GPU-based Parameterization Optimal Control for Three-dimensional Dynamic Heat Transfer Model with Application in Continuous Casting

The secondary cooling control system is a key factor for the quality of cast billets in continuous casting. The optimal method for the setting value of water flow rate in this system is based on the dynamic heat transfer equation of the billet, which is described by 3-dimensional (3D) unsteady partial differential equations with variable convection term (UPDEVCT). Therefore, an optimal control problem (OCP) for UPDEVCT is investigated. However, the solving of this OCP encounters variable convection term and high order heat transfer equations, thus the calculation process costs much time. Based on this problem’s characteristics, this paper presents a new GPU-based three-term spectral conjugate gradient algorithm (GTSCGA). Firstly, this paper establishes mathematical model of OCP for UPDEVCT, and analyzes the Lipschitz continuity of this OCP according to the adjoint approach. Secondly, a GPU-based finite difference scheme is developed for solving the UPDEVCT, and the GTSCGA is proposed. Further, the global convergence of GTSCGA is proved. Finally, the results of extensive simulations show that the GTSCGA can significantly improve the calculation performance and have a better control effect.