Optimizing the Inversion Protocol to Determine the Geometry of Vertical Cracks from Lock-in Vibrothermography

Abstract

We use low intensity lock-in vibrothermography to characterize vertical cracks of any shape. The inverse problem, consisting in finding the geometry and location of the crack from vibrothermography data is ill-posed, which makes it necessary to stabilize the inversion algorithm. In previous works, we developed a stabilized inversion procedure that was able to characterize vertical cracks of rectangular shape from lock-in vibrothermography data. In this work, we extend the method to characterize vertical cracks of arbitrary shape. For this purpose, first we improve the stabilization algorithm to obtain accurate crack shape reconstructions. Then, we optimize the protocol followed to handle data before entering the algorithm. To validate the new procedure we invert both, synthetic data with added uniform noise and experimental data on samples containing calibrated artificial cracks of different shapes. The results show that very accurate reconstructions are obtained for shallow cracks. As the depth of the crack increases, the depth is precisely obtained although the shape of the crack is rounded and its area is slightly overestimated.