Inverse Analyses and Their Applications to Nondestructive Evaluations

Inverse problems and inverse analyses, which deal with estimation of inputs or source from outputs or results, have been receiving increasing attention in various fields of science and engineering. A reasonable classification of the inverse problems is described. The nature of inverse problems and difficulties encountered in the inverse analyses are discussed. Typical inversion analysis schemes for solving the inverse problems are summarized. Nondestructive evaluations can be regarded as inverse problems. As an example of nondestructive evaluations the identification of cracks and defects from electric potential distributions observed on cracked bodies is discussed. The author and his coworkers proposed the active electric potential CT (computed tomography) method, in which the measurements of electric potential under various electric current application conditions are compared with numerical analyses of electric potential distributions for crack identification. The uniqueness and the stability of the identification are discussed. Examples of the applications of the active electric potential CT method to identification of two-dimensional cracks and threedimensional cracks are given. By using the piezoelectric film, the present author and his coworkers proposed the passive electric potential CT method, which did not require electric current application. The applicability of the passive electric potential method to identification of two-dimensional and three-dimensional cracks and delamination in composite materials are demonstrated. The enclosure method and the probe method proposed recently by Ikehata for direct reconstruction of voids and inclusions are introduced. Inverse analysis schemes related to the residual stress and strain estimation and the defect identification using thermography are also discussed.