Practical Uncertainty Quantification Guidelines for DIC-Based Numerical Model Validation

Abstract

Accurate uncertainty quantification (UQ) in digital image correlation (DIC) deformations is essential for quantitative DIC-based finite element (FE) model validation. DIC UQ is well-studied in the current literature, both from a theoretical as well as experimental point-of-view, but rarely from the model validation perspective. Moreover, the DIC uncertainties are usually considered as spatial averages over the whole field of view while local contrast variations generally lead to spatially-varying noise floors. This paper investigates how DIC UQ should be performed when validating FE models. UQ was performed using experimental stationary images of a test sample. Spatial maps of point-wise temporal standard deviation (noise) and mean (bias) were constructed to be used in the model validation process. The effectiveness of reference image averaging at reducing bias and noise was also studied. Specular reflection (‘hotspots’) was given special attention, an important additional source of uncertainty not simulated by the Digital Twin (DT) used to perform the validation. As expected, image noise was found to be the most dominant source of DIC uncertainty. The spatially-random noise on the reference stationary image was found to be responsible for the temporal bias of the displacement distribution, as the copy of noise from that initial image affects all displacement maps since this image is used for all displacement maps. Spatially-random noise on the deformed stationary images was found to be responsible for the temporal standard deviation (noise). Both temporal noise and bias were found to be comparable in magnitude, highlighting the necessity for a spatially heterogeneous model validation criterion that accounts for both. The impact of specular reflection was difficult to quantify and exhibits potential for significantly increasing DIC uncertainties. The use of polarized lights and polarizing filters can mitigate this issue but more work is needed to allow for a realistic error budget to be established for this. Heat haze (refraction from warm air flow between camera and object) and camera heating are additional effects that are difficult to error-budget for. Finally, the effect of stereo-DIC calibration errors needs to be studied further.