Image processing of full-field strain data and its use in model updating

Abstract

Finite element model updating is an inverse problem based on measured structural outputs, typically natural frequencies. Full-field responses such as static stress/strain patterns and vibration mode shapes contain valuable information for model updating but within large volumes of highly-redundant data. Pattern recognition and image processing provide feasible techniques to extract effective and efficient information, often known as shape features, from this data. For instance, the Zernike polynomials having the properties of orthogonality and rotational invariance are powerful decomposition kernels for a shape defined within a unit circle. In this paper, full field strain patterns for a specimen, in the form of a square plate with a circular hole, under a tensile load are considered. Effective shape features can be constructed by a set of modified Zernike polynomials. The modification includes the application of a weighting function to the Zernike polynomials so that high strain magnitudes around the hole are well represented. The Gram-Schmidt process is then used to ensure orthogonality for the obtained decomposition kernels over the domain of the specimen. The difference between full-field strain patterns measured by digital image correlation (DIC) and reconstructed using 15 shape features (Zernike moment descriptors, ZMDs) at different steps in the elasto-plastic deformation of the specimen is found to be very small. It is significant that only a very small number of shape features are necessary and sufficient to represent the full-field data. Model updating of nonlinear elasto-plastic material properties is carried out by adjusting the parameters of a FE model until the FE strain pattern converges upon the measured strains as determined using ZMDs.