This paper presents formulations that enable the vision-based measurement of displacement and strain fields extensively in a probabilistic manner. The proposed formulations are built on the dot centroid tracking (DCT) method by digital cameras, which measures the darkness of each pixel in gray scale, identify dots marked on a specimen, derives dot centroids using pixel darkness information and derives displacement and strain fields by tracking the centroids and interpolating the nodal displacements and strains. Under the Gaussian assumption, the proposed formulations analytically propagate the standard deviation of uncertainty in darkness measurement and estimate that in the displacement and strain field measurement. As the first step, the formulations were completed for continuous field measurement with triangular elements. Most advantageously, the proposed formulations allow discussion on measurement error bounds, which also enables the quantitative comparison of the DCT method to the other measurement techniques. For numerical validation, standard deviations of nodal displacements and strains estimated from the known darkness uncertainty were compared to those derived from large samples created with the same darkness uncertainty. The results show the validity of the proposed formulations and their potential in measurement with reliability.

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