Error evaluation of defect shape identification using charge simulation method for static electricity

Abstract

In this study, a numerical scheme for nondestructive inspection using static electricity is proposed. The relationship between the electric charges on the defect and the electric field at the observation points is described using the Fredholm integral equation for the first kind (IFK). A response function, which uses the relative coordinates between the electric charge and observation point as input variables, is derived. A system of linear equations, whose entries of the coefficient matrix are the kernels of IFK, is derived. Subsequently, an inverse algorithm is constructed to restore the electric charge distribution from the electric-field distribution. The Tikhonov regularization method is used to obtain the regularized solution because of the ill-posedness of the coefficient matrix. The optimal regularization parameter is determined using the L-curve criterion. The accuracy of the proposed method is verified through numerical experiments. The observable electric field is determined mathematically through forward analysis. A formula that quantitatively evaluates the error is then defined. It is confirmed that the inverse analysis result provides a more accurate solution than the raw data of the electric field.