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On Method of Fundamental Solution for Nondestructive Testing

Year: 2012 Volume: 6 Issue: 8 946 - 949 Pages

• Authors:
• Jieer Wu
• Zheshu Ma

Abstract: Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here.

• Keywords:
• ill-posed
• TSVD
• Laplace's equation
• inverse problem
• L-curve
• Generalized Cross Validation.

Estimating an Optimal Neighborhood Size in the Spherical Self-Organizing Feature Map

Year: 2008 Volume: 2 Issue: 6 1850 - 1854 Pages

• Authors:
• Alexandros Leontitsis
• Archana P. Sangole

Abstract: This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

• Keywords:
• Parameter estimation
• self-organizing feature maps
• spherical topology.