# Noise Reduction Based on a CEEMD-WPT Crack Acoustic Emission Dataset
## 4 Simulation Analysis  
In order to verify the noise reduction effect of CEEMD-WPT and the PIC quantization effect proposed in this paper, the AE signal digital model proposed by [PERSON] et al. [29] is introduced here for the simulation experiments. The model expression is shown in Equation (16):  
\[f(t)=\sum\limits_{i=1}^{n}{A_{i}e^{\left[{-Q_{i}(t-t_{i})}^{2}\right]}\sin[2 \pi f_{i}(t-t_{i})]} \tag{16}\]In the above equation, \(A_{i}\) is the amplitude of the signal, \(Q_{i}\) is the attenuation factor of the signal, \(t_{i}\) is the delay time of the signal, \(f_{i}\) is the frequency of the signal, and \(n\) is the number of superposition signals. The simulation parameters adopted are listed in Table 1, and the waveform and spectrum diagram are shown in the red line in Figure 2. In order to simulate the noise of the environment, white noise with a signal-to-noise ratio of 5 db is added to the analog signal. The waveform diagram and spectrum diagram of the noisy signal are shown by the black line in Figure 2. It can be seen that noise oscillates the analog waveform, and the frequency domain components become more complex, which will adversely affect the subsequent recognition of the signal. The improved CEEMD of the noisy signal is shown in Figure 2. This was carried out to obtain 10 IMF components and 1 Res, and then the Fourier transform was applied to obtain the corresponding spectrum diagram. The results are shown in Figure 3. Then, the correlation number between the IMF component and the noisy signal was calculated successively, as shown in Figure 4. The average value of the correlation number is 0.178, which is less than the set threshold value of 0.3. Finally, IMF2-4 is the strongly correlated component, and the rest are the weakly correlated components. The weak correlation component is further processed using WPT, and the processed weak correlation component and strong correlation component are reconstructed to obtain the noise reduction signal. In this paper, the traditional CEEMD and CEEMDAN noise reduction algorithms are introduced as a comparison. The waveform diagram and spectrum diagram of the three noise reduction results are drawn, respectively  
Observing the low-frequency part (the frequency is between 0 and 80 kHz), it can be found that the three noise reduction algorithms have no obvious effect. In the high-frequency part (frequency >80 kHz), it can be found that the three methods have obvious noise reduction effects, but the noise residue of the high-frequency part of the signal after the noise reduction of traditional CEEMD and CEEMDAN is higher. The high-frequency part of CEEMD-WPT has less noise residue and a better noise reduction effect. In order to further compare the noise reduction effect of the three methods, the signal-to-noise ratio, root mean square error, noise reduction error ratio, and principal interval coefficient are used to quantify the noise reduction effect. White noise with an SNR of 5 db, 10 db, and 15 db was added to the analog signal, and the noise was reduced 100 times using traditional CEEMD, CEEMDAN, and CEEMD-WPT, respectively. The results are shown in Table 2 and plotted in Figure 6. By observing Figure 6a, it can be found that, compared with traditional CEEMD and CEEMDAN, the proposed CEEMD-WPT has the largest SNR and the smallest RMS error under the three noise conditions, which proves that its noise reduction performance is better than that of traditional methods. Under the same conditions and parameters, the noise reduction results of CEEMD-WPT and CEEMDAN have smaller standard deviations, which proves that their noise reduction stability is better than that of the traditional CEEMD algorithm. Firstly, in order to verify the reliability of using the PIC as a measure of noise reduction effect, the principal interval coefficient in Table 2 is observed. It can be found that the PIC corresponding to the analog signal is the smallest at only 0.065.