Uncertainty quantification (UQ) is an increasingly important area of research. As components and systems become more efficient and optimized, the impact of uncertain parameters is likely to become critical. It is fundamental to consider the impact of these uncertainties as early as possible during the design process, with the aim of producing more robust designs (less sensitive to the presence of uncertainties). The cost of UQ with high-fidelity simulations becomes therefore of fundamental importance. This work makes use of least-squares approximations in the context of appropriately selected polynomial chaos (PC) bases. An efficient technique based on QR column pivoting has been employed to reduce the number of evaluations required to construct the approximation, demonstrating the superiority of the method with respect to full-tensor quadrature (FTQ) and sparse-grid quadrature (SGQ). Orthonormal polynomials used for the PC expansion are calculated numerically based on the given uncertainty distribution, making the approach optimal for any type of input uncertainty. The approach is used to quantify the variability in the performance of two large bypass-ratio jet engine fans in the presence of shape uncertainty due to possible manufacturing processes. The impacts of shape uncertainty on the two geometries are compared, and sensitivities to the location of the blade shape variability are extracted. The mechanisms at the origin of the change in performance are analyzed in detail, as well as the differences between the two configurations.

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