## 4 Results and Discussions
### Scenario I: Gap Detection  
The investigation results of gap detection are presented in Figures 5 and 6. Figure 5a shows the average accuracy over varying segment durations, while the average confusion matrices are shown for a selected set of durations in Figure 5b. In Figure 6, a set of clustering results are presented as examples. Figure 5a demonstrates that overall the accuracy of both sensor types steadily increases with duration until it starts to converge from a certain saturation point. This suggests that the segments longer than such saturation point can be shortened without loss of weld-relevant information. The saturation point, however, varies depending on the sensor type. Specifically, the saturation points of the structure-borne sensor signals (SB1) and the airborne sensor signals (AB) are around 50 ms and 25 ms, respectively. This difference in their saturation behavior accounts for their performance difference. If segments are longer than 40 ms, structure-borne sensor signals (SB1) slightly outperform the airborne sensor signals (AB), resulting in the maximum accuracy of 95% for the structure-borne sensor and 92.5% for the airborne sensor. This can be attributed to the information loss in higher frequencies due to attenuation in air, as shown in Figure 3. For the segments shorter than 40 ms, however, there seems to be no significant difference in performance among different sensors. If a segment is shorter than 5 ms, the accuracy of both sensors drops sharply, indicating the difficulty in extracting the weld-relevant information. A similar behavior can be observed in the confusion matrices, too (Figure 5b). Comparing the results of 100 ms and 50 ms, the difference seems to be marginal for both structure-borne sensor signals (SB1) and airborne sensor signals (AB). This again suggests that 50 ms suffices to extract the same amount of the information contained in a 100 ms segment, which enables almost 90% accuracy to distinguish Zero Gap and Gap joints. If the segments \begin{table}
\begin{tabular}{c c c} \hline \hline
**Operation** & **Parameter** & **Value** \\ \hline RLT validation & Number of iterations & 50 \\  & Segment durations & 1...100 ms \\  & Scenario I & 120 segments per class \\  & Scenario II & 30 segments per class \\  & Data split ratio & 67\% training \\  & & 33\% test \\ STFT & Sampling frequency & 6 MHz \\  & Frequency bins & 2048 \\  & Time window & 2048 samples (\(\approx\)0.341 ms) \\  & Window type & Hanning window \\  & Overlap & 50\% \\ NCA & Initialization & linear discriminant analysis \\  & Input size & 2048 \\  & Output size & \(N_{\text{class}}-1\) \\ kNN & k & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Validation parameter valuesare shorter than 5 ms, misclassification of noise segments starts to increase, also signifying that extracting the relevant information becomes more challenging. Figure 6 provides more insights into the segment separability. As an example, a set of NCA clustering results are shown for 100 ms, 50 ms, 5 ms and 1 ms segments. Here, clustering was computed using the test set, which is not used for training. In general, the distance between clusters increases with segment duration. This suggests that longer segments contain sufficient weld-relevant information, which allows NCA to learn an appropriate transformation of the segments. Comparing the separability of 100 ms and 50 ms segments in Figure 6, the separation of clusters is strikingly similar, which also indicates that the same amount of the information is preserved even if signal segments are halved from 100 ms to 50 ms. Another finding is that the clusters of the airborne sensor segments (AB) are located closer to each other than those of the structure-borne sensor segments (SB1). These results also imply that there seems to be more weld-relevant information available in the structure-borne signals when it comes to detecting joint gaps. Figure 5: Illustration of how the gap detection accuracy changes depending on the segment duration \(T\).