# Multiparameter Approach for Damage Propagation Analysis in Fiber-Reinforced Polymer Composites
## 2 Experimental Procedure
### Methodology for Data Clustering  
The different AE features provide the characteristic representation of the acoustic waveform. Many of these AE features are closely related to one another. For example, the absolute energy of the AE signal and the ASL are in direct relationship with the RMS voltage. Absolute energy is directly proportional to the square of the RMS voltage, while ASL is analogous to RMS voltage, with the only difference being that RMS voltage is measured in millivolts or microvolts, whereas ASL is measured in decibels. As such, using both RMS voltage and ASL for analyzing the signal characteristics is redundant. PCA is a multivariable data reduction technique. The core idea of PCA is to reduce the dimensionally of a dataset that has a large number of interrelated variables, which is essentially the case in this research work. The data reduction is done while retaining as much of the variation present in the dataset as possible. The data reduction is achieved by reducing the data dimensions into new correlated features called principal components, which are minimally correlated. These principal components form a symmetric matrix, where the eigenvectors of the matrix form the elements of the matrix. These eigenvectors can be defined as the characteristic vectors of the matrix. They are unique in the sense that they remain directionally invariant under linear transformation by its parent matrix. The other details about this analysis can be found in the source article presented by [PERSON] (1976). The procedure for calculating the principal components is summarized by [PERSON] and [PERSON] [PERSON] and [PERSON] (1988). The multiple parameters were reduced using PCA and the characteristic parameters were selected for analysis. Then, these selected parameters were clustered using the fuzzy c-means (FCM) data clustering method. The FCM is a data clustering method for any two-dimensional data. The dataset is clustered into a predefined number of clusters in FCM (K  
It can also be observed from Figure 4 that the I-Frequency, R-Frequency, and A-Frequency had large variations in their eigenvalues for PC 1 and PC 2 and could not be constituted into a group. This means that there existed a large variation in these parameters. Therefore, the I-Frequency and R-Frequency were considered for the analysis. From the PCA results, three parameters from the initially assigned group of six parameters were selected: amplitude, I-Frequency, and R-Frequency. Instead of going through a rigorous process of analyzing all the parameters and finding the optimal parameters for analysis, the PCA reduced the dimensionality of the dataset into three parameters. For comparison purposes, the amplitude from the ASL, amplitude, and P-Frequency group was compared with I-Frequency and R-Frequency. There was a specific reason for comparing the amplitude with these two parameters. For several years in the research of damage assessments using AE, the peak amplitude values were directly related to the damage modes. For instance, the most general trend was that the AE signals with an amplitude above 60-70 dB represent fiber breakage, 35-50 dB  
Figure 4: Principal components PC 1 and PC 2 for all the parameters selected for all specimens. Figure 3: Scree plot for the different principal components for SLS 1, SLS 2, and SLS 3.  
represents matrix cracking, and 50-60 dB represents fiber debonding or delamination. There is no definite value for this correlation of the amplitude with damage modes. Different authors use different values based on their experimental results. A summary of this information can be found in the literature [3; 20]. In recent years, however, some researchers have argued that the AE signals with high amplitudes not only represent fiber breakage but also interlaminar crack growth [4]. This is because of the mode of propagation and the degree of absorption of the AE waveforms.