Methodological developments for multi-objective optimization of industrial mechanical problems subject to uncertain parameters

In this paper, we propose a non-intrusive methodology to obtain statistics on multi-objective optimization problems subject to uncertain parameters when using an industrial software design tool. The proposed methodology builds Pareto front samples with low computational cost and proposes a convenient posterior parameterization of the solution set, to enable the statistical analysis and, in perspective, the transformation of small sets of data in large samples, thanks to an Hilbertian approach. The statistics of objects, Hausdorff distance in particular, is applied to Pareto fronts to perform a statistical analysis. This strategy is first demonstrated on a simple test case and then applied to a practical engineering problem.