Radial Basis Functions and Improved Hyperparameter Optimisation for Gaussian Process Strain Estimation

TL;DR

This paper enhances Gaussian Process-based strain estimation methods by introducing modifications like hyperparameter optimization, radial basis function approximation, and gradient-based placement to better handle high-gradient or discontinuous strain fields.

Contribution

It proposes three novel modifications to GP algorithms, improving their performance on complex strain fields with discontinuities or high gradients.

Findings

Improved accuracy in strain estimation for discontinuous fields.

Enhanced hyperparameter optimization via k-fold cross-validation.

Effective use of radial basis functions for better approximation.

Abstract

Over the past decade, a number of algorithms for full-field elastic strain estimation from neutron and X-ray measurements have been published. Many of the recently published algorithms rely on modelling the unknown strain field as a Gaussian Process (GP) - a probabilistic machine-learning technique. Thus far, GP-based algorithms have assumed a high degree of smoothness and continuity in the unknown strain field. In this paper, we propose three modifications to the GP approach to improve performance, primarily when this is not the case (e.g. for high-gradient or discontinuous fields); hyperparameter optimisation using k-fold cross-validation, a radial basis function approximation scheme, and gradient-based placement of these functions.