Sensitivity and uncertainty analysis by discontinuous Galerkin of lock-in thermography for crack characterization

This work focuses on the characterization of narrow vertical cracks of finite size using optically excited lock-in thermography (OLT). To characterize these cracks, we need to solve an ill-posed inverse problem. As a previous step to the solution of this inverse problem, we propose a sensitivity analysis to quantify the influence that the parameters involved in the model have on the surface temperature. Some of these parameters are estimated at the laboratory and they incorporate uncertainty that may severely affect the reconstruction of thin cracks. For this reason, we design a calibration criterion based on the sensitivity analysis to determine which parameters we need to include as unknowns of the inverse problem. We perform this analysis using a numerical discontinuous Galerkin method. Additionally, we propose a theoretical noise model for the thermograms. Then, we use a weighted least square method (WLS) to determine the parameters from the experimental thermograms. We also obtain a theoretical uncertainty of the reconstructed parameters in OLT-WLS fitting according to the used surface temperature dataset. Finally, we perform a numerical experiment with a 2.4 m-thick vertical crack to show the sensitivities of the surface temperature with respect to the model parameters. We also determine the uncertainty of the parameters under different datasets with known noise characteristics. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This work focuses on characterizing narrow vertical cracks of finite size using optically excited lock-in thermography, proposing a sensitivity analysis to quantify the influence of model parameters on surface temperature, and utilizing numerical methods and weighted least squares to determine and reconstruct parameters. Theoretical uncertainty of reconstructed parameters and surface temperature sensitivities are explored, along with a numerical experiment to validate the findings.