Modeling Scrap Composition in Electric Arc and Basic Oxygen Furnaces

TL;DR

This work tackles real-time estimation of scrap composition in BOF/EAF steelmaking by casting mass-balance relations into linear and nonlinear state-space models. It employs a modified Kalman filter for the linear model (Cu/Ni) and an unscented Kalman filter for the nonlinear model (Cr/S) to infer time-varying scrap fractions and, for Cr/S, partition coefficients that govern slag transfer. Real data-driven data-generation and testing demonstrate that Kalman-based estimates yield lower bias and variance in steel element fractions than windowed NNLS, improving process control and product quality. The approach supports sustainable steelmaking by enabling higher recycled content with reliable quality-conscious monitoring, while highlighting practical considerations for hyperparameter tuning and measurement noise modeling. Future work points to automated hyperparameter tuning, broader measurement-noise modeling, and integration with gas-phase behavior in steelmaking.

Abstract

This article aims to determine the composition of scrap (recycled material) used in an Electric Arc Furnace (EAF) or basic Oxygen Furnace (BOF) based on the assumption of mass balance. Accurate knowledge of this composition can increase the usage of recycled material to produce steel, reducing the need for raw ore extraction and minimizing environmental impact by conserving natural resources and lowering carbon emissions. The study develops two models to describe the behavior of elements in the EAF or BOF process. A linear state space model is used for elements transferring completely from scrap to steel, while a non-linear state space model is applied to elements moving into both steel and slag. The Kalman filter and unscented Kalman filter are employed to approximate these models, respectively. Importantly, the models leverage only data already collected as part of the standard production process, avoiding the need for additional measurements that are often costly. This article outlines the formulation of both models, the algorithms used, and discusses the hyperparameters involved. We provide practical suggestions on how to choose appropriate hyperparameters based on expert knowledge and historical data. The models are applied to real BOF data. Cu and Cr are chosen as examples for linear and non-linear models, respectively. The results show that both models can reconstruct the composition of scrap for these elements. The findings provide valuable insights for improving process control and ensuring product quality in steelmaking.

Figures (4)

• Figure 1: Schematic representation of the mass balance in steelmaking.
• Figure 2: Effects of misspecified hyperparameters in the Kalman filter for scrap type $36$, which is rarely used in the second half of the heats. Figures \ref{['fig:cu_true_f']}--\ref{['fig:cu_true_output']} use the true hyperparameters. Figures \ref{['fig:cu_small_mean_f']}--\ref{['fig:cu_large_mean_f']} show the impact of misspecification in the mean vector $\vec{q}$, causing shifts in estimated Cu when no observations are available. Figures \ref{['fig:cu_small_obs_f']}--\ref{['fig:cu_large_obs_f']} illustrate the effect of misestimating the observation covariance $H_t$, which governs trust in the data. Figures \ref{['fig:cu_small_gamma_f']}--\ref{['fig:cu_large_gamma_Q_f']} address misspecification in $\gamma$, $Q$, and $P_\infty$, which together control the rate and variability of the estimated Cu fraction.
• Figure 3: Effects of misspecified hyperparameters for UKF. Figure \ref{['fig:cr_true_output']}--\ref{['fig:cr_true_value_l']} are with the same hyperparameters when generating data. Figure \ref{['fig:cr_small_mean_f']}--\ref{['fig:cr_large_mean_l']} are about misspecification on the mean vector $\vec{q}_c$. Overestimating or underestimating $\vec{q}_c$ leads to corresponding overestimation or underestimation of the Cr fraction and partition coefficients in the UKF results. Figure \ref{['fig:cr_small_cov_f']}--\ref{['fig:cr_large_cov_l']} are about misspecification on $Q_c$. Misspecification of $Q_c$ has minimal impact on the estimation of scrap composition but significantly affects the rate and range at which partition coefficients change. The middle column shows the estimated Cr fraction of scrap type $36$, which is seldom used in the second half of heats. The right column shows the estimated partition coefficients.
• Figure 4: Results of applying windowed NNLS, Kalman filter and UKF to real data, with the left column focusing on Cu and the right column on Cr. The first row shows the error of predicted $f_{\rm steel, Cu}$ and $f_{\rm steel, Cr}$. Both the Kalman filter and UKF outperform windowed NNLS, as they yield smaller bias and lower standard deviation of error. The remaining figures display the estimated composition of different scrap types. The red bars at the bottom indicate scrap usage: scrap type $2$ is used infrequently, scrap type $36$ is often used in the first half of heats but rarely in the latter half, scrap type $37$ is used more frequently. The estimated Cu fraction by the Kalman filter and the estimated Cr fraction by the UKF are more realistic compared to the results from windowed NNLS.