Robust Principal Component Analysis of Vortex-induced Vibrations using Particle Image Velocimetry Measurements

Experimental techniques to measure fluid flow fields often contain measurement noise and corruption leading to missing velocity vectors that degrade data-driven analysis like POD, DMD etc. that are mostly based on least-squares. Here we use a statistical technique, robust principal component analysis (RPCA) to cope with this problem, RPCA removes the corrupted and misleading flow fields and fill in the missing velocity field vectors to improve the quality of the data by using the information of global coherent structures present in data before applying modal decomposition techniques like POD and DMD. RPCA takes the data matrix and decomposes this matrix into two parts first is a low-rank L matrix which contain coherent structures of flow field data and second is a S matrix which is sparse and contains corrupt entries of flow field. RPCA is applied on the numerical data (DNS) and experimental data of circular cylinder. First, we apply RPCA on the data obtained through direct numerical simulation of flow at Reynolds number 100 and add salt and pepper noise artificially to check the performance of RPCA and error analysis. Next, we investigate its performance on the experimental velocity fields data of vortex induced vibrations. Finally, we apply POD and DMD on the RPCA filtered data which are sensitive to noise and outliers. In all cases RPCA correctly identifies the coherent structures and fill in incorrect or missing information through L1 norm.