# Deep Learning Based Inversion of Locally Anisotropic Weld Properties from Ultrasonic Array Data
## 3 Results
#### TFM Reconstruction Results
However there are high levels of spatially coherent noise away from the true defect locations, which can be attributed to defocussing of the energy caused by the use of incorrect delay laws. Note that there appears to be no obvious third reflection in the image corresponding to defect C (although there is a small peak in intensity 2 mm to the left of its known location). The TFM+ algorithm was then used in conjunction with the predicted grain orientation map generated from application of the model trained DNN to the FE generated ToF data, in the pulse-echo configuration (that is we use the tomographically reconstructed grain orientation map corresponding to the plot in bottom right image of Figure 8). The travel time fields through this predicted model were calculated using the AMSFMM algorithm, and these were then used in Equation (5) to construct the TFM+ image (shown in Figure 9c, left image). The resulting image shows three clear peaks in image intensity \(I\) corresponding to the three defects present, where the upper boundary of each defect is accurately depicted (due to the size of these defects we would expect the reflections to align with the upper defect edge as this is what is illuminated by the array inspection). The signal-to-noise ratio (SNR) is calculated for both the TFM and TFM+ images within a 5 \(\times\) 5 mm window surrounding each defect, where the maximum within the window is divided by the mean of the values in the window. These values are provided in Table 2, with improvements in SNR given by the TFM+ algorithm of 2.6 and 5.3 dB for defects A and C, respectively. The SNR values for flaw B are consistent in both images. However note that this flaw lies centrally in the weld where there is little variation in grain orientation on the direct path and so the TFM in which a constant wavespeed is assumed performs very well here and the TFM+ does not improve upon the SNR. However, an improvement in axial spreading in the defect reconstruction can be observed across all three defects when the TFM+ is applied. Figure 9: (**a**) Schematics of the FEA simulations using the pulse-echo transducer array configuration of a weld region parameterised with the Test Model 1 grain orientations shown in Figure 6. On the left: three circular defects (labelled A, B and C) with 2 mm diameter are embedded within the weld. On the right: the model is embedded with a crack with length 4 mm and angled at 45\({}^{\circ}\) to simulate a lack of fusion defect at the parent weld interface. Image (**b**) arises from the application of the TFM algorithm in which a constant wave speed is assumed throughout the domain. Image (**c**) uses the TFM+ algorithm, exploiting the predicted grain orientations arising from application of the DNN to the FEA data generated by simulation of the pulse-echo inspection as depicted in Figure 8. The known boundaries of the defects are represented by the white circles. To further examine the improvements achieved when the DNN predicted map is used to correct the TFM delay laws, the simulation was run again in which the only change was the removal of the three circular defects and the embedding of a crack with length 4 mm and angled at 45\({}^{\circ}\) along the parent weld interface (Figure 9a, right hand image). A comparison between the TFM and TFM+ images can be seen in Figure 9b,c (right hand images). A significant improvement in the characterisation of the crack as a planar defect is observed when the grain map is accounted for. Furthermore, the location of the defect is more reliably portrayed and there is an improvement in SNR of 2.2 dB. These results highlight the improvements which can be achieved when the grain orientation map is accounted for.