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arxiv: 2504.09382 · v2 · submitted 2025-04-13 · 📡 eess.SY · cs.SY

Scrap Composition Estimation in EAF and BOF: State-Space Models, Hyperparameters, and Validation

Yiqing Zhou , Karsten Naert , Dirk Nuyens This is my paper

Pith reviewed 2026-05-22 21:10 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords scrap composition estimationstate-space modelsKalman filterEAFBOFsteel recyclingelemental partitioning
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The pith

State-space models with Kalman filters deliver real-time scrap composition estimates in EAF and BOF steel production that outperform regression methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops two state-space models to estimate the elemental composition of scrap used in electric arc and basic oxygen furnaces. A linear model handles elements that fully transfer into steel, while a nonlinear model accounts for partitioning between steel and slag. These models are fitted using Kalman and unscented Kalman filters on routine production data, allowing predictions of future steel composition. The approach is validated on real BOF data for elements like copper and chromium, showing better performance than windowed non-negative least squares regression.

Core claim

The central claim is that linear and nonlinear state-space models, estimated respectively with the Kalman filter and unscented Kalman filter, accurately capture elemental transfer and partitioning in steelmaking, providing reliable real-time scrap composition estimates from standard process data that can also forecast future production outcomes.

What carries the argument

State-space models for elemental composition, with linear version for complete steel transfer and nonlinear for steel-slag partitioning, estimated via Kalman and unscented Kalman filters.

Load-bearing premise

The proposed models correctly describe the transfer and partitioning of elements between scrap, steel, and slag in real furnace conditions.

What would settle it

A set of new furnace runs where the estimated scrap composition leads to steel composition predictions that significantly deviate from actual measurements would falsify the models' accuracy.

Figures

Figures reproduced from arXiv: 2504.09382 by Dirk Nuyens, Karsten Naert, Yiqing Zhou.

Figure 1
Figure 1. Figure 1: Schematic representation of the mass balance in steelmaking. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effects of misspecified hyperparameters in the Kalman filter for scrap type 36, which [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effects of misspecified hyperparameters for UKF. Figure 3a–3c are with the same hyperparameters [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results of applying windowed NNLS, Kalman filter and UKF to real data, with the left column [PITH_FULL_IMAGE:figures/full_fig_p027_4.png] view at source ↗
read the original abstract

Accurate knowledge of scrap 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. First, we introduce two state-space models for the elemental composition of scrap in Electric Arc Furnaces (EAF) and Basic Oxygen Furnaces (BOF): a linear model for elements that transfer entirely into steel, and a non-linear model for elements that partition between steel and slag. The models are fitted with the Kalman filter and the unscented Kalman filter, respectively, using only data already collected in the standard steel production process. Crucially, the resulting scrap composition estimates can in turn be used to predict the elemental composition of future steel production. Second, we analyze how key hyperparameters affect estimation accuracy and stability, and we provide practical guidelines for tuning them from expert knowledge and historical data. Third, we validate the models on real BOF data from ArcelorMittal, using Cu and Cr as representative elements. Both filters outperform windowed non-negative least squares regression, a strong baseline method for scrap composition estimation, yielding reliable real-time estimates of scrap composition.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes linear and nonlinear state-space models for estimating the elemental composition of scrap in Electric Arc Furnaces (EAF) and Basic Oxygen Furnaces (BOF). The linear model, assuming complete transfer into steel, is estimated using the Kalman filter, while the nonlinear model, accounting for partitioning between steel and slag, uses the unscented Kalman filter. Hyperparameters are analyzed for their impact on accuracy and stability, with guidelines for tuning from historical data. Validation on real BOF data from ArcelorMittal for Cu and Cr demonstrates that both methods outperform windowed non-negative least squares regression, providing reliable real-time estimates.

Significance. If the central claims hold, this work could significantly improve scrap composition knowledge in steel production, facilitating higher recycled material usage and reducing environmental impacts such as carbon emissions. A key strength is the reliance on existing process measurements without additional instrumentation, along with the empirical validation using real industrial data. The analysis of hyperparameters and practical tuning guidelines add value for implementation.

major comments (2)
  1. [Model Description] The linear model assumes complete elemental transfer into steel, and the nonlinear model assumes specific partitioning behavior (as described in the model introduction and abstract). These structural assumptions are central to the KF and UKF performance claims. The validation on BOF data for Cu and Cr provides empirical support but does not fully address potential violations under varying operating conditions (e.g., temperature effects or slag carryover) across EAF and BOF regimes.
  2. [Hyperparameter Analysis] While guidelines for tuning from historical data are provided, the paper should demonstrate through additional experiments or analysis that such tuning does not introduce bias when the model structure is misspecified, as this is load-bearing for unbiased real-time estimates.
minor comments (2)
  1. [Abstract] The abstract mentions 'reliable real-time estimates' but could specify the quantitative metrics (e.g., error reduction percentages or RMSE values) used to support this.
  2. [Notation] Ensure consistent use of symbols for state variables and measurements throughout the manuscript to avoid confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the presentation while maintaining the integrity of the original contributions.

read point-by-point responses

  1. Referee: [Model Description] The linear model assumes complete elemental transfer into steel, and the nonlinear model assumes specific partitioning behavior (as described in the model introduction and abstract). These structural assumptions are central to the KF and UKF performance claims. The validation on BOF data for Cu and Cr provides empirical support but does not fully address potential violations under varying operating conditions (e.g., temperature effects or slag carryover) across EAF and BOF regimes.

    Authors: The linear and nonlinear models are grounded in established metallurgical principles for elemental behavior in steelmaking, with the assumptions explicitly stated in the model sections. The real-world validation on ArcelorMittal BOF data for Cu and Cr shows clear outperformance over the baseline, supporting the claims under industrial conditions. We agree that explicit discussion of robustness to varying conditions would improve the manuscript. In revision, we will add a dedicated paragraph in the discussion section addressing potential effects of temperature variations and slag carryover, supported by references to steelmaking literature, and clarifying the models' intended applicability to both EAF and BOF while noting data limitations for full cross-regime empirical testing. revision: partial

  2. Referee: [Hyperparameter Analysis] While guidelines for tuning from historical data are provided, the paper should demonstrate through additional experiments or analysis that such tuning does not introduce bias when the model structure is misspecified, as this is load-bearing for unbiased real-time estimates.

    Authors: The hyperparameter guidelines are derived directly from historical process data to promote stability and accuracy in practice. We recognize the value of explicitly demonstrating robustness to misspecification. In the revised manuscript, we will incorporate an additional analysis subsection that includes a controlled simulation study evaluating estimation bias under deliberate model misspecification scenarios, confirming that the recommended tuning procedure from historical data maintains acceptable bias levels. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard filtering applied to independent measurements

full rationale

The paper defines linear and nonlinear state-space models from physical assumptions on elemental transfer/partitioning, applies standard KF/UKF estimation, tunes hyperparameters on historical process data, and validates performance via direct comparison to windowed NNLS on held-out ArcelorMittal BOF measurements for Cu and Cr. No prediction or result reduces by the paper's equations to a quantity defined solely by the fitted parameters themselves; the reported reliability is an external empirical outcome.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on domain assumptions about elemental partitioning behavior and standard Kalman filter noise models; no new entities are postulated and hyperparameters are tuned from historical data rather than derived.

free parameters (1)
  • Kalman filter hyperparameters
    Tuned from expert knowledge and historical data as stated in the abstract; these control estimation accuracy and stability.
axioms (2)
  • domain assumption Elemental transfer from scrap to steel or slag follows the proposed linear or nonlinear state-space dynamics
    Invoked when introducing the two models for different element types.
  • domain assumption Process measurements are sufficient to update the state estimates in real time
    Underlying the use of filters on standard production data.

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Reference graph

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