# Validation of Acoustic Emission Waveform Entropy as a Damage Identification Feature
## 5 Validation and Discussion
### Effect of Noise on AE Entropy  
It is worth noting that the waveforms of each event may contain some noise. This noise is impossible to filter out with the traditional AE filtration techniques (e.g., 1D localization) [44; 46; 50; 62; 63; 64; 65], as they are embedded in the waveform. The presence of noise in the waveform can affect the disorderness of the discrete probability distribution. Therefore, it has the potential to influence the calculated value of AE entropy from a waveform. Like the AE entropy, noise in the waveform can also influence the traditional AE features.  
In order to eliminate the noise embedded in the AE waveform, a few studies have proposed a signal processing approach [66; 67; 68]. These studies are based on de-noising (e.g., conditioning) the AE waveform with discrete wavelet transform (DWT) prior to extracting the features. These studies suggest that DWT is very effective in reducing the noise in a waveform. Hence, this technique was adopted in this study to investigate the effect of de-noising a waveform to calculate its AE entropy. De-noising using DWT is based on the wavelet theory. In this approach, a series of wavelet is used to obtain the wavelet coefficient of the signal to be de-noised. The series of wavelets is generated by scaling and translating a mother wavelet. The wavelet coefficients obtained are referred to as the DWT (_a,b_), which is a function of the translating \(b\) with a fixed scale factor \(a\). The DWT helps analyse the waveform at a different level of frequencies by decomposing it to several level approximations and details.  
The procedure for waveform de-noising using DWT is accomplished with three steps. Firstly, the waveform is decomposed into several levels using a series of wavelet from a mother wavelet. Each level contains approximation coefficients representing the low pass filter and a detail coefficient representing a high pass filter. Secondly, thresholding is carried out on every detail coefficient using a threshold rule (e.g., minimax, Heursure, sqtwolog, SURE), in conjunction with a hard or a soft thresholding. Finally, the signal is reconstructed by inverse DWT from the updated detail coefficient on every level and updated approximation coefficient on the final level. In this research, db8 was chosen as the mother wavelet [69], decomposition level was chosen to be 8 and a soft thresholding method was implemented. These parameters were chosen as they yielded the best de-noising performance of the AE waveform among many other set of de-noising parameters [67].  
Figure 21a,b illustrates the original and de-noised waveform of two AE events. The AE entropy of the original waveform was 10.3 and 10.5, respectively, whereas that of the de-noised waveform was 8.7 and 8.4, respectively. It is clear from this analysis that de-noising the waveform reduces the AE entropy slightly. This is because de-noising procedure decreases the disorderness in the probability distribution of the waveform. It is also evident that despite the presence of noise, the majority of the disorderness in the original waveform arises form microstructural changes in the material (as de-noising only slightly reduces the AE entropy). As a result, there is no need to perform the de-noising when AE entropy is used for damage monitoring.