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

作　　者：Zhengtao GUO Wuli CHU Haoguang ZHANG Tianyuan JI 

机构地区：[1]School of Power and Energy,Northwestern Polytechnical University,Xi’an 710072,China

出　　处：《Chinese Journal of Aeronautics》2024年第6期89-108,共20页中国航空学报（英文版）

基　　金：the National Science and Technology Major Project of China(No.J2019-I-0011);the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX2023057)for supporting the research work.

摘　　要：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 f

关 键 词：Data-driven sparse polyno-mial chaos Analysis of covariance Dependent uncertainty Aerodynamic performance Compressor cascade 

分 类 号：V235.1[航空宇航科学与技术—航空宇航推进理论与工程]