Reservoir computing based predictive reduced order model for steel grade intermixing in an industrial continuous casting tundish

TL;DR

This work addresses the prediction of steel grade intermixing during ladle changeover in continuous casting using a POD-RC-ROM framework. By fusing Proper Orthogonal Decomposition with Reservoir Computing (specifically Echo State Networks), the authors construct a non-intrusive reduced-order model that maps parameter-time dynamics to a low-dimensional modal-coefficient representation. The offline phase builds a POD basis from high-fidelity FOM data and trains the RC to interpolate modal coefficients, while the online phase delivers rapid, accurate predictions of intermixing time $T_{IM}$ with substantial computational savings (offline ~75 seconds, online ~0.42 seconds on a single core). The results demonstrate close agreement with FOM trends and reveal significant potential for real-time process monitoring, optimization, and digital-twin applications in industrial continuous casting, despite some extrapolation errors that could be reduced with more training data or tuned hyperparameters.

Abstract

Continuous casting is a widely adopted process in the steel industry, where maintaining high steel quality is paramount. Efficient prediction of grade intermixing during ladle changeover operations is critical for maintaining steel quality and minimizing material losses in the continuous casting process. Among various factors influencing grade intermixing, operating parameters play a significant role, in addition to tundish geometry and flow control devices. In this study, three-dimensional, transient, two-phase turbulent flow simulations are conducted to investigate the ladle changeover operation. During this process, the molten steel level in the tundish typically varies over time, significantly affecting the grade intermixing phenomena. The influence of ladle change time on intermixing time has been presented. However, high-fidelity full-order simulations of such complex transient phenomena are computationally expensive and are impractical for real-time monitoring or design-space exploration in industrial-scale applications. To address this issue, a reduced order modelling approach based on proper orthogonal decomposition (POD) and reservoir computing (RC) is employed to efficiently predict intermixing time. The proposed reduced order model (ROM) demonstrates excellent predictive accuracy using limited training data while requiring significantly less computational resources and training time. The results demonstrate the potential of the proposed methodology as a fast, reliable tool for real-time process monitoring and optimization in industrial continuous casting operations.

Figures (13)

• Figure 1: Schematic representation of single strand tundish Wang2021, illustrating the flow physics and key components. The tundish contains molten steel, slag, and inclusion flotation, representing a multiphase flow system. The flow modifiers, such as the impact pod (acting as a turbulent inhibitor) and the dam, improve steel quality and ensure better castability.
• Figure 2: Process diagram of the ladle changeover operation
• Figure 3: Schematic representation of an echo state network, a type of reservoir computing (RC), as defined in (\ref{['eqn:reservoir_update_rule']}). The network consists of a randomly initialized $N_\text{r} \times N_{\text{in}}$ input weight matrix $W_{\text{in}}$ that maps the $N_\text{in} \times 1$ input state vector $\mathbf{u}(t)$ into the reservoir. The reservoir dynamics are governed by a randomly selected $N_\text{r} \times N_\text{r}$ recurrent weight matrix $\mathbf{W}$, which updates the internal reservoir state vector $\mathbf{r}$ of size $N_\text{r} \times 1$. Finally, the trained readout weight matrix $\mathbf{W}_{\text{out}}$, of dimensions $N_\text{out} \times N_\text{r}$, is used to produce the final output.
• Figure 4: Computational domain of a 0.5 scaled single strand tundish. Left: Isometric view highlighting the inlet, outlet, and symmetry plane, with all other boundaries treated as walls. Right: 2D left-side view overlooking the symmetry plane.
• Figure 5: Discretized computational domain of a 0.5-scale single-strand tundish. Left: Isometric view of discretized domain; Top right: 2D symmetry plane showing the mesh refinement strategies to capture accurately the interface development and turbulence mixing phenomena; Bottom right: Inner jet impingement zone with an impact pot to enhance turbulence mixing.