A Novel Perturbed Matrix Inversion Based Method for the Acceleration of Finite Element Analysis in Crack-Scanning Eddy Current NDT

Abstract

Non-destructive testing (NDT) has a promising capability for crack detection. In this paper, a novel method for accelerating eddy current calculation for crack detection using the finite element method (FEM) is presented. This method exploits the fact that, due to the presence of a small defect, the stiffness matrix in FEM for a sample plate with the defect can be regarded as a summation of the stiffness matrix Q from the sample plate without the presence of the defect and the perturbation matrix D from the defect. The inversion of the stiffness matrix for a sample plate with the defect can, therefore, be obtained using the perturbed matrix inversion (PMI) method. PMI method only requires the inversion of a much smaller matrix and therefore improves the speed of the computation process. Numerical tests verified the effectiveness of the proposed method in shortening the computation time for crack scanning in FEM.