# A Neural Network Approach for Solving Inverse Problems in NDE

Chapter

## Abstract

Solution to inverse problems is of interest in many fields of science and engineering. In nondestructive evaluation [1], for example, inverse techniques are used to obtain quantitative estimates of the size, shape and nature of defects in materials. Inv.:rse scattering problems in electromagnetics deal with estimation of scatterer information from knowledge of incident and scattered fields. Inverse problems are frequently described by Fredholm integral equations in the form
where u(x) represents the measured data, z(y) represents the source function or the system states or parameters, and k(x,y) represents the kernel of the transformation. The objective of inverse problem is then to solve for the source or state function from known measurements. This problem is sensitive to the system parameters z, to the shape of the kernel k, and to the accuracy of the measurements u.

$$
\smallint _a^bk(x,y)z(y)dy = u(x) (c \leqslant x \leqslant d)$$

(1)

## Keywords

Inverse Problem Fredholm Integral Equation Neural Network Approach Hopfield Neural Network Hopfield Network
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© Springer Science+Business Media New York 1992