## 3 ML Algorithm Steps
### Feature Extraction  
The primary target of any feature extraction plan is the derivation of a suitable set of condition indicators in vector form from the original signal vector. These derived features are intended to be informative for the machine learning exercise [42]. The conventional feature extraction procedures can be divided into two main categories: statistical characteristics and syntactic descriptions; on the assumption of a transient signal, statistical features have proven their ability in revealing the latent discrepancies.  
Since statistical formulas can reveal non-linear features and the captured waves in the present study are transient, several statistical features were extracted from each signal.  
Statistical features can be extracted either directly from the original signal in the time domain or following a processing (transformation) step. The aforementioned processing can be performed using five well-known methods, including Fast Fourier transform (FFT), Wavelet Transform (WT), eigenvectors, time-frequency distributions, and autoregressive method [43].  
Figure 10: Comparison of the received pristine signal (solid line) and damaged signals (dotted lines) for all S-Classes.  
The feature extraction process for use in deep neural networks or machine learning classifiers can be performed manually or automatically. [PERSON] et al. [44] demonstrated that, if the parameters and features are extracted and selected correctly in a manual feature extraction and selection method, the final accuracy of the classification procedure can be even higher than the automatic process, despite the widespread belief that automatic feature extraction and selection, which is primarily used in deep neural networks, has superior performance.  
There are two main ways to use an ML classifier in this context. On the one hand, the time-series signal can be directly fed into the classifier, and the most beneficial features can then be automatically extracted via a dimension reduction technique such as Principal Component Analysis (PCA), or Linear Discriminant Analysis (LDA) [45]. On the other hand, a feature vector can be manually extracted from each signal, whether in the time, frequency, or time-frequency domain, and then added to a classifier [46]. Although finding a suitable feature in the latter case is a specialized task and implies full knowledge about the nature of the signal, the required computational capacity after the feature extraction step is much lower than the mentioned dimension reduction methods. Features such as statistical, entropy, amplitude of frequency components, and wavelet coefficients can be extracted based on the nature of the signal [47].  
Since the sampling frequency is 200 MHz, the dimension of each signal in the time domain is 1 \(\times\) 40,000, so adding it to an ML classifier without extracting the suitable features can pose computational challenges.  
In the pursuit of discerning the presence and location of the damage, i.e., the R-Classification, a dataset comprising 160 samples was built (40 different and random faults for each of the four regions \"Ri\" (Figure 7b)). For each sample test, 120 features were extracted in time, frequency, and time-frequency domain, i.e., 30 features for the signal of each of the 4 channels (sensors). The amplitudes of some of the features listed in Table 2 were found to be significantly higher than others. For example, the average value of the MDET1 vector for sensor 2 was \(-6.31\times 10^{-19}\), while the mean value of the SFDR vector for sensor 3 was equal to 62.05. To ensure impartiality in the classification phase and prevent bias due to large magnitudes, it is necessary to scale the feature vectors. This entailed rescaling all 120 feature vectors to fall within the range [0, 1].  
In order to get information on the size of the damage, i.e., the S-Classification, the same set of features as listed in Table 2 was extracted. In this case, for the feature extraction phase, the full length of the signals was selected.