Uncertainty Estimation and Experimental Design For Unsteady Flow-Field Measurements via Bootstrapping

Determination of the uncertainty associated with a measured quantity, or with statistical quantities derived from it, provides guidance for how these values should be interpreted and used. The total uncertainty of a quantity consists of precision (random, statistical) and bias (systematic). In the present work, bootstrapping is examined as a method for estimating the precision of statistics obtained from unsteady flow-field measurements using a five-hole probe capable of unsteady measurements. The objective is to demonstrate the use of bootstrapping both for experimental design—specifically, determining how data should be acquired— and for post-processing, where uncertainties of measured and derived quantities are estimated from the acquired data. The results show that the number of samples required for convergence predicted by the bootstrapping procedure generally matches or overpredicts the number of samples required when evaluated against the full dataset. In a limited number of cases, bootstrapping underpredicts the required sample count; however, the predicted and actual convergence levels always differ by no more than 2500 independent samples. These results indicate that experimental design informed by bootstrapping can accurately predict the number of independent samples required for statistical convergence and associated precision estimation, thereby optimizing experimental design while reducing oversampling.