Robust spectral proper orthogonal decomposition

Experimental measurements often present corrupted data and outliers that can strongly affect the main coherent structures extracted with the classical modal analysis techniques. This effect is amplified at high frequencies, whose corresponding modes are more susceptible to contamination from measurement noise and uncertainties. Such limitations are overcome by a novel approach proposed here, the robust spectral proper orthogonal decomposition (robust SPOD), which implements the robust principal component analysis within the SPOD technique. The new technique is firstly presented with details on its algorithm, and its effectiveness is tested on two different fluid dynamics problems: the subsonic jet flow field numerically simulated, and the flow within an open cavity experimentally analyzed in [48]. The analysis of the turbulent jet data, corrupted both with salt and pepper and Gaussian noise, shows how the robust SPOD produces more converged and physically interpretable modes than the classical SPOD; moreover, the use of the robust SPOD as a tool for de-noising data, based on the signal reconstruction from de-noised modes, is also presented. Applying robust SPOD to the open cavity flow has revealed that it yields smoother spatial distributions of modes, particularly at high frequencies and when considering higher-order modes, compared to standard SPOD.