Abstract: Uncertainties exist widely in realistic systems. To evaluate the stochastic response of the system output under various uncertainties, traditional uncertainty quantification methods such as Monte Carlo Sampling and Polynomial Chaos Expansion require large quantities of samples, which restricts their application in complex systems such as aircraft airfoils. Compressive Sensing, which has been developed rapidly in signal processing field recently, is able to precisely reconstruct the original signal with few number of samples making use of the sparsity. This feature has attracted researchers to explore the application of Compressive Sensing to uncertainty quantification research. In this work, the geometrical uncertainty of RAE2822 airfoil from manufacturing and flight was taken into consideration. The original shape was parameterized by Class-Shape Transformation method. Compressive Sensing was combined with Polynomial Chaos Expansion for uncertainty quantification. The Orthogonal Matching Pursuit algorithm was adopted to reconstruct the polynomial coefficients. In this way the means and standard deviations of aerodynamic forces and flow field quantities under geometrical uncertainty were obtained. The results were compared to that of Monte Carlo and Full-Rank Probabilistic Collocations method. Through the comparison and analyses on convergence, sample number requirement and accuracy, it showed that the Orthogonal Matching Pursuit could use less 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