An Investigation of Radial Basis Function Method for Strain Reconstruction by Energy-Resolved Neutron Imaging

Abstract

The main objective of the current work is to determine meshless methods using the radial basis function (rbf) approach to estimate the elastic strain field from energy-resolved neutron imaging. To this end, we first discretize the longitudinal ray transformation with rbf methods to give us an unconstrained optimization problem. This discretization is then transformed into a constrained optimization problem by adding equilibrium conditions to ensure uniqueness. The efficiency and accuracy of this approach are investigated for the situation of 2d plane stress. In addition, comparisons are made between the results obtained with rbf collocation, finite-element (fem) and analytical solution methods for test problems. The method is then applied to experimentally measured continuous and discontinuous strain fields using steel samples for an offset ring-and-plug and crushed ring, respectively.

A Study of the Effects of the Shape Parameter and Type of Data Points Locations on the Accuracy of the Hermite-Based Symmetric Approach Using Positive Definite Radial Kernels

“…One criterion to do this is based on the trade-off principle, that is, based on the fact that for small values of ε, the error improves while the condition number grows. The optimal value is then defined to be the smallest ε for which MATLAB did not issue a near-singular warning (Aggarwal et al, 2021). In many instances, selection of an optimal shape parameter via trial by error will end up being a rather tedious process.…”

Special Issue Advances in Neutron Imaging

“…In this Issue, a special selection of publications are presented to inform readers about various developments and to encourage them to use neutron imaging for their scientific research and work. Eleven publications report about very different topics from the application of neutron imaging, starting with an instrument at the NEUTRA facility (Switzerland) using neutrons and X-rays that was reported [1], followed by the work of the Australian imaging group, which presented new mathematical methods for reconstructing strain from energy-resolved neutron images [2]. The Swiss imaging group made a second contribution, investigating the mapping of the spatial distribution of pores using neutron microtomography [3], and from Japan a new method was presented dealing with the inner information of crystalline grain realized by wavelength-resolved neutron imaging [4].…”

Geometrically Flexible and Efficient Numerical Solution Technique for Bragg Edge Neutron Transmission Strain Tomography

“…As a result of the backscattering, the Bragg-edges do not add the scattering angle to the d-spacing error, making this technique an essential alternative for neutron applications requiring a high-resolution d distance, such as strain measurements. As no diffracted intensity beam-path is needed, the equipment can be designed more easily for particular environments, such as 2 R. Aggarwal [2] temperature, atmosphere or pressure, than for diffraction experiments. For a transmission set-up, the precise sample location is not required and, furthermore, the testing is simplified.…”

“…The descriptions of the algorithms, the comparison of approaches and the improvements in the resolution of the images are intended to serve as an entry-point guide for researchers wishing to continue this work further. Some of this research has been published in [1][2][3][4].…”