关键词: 压缩感知, 正交匹配追踪, 混沌多项式展开, 不确定性量化, 翼型不确定性, 类函数/形函数变换

Abstract:

Uncertainties exist widely in realistic systems. To evaluate the stochastic response of the system output with various uncertainties， traditional uncertainty quantification methods such as Monte Carlo Sampling （MCS） and Polynomial Chaos Expansion （PCE） require large quantities of samples， restricting their application to complex systems such as aircraft airfoils. The rapidly developed compressive sensing in signal processing field enables precise reconstruction of the signal based on the sparsity of original signals with only a small number of samples. This feature has attracted researchers to explore the application of compressive sensing to uncertainty quantification research. This study considers the geometrical uncertainty of the RAE2822 airfoil in manufacturing， assembly， and flight， and parameterizes the original shape with the Class-Shape Transformation （CST） method. We combine compressive sensing with polynomial chaos expansion for uncertainty quantification， and adopt the Orthogonal Matching Pursuit （OMP） algorithm to reconstruct the polynomial coefficients. In this way， the mean values and standard deviations of the aerodynamic forces and flow field quantities with geometrical uncertainty are obtained and compared to those of the Monte Carlo sampling and Full-Rank Probabilistic Collocations （FRPC） method. Comparison of convergence， sample number requirement and accuracy shows that the orthogonal matching pursuit can use fewer samples to obtain similar results as traditional methods. Since most of the stochastic responses of actual systems have sparse representations on polynomial chaos bases， the application of compressive sensing to uncertainty quantification can significantly decrease the required samples， thereby reducing time costs and improving computational efficiency.

Key words: compressive sensing, orthogonal matching pursuit, polynomial chaos expansion, uncertainty quantification, airfoil uncertainty, class-shape transformation