Meta-uncertainty for particle image velocimetry

Uncertainty quantification for particle image velocimetry (PIV) is critical for comparing experimentally measured flow fields with computational fluid dynamics results, and model design and validation. However, PIV features a complex measurement chain with coupled, non-linear error sources, and quantifying the uncertainty is challenging. Multiple assessments show that none of the current methods can reliably measure the actual uncertainty across a wide range of experiments, and estimates can vary. Because the current methods differ in assumptions regarding the measurement process and calculation procedures, it is not clear which method is best to use for an experiment where the error distribution is unknown. To address this issue, we propose a method to estimate an uncertainty method's sensitivity and reliability, termed the Meta-Uncertainty. The novel approach is automated, local, and instantaneous, and based on perturbation of the recorded particle images. We developed an image perturbation scheme based on adding random unmatched particles to the interrogation window pair considering the signal-to-noise of the correlation plane. Each uncertainty scheme's response to several trials of random particle addition is used to estimate a reliability metric, defined as the rate of change of the inter-quartile range of the uncertainties with increasing levels of particle addition. We also propose applying the meta-uncertainty as a weighting metric to combine uncertainty estimates from individual schemes, based on ideas from the consensus forecasting literature. We use planar and stereo PIV measurements across a range of canonical flows to assess the performance of the uncertainty schemes. Further, a novel method is introduced to assess an uncertainty scheme's performance based on a quantile comparison of the error and uncertainty distributions, generalizing the current method of comparing the RMS of the two distributions. The results show that the combined uncertainty method outperforms the individual methods, and this work establishes the meta-uncertainty as a useful reliability assessment tool for PIV uncertainty quantification.