Novel data-driven sparse polynomial chaos and analysis of covariance for aerodynamics of compressor cascades with dependent geometric uncertainties

Polynomial Chaos Expansion (PCE) has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis. However, traditional PCE suffers from two major drawbacks. First, the orthogonality of polynomial basis functions holds only for independent input variables, limiting the model's ability to propagate uncertainty in dependent variables. Second, PCE encounters the "curse of dimensionality" due to the high computational cost of training the model with numerous polynomial coefficients. In practical manufacturing, compressor blades are subject to machining precision limitations, leading to deviations from their ideal geometric shapes. These deviations require a large number of geometric parameters to describe, and exhibit significant correlations. To efficiently quantify the impact of high-dimensional dependent geometric deviations on the aerodynamic performance of compressor blades, this paper firstly introduces a novel approach called Data-driven Sparse PCE (DSPCE). The proposed method addresses the aforementioned challenges by employing a decorrelation algorithm to directly create multivariate basis functions, accommodating both independent and dependent random variables. Furthermore, the method utilizes an iterative Diffeomorphic Modulation under Observable Response Preserving Homotopy regression algorithm to solve the unknown coefficients, achieving model sparsity while maintaining fitting accuracy. Then, the study investigates the simultaneous effects of seven dependent geometric deviations on the aerodynamics of a high subsonic compressor cascade by using the DSPCE method proposed and sensitivity analysis of covariance. The joint distribution of the dependent geometric deviations is determined using Quantile-Quantile plots and normal copula functions based on finite measurement data. The results demonstrate that the correlations between geometric deviations significantly impact the variance of aerodynamic performance and the flow field. Therefore, it is crucial to consider these correlations for accurately assessing the aerodynamic uncertainty.