## 3 ML Algorithm Steps
### Signal Pre-Processing (Denoising)  
In this initial phase, collected data undergoes pre-processing for both classification procedures in order to prepare it for the next steps. Concretely, as a result of the experimental acquisitions, signals may contain noises that can threaten the effectiveness of the ML procedure, thus necessitating dedicated attention. Noise can be broadly categorized into two fundamental types: random noise and coherent noise [39]. While the period and, therefore, the frequency, can be precisely measured in coherent (purely periodic) noise, in random (non-periodic) noise the frequency can only be roughly determined, for example between a frequency band. As a result, based on the frequency of the original captured signal, random noise can be categorized as either high-frequency or low-frequency. A significant diversity of high-frequency noise originates from electronics, leading to the potential inclusion of noise generated by sources such as wires and electronic boards in the recorded signal if an analog filter is not present in the data acquisition system. Therefore, noise reduction plays a fundamental role in almost all experimental works in the field of signal processing. An inadequate management of the noise can adversely affect the feature extraction and machine learning steps. As a matter of fact, high-frequency noise was found to affect the recorded signals in the present investigations. The absence of an analog filter in oscilloscopes causes this particular type of noise, which has an electrical origin. It can stream from the oscilloscopes' circuits, nearby cables or conductors [40], and can be eliminated or at the very least diminished at the first stage of the signal processing step by using a suitable digital noise reduction technique. In this paper, different noise-reduction methods were investigated, including the Wavelet Transform (WT), a combination of Savitzky-Golay and Baseline filters (S-G and Baseline), and the Butterworth filter. It was found that the low-pass Butterworth filter [41] provided the most favorable results in terms of noise reduction, while retaining damage-related information. It is worth noting that in this process the filter is in order 4, and the cut-off corner frequency is equal to 0.01 Hz (the optimized parameters were obtained through an iterative process). Figure 9a showcases the raw noisy signals from an undamaged plate, along with its noise-reduced versions produced by the WT (Figure 9b), S-G and Baseline (Figure 9c), and Butterworth filters (Figure 9d). Figure 9: Comparison of various noise-reduction techniques for the undamaged plate signal. As can be observed from Figure 9, it is clear that the high-frequency noise in the signal was stringently eliminated by the Butterworth filter, whereas the low-frequency components are preserved for the feature extraction step. Figure 10 reveals a comparison between the signal obtained from a pristine configuration (solid line) and the signals collected by receiver S2 in a specific damage configuration (e.g., a specific region of the plate) for each cuboid size (dotted lines). At first glance, all signals appear largely, with no discernible differences. However, by thoroughly analyzing the data (zoomed area in the black circle), some discrepancies can be qualitatively observed: the different damage sizes determine different effects on the signals in terms of both signal amplitude and phase with respect to the pristine one. A first, expedient method for quantitatively discerning damage-related attributes is to extract the damage indices. The DIs set permits the straightforward identification of the most critical path, i.e., the path closest to the possible identified damage. For the example reported in Figure 10, the obtained values along the actuator S-C--receiver S2 path are 0.102, 0.105 and 0.109 for S-Class 1, 2, and 3, respectively.