# Noise Reduction Based on a CEEMD-WPT Crack Acoustic Emission Dataset
## 5 Experiment and Analysis  
In order to verify the actual noise reduction effect of the proposed method, the Acoustic Event Dataset [30] provided by HARVARD Dataverse was adopted for the noise reduction experiment. The dataset, as shown in Figure 7, has a total of 16,650 AE data, including 15,000 data in the training set and 1650 data in the test set. The data categories are divided into stretch, shear, and mixed events, each accounting for 1/3. The sample number is 1000. Firstly, a noise reduction experiment was conducted on 1650 pieces of data in the test set, and the PIC index of the original signal, traditional CEEMD, CEEMDAN, and CEEMD-WPT were calculated, respectively. As shown in Figure 8, the PIC index distribution of the original signal is relatively dispersed, mainly ranging from 0 to 0.4. This is because some of the original signals contain noise, which increases their PIC index, and a small number of signals have a large noise content, making their PIC index as high as 0.8-1. After the three noise reduction methods, the PIC index showed a decreasing trend, among which the signals of traditional CEEMD, CEEMDAN, and CEEMD-WPT concentrated in the range of 0-0.2 were 84.9%, 81.9%, and 92.9%, respectively. This shows that CEEMD-WPT has the strongest noise cancellation capability compared to other algorithms, and can reduce the PIC index of most data in the test set to 0-0.2. Secondly, the test set signal is divided into four intervals according to the PIC index, which are: [0.2-0.4], [0.4-0.6], [0.6-0.8], and [0.8-1]. Traditional CEEMD, CEEMDAN, and CEEMD-WPT denoising were carried out for these four intervals, respectively. The PIC index after denoising was calculated and the results are shown in Figure 9 and Table 3.  
Figure 6: Comparison of noise reduction quantization parameters: (**a**) SNR-RMSE; (**b**) dnSNR-PIC. Figure 7: Schematic representation of Acoustic Event Dataset. Figure 8: Denoising diagram of test set signal. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{PIC Mean} \\ \cline{2-5}  & **0.2–0.4** & **0.4–0.6** & **0.6–0.8** & **0.8–1** \\ \hline Traditional & 0.173 & 0.192 & 0.213 & 0.454 \\ CEEMD & 0.181 & 0.253 & 0.301 & 0.323 \\ CEEMD-WPT & 0.183 & 0.182 & 0.167 & 0.146 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PIC interval noise reduction. Figure 9: _Cont._  
Figure 9: Cont. By observing Figure 9 and Table 3, it can be found that the CEEMD-WPT algorithm has the best noise reduction effect for signals with a PIC between [0.4 and 1]. For a signal with a PIC between [0.2 and 0.4], the traditional CEEMD has a better noise reduction effect. As a whole, CEEMD-WPT has a wider range of adaptations, so the noise reduction effect is better than traditional CEEMD and CEEMDAN. In the observation interval [0.8-1] alone, it can be found that the noise reduction effect in order from high to low is CEEMD-WPT, CEEMDAN, and traditional CEEMD, which is consistent with the experimental results in Table 4.  
Finally, for the data with more noise in the first 20 pieces of data in the test set (the principal interval coefficient is greater than 0.8 and there are 3 pieces of data, which are the 5 th, 7 th, and 19 th pieces of data, respectively), the noise reduction effect and algorithm stability are observed, and 100 noise reduction experiments are conducted on them, respectively. The noise reduction results are shown in Figure 10, and the data are collected in Table 4.