Physics based compressive sensing approach applied to airfoil data collection and analysis

In this study, Compressive Sensing (CS), a recently developed low dimensional signal acquisition scheme, was used to reconstruct a high Reynolds number turbulent flow PIV velocity field over a NACA-4412 airfoil. The 2D PIV velocity data was obtained in the Syracuse University subsonic wind tunnel. In the CS framework, a small collection of linear random projections of a sparse signal contains sufficient information for signal recovery. The principle of CS and its feasibility has been demonstrated using the Discrete Cosine Transform (DCT) and the Proper Orthogonal Decompositon (POD)/ Principal Component Analysis (PCA) to obtain the sparsity. The reconstruction performance of CS taking different basis in which the data is sparse is compared to the performance with the traditional snapshot POD/PCA based reconstruction. When DCT is used as the saprsifying basis, acceptable performance with CS is achieved. The reconstruction performance with CS is further improved by taking the POD/PCA basis as the spasifying basis resulting in a much faster and efficient reconstruction process. Finally we demonstrate with some success, a modified snapshot POD/PCA approach that computes the correlation matrices after CS compression so as to decrease the complexity of doing the eigenvalue problem for the snapshot POD/PCA basis.