Canonical correlation decomposition of numerical and experimental data for observable diagnosis

TL;DR

This paper introduces a flow decomposition method based on canonical correlation analysis that effectively isolates observable-related flow structures from noisy data, enhancing flow diagnosis and control capabilities.

Contribution

The paper presents a novel canonical correlation-based decomposition method for extracting observable-correlated flow features from noisy numerical and experimental data.

Findings

Robustly identifies observable-correlated flow events despite high noise levels.

Effectively reduces data complexity by order reduction of flow structures.

Validated on turbulent flows, demonstrating practical applicability.

Abstract

A flow decomposition method based on canonical correlation analysis is proposed in this paper to optimally dissect complex flows into mutually orthogonal modes that are ranked by their cross-correlation with an observable. It is particularly suitable for identifying the observable-correlated flow structures while effectively excluding those uncorrelated, even though they may be highly energetic. Therefore, this method is capable of extracting coherent flow features under low signal-to-noise ratios. A numerical validation is conducted and shows that the method can robustly identify the observable-correlated flow events even though the underlying signal is corrupted by random noise that is four orders of magnitude stronger. The temporal sampling frequency and duration of the observable determine the maximum and minimum frequencies to be resolved in the cross-correlation respectively, while those of the flow are to ensure convergence. These criteria are validated using synthetic examples. The decomposition method is subsequently used to analyse a turbulent channel flow, a subsonic turbulent jet and an unsteady vortex shedding from a cylinder, showing the effectiveness of observable-correlated structure identification and order reduction. This decomposition represents a data-driven method of effective order reduction for highly noisy numerical and experimental data and is suitable for identifying the source and descendent events of a given observable. It is hoped that this method will join the existing flow diagnosis tools, in particular for observable-related diagnosis and control.