Identification of Crack Shapes by Digital Image Correlation Using Joint Estimation Maximum a Posteriori Method

Abstract

A method that estimates invisible cracks from the surface based on the surface deformation measured by digital image correlation (DIC) is being developed. An inverse problem is setup to estimate such invisible cracks from the surface deformation. Surface deformation, measured by the DIC method, contains noise. Inverse problems have ill-conditions. The regularization method applied in this study is an extension of the joint estimation maximum a posteriori (JE-MAP) method. The JE-MAP algorithm alternates between MAP method estimation and the grab-cut (GC) method to avoid ill-conditions. The physical constraints on displacement and the forces at the cracks and the crack perimeters (ligaments) are added to the MAP method. The displacement and load at the cracks and the ligaments have a cross-sparse relationship. The MAP method estimates the displacement or the load at the cracks and the ligaments. The estimated result varies greatly at the boundary between the cracks and the ligaments. This boundary is determined by the GC method based on the estimated result. This study amplified the changes at the boundary between the cracks and the ligaments in the estimated results. The amplified results were input into the GC method to improve the boundary-determination accuracy. The regularization method developed from the JE-MAP method was combined with DIC method to estimate the cracks in invisible locations. The method proposed in this study estimated cracks more accurately than L1-norm regularization in inverse problems where the observed data were strain distributions measured by the DIC method.