## 4 Results and Discussion  
### Acoustic Emission Data Preprocessing  
As mentioned in the previous section, the AE signals for this study were obtained from an AE acquisition system during steel sphere impact testing. Figure 5 presents four typical AE signal waveforms recorded in the impact experiment. The difference in the AE waveform pattern can be related to the difference in the impact location and the distance between the sensors. AE signals were subsequently processed to extract relevant features from the AE waveform. The purpose of extracting these features was to distill the complex information embedded within the signal into a set of specific, representative values that effectively capture the properties of the AE signal. In the present study, a total of 15 key features, including count, signal strength, and reverberation frequency, were derived from the initial signal. Count refers to the number of threshold crossings in the AE signal. In simpler terms, it is a measure of how many times the signal goes beyond a certain predefined limit, which can indicate the intensity of the emission. Signal strength is essentially the integral of the rectified voltage signal over the waveform duration. It provides a quantitative measure of the overall \"energy\" present in the AE signal. This feature is essential in understanding the severity of the impact or event causing the emission. Reverberation frequency is the frequency after the peak of the AE signal. Essentially, it is the dominant frequency that persists after the initial, most intense portion of the signal has passed. This feature can provide insights into the nature of the event causing the emission, as different events can have different reverberation characteristics.  
A comprehensive list of all features, along with their descriptions, is provided in Table 1. These 15 features were selected as they have shown the good performance of source locations [17]. The linear regression and random forest models proposed in this study were applied to an input dataset composed of 1200 samples, each encompassing all 15 extracted features.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parametric Features** & **Feature Descriptions** \\ \hline Amplitude & The highest magnitude observed in the AE waveform. \\ Average signal level (ASL) & The effective voltage with a characteristic time \(T_{ASL}\). \\ Root mean square (RMS) & The effective voltage with a characteristic time \(T_{RMS}\). \\ Energy & Quantification of the electrical energy contained within an AE signal. \\ Signal strength & The integral of the rectified voltage signal over the waveform duration. \\ Absolute energy & The absolute magnitude of electrical energy measured in an AE signal. \\ Rise time & The duration between the initial threshold crossing and the peak. \\ Duration & The time span encompassing the first and last threshold crossings. \\ Count & The count of instances where the signal crosses a predefined threshold. \\ Counts to peak (PCNTs) & The number of threshold crossings from the first crossing to the peak. \\ Average frequency & A parameter used to describe the overall frequency content of an AE signal. \\ Peak frequency & The frequency at which the signal exhibits its highest contribution. \\ Frequency centroid & A parameter used to characterize the overall frequency distribution or spectral content of an AE signal. \\ Reverberation frequency & The dominant frequency that persists after the initial, most intense portion of the signal has passed. \\ Initial frequency & The dominant frequency observed before the peak. \\ \hline \hline \end{tabular}
\end{table}
Table 1: AE features and their descriptions.  
Figure 5: The typical AE waveforms generated by the impact.