## 3 Simulation Analysis  
### CEEMDAN-SVD Simulation  
To test the validity of the joint CEEMDAN-SVD filtering, a simulation signal \(f(t)\) with superimposed low-frequency noise and high-frequency noise is constructed with sampling frequency \(f=100\)Hz, sampling time \(t=10\) s. The equation is as follows:  
\[f(t)=y(t)+y_{1}(t)+y_{2}(t) \tag{15}\]  
Pure signal:  
\[y(t)=10e^{-t\pi/2}\sin(16t)+5e^{-t/3}\sin(25t) \tag{16}\]  
Low-frequency noise:  
\[y_{1}(t)=8e^{-t/3}\sin(3t) \tag{17}\]  
High-frequency white noise:  
\[y_{2}(t)=4 randn(m) \tag{18}\]  
where \(t\) is the time; \(m\) is the number of samples; \(randn(m)\) is white noise. A comparison of the time history for signals \(f(t)\) and \(y(t)\) is shown in Figure 2, and a comparison of the power spectral density plot is shown in Figure 3.  
Because part of the true frequency of the pure signal will be masked by noise, the presence of noise will influence the accuracy of feature-information extraction. Filtering and denoising the acquired signal is the key step of signal analysis. In this paper, the SVD, EEMD, CEEMDAN and CEEMDAN-SVD methods are used to reduce the noise of \(f(t)\), and the noise-reduced results of each method are compared to verify the good applicability of the CEEMDAN-SVD algorithm for noisy signal filtering. The comparison of the power spectrum after noise reduction by the filtering methods are shown in Figure 4.  
Figure 2: Time history comparison of noised signal \(f(t)\) and pure signal \(y(t)\). (**a**) Time history of noised signal \(f(t)\); (**b**) Time history of pure signal \(y(t)\). From Figure 4a, we can see that although the SVD algorithm can filter out the high-frequency noise in the original signal well, there is still a large amount of residual low-frequency noise. Figure 4b presents the filtering effect of EEMD, and its filtering accuracy is low because EEMD is greatly affected by background noise. In Figure 4c, the filtering  
Figure 4: Power-spectrum comparison of four filtering methods for the noised signal \(f(t)\). (**a**) Result of SVD; (**b**) Result of EEMD; (**c**) Result of CEEMDAN; (**d**) Result of CEEMDAN-SVD. Figure 3: Power-spectrum comparison of noised signal \(f(t)\) and pure signal \(y(t)\). (**a**) Power spectrum of noised signal \(f(t)\); (**b**) Power spectrum of pure signal \(y(t)\). accuracy of CEEMDAN for high-frequency noise is low, but the effect of filtering low-frequency noise is excellent. From Figure 4d, CEEMDAN-SVD has a good filtering effect for both low-frequency and high-frequency noise. Through the analysis of the filtering effect comparison, among the four filtering methods, CEEMDAN-SVD filter can effectively remove high-frequency noise while filtering low-frequency noise, and the accuracy of feature-signal extraction is higher than the other three methods, which can effectively extract the target signal. To quantitatively evaluate the filtering capabilities of SVD, EEMD, CEEMDAN and CEEMDAN-SVD, the signal-to-noise ratio (\(SNR\)) and root mean square error (\(RMSE\)) are applied to assess the filtering capabilities of the above four methods. \[SNR=lg\left\{\frac{\frac{1}{m}\sum\limits_{i=1}^{m}f^{2}(m)}{\frac{1}{m}\sum \limits_{i=1}^{m}\left[f(m)-\widehat{f(m)}\right]^{2}}\right\}^{10} \tag{19}\]  
\[y(t)=10e^{-t\pi/2}\sin(16t)+5e^{-t/3}\sin(25t) \tag{16}\]0  
where \(f(m)\) represents the original signal; \(\widehat{f(m)}\) represents the signal after noise reduction. If the \(SNR\) is larger and the \(RMSE\) is smaller, this shows that the denoising effect of this method is better. The denoising performance of SVD, EEMD, CEEMDAN and CEEMDAN-SVD are compared, as shown in \[y(t)=10e^{-t\pi/2}\sin(16t)+5e^{-t/3}\sin(25t) \tag{16}\]1  
The two indexes calculated in Table 1 show that among the four methods of SVD, EEMD, CEEMDAN and CEEMDAN-SVD, the maximum \(SNR\) of CEEMDAN-SVD is 4.35 and the minimum \(RMSE\) is 1.07.