Band-Ensemble Spectral Proper Orthogonal Decomposition with Frequency Attribution

TL;DR

This paper introduces band-ensemble SPOD, a novel method inspired by frequency smoothing, which improves spectral resolution and reduces estimator variance without segmentation, especially effective for broadband-tonal flows.

Contribution

The paper extends SPOD with a frequency smoothing-inspired band-ensemble approach, avoiding time segmentation and enhancing spectral resolution and variance reduction.

Findings

bSPOD reduces spectral leakage compared to Welch-based SPOD

bSPOD permits increased frequency resolution

bSPOD effectively analyzes broadband-tonal flows

Abstract

This study presents band-ensemble Spectral Proper Orthogonal Decomposition (bSPOD). The approach is inspired by frequency smoothing, a method used to reduce estimator variance in power spectral density estimates, and is here extended to SPOD. The algorithm estimates SPOD modes from consecutive Fourier coefficients obtained from a single Fourier transform of the full time record and thus avoids time segmentation. In this study, bSPOD is applied to artificial test data and to a PIV data set of a broadband-tonal cavity flow. Compared to the more commonly used Welch-based SPOD formulation, bSPOD reduces spectral leakage, permits increased frequency resolution, and retains frequency information of tonal components at comparable computational cost. These features enable reduced estimator variance while maintaining low bias for tonal components, making bSPOD particularly effective for broadband-tonal flows.