# Noise Reduction Based on a CEEMD-WPT Crack Acoustic Emission Dataset
## 5 Experiment and Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Algorithm** & **PIC Mean** & **Variance (10\({}^{-2}\))** \\ \hline \multirow{4}{*}{Test set for all data} & Primary signal & 0.288 & \\  & Traditional CEEMD & 0.169 & \\  & CEEMDAN & 0.159 & \\  & CEEMD-WPT & 0.156 & \\ \hline \multirow{4}{*}{Data5} & Primary signal & 0.88 & \\  & Traditional CEEMD & 0.362 & 0.158 \\  & CEEMDAN & 0.190 & 0.016 \\  & CEEMD-WPT & 0.172 & 0.013 \\ \hline \multirow{4}{*}{Data7} & Primary signal & 0.874 & \\  & Traditional CEEMD & 0.531 & 0.010 \\ \cline{1-1}  & CEEMDAN & 0.202 & 0.016 \\ \cline{1-1}  & CEEMD-WPT & 0.188 & 0.005 \\ \hline \multirow{4}{*}{Data19} & Primary signal & 0.87 & \\  & Traditional CEEMD & 0.594 & 0.034 \\ \cline{1-1}  & CEEMDAN & 0.731 & 0.031 \\ \cline{1-1}  & CEEMD-WPT & 0.207 & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of experimental results. Figure 9: PIC interval noise reduction diagram: (**a**) 0.2–0.4; (**b**) 0.4–0.6; (**c**) 0.6–0.8; (**d**) 0.8–1. By observing Figure 10a, it can be found that all three methods can reduce the PIC index, but the PIC index of traditional CEEMD is still high after noise reduction. The PIC index of signal 7 and signal 19 is more than 0.5, and the PIC index has a large fluctuation, which proves that the noise reduction effect is limited and the noise reduction stability is poor. Although the CEEMDAN algorithm has a good effect on Data5 and Data7, it has a poor effect on Data19. On the contrary, the PIC index of CEEMD-WPT after noise reduction is about 0.2 with a small fluctuation, which proves that the proposed method has a better noise reduction effect and stability. Figure 10: _Cont._  
By comparing Figure 10b-d, it can be seen that the three methods have the effect of removing high-frequency noise from the original signal, but compared with CEEMD-WPT, traditional CEEMD has more residual noise in the high-frequency part, which is also the reason for its higher PIC index. The high-frequency noise residue of CEEMDAN on Data19 is obviously higher than that of Data5 and Data7, which is also consistent with the poor noise reduction effect on Data19. By observing Table 4, it can be found that the PIC index of CEEMD-WPT in the three experimental signals is smaller than that of traditional CEEMD and CEEMDAN, and the variance is significantly smaller than that of traditional CEEMD by one order of magnitude. The stronger stability of the noise reduction effect is mainly attributed to the following two aspects. On the one hand, due to the randomness of white noise added in traditional CEEMD, the difference between the two methods is due to the fact that the noise reduction effect is more pronounced than that of traditional CEEMD. Figure 10: Noise reduction figures of Data5, 7, and 19: (**a**) All Data. (**b**) Data5. (**c**) Data7. (**d**) Data19. CEEMD and CEEMDAN, the noise reduction effect has unstable factors, while CEEMD-WPT uses the WPT-EMD method with a more stable noise reduction effect instead of the original single EMD, so the noise reduction results are more stable. On the other hand, white noise added in traditional CEEMD and CEEMDAN smoothed the mutation points and polluted the non-mutation points at the same time, changing the non-mutation points from a low-frequency signal to a high-frequency signal. However, the effect of white noise on non-mutation points could be reduced by using WPT to filter out high-frequency noise before EMD. Thus, the noise reduction capability of the algorithm is improved.