A bubble column gas holdup prediction method based on bootstrap sampling and parameter optimization

Abstract

The application provides a bubble column gas holdup prediction method based on Bootstrap sampling and parameter optimization, and comprises the following steps: constructing and training a plurality of base models, wherein the base models adopt machine learning models, and each base model is independently trained; obtaining operation data of the bubble column, predicting the operation data by each base model, performing data fusion on the predicted results by a voting mechanism, and obtaining a prediction result of the gas holdup of the bubble column, so that the gas holdup of the bubble column can be effectively predicted.

Description

Technical Field

[0001] This invention relates to the fields of bubble column and machine learning technology, and more specifically, to a method for predicting gas holdup in bubble columns based on Bootstrap sampling and parameter optimization. Background Technology

[0002] In modern industry, bubble column towers are widely used in chemical engineering, primarily for enhancing gas-liquid reactions, conducting fermentation processes, and wastewater treatment. Bubble column towers are highly valued because they efficiently promote the interaction between gas and liquid, thereby increasing reaction and process rates. All these processes are highly dependent on gas holdup, which characterizes the volume fraction of gas within the column. Therefore, estimating gas holdup is a key issue for optimizing design parameters and operating conditions, and improving productivity and energy economy. Traditionally, gas holdup is estimated using empirical correlations and theoretical models. However, these methods often struggle to characterize the complex dynamic behavior and fluctuations under real-world conditions. In summary, traditional methods rely heavily on empirical formulas or theoretical models, making it difficult to capture the complex gas-liquid flow dynamics and nonlinear behavior within the bubble column. With increasing process complexity and data volume, the predictive power of traditional models gradually becomes insufficient, failing to effectively predict the gas holdup of bubble column towers. Summary of the Invention

[0003] In view of this, the present invention proposes a method for predicting the gas holdup of a bubble column based on Bootstrap sampling and parameter optimization. A strongly integrated method is embedded in the regression analysis of the bubble column to more accurately and reliably promote process optimization and prediction, thereby solving the problems existing in the prior art.

[0004] To achieve the above objectives, this invention proposes a method for predicting the gas holdup of a bubble column based on Bootstrap sampling and parameter optimization, comprising: Construct and train several base learners, wherein the base learners adopt machine learning models, and each base learner is trained independently. The sample set is bootstrap sampled with replacement to generate several sub-training sets, and the base learners are trained based on the sub-training sets. The Antlion optimizer was used to optimize the number of base learners and the sample ratio / number. The operation data of the bubble column is obtained, and regression prediction is performed on the operation data through an optimized base learner. The prediction results are then fused through a voting mechanism to obtain the gas holdup prediction value. The data fusion adopts either weighted average or mean fusion.

[0005] Optionally, the base learner includes decision tree models, artificial neural networks, extreme random trees, random forests, and support vector regression.

[0006] Optionally, the data fusion process includes: For classification tasks, the base learners are fused using majority voting, while for regression tasks, the base models are fused using mean calculation.

[0007] Optionally, the integrated base model may also be tested using a test set independent of the training set, wherein the metrics in the test include mean absolute error, root mean square error, variance explanation factor, relative absolute error, Pearson correlation coefficient, maximum error, standard deviation, and performance metrics.

[0008] Optionally, it also includes using a single model to predict the operating data to obtain the predicted gas holdup of the bubble column, wherein the single model includes a gradient boosting model, an extreme gradient boosting model, a random forest model, an adaptive boosting model, or a decision tree model.

[0009] On the other hand, the present invention also provides a bubble column gas holdup prediction system based on machine learning and data fusion for performing the above-described method.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention can deeply mine the hidden patterns in data and accurately capture complex interaction effects that traditional methods cannot identify; it significantly reduces the risk of overfitting of the model, enabling it to maintain stable predictive performance when faced with data fluctuations and noise in actual working conditions; at the same time, through the collective decision-making of the base learner, it effectively improves the ability to identify key influencing factors of gas holdup, providing reliable technical support for the design optimization, process control and industrial scale-up of bubbling towers, and realizing the leap from experience estimation to data-driven intelligent prediction. Attached Figure Description

[0011] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 This is a schematic diagram of the Bagging model structure in an embodiment of the present invention; Figure 2 This is a schematic diagram of the Bagging model optimization test in an embodiment of the present invention; Figure 3 The embodiment of the present invention is based on R 2 A schematic diagram comparing the models; Figure 4 This is a schematic diagram of model comparison based on numerical representation in an embodiment of the present invention; Figure 5 This is a schematic diagram of error-based model comparison in an embodiment of the present invention; Figure 6 This is a schematic diagram of model comparison based on box plots in an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the comparison of models based on evaluation indicators in an embodiment of the present invention; Figure 8 This is a schematic diagram of RMSE-based model comparison in an embodiment of the present invention; Figure 9 This is a schematic diagram of the comparative analysis of models based on mixed indicators in an embodiment of the present invention. Detailed Implementation

[0012] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0013] In various industrial processes, gas holdup estimation in bubble column bubbling towers is crucial for designing efficient, scalable, and economical systems. With advancements in modeling methods, such as computational fluid dynamics and machine learning, the accuracy and applicability of gas holdup estimation have continuously improved. Based on this, this invention focuses on the accuracy and effectiveness of several advanced machine learning models in gas holdup prediction. Regarding model optimization, 80% of the data was used for training, and 20% for testing. The main models used for predicting bubble column gas holdup include: Gradient Boosting (GB), Extreme Gradient Boosting (XGB), Random Forest (RF), Adaptive Boosting, Decision Trees (DT), and Bootstrap Aggregating (Bagging).

[0014] This invention employs machine learning methods to effectively predict the gas holdup of a bubble column. Machine learning is an important tool for improving the accuracy and efficiency of bubble column gas holdup prediction. Machine learning models can utilize massive amounts of data and complex algorithms to identify complex nonlinear relationships in the data, relationships that are often overlooked by traditional methods. Techniques such as support vector machines, neural networks, and ensemble methods have shown superior performance in modeling complex dynamics of gas-liquid interactions. Such models can continuously learn and adapt to new data, make real-time predictions, and support active process regulation. Therefore, introducing machine learning into gas holdup prediction not only improves prediction accuracy and reliability but also helps to form more efficient and scalable process optimization strategies, ultimately improving operational performance in chemical engineering applications. The relevant content regarding the machine learning model used is as follows: 1. Gradient Boosting (GB) Gradient boosting (GB) is a sequential machine learning method for regression and classification tasks where the model is built incrementally. GB constructs a strong learning model by combining the predictions of multiple base learners (typically decision trees). Its core idea is to continuously build new models to correct the prediction errors of previous models. It starts with an initial prediction and then fits a new model to the residuals of the current ensemble model. By focusing on the errors of the previous model, GB iteratively reduces the overall prediction error, thereby improving performance.

[0015] The Gradient Boosting (GB) algorithm, with its core structure comprising eight key functional modules, reveals the working principle of this ensemble learning algorithm. Its core mechanism involves progressively accumulating and combining multiple weak learners (typically shallow decision trees) into a single strong learner using an additive model. In each iteration, the newly added weak learner does not simply repeat the previous work but focuses on fitting the residual between the previous prediction and the true value, i.e., optimizing along the negative gradient direction of the loss function—hence the name "gradient boosting." To improve the model's generalization ability and prevent overfitting, multiple control strategies are provided: shrinkage (learning rate) controls the contribution weight of each tree, tree constraints limit the complexity of a single tree, penalized learning introduces a regularization term, and random sampling introduces data perturbation to enhance robustness. The GB algorithm combines simple base learners into a high-precision prediction model through serial iteration and progressive error correction, providing a theoretical basis for understanding the performance of GB in subsequent experimental results.

[0016] This process comprises three key components: a loss function, a weak learner (typically a shallow tree), and an additive model. Each stage fits a new tree to the residual error and minimizes the loss function through gradient descent optimization. Therefore, each subsequent model in the sequence aims to reduce the combined error of all preceding models, ultimately resulting in a highly accurate model. GB is highly flexible and capable of handling diverse datasets, making it widely applicable in machine learning applications.

[0017] 2. Random Forest (RF) Random Forest (RF) is an ensemble learning technique commonly used for classification and regression tasks. This method constructs multiple decision trees during training, outputting the most frequent class for classification tasks and the average of the predictions from each tree for regression tasks. It leverages the principle of "swarm intelligence": combining the predictions from multiple trees reduces the risk of overfitting and provides better generalization ability than a single decision tree.

[0018] Random forests combine multiple decision trees into a powerful predictive model through ensemble learning. Their core mechanism begins with the bootstrap process: from the original training dataset D containing (n+m) input variables, multiple distinct subsets (e.g., D1, D2, D3) are generated through random sampling with replacement. These subsets are then fed in parallel into multiple decision trees T(D1), T(D2), and T(D3) for independent training. Finally, the outputs of all decision trees are aggregated at the right-hand node, and the final robust prediction is obtained by averaging (for regression tasks). This design effectively reduces the risk of overfitting from a single decision tree by introducing randomness in the data samples and collective decision-making from multiple models, thus improving the model's generalization ability and prediction accuracy.

[0019] RF employs a Bootstrap Aggregating (Bagging) strategy, generating multiple subsets of training data through random sampling with replacement, ensuring that each tree is trained on slightly different datasets. Simultaneously, at each split of a tree, only a subset of features are randomly considered, thus maintaining diversity among the trees and reducing correlation.

[0020] The advantages of Random Forest (RF) lie in its ability to effectively handle high-dimensional, large-scale datasets and its strong robustness against noise and overfitting. The algorithm is relatively simple to implement, can handle missing values, and maintains high accuracy on most datasets. Furthermore, RF provides an internal feature importance evaluation mechanism, which helps in understanding underlying patterns in the data. Although its computational cost is higher and its interpretability is weaker than that of a single decision tree, its high accuracy and strong resistance to overfitting have led to its widespread adoption in many practical applications.

[0021] 3. Adaptive Boost (AdaBoost) Another model used in this paper is AdaBoost, or Adaptive Boosting. This is an important ensemble learning technique that aims to improve overall learning performance by sequentially training weak learners (usually decision trees). The core idea of ​​AdaBoost is to allow subsequent models to focus on samples that previous models struggled to classify correctly.

[0022] Its working mechanism is as follows: In each iteration, AdaBoost assigns weights to each training sample, initially with equal weights; then, it adjusts the sample weights based on whether the weak learner correctly classifies the sample. The weights of misclassified samples are increased, causing subsequent models to pay more attention to these difficult samples. This process is repeated iteratively.

[0023] In the machine learning training-testing process: First, from the original feature and target dataset, samples are randomly divided into an 80% training subset and a 20% test subset. Next, the AdaBoost model is trained on the training subset. The core of this algorithm lies in iteratively adjusting sample weights, making subsequent weak learners pay more attention to previously misclassified difficult examples. Then, the trained model is applied to the test subset for prediction. During the prediction phase, the target value must be "ignored," meaning the model can only make inferences based on input features to ensure the objectivity of the evaluation. Finally, the model's test prediction results are compared with the actual test target value, and the model's prediction accuracy is objectively evaluated by calculating accuracy or error metrics. This demonstrates the complete operational flow of AdaBoost in practical applications, emphasizing the importance of data splitting and independent validation for ensuring the model's generalization ability.

[0024] AdaBoost's final prediction is determined by a weighted majority vote of all weak learners. Each learner's weight depends on its accuracy; the more accurate the learner, the higher its weight. This mechanism allows AdaBoost to combine multiple weak models into a strong classifier, making it well-suited for complex datasets and possessing strong generalization capabilities. AdaBoost is also renowned for its ability to handle noisy data and complex classification problems, thus it is widely used in practical applications requiring high accuracy.

[0025] 4. Extreme Gradient Boosting (XGB) XGB is one of the best-performing machine learning techniques currently available, demonstrating excellent performance on structured data problems. The algorithm works by generating a series of decision trees, each of which "learns" the mistakes made by the preceding trees and attempts to correct them. This process iterates until the model reaches its optimal performance or meets a preset stopping condition.

[0026] XGB employs a relatively complex objective function, composed of a loss function and a regularization term, to effectively manage model complexity and prevent overfitting. Leveraging gradient descent optimization and tree pruning techniques, XGB achieves high computational efficiency while improving prediction accuracy. It also supports parallel processing, thus exhibiting excellent scalability on large-scale datasets.

[0027] The complete experimental framework and workflow of the XGBoost (Extreme Gradient Boosting) model are presented from top to bottom, clearly showing three core layers: First, in the data preparation layer, all available data is divided into 2 / 3 training set and 1 / 3 test set; then, in the model building and optimization layer, on the left, grid search is used to tune the hyperparameters of XGBoost to determine the optimal parameter combination, and on the right, 1000 XGBoost models (GBM1 to GBM) are built in parallel using this optimal set of parameters. 1000 Each model corresponds to a decision tree structure. Finally, in the result aggregation layer, the left side aggregates a ranking list of the feature importance of 1000 models to analyze the influence weight of input variables, while the right side uses all 1000 models to predict the test set, and averages all prediction results to output the final test set prediction result. The core idea of ​​XGBoost to improve prediction accuracy through the "group decision" strategy is to build a large-scale model group based on optimal parameters and reduce the volatility of individual models by averaging the results, thereby obtaining more stable and reliable prediction performance.

[0028] In practice, XGB is widely used for various tasks such as classification, regression, and ranking. It can handle complex feature interactions and effectively manage missing data, making it particularly suitable for diverse and dynamic real-world data. Furthermore, its flexible objective function and parameter configuration make it applicable to different modeling scenarios, thus making it very popular in both competitive and industrial settings.

[0029] 5. Decision Tree (DT) Decision trees (DTs) are one of the most common methods in machine learning, widely used for classification and regression problems in supervised learning. This method recursively divides the input space into smaller regions, each corresponding to a specific class label or regression result. Decision trees typically have a hierarchical structure: internal nodes make decisions based on feature values, and leaf nodes provide the final prediction or classification result.

[0030] This structure is highly interpretable and transparent because the decision-making process relies entirely on the input features, making it easy to understand and reason. During training, at each node, DT selects the feature and split point that yields the maximum information gain (classification) or the minimum variance (regression). This process is repeated recursively until a stopping condition is met, such as the tree depth reaching its limit or the purity metric no longer improving.

[0031] The basic structure of the decision tree model and its extension path to ensemble learning include: the original dataset is divided into training and test sets, with the training set used to build the decision tree model. Based on the Bagging mechanism, multiple sub-training sets and corresponding sub-test sets can be generated from the original training set through sampling with replacement. This process further points upwards to "random forests," indicating that when decision trees are combined with Bagging and random feature selection is introduced during node splitting, a random forest algorithm can be constructed. The application scenario of the model is clarified through the "classification" task type. Finally, after the above process, a mature model that can be used for prediction is obtained. The decision tree, as the training-test paradigm of the basic model, is upgraded to a random forest through the Bagging mechanism.

[0032] Decision trees are intuitive, interpretable, and can handle both numerical and categorical data. However, without proper regularization or pruning, they are prone to overfitting. Common methods to improve the predictive performance and generalization ability of decision trees include pruning techniques, ensemble methods such as random forests, and boosting methods such as gradient boosting.

[0033] 6. Bootstrap Bagging The final model used was Bagging, or Bootstrap Aggregating. This is an ensemble learning technique designed to improve the stability and accuracy of individual machine learning models. Its process involves generating multiple subsets from the original dataset through sampling with replacement, and then independently training a base learner (e.g., a decision tree) on each subset. The final result is obtained by aggregating the outputs of all base models: majority voting for classification tasks and the average for regression tasks.

[0034] like Figure 1-2As shown, the core idea of ​​the Bagging ensemble learning algorithm can be summarized as improving the predictive performance of the model through data perturbation and collective decision-making. Bagging first performs Bootstrap sampling (random sampling with replacement) on the original training set, generating multiple different subsets D1, D2, and D3. Each subset independently trains a base learner—usually a decision tree (DT) as the base model. During parallel training, each subset corresponds to a decision tree T(D1), T(D2), and T(D3), and all trees grow independently without interfering with each other. Finally, when new test data is input, all parallel base models (Model-1 to Model-6) make predictions respectively, and their results are aggregated through a voting mechanism (majority voting for classification tasks, and average value for regression tasks as described in this paper) to obtain the final output. This strategy of parallel training and average output effectively reduces the risk of overfitting by a single model and the prediction variance, thus achieving more stable and accurate generalization performance than any single model.

[0035] Bagging can reduce variance, reduce model overfitting, and improve overall prediction performance.

[0036] Based on the above model, this paper aims to propose a new Bagging application method, namely, to optimize the Bagging algorithm using the Antlion Optimizer (ALO) to solve the regression problem of bubble column gas holdup prediction. The optimization objective is the relevant performance indicators of the Bagging algorithm.

[0037] The dataset for predicting gas take-off in bubble column data is derived from literature data and extracted and organized using the Engauge Digitizer tool. This dataset contains one dependent variable, gas take-off, and several independent variables representing predictors, including apparent gas velocity, apparent liquid velocity, liquid viscosity, liquid surface tension, liquid density, gas density, column diameter, distributor type and aperture, temperature, pressure, solids take-off (if a gas-liquid-solid system is involved), liquid properties (such as electrolyte or surfactant concentration), operating mode (batch / continuous), and operating conditions and physical properties affecting gas-liquid interaction, such as column height or height-to-diameter ratio. This dataset supports the application of various machine learning techniques, including Artificial Neural Networks (ANN), Extra Trees, Random Forests (RF), and Support Vector Regression (SVR), in addition to the aforementioned decision trees.

[0038] In addition, data preprocessing includes splitting the data into training and test sets. This splitting is crucial for building and evaluating machine learning models. The training set is used to fit the model parameters, while the test set is used to perform an unbiased evaluation of the model's performance on new data. Ultimately, 218 data points (80%) were assigned to the training set in the final experimental dataset, and the remaining 55 data points (20%) were retained as the test set. Both the training and test datasets were collected or constructed through actual work or simulations of real-world scenarios.

[0039] Therefore, the optimized Bagging algorithm was applied to a new dataset specifically constructed for this study. The models compared in this paper include GB, RF, AdaBoost, XGB, and DT, and are compared with the selected Bagging method using various performance metrics and results from the training / testing phases.

[0040] Furthermore, the hyperparameters selected for each model tuning are determined based on their significant impact on model performance and generalization ability; other hyperparameters are excluded to simplify the tuning process and improve computational efficiency. For BaggingRegressor, the main hyperparameters tuned, or optimized by the optimizer, are n_estimators and max_samples, as they directly affect model complexity, convergence, and capacity. Other hyperparameters are not included in the tuning to reduce tuning complexity.

[0041] In the Bagging ensemble learning algorithm, `n_estimators` and `max_samples` are two core hyperparameters that jointly control the model's construction method and final performance. `n_estimators` refers to the number of base learners, i.e., the total number of decision trees in the ensemble model, while `max_samples` controls the number or proportion of samples that each base learner can use during training. The hyperparameters are shown in Table 2. Table 2 ; We also addressed the overfitting problem. Overfitting occurs when a model performs exceptionally well on the training data but poorly on other datasets. To avoid this problem, this paper takes the following measures: First, use an independent test set to accurately evaluate the model's generalization ability, avoiding overfitting, which is common in mathematical simulations of data.

[0042] Second, a balance needs to be struck between regularization and model complexity to enhance the model's ability to generalize to unknown data.

[0043] Third, increase the size and diversity of the training dataset so that the model can learn more universal patterns.

[0044] Fourth, remove unnecessary data parameters or features from the model.

[0045] In addition, monitoring overfitting during training using an appropriate validation set, introducing regularization techniques (such as dropout) into deep learning models, and employing early stopping mechanisms when validation performance no longer improves can also help prevent model overfitting.

[0046] The selected evaluation indicators are shown in Table 3.

[0047] Table 3 ; The parameters and their meanings are listed in Table 3 as follows: This represents the true value of the i-th sample. This represents the corresponding model prediction value. The total number of samples, It is the mean of all true values; It is often used to represent the true value (target value) of the nth sample. This represents the corresponding predicted value. and These are the mean values ​​of the actual value and the predicted value, respectively. This usually refers to the observation value (e.g., error) of the i-th sample. Its mean; The variance represents the true value. The variance represents the prediction error; and These represent the true value vector and the predicted value vector, respectively.

[0048] In summary, this study defines input and output parameters, divides the data into training and testing sets, constructs various advanced machine learning models, and conducts comparative analysis based on multiple robust evaluation metrics to evaluate the performance of each model and select the best model for predicting the gas holdup of the bubble column.

[0049] This section provides a detailed analysis of the performance of the Bagging algorithm in predicting gas holdup in bubble column gas flow and compares it with several established machine learning models. Multiple metrics are used to comprehensively evaluate the prediction accuracy, including mean squared error and R². 2 The results are presented using visualization methods such as values, fitting plots, and regression plots. These results demonstrate the relative advantages and limitations of Bagging compared to GB, RF, AdaBoost, XGB, and DT. Furthermore, the significance of these results for optimizing gas holdup prediction models is discussed, and directions for future research and improvement are pointed out.

[0050] like Figure 3 As shown, AdaBoost's performance is significantly inferior to other models. It achieves the highest MAE, MAPE, and RMSE on both the training and test sets, while VAF and R... 2 Both the error rate and explained variance were the lowest. This indicates that while AdaBoost can capture some data patterns, its accuracy and consistency are poor, especially in worst-case prediction. The high error rate and low explained variance suggest its limited modeling ability, making it the worst-performing model among those evaluated.

[0051] like Figure 4 As shown, Bagging consistently achieves the highest VAF on both the training and test sets, indicating its ability to explain the largest variance in the data. On the training set, Bagging's VAF is 99.998519, slightly higher than XGB and RF; on the test set, Bagging's VAF remains the highest at 99.999460, demonstrating its robustness across different datasets. Conversely, AdaBoost has the lowest VAF on both the training and test sets, at 99.563143 and 98.595065 respectively, indicating a weaker ability to explain data variance.

[0052] R 2 The trend of change is similar to that of VAF. On the training set, Bagging's R... 2 AdaBoost's R score was 0.999985, ranking first, followed by XGB; on the test set, Bagging again topped the list with 0.999995, followed closely by XGB. 2 The lowest value was 0.995583 on the training set and 0.985266 on the test set. This indicates that although most models perform well overall, AdaBoost is the weakest in explaining the variance of the target variable.

[0053] like Figure 5 As shown, Bagging has the lowest MAE on the training set, at only 0.000095, indicating its optimal prediction accuracy. On the test set, its MAE remains low at 0.000138, demonstrating stable performance. In contrast, AdaBoost achieves the highest MAEs on both the training and test sets, at 0.005837 and 0.007369 respectively, indicating the largest average bias among all models.

[0054] like Figure 6As shown, in terms of MAPE, Bagging also performs best on the training set with a value of 0.001859; in the testing phase, it is 0.003939, which is slightly higher than the training set, but still the lowest among all models. AdaBoost's MAPE reaches 0.184943 on the training set and 0.354997 on the testing set, indicating that it has the largest percentage error and the worst reliability.

[0055] In terms of maximum error (MaxError), XGB has the lowest MaxError on the training set at 0.002213; Bagging also performs well at 0.012938. On the test set, XGB continues to perform well, while Bagging's MaxError is also very low at 0.001026. AdaBoost's MaxError on the training and test sets are 0.038339 and 0.035860 respectively, indicating a more significant outlier error in its predictions.

[0056] like Figures 7-8 As shown, the RMSE results indicate that Bagging has the lowest RMSE on both the training and test sets, at 0.000459 and 0.000196 respectively, demonstrating its most accurate performance in reducing squared error. XGB also performs well, with RMSEs of 0.000577 and 0.000687 on the training and test sets respectively. Conversely, AdaBoost has the highest RMSE, at 0.007934 on the training set and 0.010247 on the test set, indicating its poor performance in controlling squared error.

[0057] like Figure 9 As shown, Bagging also has the highest explained variance on the training and test sets, at 0.999985 and 0.999995 respectively, indicating its extremely strong ability to explain data variance. XGB performs similarly to Bagging, while AdaBoost has the lowest explained variance on both datasets, further demonstrating its relative inefficiency in modeling changes in the target variable. The error metrics obtained from the mixed model implementation on the training and test sets are shown in Tables 4 and 5.

[0058] Table 4 ; Table 5 ; In summary, Bagging demonstrates the most robust and accurate performance on both the training and test sets. It consistently leads in several key metrics, including the lowest MAE, MAPE, MaxError, and RMSE, and the highest VAF and R². 2 And the explained variance. This shows that Bagging not only fits the training data better, but also has a stronger generalization ability to new data, making it the most reliable model in this comparison.

[0059] Furthermore, this paper compares the results with existing studies on similar datasets, showing that the optimal model in this study achieves R0. 2 The value is 0.99, which is significantly better than other existing technologies.

[0060] A thorough understanding of gas holdup in bubbling towers is crucial for the design of gas-liquid bubbling towers in various industrial processes and for improving the quality of gas holdup prediction. Although modern science and technology are constantly improving the efficiency and innovation of gas-liquid bubbling tower production processes, they are also bringing greater challenges to the construction of gas holdup prediction models and evaluation systems.

[0061] This study constructed an accurate and reliable bubble column gas holdup prediction model by comparing six machine learning models. After rigorous comparison, the most promising model was identified as Bagging. The results show that Bagging performs particularly well in bubble column gas holdup prediction, outperforming other common models such as GB, XGB, RF, DT, and AdaBoost.

[0062] Among the compared models, Bagging achieved the highest VAF (99.9985) and R² on the training set. 2 (0.9999); it also achieved the highest VAF (99.9994) and R on the test set. 2 (0.9999). This means it has a stronger explanatory power for gas holdup fluctuations and is more robust under different operating conditions. Meanwhile, it has the lowest RMSE on the training set (0.0004), the lowest RMSE on the test set (0.0001), the lowest MAE on the training set (0.00009), and the lowest MAE on the test set (0.0001). This fully demonstrates the high accuracy of Bagging in gas holdup prediction.

[0063] While models such as XGB and RF also demonstrate good performance, Bagging excels in error control and handling data fluctuations, making it most effective in this specific application scenario. This demonstrates that Bagging is a highly suitable method when high-accuracy and reliable predictions of gas holdup are required, making it a valuable tool in chemical engineering process optimization.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the gas holdup of a bubble column based on Bootstrap sampling and parameter optimization, characterized in that, include: Construct and train several base learners, wherein the base learners adopt machine learning models, and each base learner is trained independently. The sample set is bootstrap sampled with replacement to generate several sub-training sets, and the base learners are trained based on the sub-training sets. The Antlion optimizer was used to optimize the number of base learners and the sample ratio / number. The operation data of the bubble column is obtained, and regression prediction is performed on the operation data through an optimized base learner. The prediction results are then fused through a voting mechanism to obtain the gas holdup prediction value. The data fusion adopts either weighted average or mean fusion.

2. The method according to claim 1, characterized in that, The base learners include decision tree models, artificial neural networks, extreme random trees, random forests, and support vector regression.

3. The method according to claim 1, characterized in that, The data fusion process includes: For classification tasks, the base learners are fused using majority voting, while for regression tasks, the base models are fused using mean calculation.

4. The method according to claim 1, characterized in that, It also includes testing the optimized base learner using a test set independent of the training set, wherein the metrics in the test include mean absolute error, root mean square error, variance explanation factor, relative absolute error, Pearson correlation coefficient, maximum error, standard deviation, and performance metrics.

5. The method according to claim 1, characterized in that, It also includes using a single model to predict the gas holdup of the bubbling tower based on the operating data. The single model can include gradient boosting model, extreme gradient boosting model, random forest model, adaptive boosting model, or decision tree model.

6. A bubble column gas holdup prediction system based on machine learning and data fusion, characterized in that, Used to perform the method described in any one of claims 1-5.

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