Track benchmarking method for uncertainty quantification of particle tracking velocimetry interpolations

The track benchmarking method (TBM) is proposed for uncertainty quantification of particle tracking velocimetry (PTV) data mapped onto a regular grid. The method provides statistical uncertainty for a velocity time-series and can in addition be used to obtain instantaneous uncertainty at increased computational cost. Interpolation techniques are typically used to map velocity data from scattered PTV (e.g. tomographic PTV and Shake-the-Box) measurements onto a Cartesian grid. Recent examples of these techniques are the FlowFit and VIC+ methods. The TBM approach estimates the random uncertainty in dense velocity fields by performing the velocity interpolation using a subset of typically 95% of the particle tracks and by considering the remaining tracks as an independent benchmarking reference. In addition, also a bias introduced by the interpolation technique is identified. The numerical assessment shows that the approach is accurate when particle trajectories are measured over an extended number of snapshots, typically on the order of 10. When only short particle tracks are available, the TBM estimate overestimates the measurement error. A correction to TBM is proposed and assessed to compensate for this overestimation. The experimental assessment considers the case of a jet flow, processed both by tomographic PIV and by VIC+. The uncertainty obtained by TBM provides a quantitative evaluation of the measurement accuracy and precision and highlights the regions of high error by means of bias and random uncertainty maps. In this way, it is possible to quantify the uncertainty reduction achieved by advanced interpolation algorithms with respect to standard correlation-based tomographic PIV. The use of TBM for uncertainty quantification and comparison of different processing techniques is demonstrated.