Focusing on the problem of strip shape quality control in the finishing process of hot rolling, a shape model based on metal flow and stress release with the application of varying contact rolling parameters is introduced. Combined with digital twin technology, the digital twin framework of the shape model is proposed, which realizes the deep integration between physical time–space and virtual time–space. With the utilization of the historical data, the parameters are optimized iteratively to complete the digital twin of the shape model. According to the schedule, the raw material information is taken as the input to obtain the simulation of the strip shape, which shows a variety of export shape conditions. The prediction absolute error of the crown and flatness are less than 5 μm and 5 I-unit, respectively. The results prove that the proposed shape simulation model with strong prediction performance can be effectively applied to hot rolling production. In addition, the proposed model provides operators with a reference for the parameter settings for actual production and promotes the intelligent application of a shape control strategy.

For the high temperature superconducting magnetic energy stor-age (HTS SMES) magnet with large capacity, in order to reduce the leakage magnetic field and the vertical magnetic field compo-nent on the wire, it mostly adopts the toroidal magnet structure. However, this structure has imposed new challenges in calculat-ing the AC loss of the magnet. Due to the particularity structure of the toroidal magnet, that is, its magnetic field is not distributed in the 2D axisymmetric manner, it is impossible to calculate the AC loss in the toroidal magnet with a traditional 2D computation model. At the same time, the 3D model has its problems, such as the modeling is complicated; the calculation efficiency is low; the demand for computation is enormous, and so on. In order to provide a solution for calculating the AC loss in the magnet with a non-2D axisymmetric distributed magnetic field, a method of “dimensionality reduction and inversion” is proposed. In this method, the magnetic field distribution in the toroidal magnet is calculated by using a 3D model intended for uniform flow, and the AC loss is calculated by using a 2D model. The practical ap-plication shows that this method can provide a solution for calcu-lating the AC loss in the magnet with a non-2D axisymmetric dis-tribute magnetic field, and the calculated results meet the re-quirements of engineering calculation.

Flatness is a vital quality index that determines the dimensional accuracy of the cold-rolled strip. This paper designs a local shape wave extraction algorithm and a fuzzy classification algorithm for overall flatness defect classification based on cosine distance. By introducing the small displacement buckling theory of thin plates, the plate stress buckling model of overall and local shape waves is studied, and the critical buckling elongation difference of the overall shape and the local shape under the given conditions are obtained. Finally, using the multi-objective decision-making evaluation method, a comprehensive evaluation model of the flatness quality is established. The model is applied to the actual cold rolling production. The on-site flatness data are used to verify the flatness quality determination model both locally and overall. The results show that the model can accurately identify the local and overall flatness defects of cold-rolled strips, realizes the accurate identification and evaluation of the cold-rolled flatness quality, and provides strong support for the optimization of rolling process parameters and the improvement of the quality of thin strip products.