# Uncertainty Quantification in Particle Image Velocimetry

Particle Image Velocimetry (PIV) is a non-invasive measurement technique which resolves the flow velocity by taking instantaneous snapshots of tracer particle motion in the flow and uses digital image cross-correlation to estimate the particle shift up to subpixel accuracy. The measurement chain incorporates numerous sets of parameters, such as the particle displacements, the particle image size, the flow shear rate, the out-of-plane motion for planar PIV and image noise to name a few, and these parameters are interrelated and influence the final velocity estimate in a complicated way. In the last few decades, PIV has become widely popular by virtue of developments in both the hardware capabilities and correlation algorithms, especially with the scope of 3-component (3C) and 3-dimensional (3D) velocity measurements using stereo-PIV and tomographic-PIV techniques, respectively. The velocity field measurement not only leads to other quantities of interest such as Pressure, Reynold stresses, vorticity or even diffusion coefficient, but also provides a reference field for validating numerical simulations of complex flows. However, such a comparison with CFD or applicability of the measurement to industrial design requires one to quantify the uncertainty in the PIV estimated velocity field. Even though the PIV community had a strong impetus in minimizing the measurement error over the years, the problem of uncertainty estimation in local instantaneous PIV velocity vectors have been rather unnoticed. A typical norm had been to assign an uncertainty of 0.1 pixels for the whole field irrespective of local flow features and any variation in measurement noise. The first article on this subject was published in 2012 and since then there has been a concentrated effort to address this gap. The current dissertation is motivated by such a requirement and aims to compare the existing 2D PIV uncertainty methods, propose a new method to directly estimate the planar PIV uncertainty from the correlation plane and subsequently propose the first comprehensive methods to quantify the measurement uncertainty in stereo-PIV and 3D Particle Tracking Velocimetry (PTV) measurements.

The uncertainty quantification in a PIV measurement is, however, non-trivial due to the presence of multitude of error sources and their non-linear coupling through the measurement chain transfer function. In addition, the advanced algorithms apply iterative correction process to minimize the residual which increases the complexity of the process and hence, a simple data-reduction equation for uncertainty propagation does not exist. Furthermore, the calibration or a reconstruction process in a stereo or volumetric measurement makes the uncertainty estimation more challenging. Thus, current uncertainty quantification methods develop a-posterior models utilizing the evaluated displacement information and combine it with either image information, correlation plane information or even calibration “disparity map” information to find the desired uncertainties in the velocity estimates.