## 4 Results and Discussions
### Scenario II: Identification of Gap Size
#### 4.3.2 Separability Analysis Using Relative Recall  
Contrary to Scenario I, visualizing the separability of five classes is not trivial as the clustering outputs consist of four features, requiring 4D plots. However, considering only two classes at a time enables to handle the classification results as that of binary classification. One metric to evaluate binary classification is recall, also known as the true positive rate. The recall is essentially a ratio of the true positive to all positive predictions. As an example, consider the confusion matrix of the structure-borne sensor (SB1) for 25 ms shown in Figure 7b. Its relative recall of the Gap 0.1 class with respect to Zero Gap one can be computed as \(\frac{0.76}{(0.76+0.16)}=0.826\). The reason for using recall to evaluate the class separability is that the relative recall represents the misclassification rate. If, for instance, Gap 0.1 segments tend to be misclassified as Zero Gap one, then the Gap 0.1 cluster is likely to be very close to the Zero Gap cluster than other clusters whose misclassification rate is low. This means that a high relative recall indicates good separability of the reference class from another one and vice versa. The relative recall results over varying durations are presented in Figure 8. Figure 8a shows the relative recall with respect to the Zero Gap class, aiming to demonstrate how separable the Zero Gap cluster is from the other classes. Using the same analogy, Figure 8b presents the relative recall with respect to the Noise class. Focusing on the results shown in Figure 8a, two things are common for both sensor types. First, the Gap 0.1 segments seem to be very difficult to distinguish from the Zero Gap ones. Here, even 100 ms segments can achieve only around 85% recall, demonstrating that making a segment longer does not necessarily increase the sensitivity with regard to the gap size. This can be attributed to two factors. On the one hand, the actual gap size of Zero Gap patches is not exactly zero, as discussed in Section 3.1, making the distinction between these two classes ambiguous. On the other hand, the laser spot diameter (0.6 mm) is large relative to the gap size of 0.1 mm. Such a relatively large laser beam can ignore a small-sized gap and may produce acoustic process emissions very similar to the one that is produced with Zero Gap joints. Another finding is that the relative recall of the Gap 0.3 class is and remains very high up to 1 ms. This suggests high separability of the Zero Gap and the Gap 0.3 clusters. This is also true for the Noise class, yet its recall reduces slightly more than that of the Gap 0.3 class if the segments are shorter than 5 ms.  
A striking difference among different sensor types can be observed with the relative recall of the Gap 0.2 class. In the same way as the confusion matrices, the structure-borne sensor signal (SB1) exhibits a much lower recall regardless of the segment duration. This is suspected to result from the aforementioned inconsistency in the signals. In contrast, the airborne sensor signals (AB) yield a very high recall of the Gap 0.2 class, indicating that the Zero Gap class is also well separable from the Gap 0.2 class. Comparing the airborne sensor results (AB) of the Gap 0.2 and the Gap 0.3 class, the Zero Gap cluster seems slightly closer to the Gap 0.2 cluster than to the Gap 0.3 one. The same behavior can be seen in the relative recall of the Gap 0.2 class with respect to the Noise class in Figure 8b. Here again the structure-borne sensor signals (SB1) yield a much lower recall of the Gap 0.2 class than other classes, exhibiting the difficulty in correctly classifying the Gap 0.2 segments. Considering its relative recall to the Zero Gap as well, it is highly likely that the Gap 0.2 data have a larger variance than other classes. For the rest of the classes, the relative recall with respect to the Noise class is very high (>97.5%) up to 10 ms.