Corner stall receives noticeable attention in the aeroengine field as an important phenomenon in highly-load compressors. Non-uniform leading-edge tubercles, as an effective method to delay stall, are introduced into the compressor. In this paper, the shape of leading-edge tubercles was controlled by a third-order Fourier function. To judge corner stall, a more precise stall indicator for compressor cascade with flow control methods was defined. Besides, the total kinetic energy of the secondary flow at large incidence was adopted as a parameter for stall evaluation to save computing resources. The results of multi-objective optimization reveal that the loss coefficient exhibited negligible variation at design incidence, while the total kinetic energy of secondary flow showed a significant reduction at large incidence, resulting in a substantial increase in stall incidence. In the optimal profiling cases, thestall incidencewas delayed from 7.9° to 11.6°. The major purpose of the research is to provide proper design guidelines for non-uniform leading-edge tubercles and uncover the flow control mechanisms of leading-edge profiling. Hence, the geometric features that meet different optimization objectives were extracted through geometric analysis near the Pareto Front and through Self-Organizing Map (SOM) data mining methods in the optimization database. Besides, flow field analysis reveals the flow control mechanism of leading-edge tubercles. The convex-concave-convex structure at the 0%–70% blade height region can form two branches of leading-edge vortex pairs that are opposite in the rotation direction to the passage vortex. The two branches of leading-edge vortex pairs mixed with the leading-edge separation vortex to form two stronger mixed vortices, which can effectively suppress the development of passage vortex and delay stall incidence.

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.