## 3 Dataset and Cluster Analysis  
### Signal Analysis  
In this section, measurement data are briefly analyzed based on their spectrograms. A set of exemplary results are shown in Figure 3, where two metal sheets with two 0.3 mm gaps (Figure 1) are welded using a laser beam. For the purpose of visualization, two sensor signals are selected: the structure-borne sensor placed at the beginning of the specimen (SB1) and the airborne ultrasound sensor (AB). For computing the spectrograms, we used 2048 frequency bins with a window size of 2048, which is equivalent to 0.328 ms. The window type used here is the Hanning window [23] with an overlap of 50%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Type** & **Specifications** & **Distance** \\ \hline IZFP RI-MA71 RC & Airborne & Center frequency: 520 kHz & \\ (AB) & ultrasound & Transducer diameter: 23 mm & \(a_{\mathrm{mic}}=297\,\mathrm{mm}\) \\  & sensor & Focal point: 50 mm & \\ QASS QWT sensors & Structure borne & & \\ (SB1: at the start, & ultrasound & Max frequency: 100 MHz & \(a_{\mathrm{sensor}}=114\,\mathrm{mm}\) \\ SB2: at the end) & sensor & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical specifications of the used airborne and structure-borne-sound sensors. Figure 2: Experimental setup: (**a**) schematic illustration and (**b**) actual photograph of the set up. In general, the acoustic process emissions consist of four types of signals: signals correlated with properly welded joints in the Zero Gap sections, signals correlated with erroneous joints in the Gap sections, the acoustic emissions from the robotic arm movement and the environmental noise. In this work, the former two signals are denoted as weld-relevant signals, from which the information relevant to the welding process is attainable, and the latter two as the ambient noise. As mentioned in Section 2.2, acoustic emissions from a cross jet are not included in this study. Our results in Figure 3a,b show that the weld-relevant signals are present below 400 kHz in the structure-borne sensor signal (SB1). In the airborne sensor signal (AB), the frequency range for the same information is reduced to below 125 kHz due to attenuation in the air (Figure 3c,d). Above those ranges, no weld-relevant signals can be visually perceived in the spectrograms for both sensor types. However, the relevant frequency range should be selected with care. To determine the frequency range, a significant reduction in the signal energy of interest needs to be identified. However, such reduction cannot be identified meaningfully without filtering out the ambient noise. It is even reported that some intrinsic changes in the signals are not easily perceptible for visual inspections [12]. Furthermore, weld-relevant signals were reported to be clearly observed in the frequencies above 1 MHz, when the measurements were conducted using three different types of steels (DC04, DX51D, and S235 JR+Z) with a focus spot diameter of 600 um and the laser power of 2 kW at the welding speed of 1.2 m/min [16]. Unquestionably, the selection of specimen materials and/or the measurement configurations highly affect the frequency range. Yet, these  
Figure 3: Exemplary measurement results of a specimen with 0.3 mm gaps. Top row (**a,b**): the spectrograms of the structure-borne sensor signal placed at the beginning of the specimen (SB1), bottom row (**c,d**): the spectrograms of the airborne sensor signal (AB). For both rows, the entire frequency range (approximately 3.125 MHz) is shown in the left column, whereas the lower frequency range (\(<\)760 kHz) is presented in the right column. Here, the measurement data up to 1.3 s are shown for the sake of presentation. suggest that there may be relevant information in higher frequencies of our measurement data, which is not visually observable in their spectrograms. Nevertheless, visual inspection of the spectrograms can further confirm the correlation between the acoustic process emissions and the presence of a butt-joint gap or lack thereof.