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

2021 ◽  
Vol 11 (1) ◽  
pp. 391
Author(s):  
Riya Aggarwal ◽  
Bishnu P. Lamichhane ◽  
Michael H. Meylan ◽  
Chris M. Wensrich
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Optimization Problem ◽  
Neutron Imaging ◽  
Test Problems ◽  
Equilibrium Conditions ◽  
Radial Basis ◽  
Solution Methods ◽  
Radial Basis Function Method ◽  
Elastic Strain Field

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.

scholarly journals A Frame-Based Conjugate Gradients Direct Search Method with Radial Basis Function Interpolation Model

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowei Fang ◽  
Qin Ni
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Direct Search ◽  
Search Method ◽  
Conjugate Gradients ◽  
Test Problems ◽  
Interpolation Model ◽  
Direct Search Method ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising.

scholarly journals The Conical Radial Basis Function for Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
J. Zhang ◽  
F. Z. Wang ◽  
E. R. Hou
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Computational Cost ◽  
Basis Functions ◽  
Simple Scheme ◽  
Collocation Points ◽  
Radial Basis ◽  
Radial Basis Function Method

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

scholarly journals A symmetric integrated radial basis function method for solving differential equations

2018 ◽  
Vol 34 (3) ◽  
pp. 959-981 ◽  
Author(s):  
Nam Mai-Duy ◽  
Deepak Dalal ◽  
Thi Thuy Van Le ◽  
Duc Ngo-Cong ◽  
Thanh Tran-Cong
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Radial Basis ◽  
Radial Basis Function Method

Accuracy of the Hill–radial basis function method and the Barrett Universal II formula

2020 ◽  
pp. 112067212090295 ◽  
Author(s):  
Gabor Nemeth ◽  
Laszlo Modis
Keyword(s):  
Radial Basis Function ◽  
Intraocular Lens ◽  
Basis Function ◽  
Function Method ◽  
Theoretical Formula ◽  
Refractive Errors ◽  
Radial Basis ◽  
The Mean ◽  
The Hill ◽  
Radial Basis Function Method

Purpose: The aim was to assess the postoperative results of a biometric method using artificial intelligence (Hill–radial basis function 2.0), and data from a modern formula (Barrett Universal II) and the Sanders–Retzlaff–Kraft/Theoretical formula. Methods: Phacoemulsification and biconvex intraocular lens implantation were performed in 186 cataractous eyes. The diopters of intraocular lens were established with the Hill–radial basis function method, based on biometric data obtained using the Aladdin device. The required diopters of the intraocular lens were also calculated by the Barrett Universal II formula and with the Sanders–Retzlaff–Kraft/Theoretical formula. The differences between the manifest postoperative refractive errors and the planned refractive errors were calculated, as well as the percentage of eyes within ±0.5 D of the prediction error. The mean- and the median absolute refractive errors were also determined. Results: The mean age of the patients was 70.13 years (SD = 10.67 years), and the mean axial length was 23.47 mm (range = 20.72–28.78 mm). The percentage of eyes within a prediction error of ±0.5 D was 83.62% using the Hill–radial basis function method, 79.66% with the Barrett Universal II formula, and 74.01% in the case of the Sanders–Retzlaff–Kraft/Theoretical formula. The mean- and the median absolute refractive errors were not statistically different. Conclusion: Clinical success was the highest when using the biometric method, based on pattern recognition. The results obtained using Barrett Universal II came a close second. Both methods performed better compared to a traditionally used formula.

Sign in / Sign up

Export Citation Format

Share Document