Spatio-temporal principal component analysis of full-field deformation data

Full-field displacements are the output of several non-contact experimental mechanics techniques such as the Grid method or Digital Image Correlation (DIC). Although it appears that an enormous amount of data is available from such measurements, such data are often highly redundant. In the past, orthogonal shape descriptors such as Zernike moments, Fourier-Zernike moments (Patki and Patterson, Exp Mech 1:1-13, 2011) and Tchebicheff moments (Sebastian et al., Appl Mech Mater 70:63-68, 2011) have been proposed to reduce dimensionality. We recently proposed the use of Principal Components Analysis (PCA) to reduce the dimensionality of full-field displacement data, identify primary spatial variations and compute strains without any a priori assumptions on the form the shape descriptors. In this work, we extend this idea to time-dependent problems and investigate spatio-temporal PCA to identify evolution of the primary displacement patterns with time in a deforming solid. The proposed method is applied to synthetic data obtained from a finite-element analysis of a thin visco-plastic solder specimen subjected to cyclic shear loading. Progressive damage is introduced into the specimen through the reduction of element stiffness at a specific location after pre-determined number of cycles. Displacement fields collected at periodic intervals are analysed using spatio-temporal PCA and the possibility of inferring local damage from the time-evolution of the eigenfunctions and their singular values is demonstrated. © The Society for Experimental Mechanics, Inc. 2014.