<p>The precise prediction of end-point carbon content in electric arc furnace (EAF) steelmaking is a prerequisite for ensuring primary liquid steel quality and optimizing downstream refining costs. However, the EAF smelting process exhibits strong non-linearity and transient dynamics. Consequently, existing data-driven models are susceptible to physically inconsistent extrapolations under distribution shifts. Moreover, these deterministic models lack the capability to quantify prediction uncertainty. To address these limitations, this paper proposes a novel framework that integrates a Bayesian Physics-Informed Neural Network (BPINN) for end-point carbon prediction and risk-aware control. By taking 20-dimensional process parameters as inputs, the proposed method embeds the carbon oxidation mass conservation equation into a variational inference (VI) framework as a soft constraint. This design incorporates metallurgical physical priors into statistical inference to constrain the solution space. Extensive validation using 9673 production heats from a 130 t direct-current (DC) EAF demonstrates that the BPINN reduces the mean absolute error (MAE) to 0.0072 pct, achieving a standard-level hit rate (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\pm 0.02 \text{p}\text{c}\text{t}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>0.02</mn> <mtext>pct</mtext> </mrow> </math></EquationSource> </InlineEquation>) of 91.7 pct. Under extreme out-of-distribution (OOD) scenarios, such as the deep decarburization stage—where the rate-limiting step shifts from oxygen supply to carbon mass-transfer diffusion, causing strongly non-linear carbon evolution that data-driven models struggle to extrapolate—and scrap surges—where sudden changes in scrap composition destabilize the input feature distribution and cause conventional models to produce severely miscalibrated predictions—the model mitigates performance degradation by enforcing physical constraints. Based on this model, a risk-aware hierarchical control system is established, which utilizes the single-heat prediction interval width to classify control instructions into automatic control, manual review, and emergency intervention. This study provides a reliable pathway from deterministic numerical prediction to risk-aware control in highly uncertain metallurgical processes.</p>

A Bayesian Physics-Informed Neural Network for End-Point Carbon Prediction and Risk-Aware Control in Electric Arc Furnaces

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发表日期：

2026年6月16日

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Yangchun Wang,
Liguang Zhu,
Pengcheng Xiao

摘要

The precise prediction of end-point carbon content in electric arc furnace (EAF) steelmaking is a prerequisite for ensuring primary liquid steel quality and optimizing downstream refining costs. However, the EAF smelting process exhibits strong non-linearity and transient dynamics. Consequently, existing data-driven models are susceptible to physically inconsistent extrapolations under distribution shifts. Moreover, these deterministic models lack the capability to quantify prediction uncertainty. To address these limitations, this paper proposes a novel framework that integrates a Bayesian Physics-Informed Neural Network (BPINN) for end-point carbon prediction and risk-aware control. By taking 20-dimensional process parameters as inputs, the proposed method embeds the carbon oxidation mass conservation equation into a variational inference (VI) framework as a soft constraint. This design incorporates metallurgical physical priors into statistical inference to constrain the solution space. Extensive validation using 9673 production heats from a 130 t direct-current (DC) EAF demonstrates that the BPINN reduces the mean absolute error (MAE) to 0.0072 pct, achieving a standard-level hit rate ( $\pm 0.02 \text{p}\text{c}\text{t}$ $\pm 0.02 pct$ ) of 91.7 pct. Under extreme out-of-distribution (OOD) scenarios, such as the deep decarburization stage—where the rate-limiting step shifts from oxygen supply to carbon mass-transfer diffusion, causing strongly non-linear carbon evolution that data-driven models struggle to extrapolate—and scrap surges—where sudden changes in scrap composition destabilize the input feature distribution and cause conventional models to produce severely miscalibrated predictions—the model mitigates performance degradation by enforcing physical constraints. Based on this model, a risk-aware hierarchical control system is established, which utilizes the single-heat prediction interval width to classify control instructions into automatic control, manual review, and emergency intervention. This study provides a reliable pathway from deterministic numerical prediction to risk-aware control in highly uncertain metallurgical processes.