High-fidelity quantification of manufacturing-induced uncertainty in supersonic flow fields via deep autoencoder and spatially-adaptive polynomial chaos

The precision of high-load compressor blade machining critically determines the research, development, and operational costs of aero-engines. Supersonic compressor blades require particularly stringent geometric tolerances, since minor geometric deviations can trigger highly nonlinear and localized flow anomalies, such as shock oscillations and shock–boundary layer interactions, that substantially fluctuate aerodynamic performance. Conventional Uncertainty Quantification (UQ) methods, including standard Polynomial Chaos Expansion (PCE) based on least angle regression, often fail to efficiently and accurately represent these high-dimensional, strongly nonlinear uncertainty propagation processes. To overcome these limitations, the study proposes an integrated UQ framework that combines a Deep Autoencoder (DAE) and a spatially-adaptive PCE for modeling of supersonic flow fields. The developed DAE substantially alleviates the curse of dimensionality associated with high-dimensional manufacturing blade data, outperforming Principal Component Analysis (PCA) in reconstruction fidelity and parameter compactness. The proposed spatially-adaptive PCE employs recursive domain partitioning and local spectral expansions to resolve localized or high-gradient flow features, achieving accelerated convergence in quantifying shock-related nonlinearities. Applied to the ARL-SL19 supersonic compressor blade, the framework uncovers bimodal and multimodal probability distributions of flow parameters in shock and separation regions, revealing strong nonlinear dependencies on geometric deviations. Sensitivity decomposition identifies the leading edge geometry and the streamwise location of maximum thickness on the suction surface as the dominant parameters influencing performance variability, with the former primarily modulating the first passage shock and the latter significantly affecting the second. Based on these insights, geometric tolerance specifications are optimized, resulting in a 2.84-fold increase in mean total pressure loss reduction and a 66.8% reduction in standard deviation, providing suggestions for the refined design of the new generation of aero-engines.