# Acoustic Emission-Based Method for IFSS Characterization in Single-Fiber Fragmentation Tests
## 2 Materials and Methods
### Fragment Count: AE Method  
Fragment generation in the sample can be quantified by detecting bursts in the AE signal measured during tensile testing. The conventional approach for this purpose is the fixed threshold method; however, it presents significant limitations when applied to AE signals with a high density of bursts occurring within a short time window. When two or more bursts occur sufficiently close in time, they may be interpreted as a single, large event, resulting in the loss of information associated with individual events. Since fracture events do not follow any periodic pattern, it cannot be ensured that the bursts generated by fiber breakage will be sufficiently separated in time to be individually detected using the fixed threshold method. [PERSON] [31] proposed a burst detection method designed to accurately identify events under such AE signal conditions. The core premise of this approach is the progressive simplification of the AE signal to obtain a triangular envelope, which enables the identification of individual bursts contained within the signal. The processed signal is generated by applying a series of processing steps, as shown in Figure 3.  
* Step 1: An envelope of the raw AE signal is obtained by calculating the norm of the Hilbert transform on a logarithmic scale. This process reduces the difference between high and low-amplitude AE-bursts, thus enhancing their detectability.
* Step 2: A smoothing process is applied to reduce small fluctuations present in the signal obtained in Step 1. Smoothing is achieved by averaging the signal points using a moving window.
* Step 3: Eliminate all points in the signal obtained in the previous step that do not correspond to peaks. Since AE signals are measured at a high sampling rate, this process is performed twice to ensure the removal of non-relevant points for burst detection.
* Step 4: Apply a second smoothing using the same method as in Step 2.
* Step 5: The points of the signal that do not correspond to peaks or valleys are removed. Then, using a \"local threshold\" value, each point is compared with its neighborhood.  
Figure 3: Burst detection method: triangular envelope.  
If the amplitude difference between two neighboring points is smaller than the local threshold, the point with the smaller amplitude is removed, which helps to simplify the signal and improve the burst detection.  
Step 5 is applied iteratively using progressively increasing values of the local threshold. The resulting signal from this process is an envelope composed of triangles, where each triangle with a peak amplitude exceeding a predefined detection threshold is identified as a burst. The start and end times of each triangle in the triangular envelope are obtained, and these values are used to extract the corresponding burst from the raw AE signal. Once the multiple AE-bursts have been identified, their number is counted for the IFSS calculation. The processing parameters of this method are the window size (Steps 2 and 4), the local threshold value (Step 5), and the detection threshold (Step 5). For burst detection in the AE signals measured during the tests of this study, a window size of 10 points is used. The local threshold is set at 35% of the maximum AE amplitude, and the detection threshold is defined as 0.005 V.