Breaking the geometry-performance tradeoff in compressor deviation modeling: Nested principal component analysis

Uncertainties in the aerodynamic performance of compressors, introduced by manufacturing variations, have received more and more attentions in recent years. The deviation model plays a crucial role in evaluating this uncertainty and facilitating robust design. However, current deviation models with a few variables cannot simultaneously achieve a precise geometric approximation of deviation and provide an accurate assessment of performance uncertainty. This paper introduces a novel deviation modeling method named Nested Principal Component Analysis (NPCA) to break this tradeoff. In this method, both geometry-based and performance-based modes are utilized to describe manufacturing variations. By considering aerodynamic sensitivity, surface deformations that significantly impact aerodynamic performance can be extracted for deviation modeling. To demonstrate the superiority of this newly proposed method, ninety-eight newly manufactured compressor rotor blades were measured using a coordinate measurement machine, and both NPCA and Principal Component Analysis (PCA) were employed to model the real manufacturing variations. The results indicate that, in comparison to the PCA method, the NPCA method achieves an equivalent level of accuracy in geometric reconstruction and evaluation of mean performance. Furthermore, the same level of accuracy can be obtained with eight NPCA modes and fifty PCA modes when assessing the scatter in aerodynamic performance. Finally, the working mechanism of the NPCA method for accurate uncertainty quantification was further investigated.