Innovative methodologies for Robust Design Optimization with large number of uncertainties using modeFRONTIER
CHALLENGE - As proven by recent studies, one of the most efficient methodology to accurately manage the uncertainties is the application of Polynomial Chaos expansion. This however requires a minimum number of samples which increases heavily with the number of uncertainties, and a typical industrial optimization case can hardly be considered a feasible task. For this reason, specific approaches are proposed to handle industrial problems of this kind, both in Uncertainty Management (UQ) and Robust Design Optimization (RDO).
SOLUTION - For UQ, the methodologies allow for the identification of uncertainties that have higher statistical effects on the performances of the system, allowing the application of Polynomial Chaos expansion to a smaller number of uncertainties. Two different UQ methodologies have been proposed, one based on SSANOVA and one based on a step-wise regression methodology. In RDO methodologies, a methodology based on the minmax formulation of objectives is proposed, which guarantees the reduction of objectives with respect to a classical RDO approach. The approach is based on the exploitation of Polynomial Chaos coefficients to evaluate the percentiles of the quantities to be optimized/constrained. This methodology is also called reliability-based design optimization. Aeronautical test cases proposed by the UMRIDA consortium are used to verify the validity of the methodologies and they are implemented in the software platform modeFRONTIER. The aeronautical test case applied uses drag minimization as the objective.
BENEFITS - As seen in the table above, a comparison of the performances (mean and standard deviation values) of the baseline configuration and of the optimized configuration obtained in each approach (also in this case SIMPLEX has been used). The optimized solution is generally slightly different, considering the performance distributions, following the two approaches, but in both cases the constraints are respected and the selected objective is minimized.