A precision on-line model for the prediction of thermal crown in hot rolling processes

The tendency towards an increase in rolling speeds, which is characteristic of the development of modern sheet rolling, causes an increase requirement of accurate prediction on-line control models for the thermal crown of work rolls. In this paper, a precision on-line model is proposed for the prediction of thermal crown in hot-strip rolling processes. The heat conduction of the roll temperature can be described by a nonlinear partial differential equation (PDE) in the cylindrical coordinate. After selecting a set of proper basis functions, the spectral methods can be applied to time/space separation and model reduction, and the dynamics of the heat conduction can be described by a model of high-order nonlinear ordinary differential equations (ODE) with a few unknown nonlinearities. Using a technique for further reducing the dimensions of the ODE system, neural networks (NNs) can be trained to identify the unknown nonlinearities. The low-order predicted model of the thermal crown is given in state-space formulation and efficient in computation. The comparisons of prediction values for the thermal crown with the production data in an aluminum alloy hot rolling process show that the proposed method is effective and has high performance.