Tailoring material scatter for metal forming processes based on inverse robust optimization

Robust optimization is a powerful method to find the parameters for a process at which its output is least sensitive to the variation of the input parameters. In this method, measured or estimated noise parameters are used to estimate the scatter of the output. At the optimum design, the variation in noise parameters leads to a minimum scatter of the output. If this minimum scatter of the output does not meet the specified tolerance, then the input noise must be adjusted accordingly. This means for example that materials with a tighter specification must be ordered, which usually incurs additional costs. In this article, an inverse method is presented to tailor the variation of noise parameters based on the allowable tolerance in the output. This method is successfully applied to a non-linear process, lab-type B-pillar part. The results show how to adjust the input noise parameters at a minimum cost to meet the required output tolerance.