Evaluation and assessment of non-normal output during robust optimization

Abstract

A robustness criterion that employs skewness of output is presented for a metamodel-based robust optimization. The propagation of a normally distributed noise variable via nonlinear functions leads to a non-normal output distribution. To consider the non-normality of the output, a skew-normal distribution is used. Mean, standard deviation, and skewness of the output are calculated by applying an analytical approach. To show the applicability of the proposed method, a metal forming process is optimized. The optimization is defined by an objective and a constraint, which are both nonlinear. A Kriging metamodel is used as nonlinear model of that forming process. It is shown that the new robustness criterion is effective at reducing the output variability. Additionally, the results demonstrate that taking into account the skewness of the output helps to satisfy the constraints at the desired level accurately.