A dimensionality reduction method for uncertainty study of geometric variations of turbomachinery blades

Abstract

Studies on performance impact due to the high-dimensional geometric uncertainties face the “curse of dimensionality” problem, making the cost of uncertainty quantification (UQ) unaffordable. To reduce the number of uncertainties, a sensitivity-based deep dimensionality reduction (SBDDR) method is introduced, verified and applied to the UQ studies of a low-pressure turbine cascade considering geometric variations. The basis modes of geometric variations are extracted from more than one thousand casting turbine blades using principal component analysis (PCA) and ordered by eigenvalues. However, the selection of primary basis mode by PCA neglects the performance impact of geometric variations. In the study, total-order sensitivities of performance parameters to the basis modes are calculated by Sobol analysis, in which fast performance prediction methods are employed. The total-order sensitivities are given in detail, by which the basis modes previously obtained by PCA are reordered. Furthermore, considering different numbers of basis modes ordered by PCA and SBDDR, the statistical means and standard deviations of performance changes are calculated and compared with those obtained by the direct Monte Carlo simulation (MCS). The results show that the SBDDR-based statistics are closer to the MCS ones, especially in the cases considering a limited number of basis modes.