## 3 Simulation Signal Analysis  
To verify the effectiveness and superiority of the proposed noise reduction method, the simulated signals that are used for analysis are based on MATLAB 2020b software. The following simulation signal expression is constructed here:  
\[\left\{ \begin{array}{l}x(t)=s(t)+n(t)=\sum\limits_{i}A_{i}h(t-iT)+n(t)\\ h(t)=\exp(-Ct)\cos(2\pi f_{n}t)\\ A_{i}=1+A_{0}\cos(2\pi f_{r}t)\end{array} \right. \tag{26}\]  
where \(s(t)\) is the periodic shock component, \(A_{i}\) is the variable shock amplitude, \(A_{o}\) is 0.3; the rotation frequency \(f_{r}\) is 30; the attenuation coefficient C is 700; the resonance frequency \(f_{n}\) is 4; the problematic eigenfrequency is \(f_{i}=1/T=120\)Hz; and \(n(t)\) is the white Gaussian noise component. The sampling frequency of the signal is set to 16 kHz. Due to the large noise of the vibration signal, the overall signal-to-noise ratio of the signal is low; in order to ensure that the signal-to-noise ratio of the simulated signal model is \(-13\), a Gaussian white noise signal with a signal-to-noise ratio of 0 is added to the signal. The time-domain signal is shown in Figure 2, and it can be seen that the time-domain waveform signal is completely submerged after adding the noise. Figure 1: Noise Reduction Technology Roadmap. Noise-containing analog signals are individually decomposed using the EMD, EEMD, CEEMD, CEEMDAN, and modified CEEMDAN methods with the standard deviation of the added noise set to 0.2 and the number of loops to 100 for EEMD, CEEMD, CEEMDAN, and modified CEEMDAN. The decomposed IMFs of each order are shown in Figure 3.  
Through the decomposition of each order's IMF, it is evident that the first six-order components possess greater information and exhibit more complex signal characteristics. To identify the high noise components for subsequent noise reduction, this study analyzes the similarity and correlation between the original signal, each IMF component, and among the IMF signals. The analysis focuses on metrics such as cross-correlation coefficient, kurtosis, and sample entropy values. Specifically, the cross-correlation coefficient, kurtosis, and sample entropy values are calculated for each order of IMF. The resulting values for the first six orders are presented in Table 1. This table provides a comprehensive overview of the cross-correlation coefficients, kurtosis values, and sample entropy for each IMF component. The purpose of this analysis is to determine the components with higher noise content, enabling effective selection for the subsequent noise reduction process. By evaluating these metrics, the study gains insights into the characteristics and relationships among the IMF components and the original signal. In the first six orders of IMF components, the overall number of cross-correlation coefficients is at a low level, indicating that the signal has been decomposed relatively well. After decomposition, the IMF with higher energy reflects the true extent of the vibration signal more accurately. Based on the classification criterion, the components can be categorized as spurious or valid components. The criterion involves comparing each IMF signal with the original data and calculating their correlation coefficient. The highest correlation coefficient is identified, and a threshold is set at one-tenth of this maximum correlation coefficient. IMF components with correlation coefficients below this threshold are considered spurious components, while those above the threshold are considered valid components [36]. For the EMD method, the valid components are IMF1-IMF3. For the CEEMD method, the valid components are IMF1-IMF3 and IMF5. In the case of the improved CEEMDAN method, the valid components are IMF1-IMF5. By comparing the results obtained from EMD, EEMD, and CEEMD, it is observed that the improved CEEMDAN decomposition produces more valid components and fewer spurious components.