# Noise Reduction Based on a CEEMD-WPT Crack Acoustic Emission Dataset
## 4 Simulation Analysis
With the increase in noise to the analog signal, the PIC rises to about 0.8, and the smaller the SNR of the increase in noise, the higher the PIC rises. This phenomenon confirms the inference in Section 3.4 that the higher the noise content in the signal, the larger the PIC. Secondly, by observing Figure 6b, it can be found that the PIC has the same trend as the RMSE, and decreases with the increase in the SNR. In addition, the noise reduction effect measured using the PIC as the noise reduction index is consistent with the SNR and RMSE, and the noise reduction effect from high to low is CEEMD-WPT, CEEMDAN, and traditional CEEMD. In summary, the use of the PIC as a measure of noise reduction effect has high reliability. Figure 2: Analog signal: (**a**) Analog signal waveform diagram. (**b**) Analog signal spectrum diagram. Figure 3: Expanded view of noisy signals. Figure 4: Distribution of correlation numbers. Figure 2.0 _Cont._  
Figure 2.1 The noise reduction effect of a noisy signal: (**a**) Noise reduction rendering of traditional CEEMD. (**b**) CEEMDAN noise reduction effect diagram. (**c**) Noise reduction effect diagram of CEEMD-WPT. (**d**) Noise reduction spectrum map of traditional CEEMD. (**e**) CEEMDAN noise reduction spectrum map. (**f**) Noise reduction spectrum map of CEEMD-WPT. By comparing the use of the dnSNR as the measurement index of the noise reduction effect, it can be seen in Table 2 and Figure 6b that, although the dnSNR index of the three noise reduction algorithms has the same trend as that of the RMSE, the noise reduction effect determined by this parameter is contradictory to that of the SNR and RMSE. The noise reduction effect from high to low is as follows: CEEMDAN, traditional CEEMD, and CEEMD-WPT. Considering the high-frequency noise residue observed in Figure 5 and the inherent theoretical defects of this index, it can be concluded that the reliability of using the dnSNR to measure the noise reduction effect is poor. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Add Noise SNR**} & \multicolumn{2}{c}{**5 db**} & \multicolumn{2}{c}{**10 db**} & \multicolumn{2}{c}{**15 db**} \\ \cline{3-8}  & & \multirow{2}{*}{**Mean**} & \multicolumn{1}{c}{**Variance (10\({}^{-2}\))**} & \multirow{2}{*}{**Mean**} & \multicolumn{1}{c}{**Variance (10\({}^{-2}\))**} & \multirow{2}{*}{**Mean**} & \multicolumn{1}{c}{**Variance (10\({}^{-2}\))**} \\ \hline \multirow{4}{*}{SNR} & Traditional & \multirow{2}{*}{10.136} & \multirow{2}{*}{107.745} & \multirow{2}{*}{13.890} & \multirow{2}{*}{175.306} & \multirow{2}{*}{16.362} & \multirow{2}{*}{439.393} \\  & CEEMDAN & & & & & & \\ \cline{1-1}  & CEEMDAN & 11.020 & 5.575 & 15.289 & 10.068 & 19.908 & 13.584 \\  & CEEMD-WPT & 12.548 & 9.992 & 17.186 & 9.765 & 21.663 & 16.517 \\ \hline \multirow{4}{*}{RMSE} & Noisy signal & \multirow{2}{*}{0.535} & \multirow{2}{*}{0.301} & \multirow{2}{*}{0.099} & \multirow{2}{*}{0.169} & \multirow{2}{*}{0.146} \\  & Traditional & & & & & & \\ \cline{1-1}  & CEEMD & 0.293 & 0.122 & 0.190 & 0.099 & 0.146 & 0.166 \\ \cline{1-1}  & CEEMDAN & 0.280 & 0.007 & 0.166 & 0.002 & 0.098 & 0.004 \\ \cline{1-1}  & CEEMD-WPT & 0.225 & 0.006 & 0.129 & 0.002 & 0.077 & 0.001 \\ \hline \multirow{4}{*}{dnSNR} & Traditional & \multirow{2}{*}{1.162} & \multirow{2}{*}{0.638} & \multirow{2}{*}{0.527} & \multirow{2}{*}{0.231} & \multirow{2}{*}{0.307} & \multirow{2}{*}{0.297} \\  & CEEMDAN & & & & & & \\ \cline{1-1}  & CEEMD-WPT & 1.191 & 0.054 & 0.578 & 0.005 & 0.352 & 0.0008 \\ \hline \multirow{4}{*}{PIC} & Primary signal & \multirow{2}{*}{0.065} & \multirow{4}{*}{0.842} & \multirow{4}{*}{0.792} & \multirow{4}{*}{0.553} \\  & Noisy signal & \multirow{2}{*}{0.557} & \multirow{2}{*}{0.016} & \multirow{2}{*}{0.426} & \multirow{2}{*}{0.048} & \multirow{2}{*}{0.335} \\  & Traditional & & & & & \\ \cline{1-1}  & CEEMD & & & & & & \\ \cline{1-1}  & CEEMDAN & 0.338 & 0.118 & 0.314 & 0.032 & 0.282 & 0.007 \\ \cline{1-1}  & CEEMD-WPT & 0.214 & 0.004 & 0.164 & 0.003 & 0.111 & 0.004 \\ \hline \hline \end{tabular}
\end{table}