An optimization method for stochastic reconstruction from empirical data - A limestone rock strain fields study-case using digital image correlation data

Abstract

Stochastic field reconstruction is a crucial technique to improve the accuracy of modern rock simulation. It allows explicit modelling of field conditions, often employed in uncertainty quantification analysis and upsampling and upscaling procedures. This paper presents a case-study of a framework for the stochastic reconstruction of rock’s strain field using experimental data. The proposed framework is applied to a limestone outcrop in which the strain field is measured using Digital Image Correlation (DIC). Assuming that the strain fields of these rocks are well-represented by Gaussian random fields, we capitalize on the algorithms used for training Gaussian processes to estimate the correlation family and the parameters that best represent these fields. Although the spherical and exponential kernels often correspond to the best fit, our results depict that each field shall be analyzed separately and no general rule can be defined. We show that the method is versatile and can be employed in any measurable field reasonably represented by a Gaussian random field. Therefore, the present work aims to highlight the following topics: • A study-case of stochastic strain field reconstruction aims to contribute to uncertainty quantification of rock experimental procedures. • A stochastic minimization algorithm is presented to solve the maximum likelihood estimation to define the most suitable hyper-parameter: correlation length. • The calculated hyper-parameters of a set correlation functions are presented to best reproduce the strain fields of a rock sample.

Keywords

• Stochastic Reconstruction of Limestone Rock Strain Fields Using Digital Image Correlation Data