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<p>Titanium dioxide (TiO<sub>2</sub>) is the primary component of high titanium slag, renowned for its exceptional physical and chemical properties, making it indispensable in numerous industrial applications, particularly in the production of titanium dioxide itself. In this study, an ensemble of random forest, gradient boosting machine, and support vector regression was adopted as a stacked regression model with linear regression as a meta-model, applying ensemble learning to optimize the prediction accuracy of TiO<sub>2</sub> grade in high-Ti slag. A representative dataset was created from the factory’s raw data, capturing the material ratios and TiO<sub>2</sub> quality in the metallurgical process. Initially, 33 feature variables were considered, which were later reduced to 15 key features through dimensionality reduction to identify the most influential variables. The stacked model shows an <i>R</i><sup>2</sup> value of 0.9249, with MAPE values of 0.29 and 0.30%, and MSE values of 0.177 and 0.182 on the validation and test sets, outperforming individual models. The mass ratio of TiO<sub>2</sub> to FeO and the C content, among other feature variables, show high average absolute SHAP values, indicating that these variables, within certain ranges, can lead to higher product quality. Based on 5000 Monte Carlo experiments and extensive data simulation, the optimal value ranges of key features, such as the TiO<sub>2</sub>/FeO ratio (1.70 to 2.12) and TiO<sub>2</sub>/C ratio (0.50 to 0.58), were identified. By introducing the stacked model into the metallurgical process of high-titanium slag production, energy waste caused by traditional experience-based material mixing is not only avoided, but the entire process also becomes more intelligent, efficient, and environmentally friendly, thereby achieving energy-saving goals.</p> Graphical Abstract <p></p>

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Stacked Ensemble Learning Model-Based Prediction and Optimization of the Grade of Titanium Dioxide in High-Titanium Slag

  • 期刊论文

  • 发表日期：

    2025年3月20日

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  • Jinqiu Cai,
  • Yanqing Hou,
  • Jianguo Wang,
  • Kaixuan Wang,
  • Ni Yang,
  • Gang Xie

摘要

Titanium dioxide (TiO2) is the primary component of high titanium slag, renowned for its exceptional physical and chemical properties, making it indispensable in numerous industrial applications, particularly in the production of titanium dioxide itself. In this study, an ensemble of random forest, gradient boosting machine, and support vector regression was adopted as a stacked regression model with linear regression as a meta-model, applying ensemble learning to optimize the prediction accuracy of TiO2 grade in high-Ti slag. A representative dataset was created from the factory’s raw data, capturing the material ratios and TiO2 quality in the metallurgical process. Initially, 33 feature variables were considered, which were later reduced to 15 key features through dimensionality reduction to identify the most influential variables. The stacked model shows an R2 value of 0.9249, with MAPE values of 0.29 and 0.30%, and MSE values of 0.177 and 0.182 on the validation and test sets, outperforming individual models. The mass ratio of TiO2 to FeO and the C content, among other feature variables, show high average absolute SHAP values, indicating that these variables, within certain ranges, can lead to higher product quality. Based on 5000 Monte Carlo experiments and extensive data simulation, the optimal value ranges of key features, such as the TiO2/FeO ratio (1.70 to 2.12) and TiO2/C ratio (0.50 to 0.58), were identified. By introducing the stacked model into the metallurgical process of high-titanium slag production, energy waste caused by traditional experience-based material mixing is not only avoided, but the entire process also becomes more intelligent, efficient, and environmentally friendly, thereby achieving energy-saving goals.

Graphical Abstract