# Multiparameter Approach for Damage Propagation Analysis in Fiber-Reinforced Polymer Composites
## 1 Introduction  
The acoustic emission (AE) technique is based on the detection and interpretation of sound waves that are caused by rapid internal displacements in a material and traveling at an ultrasonic velocity [1, 2]. The formation and propagation of cracks due to different damage sources are the sources of these acoustic signals. In simple words, when a material is locally and irreversibly deformed, it releases energy in the form of elastic waves and the AE technique is based on the analysis of these elastic waves. The characteristics of these elastic waves are studied in their frequency domain or time-frequency domain using different types of waveform analysis [3]. The waveform analysis involves post-processing of the acoustic signals after their acquisition. This post-processing sometimes requires high computational power and consumes lots of storage space. In particular, when the continuous acoustic signals are studied in their time-frequency domain, the data processing consumes lots of time. For these reasons, the acoustic signals can be characterized in terms of their energy, peak amplitude, duration, rise time, and so many other different parameters. These parameters are derived from the acoustic signals that can define the characteristics of the acoustic source. There exists a longstanding debate on which are the most relevant parameters that can be used for describing the damage characteristics most efficiently [3]. The peak amplitude and peak frequency of the waveform often stand out as the best parameters for defining the characteristics of the acoustic source. In the last 5 years, several researchers have shown that the peak amplitude and peak frequency of the acoustic waveform provide misleadinginformation about the damage characteristics, especially in fiber-reinforced polymer (FRP) composites [4; 5; 6]. This is because several damage characteristics release acoustic waveforms with the same peak frequency. For instance, in a carbon-fiber-reinforced polymer (CFRP) material, the fiber breakage during static tension loading releases acoustic signals with the same frequency as interlaminar crack propagation [4]. Analyzing the acoustic emission signals based only on their peak frequency is the reason for this anomaly. To avoid this erroneous description of the damage characteristics of the acoustic source, a multiparameter approach is required. The debate resumed once again on the conception of the multiparameter approach: what are the parameters that can be selected? A few researchers have used the rise time and rise angle (RA) of the acoustic waveforms [7], while some others have used absolute energy [8]. A definite set of parameters has not been specifically defined as the optimal set of parameters for analyzing the damage characteristics. Recently, [PERSON] et al. [9] used a multiparameter approach by integrating the acoustic results recorded from two different types of piezoelectric sensors. The parameters they used for this analysis were centroid frequency, peak frequency, and energy. Although these parameters have been commonly used by several researchers in the past, [PERSON] et al. used an exploratory data analysis for selecting these parameters [9]. Nonetheless, the parameters they used for analysis are quite common in the literature. In this research work, principal component analysis (PCA) was used for identifying the sets of parameters for analysis. The initial parameter set that was considered were the peak amplitude, absolute signal level (ASL), initiation frequency (I-Frequency), peak frequency (P-Frequency), average frequency (A-Frequency), and reverberation frequency (R-Frequency). These parameters may represent the characteristic features of the waveform. Furthermore, during the preliminary analysis and our previous research works [6], the authors have identified that the acoustic signals observed from different damage modes are highly asymmetrical. The propagation of the acoustic signals released from the different damage sources may be responsible for the asymmetry of these signals.