# An error threshold criterion for singular value decomposition modes extracted from PIV data

An error threshold criterion for singular value decomposition modes extracted from PIV data Singular value decomposition (SVD) is often used as a tool to analyze particle image velocimetry (PIV) data. However, experimental error tends to corrupt higher SVD modes, in which the root mean square velocity value is smaller than the experimental error. Therefore, we suggest that the threshold criterion, $$s_k >\sqrt{DT}\epsilon,$$ can be used as a rough limit of the validity of SVD modes extracted from experimental data (where s k is the singular value of mode k, D and T are the number of data sites and time steps, respectively, and $$\epsilon$$ is the root mean square PIV error). By synthesizing the relationship between the general SVD procedure and its two special cases—biorthogonal decomposition (BOD) and proper orthogonal decomposition (POD)—we show that our criterion can be used to assess modes extracted by either BOD or POD. We apply our threshold criterion to PIV data of the wake behind a live swimming Giant Danio (Danio aequipinnatus). The biorthogonal decomposition of the fish wake, which is a reverse-Kármán street, reveals that the first four modes are similar to the modes of a regular Kármán street created in the wake of a stationary cylinder and that higher modes are corrupted by experimental error. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

# An error threshold criterion for singular value decomposition modes extracted from PIV data

, Volume 48 (2) – Oct 1, 2009
13 pages

/lp/springer_journal/an-error-threshold-criterion-for-singular-value-decomposition-modes-qnKxRxXOpp
Publisher
Springer-Verlag
Subject
Engineering; Engineering Thermodynamics, Heat and Mass Transfer; Fluid- and Aerodynamics; Engineering Fluid Dynamics
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-009-0740-4
Publisher site
See Article on Publisher Site

### Abstract

Singular value decomposition (SVD) is often used as a tool to analyze particle image velocimetry (PIV) data. However, experimental error tends to corrupt higher SVD modes, in which the root mean square velocity value is smaller than the experimental error. Therefore, we suggest that the threshold criterion, $$s_k >\sqrt{DT}\epsilon,$$ can be used as a rough limit of the validity of SVD modes extracted from experimental data (where s k is the singular value of mode k, D and T are the number of data sites and time steps, respectively, and $$\epsilon$$ is the root mean square PIV error). By synthesizing the relationship between the general SVD procedure and its two special cases—biorthogonal decomposition (BOD) and proper orthogonal decomposition (POD)—we show that our criterion can be used to assess modes extracted by either BOD or POD. We apply our threshold criterion to PIV data of the wake behind a live swimming Giant Danio (Danio aequipinnatus). The biorthogonal decomposition of the fish wake, which is a reverse-Kármán street, reveals that the first four modes are similar to the modes of a regular Kármán street created in the wake of a stationary cylinder and that higher modes are corrupted by experimental error.

### Journal

Experiments in FluidsSpringer Journals

Published: Oct 1, 2009

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