# Welding Bead Inspection Using Image and Multi-Sensor Fusion
## 4 Experimental Results
### Experiment Results  
First, experiments were conducted separately for the sensor inspection, image inspection, and the combined inspection method proposed in this study, and the results are shown in Table 2. For the good samples, all three inspection methods accurately classified them as good. However, in the sensor inspection, one bad sample was not classified, and in the image inspection, two bad samples were not classified. In contrast, the combined inspection method successfully classified all the bad samples. The results of the image inspection performed in this study are shown in Figures 6-8. Figure 6 shows the results of testing the good samples, where Figure 6a,c represent the ROI of the welding bead, Figure 6b shows the result of detecting the welding bead from Figure 6a, and Figure 6d shows the result of detecting the welding bead from Figure 6c. Figure 7 displays the results of testing the bad samples, where Figure 7a,c represent the detected width of the welding bead, and Figure 7b,d represent the detected height. As observed in the results of the image inspection, some measurement errors occurred, but it was possible to detect the significant width and height of the welding bead. On the other hand, Figure 8 shows two bad samples that were not classified during the image inspection experiments. In other words, these are incorrectly inspected image results. Figure 8a,c represent the results of detecting the width of the welding bead, while Figure 8b,d represent the results of detecting its height. As evident from the experimental results in Figure 8, it was possible to detect the width of the welding bead, but its height remained undetected. Consequently, in image inspection, what was actually 'bad' was misclassified as 'good' in the inspection results. This was attributed to the small size of the welding beads and the high brightness values of the base material, resulting in a small difference between \(MB_{[min(pixel)]}\) and \(MB_{[max(pixel)]}\) in the image histogram, as shown in Figure 4.  
Based on the confusion matrix, we calculated several evaluation metrics, such as accuracy, precision, recall, and F1 score, using the following formulas:  
\[\text{Accuracy}=(TP+TN)/(TP+TN+FP+FN), \tag{9}\]  
\[\text{Precision}=TP/(TP+FP), \tag{10}\]  
\[\text{Recall}=TP/(TP+FN), \tag{11}\]  
\[\text{F1 score}=2\times\{(Precision\times Recall)/(Precision+Recall)\}. \tag{12}\]  
We calculated the performance metrics outlined in Table 2 using the four evaluation metrics mentioned above, and the results are shown in Table 3. In sensor inspection, image inspection, and combined inspection, all performance metric values exceeded 99%, with computation times of 2 s, 27 s, and 26 s, respectively. This indicates that each inspection method individually achieved a sufficiently high performance. However, the combined method of the two inspection approaches allowed for the accurate classification of all experimental data. In addition, when conducting sensor inspection alone, it only took 2 s, but when combining image inspection into the combined inspection, it can be concluded that there was only a slight improvement in performance, while significantly sacrificing in terms of its speed. However, it is crucial to verify whether the welding bead is properly placed (position) and whether the width and size of the welding bead are consistent (shape), as it is related to its safety. When using sensor inspection alone, it was not possible to confirm the location and shape of the welding. Therefore, when conducting sensor and image inspections together, it was possible to perform accurate inspections. Furthermore, in order to increase the speed of image inspection, we reduced the resolution. However, due to its reduced accuracy, we analyzed it at a size of 256 \(\times\) 256. Therefore, the proposed  
Figure 8: Experimental results of the proposed method for misclassified bad products. (**a**) Vertical direction inspection of bad-3. (**b**) Horizontal direction inspection of bad-3. (**c**) Vertical direction inspection of bad-4.