Moving least squares response surface approximation: Formulation and metal forming applications

We focus on a successive response surface method for the optimization problems. The response surfaces are built using Moving Least Squares approximations constructed within a moving region of interest. Our first approach is an extension of pattern search algorithms with a fixed pattern panned and zoomed in a continuous manner across the design space. In the second one, the region of interest moves across a predefined discrete grid of authorized experimental designs. Two examples of the sheet metal forming process are used to demonstrate the robustness of the method. We use the one-step Inverse Approach as a surrogate model during the optimization. The final designs is validated with Stampack commercial code based on Explicit Dynamics Approach.