Modeling and Monitoring for Laminar Cooling Process of Hot Steel Strip Rolling with Time–Space Nature

Abstract

The laminar cooling process is an important procedure in hot steel strip rolling. The spatial distribution and the drop curve of the strip temperature are crucial for the production and the quality of the steel strip. Traditionally, lumped parameter methods are often used for the modeling of the laminar cooling process, making it difficult to consider the impact of the variation of state variables and related parameters on the system, which seriously affect the stability of the steel strip quality. In this paper, a modeling and monitoring method with a time–space nature for the laminar cooling process is proposed to monitor the spatial variation of the strip temperature. Firstly, the finite-dimensional model is obtained by time–space separation to describe the temperature variation of the steel strip. Next, a global model is constructed by using the multi-modeling integration method. Then, a residual generator is designed to monitor the strip temperature where the statistics and the threshold are calculated. Finally, the superiority and reliability of the proposed method are verified by the actual-process data of the laminar cooling process for hot steel strip rolling, and different types of faults are detected successfully.

Integrated spatio‐temporal process monitoring and fault spatial location for the laminar cooling of hot‐rolled strip steel

“…𝜙 i (z )(i = 1, 2 … , m) are basic functions of the state variables in a pre-defined m-dimensional function subspace S and S = [𝜙 1 (z ) ⋯ 𝜙 m (z )] and the meaning of the spatial functions in LCP is the weight of each node temperature in the direction of the thickness. Here we adopt FEM to solve Equation ( 2) in [46], and the number of the grid in z-direction is m + 1.…”

“…where 𝜂 i (x) is the direction of process variables. Substitute Equation (46) into Equation ( 43) we get…”

“…\end{equation}$$$${{\phi }_{i}}(z)(i=1,2\ldots ,m )$$ are basic functions of the state variables in a pre‐defined m ‐dimensional function subspace S and $$S=[ \begin{matrix} {\phi }_{1}(z) & \cdots & {{\phi }_{m}}(z) \end{matrix} ]$$ and the meaning of the spatial functions in LCP is the weight of each node temperature in the direction of the thickness. Here we adopt FEM to solve Equation (2) in [46], and the number of the grid in z ‐direction is $$m+1$$. Then the state space model can be obtained with the following description: $$$$\begin{equation} \dot{\alpha }(t)=A\alpha (t)+Bu(t), \end{equation}$$$$where $$\alpha (t)={{[ \begin{matrix} {\alpha }_{1}(t) & \cdots & {{\alpha }_{m}}(t) \end{matrix} ]}^{T}}$$ is the temporal base in each cooling zone.…”

Quality-Related Process Monitoring and Diagnosis of Hot-Rolled Strip Based on Weighted Statistical Feature KPLS

“…Hot rolling is a complex multi-process collaborative industrial production process [32]. It mainly includes heating, roughing mill, finishing mill, laminar cooling, coiling, and other processes, as shown in Figure 1.…”

Numerical Modelling of Thermo-Mechanical Processes in Steels - An Overview and Recent Progress

“…Colorado School of Mines group has developed several models for microstructure evolution to enhance industrial processing [9][10]. Numerical modelling tools are also developed by several other research groups [11][12][13][14]. The benefit of the numerical process modelling is to reduce the expensive production trials and to provide understanding of the most important factors affecting the metallurgical industrial processes.…”