Comparison of two techniques for implementing the proper orthogonal decomposition method in damage detection problems

The viability of using the reduced-order proper orthogonal decomposition (POD) (alsocalled principal component analysis) methods to reduce the total computational time to detect damages using eddy current nondestructive evaluation techniques was demonstrated in a previous paper [1]. In this paper, we concentrate on various alternatives used to form the reduced-order solution to the forward problem, still in the context of eddy current damage detection. In particular, we focus on two different algorithms, a POD/Galerkin technique and a POD/interpolation technique. The POD/Galerkin method is a popular choice in the implementation of the POD method; however, in this paper, we will point out some of the problems in the traditional implementation of the reduced-order POD/Galerkin method when used in conjunction with eddy current damage detection. We will also compare the POD/Galerkin method to the POD/interpolation method and argue that in certain circumstances, the POD/interpolation method may be a better choice.