title: Kriging regression in digital image correlation for error reduction and uncertainty quantification
Creators: name: Wang, Dezhi
Publisher: name: University of Liverpool Repository
Year: 2016

description: Digital Image Correlation (DIC) is a widely used full-field measurement technique in the field of experimental mechanics because of its simplicity and ease of implementation. However, owing to the inherent complexity of DIC error sources, the problem of DIC error reduction and uncertainty quantification is still unsolved and has received considerable attention in recent years. The existing work on DIC error reduction is usually focused on specific error sources, e.g. local smoothing techniques are normally applied to reduce errors due to image acquisition noise. Moreover, DIC uncertainty quantification methods are usually derived from a subset-based DIC framework with an assumption of Gaussian image noise. Established methods are normally subject to an ad-hoc choice of parameterisation and might only be able to achieve a local optimum. On the other hand, originally developed in geo-statistics, Kriging is known as optimal interpolation to predict interpolated values using random variables as a realization of a Gaussian process. The Kriging technique has the excellent capability in global optimisation and uncertainty quantification. It is advisable to make an attempt to introduce the Kriging method to DIC to facilitate the solution of error and uncertainty issue. The main purpose of this thesis is to offer a generic and global method that can reduce general DIC errors and quantify measurement uncertainty for displacement and strain results based on Kriging regression from Gaussian Process (GP) and Bayesian perspective. Firstly, a new global DIC approach known as Kriging-DIC was developed through incorporating the Kriging regression model into the classical global DIC algorithm as a full-field shape function. The displacement field of the Region of Interest (RoI) is formulated as a best linear unbiased realisation that contains correlations between all the samples. The measurement errors of control points are accounted for through a global regularisation technique using a global error factor. With the aid of the Mean Squared Error (MSE) determined from the Kriging model, a self-adaptive updating strategy was developed to achieve an optimal control grid without artificial supervision. The developed Kriging DIC method was compared with subset-based DIC, FE-DIC and B-Spline DIC by using synthetic images and open-access experimental data. The effectiveness and robustness of Kriging DIC was verified by numerical examples and an experimental I-section beam test. Secondly, a Kriging-based DIC uncertainty quantification method was proposed to quantify uncertainty of displacement and strain results of the subset-based DIC through a post-processing analysis based on Kriging regression. The subset-by-subset uncertainty was estimated through the subset-based DIC framework and derived as a function of the inverse of the Hessian matrix and residual of Sum of Squared Difference (SSD). This local subset-based uncertainty was then integrated into Kriging regression formula allowing uncertainty quantification of displacement field from a global sense. Based on Cholesky decomposition and covariance matrix solved by the Kriging formula, a multivariate normal sampling process was used to quantify the strain uncertainty whereas displacement gradients were calculated by a Finite Difference technique. Both numerical case studies and an experimental cantilever beam test were employed to test the method, which was found to be able to improve the accuracy of displacement and strain results and quantify corresponding uncertainties. Furthermore, a new approach was developed to calculate strain results by means of Kriging gradients, which was also compared with a state-of-the-art PLS local fitting algorithm. In summary, the main contribution of this thesis is the development of a global DIC algorithm (i.e. Kriging-DIC) and a Kriging-based DIC uncertainty quantification approach. These two methods provide great potential to globally improve DIC measurement accuracy and quantify uncertainties of displacement and strain results.