The distribution of phosphorus between slag and molten steel reflects the slag’s capacity to retain phosphorus, which significantly influences the final phosphorus content in steel. This study investigated the prediction of the phosphorus distribution ratio in CaO–SiO2–MgO–FeO–P2O5 converter slags using feature engineering derived from the Ion and Molecule Coexistence Theory (IMCT). Three datasets were utilized: Dataset 1 (endpoint molten steel chemical compositions and temperature), Dataset 2 (slag chemical compositions), and Dataset 3 (IMCT-derived mass action concentrations of slag components). Comparative analysis indicated that integrating all three datasets—actual production data together with IMCT-based features—yielded the highest predictive accuracy. Building on these insights, a BSE-IMCT model incorporating multiple heterogeneous learners was proposed. The model adopts a two-layer stacking framework and an n-repeated k-fold bagging strategy to aggregate base-learner outputs. This approach consistently outperformed individual ensemble methods across several metrics. Experimental results demonstrated that the model achieved MSE, RMSE, MAE, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${R}^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> values of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$1.28\times 10^{-3}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.28</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$3.58\times 10^{-2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.58</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$2.90\times 10^{-2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.90</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$9.57\times 10^{-1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>9.57</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, respectively. The robustness of the BSE-IMCT model was further validated through regression fitting and prediction error band plots, where predicted values closely matched actual observations, with the majority of data points falling within the 95 pct confidence interval—indicating minimal bias and variance. By applying IMCT-based feature engineering to converter production data and leveraging the proposed BSE-IMCT model, more accurate predictions of the phosphorus distribution ratio were achieved, providing valuable guidance for decision-making in converter steel tapping operations.

IMCT-Based Stacked Model for Predicting Phosphorus Distribution Ratio in Converter Steelmaking

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发表日期：

2025年12月1日

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Peng Li,
Dongping Zhan,
Xudong Dou,
Zhouhua Jiang,
Huishu Zhang

摘要

The distribution of phosphorus between slag and molten steel reflects the slag’s capacity to retain phosphorus, which significantly influences the final phosphorus content in steel. This study investigated the prediction of the phosphorus distribution ratio in CaO–SiO₂–MgO–FeO–P₂O₅ converter slags using feature engineering derived from the Ion and Molecule Coexistence Theory (IMCT). Three datasets were utilized: Dataset 1 (endpoint molten steel chemical compositions and temperature), Dataset 2 (slag chemical compositions), and Dataset 3 (IMCT-derived mass action concentrations of slag components). Comparative analysis indicated that integrating all three datasets—actual production data together with IMCT-based features—yielded the highest predictive accuracy. Building on these insights, a BSE-IMCT model incorporating multiple heterogeneous learners was proposed. The model adopts a two-layer stacking framework and an n-repeated k-fold bagging strategy to aggregate base-learner outputs. This approach consistently outperformed individual ensemble methods across several metrics. Experimental results demonstrated that the model achieved MSE, RMSE, MAE, and ${R}^2$ $R^{2}$ values of $1.28\times 10^{-3}$ $1.28 \times 10^{- 3}$ , $3.58\times 10^{-2}$ $3.58 \times 10^{- 2}$ , $2.90\times 10^{-2}$ $2.90 \times 10^{- 2}$ , and $9.57\times 10^{-1}$ $9.57 \times 10^{- 1}$ , respectively. The robustness of the BSE-IMCT model was further validated through regression fitting and prediction error band plots, where predicted values closely matched actual observations, with the majority of data points falling within the 95 pct confidence interval—indicating minimal bias and variance. By applying IMCT-based feature engineering to converter production data and leveraging the proposed BSE-IMCT model, more accurate predictions of the phosphorus distribution ratio were achieved, providing valuable guidance for decision-making in converter steel tapping operations.