Adaptive moment descriptors for full-field strain and displacement measurements

Recent advances in measurement techniques such as digital image correlation, automated photoelasticity, electronic speckle pattern interferometry and thermoelastic stress analysis allow full-field maps (images) of displacement or strain to be obtained easily. This generally results in the acquisition of large volumes of highly redundant data. Fortunately, image decomposition offers feasible techniques for data condensation while retaining essential information. This permits data processing such as the validation of computational models, modal testing or structural damage assessment efficiently and in a straightforward way. The selection, or construction, of decomposition bases (kernel) functions is essential to data reduction and has been shown to produce features, or attributes, of the full-field image that are effective in reproducing the measured information, succinct in condensation and robust to measurement noise. Among the most popular kernel functions are the orthogonal Fourier series, wavelets and Legendre polynomials, which are defined on continuous rectangular domains, and Zernike polynomials and Fourier–Mellin functions, which are defined on continuous circular domains. The discrete orthogonal polynomials include Tchebichef, Krawtchouk and Hahn functions that are directly applicable to digital images and avoid the approximate numerical integration that becomes necessary with the sampling of continuous kernel functions. In practice, full-field measurements of the engineering components are usually non-planar within irregular domains – neither rectangular nor circular, so that the classical kernel functions are not immediately applicable. To address this problem, a complete methodology is described, consisting of (1) surface parameterisation for the mapping of three-dimensional surfaces to two-dimensional planar domains, (2) Gram–Schmidt orthogonalisation for the construction of orthogonal kernel functions on arbitrary domains and (3) reconstruction of localised image features, such as regions of high strain gradient, by a windowing technique. Application of this methodology is demonstrated in a series of illustrative examples