Proper orthogonal decomposition truncation method for data denoising and order reduction

Proper orthogonal decomposition (POD) is used widely in experimental fluid dynamics for reducing noise in a measured flow field. The efficacy of POD is governed by the selection of modes used for the velocity field reconstruction. Currently, the determination of which or how many modes to keep is a user-defined subjective choice, where an arbitrary amount of energy to retain in the reconstruction, such as 99% cumulative energy, is chosen. Here, we present a novel, fully autonomous, and objective mode-selection method, which we term the entropy-line fit (ELF) method. The ELF method computes the Shannon entropy of the spatial discrete cosine transform of the eigenmodes, and using a two-line fit of the entropy mode spectrum, distinguishes between the modes carrying meaningful signal and those containing noise. We compare the ELF and existing methods using the analytical Hama flow field, synthetic PIV velocity fields derived from DNS turbulent channel flow data, and experimental particle image velocimetry vortex ring data. Overall, the ELF method improves the effectiveness of POD at removing noise from experimentally measured flow fields and subsequently the accuracy of post-processing calculations.