Robustness Measures for Multi-objective Robust Design

A significant step to engineering design is to take into account uncertainties and to develop optimal designs that are robust with respect to perturbations. Furthermore, when multiple optimization objectives are involved it is important to define suitable descriptions for robustness. We introduce robustness measures for robust design with multiple objectives that are suitable for considering the effect of uncertainties in objective space. A direct formulation and a two-phase formulation based on expected losses in objective space are presented for finding robust optimal solutions. We apply both formulations to the robust design of an airfoil. Fluid mechanical quantities are optimized under the consideration of aleatory uncertainties. The uncertainties are propagated with the help of the non-intrusive polynomial chaos approach. The resulting multi-objective optimization problem is solved with a constraint-based approach, that combines adjoint-based optimization methods and evolutionary methods evaluated on surrogate models.