Construction of Shape Features for the Representation of Full-Field Displacement/Strain Data

Abstract

The achievement of high levels of confidence in finite element models involves their validation using measured responses such as static strains or vibration mode shapes. A huge amount of data with a high level of information redundancy is usually obtained in both the detailed finite element prediction and the full-field measurements so that achieving a meaningful validation becomes a challenging problem. In order to extract useful shape features from such data, image processing and pattern recognition techniques may be used. One of the most commonly adopted shape feature extraction procedures is the Fourier transform in which the original data may be expressed as a set of coefficients (coordinates) of the decomposition kernels (bases) in the feature space. Localised effects can be detected by the wavelet transform. The acquired shape features are succinct and therefore simplify the model validation, based on the full-field data, allowing it to be achieved in a more effective and efficient way. In this paper, full-field finite element strain patterns of a plate with a centred circular hole are considered. A special set of orthonormal shape decomposition kernels based on the circular Zernike polynomials are constructed by the Gram-Schmidt orthonormalization process. It is found that the strain patterns can suitably be represented by only a very small number of shape features from the derived kernels.

Decomposition-based calibration/validation metrics for use with full-field measurement situations

“…A number of other decomposition methods have been compared to the PCA-SVD method in recent research. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] This work reviewed image classification methods that can be grouped into three categories: (1) Fourier transform signatures, (2) minutiae matching and (3) moment descriptors. Of the three categories, moment descriptor methods were found to be the most promising with respect to the development of a calibration/validation metric similar to the PCA-SVD method.…”

“…Moment descriptor method: 27,29,32–44 a set of 2D moments are computed for the image intensity functions (essentially, Figures 4 and 5) using a set of basis kernels ranging from simple monomials to OPs. These sets of moments form the features which are then used for final comparison to classify the images.…”

The validation of a full-field deformation analysis of an aircraft panel: A case study

“…In the field of solid mechanics, a series of European collaborative research projects, including ADVISE, 4 VANESSA 5 and MOTIVATE 6 have explored the challenges of utilising full-field maps, such as strain fields, and implementing a validation process in an industrial environment. Research activities in the frame of these projects have led to the development of effective tools for processing full-field maps using image decomposition 7 and for comparing the outputs using quantitative statistical methods 8 at different length scales, that is ranging between small and large scale components.…”

“…Over the last decade, image decomposition techniques have been intensively studied to process measured and predicted strain and displacement fields. 7,[9][10][11] The measured fields obtained using an optical measurement technique, such as digital image correlation (DIC), are typically treated as images, and can be visually compared with the corresponding images obtained from a simulation, for example using finite element analysis. However, for a quantitative comparison within the scope of validation, further processing is necessary because the image pairs could have different co-ordinate systems, pixel spacing or colour bars, which does not allow a direct comparison between two sets of data.…”

On the integration of validation, quality assurance and non-destructive evaluation

“…Recently, Hack et al 2 have suggested that the validation of a computational solid mechanics model can be performed over the entire surface of a component based on strain data obtained using full-field techniques from experimental mechanics, such as photoelasticity, interferometry, thermoelastic stress analysis and digital image correlation. Digital image correlation, 3 which has become very popular in recent years due to the relatively low cost of equipment and operation, provides an excellent source of data for performing the more comprehensive type of validation recommended by Hack et al 2 Wang et al 4 have shown that the data-rich maps of strain generated by digital image correlation and other experimental techniques can be represented accurately and at reduced dimensionality based on orthogonal shape descriptors, which can be used for updating of numerical models and for their validation. 5…”