A novel framework for distributed multi-output prediction tasks in rolling processes: A case study on cold rolling strip flatness

Abstract

Strip flatness in tandem cold rolling is a distributed quality attribute characterized by a widthwise profile, whereas most data-driven predictors use only discrete process parameters and cannot accurately capture this spatially distributed target. Mechanism-based models can describe flatness behavior but are often unsuitable for industrial use because of computational burden and simplifying assumptions. To address this input–output mismatch, we develop a data–mechanism-integrated multimodal framework that incorporates distributed rolling information. The influence function method (IFM) computes two-dimensional mechanistic fields representing widthwise rolling pressure, roll-stack deformation, and strip thickness. A Multi-Modal Parallel Network (MMPN) combines a deep neural network (DNN) encoder for global operating states with a convolutional neural network (CNN) encoder containing residual blocks (ResBlocks) and squeeze-and-excitation (SE) modules for seven mechanistic maps. The fused features directly predict the 35-channel flatness profile. A two-stage hyperparameter optimization strategy refines the network architecture and training configuration. Validation using industrial production data shows that MMPN achieves a mean absolute error (MAE) of 0.7802 and a root mean square error (RMSE) of 1.1648, reducing these errors by 17.13% and 18.98%, respectively, relative to the best baseline. MMPN also reconstructs widthwise profiles more faithfully across diverse rolling conditions. The results show that aligning inputs and architecture with the distributed nature of flatness provides a practical, physically consistent route to high-precision prediction in tandem cold rolling.