Uncertainty analysis of acceleration and velocity fields measured via DIC

Abstract

Digital image correlation is used to obtain full-field displacement measurements in a variety of applications. Since DIC measurements are obtained by comparing digital reconstructions of images captured during an experiment, noise in digital image data will introduce error in the displacement measurements which then propagate into derived field quantities such as displacement gradients, strains, velocity, and acceleration. The propagation of displacement error into velocities and accelerations is of significance in high-rate loading experiments such as direct impact or split Hopkinson pressure bar tests where accurate pointwise velocity and acceleration measurements are important, especially during the early transient stages of loading. While numerous studies have focused on quantifying displacement uncertainty in DIC, displacement uncertainty propagation into the derived velocity and acceleration fields has not been well explored. Employing well-known first and second order differentiation formulae with DIC-measured displacements to determine pointwise velocity and acceleration metrics, the enclosed study presents an error analysis and uncertainty quantification for these field quantities as a function of displacement noise and camera frame rate. When using central difference algorithms, theoretical analysis indicates that (a) uncertainty in acceleration is directly proportional to the product of frame rate squared and standard deviation in displacement and (b) uncertainty in velocity is directly proportional to the product of frame rate and standard deviation in displacement. The uncertainty analysis noted above is supported by results obtained for (a) numerical rigid body translation experiments and (b) a series of both static and wave-induced quasi-rigid motion dynamic experiments where images are obtained using a high-speed camera at frame rates from 100,000 to 5 million frames per second.