Optimization of Total Variation regularization to improve the accuracy of the characterization of vertical cracks by lock-in vibrothermography

Abstract

We use lock-in vibrothermography to characterize vertical cracks. In the presence of ultrasounds, the rubbing of the crack faces produces heat which induces a temperature rise at the surface that is measured with an infrared camera. We fit data obtained by modulating the amplitude of the ultrasounds at several modulation frequencies. The inverse problem consisting of finding the geometry and location of the heat source from vibrothermography data is ill-posed, which makes it necessary to stabilize the inversion algorithm. We analyze the effect of the stabilizing term on the accuracy of the reconstructions. Ultrasound excited thermography is a very suitable technique for the detection of kissing cracks. The friction between crack lips in the presence of ultrasounds turns the crack into a heat source producing a temperature rise at the surface, on top of the crack. The goal of this work is to retrieve the dimensions and location of the heat source from lockin vibrothermography data. This inverse problem is ill-posed and as a consequence the minimization process is unstable. The algorithm can be stabilized by introducing a regularization term that is added to the residual to be minimized. In this work we analyze the effect of the regularization term and of the quality of the data on the quality of the reconstruction. To this purpose, we first calculate the surface temperature corresponding to a modulated vertical heat source. Then we invert synthetic data with added white noise by implementing two different regularization terms based on isotropic and anisotropic Total Variation functionals and we also check the effect of normalizing input data. Finally, we invert experimental data obtained on samples containing calibrated heat sources. The results show that it is possible to characterize 1 mm side square vertical cracks down to depths of about 3 mm. 2. Inverse problem and inversions of synthetic data