Displacement Uncertainty Quantifications in T3-Stereocorrelation

Abstract

Background: Uncertainty quantifications are required for any measurement result to be meaningful. Objective: The present work aims at deriving and comparing a priori estimates of displacement uncertainties in T3-stereocorrelation for a setup to perform high temperature tests. Methods: Images acquired prior to the actual experiment (i.e., at room temperature) were registered using 3-noded triangular elements (T3-stereocorrelation) to determine displacement uncertainties for different positions of the experimental setup. Results:The displacement uncertainties were then compared to their a priori estimates. Conclusions:

On the validation of a priori estimates of standard displacement uncertainties in T3-stereocorrelation

“…For artificial cases, the multiplicative constant Σ u was found equal to 1.2 ± 0.3 for global T3-stereocorrelation [25]. More refined analyses have shown that a lower bound to Σ u was 1.08 [21] when threenoded elements were used. This last value was selected for the results reported herein.…”

“…Such approaches allow the systemic errors to be avoided. However, they may occur in practice, and the previous analyses call for experimental validations [20,21]. As maturity increases in the use of stereocorrelation, some systemic errors (e.g.…”

“…If acquisition noise can be modeled with Gaussian variables, then one important piece of information is related to the covariance matrix of the measured quantities when analyzing the performance of DIC and stereoDIC tools [24]. For FE-based stereocorrelation, it was shown that the covariance matrix of the measured nodal displacements was equal to the inverse of the Hessian matrix used in the minimization scheme of the weighted cost function in which the gray level differences were scaled by their corresponding variances [21,25]. Such result corresponds to the so-called Rao and Cramér lower bounds [26,27] applied to the evaluation of displacement uncertainties.…”

Brightness and contrast corrections for stereocorrelation

“…The nodal displacement can be obtained through a Gauss-Newton scheme [16,32]. Hence, at each iteration, the stereocorrelation Hessian matrix [H U ] and second member {h U } are computed…”

Damage Detection and Quantification via Multiview DIC at Varying Scales

“…Multiscale and multiview DIC approaches were developed separately in previous works. Measurement uncertainties in DIC depend on the number of pixel per the size of subsets in the local approaches [32,31,17] or element size in global approaches [15,6]. For a given resolution, bigger elements contain more pixels and thus yield lower measurement uncertainties.…”