generalization ability. Summary of the invention

[0009] In order to solve the problem of generating redundant or even inferior sub-models in ensemble learning, which leads to model overfitting, the present invention proposes a selective ensemble learning soft measurement method based on double error measurement and game theory. The method uses double error measurement to calculate the diversity weight of the sub-model, and uses the idea of ​​game theory to fuse the precision weight and diversity weight of the sub-model to obtain a comprehensive weight that takes both into account. In the model screening stage, the comprehensive weight can be used to balance precision and diversity to obtain a model that is accurate and has high generalization ability.

[0010] A selective ensemble learning soft sensing method based on double error measurement and game theory is used to predict quality variables in a specific industrial process. The method includes:

[0011] Step 1: Collect historical data from specific industrial processes as samples required for modeling, and perform data preprocessing to obtain a training data set.

[0012] Step 2: Use the random resampling method in the Bagging algorithm to generate J groups of sub-datasets from the training data set, and use the J sub-datasets to build J GPR sub-models to obtain a sub-model pool.

[0013] Step 3: For the test sample x new , calculate the Euclidean distance between it and each data in the training data set, and select the N samples with the closest distance as the validation set, recorded as Among them, {x' i ,y' i} are the input values ​​and true values ​​after renumbering the selected samples.

[0014] Step 4: On the validation set, calculate the accuracy weight ω of each model in the sub-model pool MSE and the diversity weight ω RDF .

[0015] Step 5: Comprehensive precision weight ω according to game theory strategy MSE and the diversity weight ω RDF , and get the optimal comprehensive weight W′.

[0016] Step 6: Normalize the optimal comprehensive weights and sort them in descending order. Select the first M models whose cumulative weights reach the set threshold T as high-quality models, denoted as {h'1,h'2,…,h' M}.

[0017] Step 7: Calculate the posterior probability of the sample to be predicted for each high-quality model, and fuse the output according to the Bayesian posterior probability idea to obtain the final prediction value.

[0018] The double error metric is an indicator used to measure the common classification errors of two models in classification tasks. The larger the double error metric, the greater the ratio of the common classification errors of the two models, and the smaller the diversity between the models; the smaller the double error metric, the smaller the ratio of the common classification errors of the two models, and the greater the diversity between the models. The calculation formula of the double error metric is as follows:

[0019]

[0020] The existing double error metric is calculated using all sub-models, which will make the denominator too large, resulting in DF being 0, making the double error metric matrix unsolvable and unable to calculate the weight coefficient; this application calculates the double error metric between two sub-models. It is extended to regression prediction. There is a deviation between the prediction result and the true value of each sample point in the regression task. It is defined that when the absolute values ​​of the relative errors of the two models for the sample point are both greater than a certain threshold, it is judged that the two models have a common prediction error for this sample point.

[0021] The absolute value of the relative error of the jth model for the nth data point is defined as follows:

[0022]

[0023] Where y n Represents the true value of the nth data point, y n,j represents the predicted value of the jth model at the nth data point. For the nth data point, the judgment condition that the two models make a common prediction error is:

[0024] dp n,p &dp n,q >mean({dp n,j} n＝1,2,…,N；j＝p,q ) (2)

[0025] In the formula, N represents the total amount of data, J represents the number of sub-models, dp n,p and dp n,q Represents the absolute value of the relative error between any two sub-models at the nth data point. mean({dp n,j} n＝1,2,…,N；j＝p,q ) is the mean of the absolute values ​​of the relative errors of the p-th and q-th sub-models at all data points.

[0026] According to equations (1) and (2), we can obtain the double error measurement matrix DF between J sub-models and the double error measurement DF between the j-th sub-model and other sub-models: j for:

[0027]

[0028]

[0029] Among them, J represents the number of sub-models, DF j,t is the double error measure between the j-th sub-model and the t-th sub-model.

[0030] The step 4 comprises:

[0031] Step 4.1: First calculate the accuracy weight;

[0032] The prediction mean square error of the j-th sub-model on the validation set is calculated according to the following formula:

[0033]

[0034] Among them, h j (x i ) represents the predicted value of the jth sub-model on the i-th data sample, y i is the true value of the i-th sample, and N is the length of the validation set Z.

[0035] Finally, we can get the MSE vector of all sub-models: MSE = [MSE1, MSE2, …, MSE J ]. The jth precision-based weight calculation formula is:

[0036]

[0037] In the formula, med(MSE) is the median of the accuracy weights of all sub-models. Finally, the weight vector ω based on accuracy is obtained MSE =[ω 1,1 ,ω 1,2 ,…,ω 1,J ].

[0038] Step 4.2: Calculate diversity weights;

[0039] The double error metric vector DF calculated in step 3 is DF=[DF1, DF2,…, DF J ]. The jth diversity-based weight calculation formula is:

[0040]

[0041] In the formula, med(DF) is the median of the accuracy weights of all sub-models. Finally, the weight vector ω based on diversity is obtained RDF =[ω 2,1 ,ω 2,2 ,…,ω 2,J ].

[0042] When there are m weights obtained using m standards, these m weights are combined so that the final weight takes into account different standards. The final weight is a linear combination of the above m weights, as follows:

[0043]

[0044] By optimizing the weight coefficient α k The optimal comprehensive weight vector W′ is obtained. The optimization goal is to minimize the comprehensive weight W and ω i The deviation is as follows:

[0045]

[0046] Calculate formula (9) to get the optimal weight coefficient The optimal comprehensive weight is

[0047]

[0048] Obtain W′={ω1′,ω2′,…,ω k ′}.

[0049] Then the optimal comprehensive weight is normalized.

[0050]

[0051] Get the final weight W″={ω1″,ω2″,…,ω k ″}.

[0052] The beneficial effects that the present invention can achieve are:

[0053] A selective ensemble learning soft measurement method based on double error measurement and game theory is proposed. The double error measurement method is used to calculate the diversity weight of the model, and the precision weight and diversity weight of the sub-model are integrated with the idea of ​​game theory to obtain a comprehensive weight that takes both into account. In the model screening stage, the comprehensive weight can be used to balance precision and diversity to obtain an accurate model with high generalization ability, so as to solve the problem of model overfitting caused by the generation of redundant or even inferior sub-models in the ensemble learning process. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0055] Figure 1 This is the framework diagram of the DFG-GPR model;

[0056] Figure 2 This is a comparison chart of the RMSE of penicillin concentration prediction by the DFG-GPR model under different thresholds T;

[0057] Figure 3 This is a comparison chart of the prediction errors of penicillin concentration obtained under the three modeling methods;

[0058] Figure 4 Box plot of the prediction error of penicillin concentration under three modeling methods. DETAILED DESCRIPTION

[0059] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0060] Embodiment 1:

[0061] This embodiment provides a selective ensemble learning soft-sensing method based on double-error metric and game theory, the method comprising:

[0062] Step 1: Collect historical data from a specific industrial process and preprocess the historical data to obtain a training data set;

[0063] Specific industrial processes include petrochemicals, blast furnace refining, fermentation processes, etc.; and for different industrial processes, the corresponding historical data may be different.

[0064] For fermentation processes, such as the penicillin process, historical data include: stirring power, substrate feed rate, dissolved oxygen concentration, heat generated, culture volume, carbon dioxide concentration, pH value, penicillin concentration, etc.

[0065] Preprocessing includes: data cleaning, data conversion, feature engineering, data integration, etc.

[0066] Step 2: Resample the training data set to generate J groups of sub-data sets, and use the J sub-data sets to establish J GPR sub-models to obtain a sub-model pool;

[0067] The training data set obtained in step 1 is resampled by the random resampling method in the Bagging algorithm to obtain J groups of sub-data sets, and J GPR sub-models are established by the GPR method to obtain a sub-model pool.

[0068] Step 3: For the test sample x new , calculate the Euclidean distance between it and each data in the training data set, and select the N samples with the closest distance as the validation set, recorded as Among them, {x′ i ,y′ i} is the input value and true value after renumbering the selected samples;

[0069] Calculate double error measures between sub-models and other sub-models;

[0070] The absolute value of the relative error of the jth sub-model for the nth data point is defined as follows:

[0071]

[0072] Where y n Represents the true value of the nth data point, y n,jrepresents the predicted value of the jth model at the nth data point. For the nth data point, the judgment condition that the two models make a common prediction error is:

[0073] dp n,p &dp n,q >mean({dp n,j} n＝1,2,…,N；j＝p,q ) (2)

[0074] In formula (2), N represents the total amount of data, dp n,p and dp n,q Represents the absolute value of the relative error between any two sub-models at the nth data point, mean({dp n,j} n＝1,2,…,N；j＝p,q ) is the mean of the absolute values ​​of the relative errors of the p-th and q-th sub-models at all data points;

[0075] According to equations (1) and (2), we can obtain the double error measurement matrix DF between J sub-models and the double error measurement DF between the j-th sub-model and other sub-models: j for:

[0076]

[0077]

[0078] Among them, J represents the number of sub-models, DF j,t is the double error measure between the j-th sub-model and the t-th sub-model.

[0079] Step 4: On the validation set, calculate the accuracy weight ω of each model in the sub-model pool MSE and the diversity weight ω RDF ;

[0080] 4.1: Calculate the precision weight;

[0081] The prediction mean square error of the j-th sub-model on the validation set is calculated according to the following formula:

[0082]

[0083] Among them, h j (x i ) represents the predicted value of the jth sub-model on the i-th data sample, y i is the true value of the i-th sample, and N is the length of the validation set Z;

[0084] Finally, we can get the MSE vector of all sub-models: MSE = [MSE1, MSE2, …, MSE J ], the jth precision-based weight calculation formula is:

[0085]

[0086] In the formula, med(MSE) is the median of the accuracy weights of all sub-models, and finally the accuracy-based weight vector ω is obtained MSE =[ω 1,1 ,ω 1,2 ,…,ω 1,J ];

[0087] 4.2: Calculate diversity weights;

[0088] The double error metric vector DF calculated in step 3 is DF=[DF1, DF2,…, DF J ], the j-th diversity-based weight calculation formula is:

[0089]

[0090] In the formula, med(DF) is the median of the accuracy weights of all sub-models, and finally the weight vector ω based on diversity is obtained RDF =[ω 2,1 ,ω 2,2 ,…,ω 2,J ].

[0091] Step 5: Comprehensive precision weight ω according to game theory strategy MSE and the diversity weight ω RDF , get the optimal comprehensive weight W′;

[0092] The game theory strategy is that when there are m weights obtained using m criteria, these m weights are integrated so that the final weight takes into account different criteria. The final weight is a linear combination of the above m weights, as follows:

[0093]

[0094] By optimizing the weight coefficient α k The optimal comprehensive weight vector W′ is obtained, and its optimization goal is to minimize the comprehensive weight W and ω i The deviation is as follows:

[0095]

[0096] Calculate formula (9) to get the optimal weight coefficient The optimal comprehensive weight is:

[0097]

[0098] Obtain W′={ω1′,ω2′,…,ω k ′}.

[0099] In this solution, there are two weights: precision weight and diversity weight, so m=2 in the above formulas (8)-(10).

[0100] Step 6: Normalize the optimal comprehensive weights and sort them in descending order. Select the first M models whose cumulative weights reach the set threshold T as high-quality models, denoted as {h′1,h′2,…,h′ M};

[0101] Normalize the optimal comprehensive weight,

[0102]

[0103] Get the final weight W″={ω1″,ω2″,…,ω k ″}.

[0104] Step 7: Calculate the posterior probability of the sample to be predicted for each high-quality model, and fuse the output according to the Bayesian posterior probability idea to obtain the final prediction value.

[0105] Embodiment 2:

[0106] This embodiment provides a method for predicting penicillin concentration in a penicillin fermentation process. The method uses the selective ensemble learning soft measurement method based on double error measurement and game theory given in Example 1 to predict the penicillin concentration in the penicillin fermentation process. The penicillin fermentation process is the metabolic activity of penicillin-producing bacteria in which the bacteria grow and synthesize antibiotics under the premise of a suitable fermentation environment, and is widely used in the research of soft measurement modeling.

[0107] Using the PenSim simulation platform, seven highly correlated variables were selected as input variables, penicillin concentration was used as the dominant variable, simulation experiments were designed, and the required experimental data were collected. The variables involved in the modeling process are shown in Table 1.

[0108] Table 1 Variables used to establish the penicillin concentration prediction model

[0109]

[0110]

[0111] In the PenSim penicillin fermentation simulation platform, the fermentation time of penicillin was set to 400 hours and the sampling time interval was 0.2 hours. A total of 2000 sets of process data were collected, of which 1500 sets were used as training sets for the modeling algorithm and 500 sets were used as test sets for the modeling algorithm.

[0112] In order to verify the effectiveness of the method proposed in this paper, the soft sensor model constructed in this application is experimentally compared with two other existing soft sensor models to compare their prediction performance indicators:

[0113] (i) GPR global model;

[0114] (ii) Bagging-based GPR multi-model (abbreviated as B-GPR), please refer to the detailed introduction in "Zhao Shuai. Research on Gaussian process regression soft sensor modeling method based on ensemble learning [D]. Jiangnan University, 2018 (Chapter 2)";

[0115] (iii) DFG-GPR (the method proposed in the present invention).

[0116] This application scheme selects root mean squared error (RMSE), correlation coefficient (COR) and coefficient of determination (R 2 ) is used to evaluate the prediction performance and tracking ability of the model. The calculation method is as follows:

[0117]

[0118]

[0119]

[0120] Among them, |L| is the test sample length, and i are the estimated value and actual value of the i-th test sample, respectively. and are the average values ​​of the estimated value and the actual value of the test sample, respectively. COR reflects the degree of linear correlation between the estimated value and the true value. The larger the value, the higher the prediction accuracy of the model. 2 It measures how well the model fits the data. When the predicted value is exactly equal to the actual value, its value is 1, indicating a perfect fit.

[0121] When selecting a high-quality model, different thresholds T for cumulative weighting will affect the performance of the model. Therefore, simulation tests are conducted under different thresholds. Figure 2 This is a graph showing the change of RMSE of penicillin concentration as the threshold T changes in the experiment using the DFG-GPR model method.

[0122] from Figure 2 It can be seen that in multiple experiments, changes in the threshold will also affect the performance of the final model. When T = 0.4, the RMSE value of the model reaches the minimum. Therefore, in subsequent experiments, the threshold T is set to 0.4.

[0123] Table 2 Comparison of penicillin concentration prediction performance indicators under three modeling methods

[0124]

[0125] Table 2 shows the comparison of penicillin concentration prediction performance indicators obtained under the three modeling methods. The results show that the DFG-GPR method proposed in this application has better prediction performance and tracking performance. It can be seen from the RMSE value that its model has the highest accuracy; its COR value is closest to 1, indicating that the prediction value of the model established by this method for new sample points is closer to the true value; in addition, R 2 The value is also closest to 1, which means that the degree of fit of the model is higher than that of GPR and B-GPR.

[0126] Figure 3 A real-time comparison of the prediction errors of penicillin concentration using three modeling approaches is shown. Figure 3 It can be seen that the real-time prediction error of the DFG-GPR method proposed in this paper is more stable near 0 and has a smaller fluctuation range. Compared with the GPR and B-GPR methods, the prediction accuracy of this model is higher and the stability is better.

[0127] Figure 4 Box plots showing the prediction errors of penicillin concentration under the three modeling methods. Figure 4 It can be seen that compared with the other two methods, the box height of the method proposed in this article is smaller, indicating that the data fluctuation is smaller; the upper and lower dotted lines are shorter, indicating that the data outside the upper and lower quartiles change less and the variance of the overall data is also smaller.

[0128] In addition, in order to observe the impact of noise on the model established in this paper in the actual process, three methods under different signal-to-noise ratios were added to simulate the prediction of penicillin concentration. As can be seen from Table 3, even under different signal-to-noise ratios, the DFG-GPR model established in this paper still has the best prediction performance compared with the GPR and B-GPR methods.

[0129] Table 3 Prediction performance indicators of penicillin concentration by three modeling methods at different signal-to-noise ratios

[0130]

[0131] according to Figures 2 to 4 The simulation results shown in Tables 2 and 3 show that the DFG-GPR method combines the precision weight and diversity weight of the sub-models, and deletes the inferior and redundant models in the selection integration process. In the penicillin fermentation process, the DFG-GPR method shows good prediction performance in the task of estimating penicillin concentration, and achieves better prediction results than the GPR and B-GPR methods.

[0132] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0133] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A selective ensemble learning soft-sensing method based on double-error metric and game theory, characterized in that: The method comprises: Step 1: Collect historical data from a specific industrial process and preprocess the historical data to obtain a training data set; Step 2: Resample the training data set to generate J sub-data sets, and use the J sub-data sets to establish J GPR sub-models to obtain a sub-model pool; Step 3: For the test sample x new , calculate the Euclidean distance between it and each data in the training data set, and select the N samples with the closest distance as the validation set, recorded as Among them, {x' i ,y' i } is the input value and true value after renumbering the selected samples; Step 4: On the validation set, calculate the accuracy weight ω of each model in the sub-model pool MSE and the diversity weight ω RDF ; Step 5: Comprehensive precision weight ω according to game theory strategy MSE and the diversity weight ω RDF , get the optimal comprehensive weight W′; Step 6: Normalize the optimal comprehensive weight and arrange them in descending order to obtain M high-quality sub-models denoted as {h′1,h′2,…,h′ M }; Step 7: Calculate the posterior probability of the sample to be predicted for each high-quality sub-model, and fuse the output according to the Bayesian posterior probability idea to obtain the final prediction value.

2. The method according to claim 1, characterized in that The step 3 comprises: Calculate double error measures between sub-models and other sub-models; The absolute value of the relative error of the jth sub-model for the nth data point is defined as follows: Where y n Represents the true value of the nth data point, y n,j represents the predicted value of the jth sub-model at the nth data point. For the nth data point, the judgment condition for the common prediction error of the two sub-models is: dp n,p &dp n,q >mean({dp n,j } n＝1,2,…,N；j＝p,q ) (2) In formula (2), N represents the total amount of data, dp n,p and dp n,q Represents the absolute value of the relative error between any two sub-models at the nth data point, mean({dp n,j } n＝1,2,…,N；j＝p,q ) is the mean of the absolute values ​​of the relative errors of the p-th and q-th sub-models at all data points; According to equations (1) and (2), we can obtain the double error measurement matrix DF between J sub-models and the double error measurement DF between the j-th sub-model and other sub-models: j for: Among them, J represents the number of sub-models, DF j,t is the double error measure between the j-th sub-model and the t-th sub-model.

3. The method according to claim 2, characterized in that The step 4 comprises: Step 4.1: Calculate the precision weight; The prediction mean square error of the j-th sub-model on the validation set is calculated according to the following formula: Among them, h j (x i ) represents the predicted value of the jth sub-model on the i-th data sample, y i is the true value of the i-th sample, and N is the length of the validation set Z; Finally, we can get the MSE vector of all sub-models: MSE = [MSE1, MSE2, …, MSE J ], the jth precision-based weight calculation formula is: In the formula, med(MSE) is the median of the accuracy weights of all sub-models, and finally the accuracy-based weight vector ω is obtained MSE =[ω 1,1 ,ω 1,2 ,…,ω 1,J ]; Step 4.2: Calculate diversity weights; The double error metric vector DF calculated in step 3 is DF=[DF1, DF2,…, DF J ], the j-th diversity-based weight calculation formula is: In the formula, med(DF) is the median of the accuracy weights of all sub-models, and finally the weight vector ω based on diversity is obtained RDF =[ω 2,1 ,ω 2,2 ,…,ω 2,J ].

4. The method according to claim 3, characterized in that The step 5 comprises: The game theory strategy is that when there are m weights obtained using m criteria, these m weights are integrated so that the final weight takes into account different criteria. The final weight is a linear combination of the above m weights, as follows: By optimizing the weight coefficient α k The optimal comprehensive weight vector W′ is obtained, and its optimization goal is to minimize the comprehensive weight W and ω i The deviation is as follows: Calculate formula (9) to get the optimal weight coefficient The optimal comprehensive weight is: We get W′={ω′1,ω′2,…,ω′ k }, in formulas (8)-(10), m=2.

5. The method according to claim 4, characterized in that The step 6 comprises: Normalize the optimal comprehensive weight, Get the final weight W″={ω1″,ω2″,…,ω k ″}.

6. The method according to claim 5, characterized in that The resampling method in step 2 is the random resampling method in the Bagging algorithm.

7. The method according to claim 6, characterized in that In step 6, the high-quality sub-models are the first M sub-models whose cumulative weights reach the set threshold T.

8. The method according to claim 1, characterized in that The industrial processes include petrochemicals, blast furnace refining, and fermentation processes.

9. A method for predicting penicillin concentration in a penicillin fermentation process, characterized in that: The method predicts the concentration of penicillin using the method described in any one of claims 1 to 7.

10. The method according to claim 9, characterized in that The historical data in the penicillin fermentation process include stirring power, substrate feed rate, dissolved oxygen concentration, heat generation, culture volume, carbon dioxide concentration, pH value, and penicillin concentration.

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