An efficient streaming algorithm for spectral proper orthogonal decomposition

TL;DR

This paper introduces a streaming algorithm for spectral proper orthogonal decomposition (SPOD) that updates eigenbases incrementally, enabling real-time analysis of stationary processes with low memory use.

Contribution

The paper presents a novel streaming algorithm for SPOD that efficiently updates eigenbases with new data, suitable for real-time applications and long data streams.

Findings

Reliable convergence of the most energetic SPOD modes demonstrated

Algorithm performs well on turbulent jet simulation data

Effective on optical flow data from high-speed camera recordings

Abstract

A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated cross-spectral density (CSD) matrix is performed. The algorithm converges orthogonal sets of SPOD modes at discrete frequencies that are optimally ranked in terms of energy. We define measures of error and convergence, and demonstrate the algorithm's performance on two datasets. The first example is that of a high-fidelity numerical simulation of a turbulent jet, and the second optical flow data obtained from high-speed camera recordings of a stepped spillway experiment. For both cases, the most energetic SPOD modes are reliably converged. The algorithm's low memory requirement enable real-time deployment and allow for the convergence of second-order statistics from arbitrarily long streams of data.