Confidence estimation using dependent circular block bootstrapping: application to the statistical analysis of PIV measurements

Abstract

In this paper the authors show an original application to time-resolved PIV of an existing method for confidence level and error determination, called dependent bootstrapping. Due to the high sampling frequencies the measured velocity samples are no longer uncorrelated making classical statistical procedures not applicable. Examples show that the various ways in calculating the number of independent samples based on the autocorrelation function question the reliability of the rarely, if ever, mentioned confidence levels in literature. Instead, the dependent bootstrapping technique reports consistent results of confidence estimates for both correlated and uncorrelated PIV velocity samples making this technique robust and general for further applications. The step-by-step description of the dependent circular block bootstrap implementation is given. The practical application and viability of the method are illustrated by two experimental cases.