# Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis
## 3 Simulation
### Optimized CEEMD Method  
The simulation signal \(X(t)\) is decomposed by CEEMD, and the decomposed time and frequency domain diagram is shown in Figure 5. Impact signals can be observed in the time-domain diagram. The signal in the frequency-domain diagram still has mode aliasing and contains some noise, which will affect the extraction of fault feature signals. Therefore, this paper proposes to use MSE to optimize the decomposition of CEEMD. Figure 4: Simulation signal. (**a**) Time domain of simulation signal, (**b**) Frequency domain of simulation signal. The scale factor \(Q\) of the multi-scale sample entropy will affect the MSE value, and different \(Q\) values have different MSE values. According to the decomposition characteristics of CEEMD, each layer of IMF has a different SNR. In order to accurately determine the MSE value of each IMF, the different IMFs must be accurately distinguished. In this paper, the values of the scale factor \(Q\) range from 1 to 20 are taken, and the SNR is respectively taken as \(-\)30 dB, \(-\)20 dB, \(-\)10 dB, 1 dB, and 10 dB for simulation. The results are shown in Figure 6. The signals with the same SNR in the figure have different MSE values due to different \(Q\) values  
To eliminate the signal with larger MSE value in IMFs, it is necessary to determine the appropriate threshold. In this paper, the MSE values of 10,000 sets of noise signals (the signal length of each group of random noise is the same as the simulated signal) are calculated separately. The signal length of each group of random noise is the same as the vibration signal and the values are normalized, and the graph is drawn in Figure 7. The MSE value of the noise signal in Figure 7 varies from 0.55 to 1.0. In this paper, the minimum value of the MSE value in the 10,000 sets of noise signals is selected as the threshold for eliminating IMFs. 10,000 sets of random noise are randomly obtained, so the threshold in this paper is a dynamically changing value. After a lot of simulation, the minimum threshold fluctuates in a small range, so it is reasonable to choose the minimum value of 10,000 groups of noise as the threshold in this paper. In this paper, the scale factor \(Q=10\) is used to calculate the MSE values of IMFs and 10,000 sets of random noise, at the same time, the minimum value of 10,000 sets of random noise is used as the threshold, and Figure 8 is drawn. In Figure 8, the pink line is the minimum value of 10,000 groups of random noise, and the red bar is the MSE value of each IMF. In this paper, IMFs signals larger than the threshold are eliminated, so the IMF1-IMF4 signals are eliminated. Reconstruct the remaining IMF5-IMF10 signals and perform FFT transformation to obtain Figure 9. In Figure 9, the red line is the reconstructed signal, and the blue is the original signal. It can be seen that the high-frequency noise part of the signal is removed from 400 Hz to 1000 Hz, which achieves the purpose of noise reduction. Figure 8: MSE of each IMF component. Figure 7: Multi-scale sample entropy (MSE) values of 10,000 sets of random noise. According to the method mentioned in this article, the reconstructed signal needs to be decomposed again by the CEEMD method, and the MSE value of each component signal is calculated. The MSE value is compared with the dynamic threshold value, and if there is an IMFs component signal greater than the threshold, it is removed, and the remaining signal is reconstructed and CEEMD decomposition is performed again. After multiple iterations, it is finally obtained that there is no case where the MSE value of the component signal is greater than the threshold, so the iteration is terminated. The time and frequency domain diagrams of signal decomposition at the end of the iteration are shown in Figure 10. The fault frequencies of 50 Hz and 130 Hz of the simulated signal in Figure 10 were extracted, which verified the effectiveness of the proposed method.