Multi-fidelity optimization for sheet metal forming process

Traditional design optimization for industry problems often requires many runs of costly high-fidelity finite element models. Multi-fidelity techniques offer a means to reducing prohibitive computational cost by combining cheap low-fidelity analyses with more accurate but more expensive high-fidelity solutions. This paper proposes a two-stage multi-fidelity method to better compromise the uses of low-fidelity and high-fidelity solutions. A correction response surface (RS) was first constructed based on the ratio or difference between high-fidelity and low-fidelity solutions at fewer sample points. Then the low-fidelity analysis is further replaced by a moving least square (MLS) approximation to enhance its accuracy. To demonstrate the present design procedure, multiobjective optimization of draw-bead restraining forces for an automobile inner panel is exemplified herein, where the high-fidelity model employs an incremental solver, while the low-fidelity model adopts a one-step solver. The results significantly improved the computational efficiency and accuracy of optimizing sheet-metal formability without wrinkle and fracture.