# Multiparameter Approach for Damage Propagation Analysis in Fiber-Reinforced Polymer Composites
## 2 Experimental Procedure
### Fuzzy c-Means Data Clustering Results  
The I-Frequency and R-Frequency with respect to the different amplitudes of the recorded AE events were clustered using the FCM clustering technique. Initially, for selecting the optimal number of clusters, the Davies-Bouldin Index (DBI) was calculated for the abovementioned data. The DBI with the minimum value for the different clusters \(N=1,2,\ldots,6\) is supposed to be selected as the optimal number of clusters. For all sets of data recorded for SLS 1, SLS 2, and SLS 3, the DBI returned the lowest value for \(N=3\). The FCM was used for clustering I-Frequency and R-Frequency into three clusters. The clustered data of I-Frequency and R-Frequency with respect to amplitude is presented in Figures 5 and 6, respectively, for all SLS specimens. Figure 5: I-Frequency vs. amplitude plotted as three clusters using FCM for the (**a**) SLS 1, (**b**) SLS 2, and (**c**) SLS 3 specimens. The clustered data in Figure 5 shows that despite the peak amplitude level, the R-frequency of the recorded waveforms varied significantly. Similar results are also observed in Figure 6 for the R-Frequency. Furthermore, the frequency levels for I-Frequency and R-Frequency in Figures 5 and 6 were not very similar for all the AE signals. They differed significantly in several instances. For example, in Figure 5a,b, which shows the I-Frequency of the recorded signals, there were very few AE events recorded between the frequencies of 100 and 200 kHz in cluster 2, and even less AE signals between 100 and 300 kHz below 90 dB in cluster 3. However, in Figure 6a,b, which shows the R-Frequency, the number of AE signals in the frequency range of 100 to 300 kHz was significantly higher. This also meant that the frequency rate of absorption, which can be indicated by the R-Frequency, varied significantly from the I-Frequency. A question may arise: why did the I-Frequency range from 0 to 1000 kHz, while the R-Frequency was only below 500 kHz. The I-Frequency was calculated using Equation (4), which is the ratio of P.Counts to the rise time. If the second or third count of the AE waveform has the largest amplitude, then P.Counts is counted as 1 or 2, respectively. This also means that there was a huge possibility that the rise time could be very short during these instances. By considering the large differences between the short duration of the rise time and the duration of the AE signal, the variation between the I-Frequency and R-Frequency was quite common. This was the reason for the wide range of I-Frequency compared to the R-Frequency. The I-Frequency clusters can be classified as follows: cluster 1 had AE signals with a low amplitude but with the I-Frequency spread between 0 and 1000 kHz; cluster 2 had AE  
Figure 6: R-Frequency vs. amplitude plotted as three clusters using FCM for the (**a**) SLS 1, (**b**) SLS 2, and (**c**) SLS 3 specimens. signals with a moderate amplitude (mostly between 55 and 75/80 dB) with the I-Frequency spread between 0 and 700 kHz; cluster 3 had the signals with higher amplitude (>75/80 dB) but with the I-Frequency spread between 0 and 500 kHz, ignoring the outliers. Since I-Frequency is inversely proportional to the rise time, it can be used as a parameter for classifying the type of damage mode that the AE signals have as their source. Several reports have indicated that the AE signals with a larger peak amplitude and a shorter rise time correspond to an interlaminar crack as the source, while the signals with a smaller peak amplitude and a longer rise time may correspond to the shearing mode under tensile loading. Analogous with these observations, the differences between the shearing mode and the interlaminar crack can be identified [3,5,7]. A detailed explanation of how to identify the damage sources is presented in the next section. The R-Frequency represents the amount of absorption of the AE signals. The AE signals generally propagate in two different modes: symmetrical and asymmetrical.