arXiv subjects

Karsten Naert

Publications and source records attributed to Karsten Naert.

4 recordsLinked to original sources

arXiv2025

Sensitivity Analysis of State Space Models for Scrap Composition Estimation in EAF and BOF

This study develops and analyzes linear and nonlinear state space models for estimating the elemental composition of scrap steel used in steelmaking, with applications to Electric Arc Furnace (EAF) and Basic Oxygen Furnace (BOF) processes. The models incorporate mass balance equations and are fitted using a modified Kalman filter for linear cases and the Unscented Kalman Filter (UKF) for nonlinear cases. Using Cu and Cr as representative elements, we assess the sensitivity of model predictions to measurement noise in key process variables, including steel mass, steel composition, scrap input mass, slag mass, and iron oxide fraction in slag. Results show that the models are robust to moderate noise levels in most variables, particularly when errors are below $10\%$. However, accuracy significantly deteriorates with noise in slag mass estimation. These findings highlight the practical feasibility and limitations of applying state space models for real-time scrap composition estimation in industrial settings.

eess.SY↗

arXiv2025

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

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.

eess.SY↗

arXiv2019

Suzuki-Ree groups as algebraic groups over $\mathbb{F}_{\sqrt{\smash[b]p}}$

Among the infinite classes of finite simple groups, the most exotic classes are probably the Suzuki groups and the Ree groups. They are "twisted versions" of groups of Lie type, but they cannot be directly obtained as groups of rational points of a suitable linear algebraic group. We provide a framework in which these groups do arise as groups of rational points of algebraic groups over a "twisted field"; in the finite case, such a twisted field can be interpreted as a "field with $\sqrt{\smash[b]p}$ elements". Our framework at once allows for other, perhaps less known, exotic families of groups. Most notably, there is a class of "mixed groups", introduced by J. Tits but also apparent in the work of Steinberg, and we show that they can be obtained as groups of rational points of algebraic groups over a "mixed field". We show that a base change from $\mathbb{F}_{\sqrt{\smash[b]p}}$ to $\mathbb{F}_p$ transforms twisted groups into mixed groups, and we formulate a notion of "twisted descent" that allows to detect which mixed groups arise in this fashion.

math.GR↗

arXiv2017

Twisting and Mixing

We present a framework that connects three interesting classes of groups: the twisted groups (also known as Suzuki-Ree groups), the mixed groups and the exotic pseudo-reductive groups. For a given characteristic p, we construct categories of twisted and mixed schemes. Ordinary schemes are a full subcategory of the mixed schemes. Mixed schemes arise from a twisted scheme by base change, although not every mixed scheme arises this way. The group objects in these categories are called twisted and mixed group schemes. Our main theorems state: (1) The twisted Chevalley groups ${}^2\mathsf B_2$, ${}^2\mathsf G_2$ and ${}^2\mathsf F_4$ arise as rational points of twisted group schemes. (2) The mixed groups in the sense of Tits arise as rational points of mixed group schemes over mixed fields. (3) The exotic pseudo-reductive groups of Conrad, Gabber and Prasad are Weil restrictions of mixed group schemes.

math.GR↗