An error threshold criterion for singular value decomposition modes extracted from PIV data
Epps, Brenden P.
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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, sk [ ffiffiffiffiffiffiffi DT p ; can be used as a rough limit of the validity of SVD modes extracted from experimental data (where sk is the singular value of mode k, D and T are the number of data sites and time steps, respectively, and 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-Ka´rma´n street, reveals that the first four modes are similar to the modes of a regular Ka´rma´n street created in the wake of a stationary cylinder and that higher modes are corrupted by experimental error