A numerical study of the POD method in NDE

In a previous paper [H.T. Banks, M.L. Joyner, B. Wincheski, W.P. Winfree, Real-time computational algorithms for eddy current-based damage detection, Inverse Problems 18 (2002) 795–823], we demonstrated the viability of using the proper orthogonal decomposition (POD) (also called principal component analysis) method in conjunction with eddy current nondestructive evaluation techniques when using either simulated or experimental data. In this paper we explore which factors impact the effectiveness of the POD method in the NDE damage detection problem. We examine whether or not the number of snapshots used to form the POD basis affects the accuracy of the estimation of the damage parameter. We also consider whether or not it is necessary to vary the damage parameters in the set of snapshots incrementally or whether it is possible to utilize random damage parameters and result in the same order of accuracy in the damage estimation. In addition, we examine how much relative error in the POD approximation we can sustain and still obtain fairly precise results in the inverse problem. We also consider whether or not the answers to the above questions are the same for different damage parameters or if the parameter we wish to approximate has an impact on the answers to these questions.