Abstract
Engineering design often involves the determination of design variable settings to optimize competing performance requirements. In the early design stages we propose narrowing down the domain of design solutions using metamodels of principal components of the multiple performance levels that have been scaled by a multivariate quadratic loss function. The multivariate quadratic loss function is often used as the objective function in reaching optimal solutions because it utilizes the correlation structure of the design's performance metrics and penalizes off-target performance in a symmetrical manner. We also compare the computational performance of these loss-scaled principal components when used to solve for the design with minimal expected multivariate quadratic loss under three modeling approaches: response surface methodology, multivariate adaptive regression splines, and spatial point modeling. We demonstrate the technique on the design of the mechanical frame of an electric vehicle with six desired performance levels determined simultaneously by the dimensions of eight mechanical design elements. The method is the focus in this work.