## 4 Experimental Applications
### Cross-Comparison of the Estimated Weld Models  
Thanks to the two mock-ups being sampled from a same weld, we can perform a cross-comparison of the results. In a first step, the 100 weld models obtained with the OL0\({}^{\circ}\) inspection are compared with the 100 weld models resulting from the OL60\({}^{\circ}\) inspection in order to find a common model. The second step consists in applying the reconstruction models obtained for the 100 trials in the OL0\({}^{\circ}\) case to the signals recorded with the OL60\({}^{\circ}\) case, and vice-versa. In order to determine common models, a tolerance error is defined that indicates the minimum admissible difference for models to be similar. This criterion is set to 10 GPa for the elastic components, 0.5 mm for \(D_{1,2}\), 3\({}^{\circ}\) for both \(\alpha_{1,2}\) and \(\zeta\), and 0.25 A.U. for both \(T_{1,2}\) and \(\eta_{1,2}\). However, after comparison, none of the models satisfies the fixed tolerance error, which means that no model is common to the results of the 100 optimization trials in the OL0\({}^{\circ}\) case and to the 100 trials in the OL60\({}^{\circ}\) case. The dispersion of the results is here again too large to find a common model. Let us consider now the 100 weld models obtained from the OL0\({}^{\circ}\) inspection and apply them to the set of signals recorded with the OL60\({}^{\circ}\) configuration. It turns out that none of the models produces a satisfactory image. On the contrary, the images are as degraded as with an isotropic reconstruction model. An example is presented in Figure 9(b). Nonetheless, if we consider the 100 weld models resulting from the OL60\({}^{\circ}\) inspection and apply them to images computed with the OL0\({}^{\circ}\) acquisition, we find that one model is able to correct the image with the OL0\({}^{\circ}\) configuration. This image is displayed in Figure 9(a) and the associated weld model parameters are indicated in Table 5. It would be interesting to compare these values with those resulting from another experimental characterization setup to see how realistic or unrealistic these results are. Figure 9: Slowness curves of QL waves estimated with PSO (**a**): slowness curves for the OL0\({}^{\circ}\) inspection (red), the OL60\({}^{\circ}\) inspection (purple) and the base material (orange). Table of the material properties values after optimization (**b**). This experimental application of the optimization procedure confirms the results of the numerical study: the optimization is very efficient in correcting the degradation of TFM images and produces high quality images, but the weld model parameters cannot be accurately estimated as the optimization only relies on the observation of a single isolated defect. In this section, two samples extracted from the same weld were considered, however the dispersion of the estimated weld parameters is too strong to find a common model between both cases. At the end, only one model is able to both correct the images of the inside of the two samples. Figure 10: Images in a 316L stainless steel V-shape weld with experimental signals: images computed from the acquisition with the OL0\({}^{\circ}\) experimental setup and by using a weld model provided by the optimization of the image for the OL60\({}^{\circ}\) configuration (**a**); image from the OL60\({}^{\circ}\) configuration computed with a weld model resulting from the optimization of the image for the OL0\({}^{\circ}\) configuration (**b**). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **OL60\({}^{\circ}\) Estimated Values** \\ \hline C\({}_{11}\) (GPa) & 229 \\ C\({}_{13}\) (GPa) & 137 \\ C\({}_{33}\) (GPa) & 257 \\ C\({}_{55}\) (GPa) & 129 \\ \hline \(T_{1}\) (A.U.) & 1.1 \\ \(T_{2}\) (A.U.) & 1.0 \\ \(D_{1}\) (mm) & 3.7 \\ \(D_{2}\) (mm) & 0.6 \\ \(\alpha_{1}\) (\({}^{\circ}\)) & 32.1 \\ \(\alpha_{2}\) (\({}^{\circ}\)) & 5.0 \\ \(\eta_{1}\) (A.U.) & 0.8 \\ \(\eta_{2}\) (A.U.) & 1.1 \\ \hline \(\xi\) (\({}^{\circ}\)) & \(-\)28.5 \\ \hline \hline \end{tabular}
\end{table}