The adjoint method for an inverse design problem in continuous steel slab casting processes

This work proposes using the adjoint method, the central contribution of the work, to address an inverse design problem in the continuous steel slab casting process, aiming to optimize the process and reduce computational costs based on a novel target-made approach. Regarding this methodology, two sets of design parameters are considered: (1) Set one includes the temperature of cooling nozzles in the secondary cooling zone, interfacial heat transfer coefficient of the cooling systems, and casting speed, and (2) set two comprises the transported heat flux, and casting speed. Firstly, the target approach, revolving around a near-to-ideal thermal target field, is developed using thermal constraints corresponding to the production of a sound strand. Although the target method seems to be a widely used mature strategy in the literature, a simple but novel method, as compared to some rather conventional feedback control models, is proposed here to create a new target distribution based on technological and metallurgical constraints. The constraints include the minimum solid shell thickness to avoid strand breakout, the Niyama criterion to avoid shrinkage porosity formation, the desired metallurgical length, the strand surface temperature at a few points, and a new crack-related term to avoid cracking at the strand’s unbending point. Afterward, optimization models are formulated and coupled with a comprehensive thermophysical database (based on the calculation of phase diagrams) used in direct physical and adjoint PDEs. Then, a gradient-based optimization algorithm is employed to find optimal values for design parameters such that the mismatch between the working temperature profile and the thermal target distribution becomes minimal. Later, the optimization problem is solved numerically for two typical commercial steel grades, and the optimal design variables are obtained. Finally, optimally numerical results are compared with experimental data obtained through plant tests to demonstrate the proposed design methodology’s success and reliability. The comparison shows that the difference between simulation and experimental results is less than %5 percent, indicating the acceptability of the proposed design method.