Stereo-PIV Uncertainty Quantification
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Stereo-PIV Uncertainty Quantification

Most physical flows are complex and three-dimensional (3D) and all three velocity components (3C) are required to fully characterize the fluid motion. Stereo Particle Image Velocimetry (SPIV) is a non-invasive, 2D3C velocimetry measurement which offers a balance between accuracy — 2D PIV fails to resolve out of plane motion — and computational complexity — volumetric methods are most accurate but computationally intensive. Thus, SPIV has become the standard approach for typical PIV measurements and is even used for volumetric measurements by scanning several slices along a volume. The primary sources of error in this two-camera measurement arise from the individual camera image correlation and registration between the two camera images. Several studies have focused on quantifying the overall measurement error and some recent work has focused on the uncertainty estimation for in-plane camera image correlations; however, no complete methodology exists for uncertainty quantification in stereo PIV. In particular, the nonlinear combination of the multiple error sources (e.g. particle image size, shear rate, image noise, disparity or registration error etc.) makes the measurement uncertainty quantification challenging.

Figure 1.

Figure 1: The stereo-PIV measurement chain consists of several steps which combine and propagate the error in calibration and image cross-correlation to the final measurement. The degree of mismatch between registered camera images contributes to the uncertainty in the camera calibration and subsequently determines the camera angle uncertainty. The developed methodology extracts this angle uncertainty and combines it with planar cross-correlation uncertainty to predict the correct uncertainty level in the 3-component velocity field.

In the current work, we present a comprehensive framework to quantify the uncertainty stemming from stereo registration error and combine it with the underlying 2D correlation uncertainties. After correcting for any registration error or disparity, the stereo PIV uncertainty prediction method is more sensitive to the 2D correlation uncertainty estimates than to the camera calibration mapping function uncertainty, although the latter is not negligible for non-zero disparity. Overall, the presented uncertainty quantification framework showed excellent agreement between the error and uncertainty RMS values for both synthetic and experimental data and demonstrated reliable uncertainty prediction coverage.

Figure 2: The article shows uncertainty prediction for an experimental vortex ring case. The spatial contours indicate higher RMS uncertainty in the vortex core region and are in agreement with the RMS error values (the expected true uncertainty levels). The contribution fraction of camera angle uncertainty and the planar cross-correlation uncertainty shows that, for a properly calibrated system, the planar uncertainty estimate has the more significant contribution.

Published Paper

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