## 5 Comparison Analysis  
In order to further analyze the noise reduction effect of the WOA-VMD algorithm, the CEEMDAN algorithm with adaptive ability, the traditional VMD algorithm and WOAVMD algorithm are respectively applied to decompose three groups of measured signals induced by tunnel blasting in the portal section (as shown in Figure 6), and MPE is used to determine the noise composition. The parameters [\(K\), \(\alpha\)] of the three algorithms are shown in Table 3, and the parameters of traditional VMD algorithm are all processed manually by the method used in the literature [13]. Figure 6 is the signal comparison before and after noise reduction, and the signal-to-noise ratio s and the root mean square error \(\varepsilon\) of the denoised signal and the original signal are calculated in Table 3.  
According to the waveform curve (Figure 6), the blasting vibration signals of the tunnel portal before and after noise reduction were compared and analyzed. The CEEMDAN, VMD, and WOAV-VMD algorithms all achieved a certain degree of noise reduction effect and removed part of the high-frequency noise, among which the WOA-VMD algorithm obtained the best waveform and the least noise. According to Table 3, comparing the noise reduction effect indexes of the three groups of signals, the signal-to-noise ratio s of the WOA-VMD and VMD algorithms is greater than that of the CEEMDAN algorithm, and the root mean square error \(\varepsilon\) of the WOAV-VMD and VMD algorithm is smaller than that of the CEEMDAN algorithm. It shows that the denoising effect of the VMD algorithm is better than that of the CEEMD class decomposition algorithm.  
Comparing the noise reduction effect of the WOAV-VMD and VMD algorithms, it can be seen that there are differences in the mode number \(K\) and penalty factor \(\alpha\) determined by the WOA optimization algorithm and manual determination for different signals. For signal s1, the two methods obtain the same mode number, but the penalty factor is slightly different, and the noise reduction effect is not different. However, for signals s2 and s3, the modal number \(K\) obtained by WOAV-VMD decomposition are 1-2 more modal functions  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Original Signal** & \begin{tabular}{c} **Noise Reduction** \\ **Algorithm** \\ \end{tabular} & **Modal Number K** & **Penalty Factor \(\alpha\)** & \
\begin{tabular}{c} **Signal to Noise** \\ **Ratio s/dB** \\ \end{tabular} &
\begin{tabular}{c} **Root Mean** \\ **Square Error \(\varepsilon\)** \\ \end{tabular} \\ \hline \multirow{3}{*}{s1} & CEEMDAN & 10 & - & 14.021 & 0.095 \\  & VMD & 8 & 4800 & 18.242 & 0.057 \\  & WOA-VMD & 8 & 5600 & 18.322 & 0.055 \\ \hline \multirow{3}{*}{s2} & CEEMDAN & 6 & - & 13.871 & 0.101 \\  & VMD & 6 & 4800 & 16.520 & 0.070 \\  & WOA-VMD & 7 & 6100 & 18.325 & 0.061 \\ \hline \multirow{3}{*}{s3} & CEEMDAN & 8 & - & 10.210 & 0.125 \\  & VMD & 8 & 5000 & 14.525 & 0.081 \\ \cline{1-1}  & WOA-VMD & 10 & 6000 & 16.658 & 0.072 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Denoised effect index.  
than that obtained by VMD algorithm, the decomposition is more refined, and the denoising effect is better.  
From the analysis of the waveform and evaluation index, it is found that the denoising effect of the WOA-VMD algorithm is better than that of other methods, and the high-frequency noise in signal is more effectively removed. At the same time, the algorithm has strong adaptive energy, avoids the error of manual intervention, and has obvious superiority in the noise reduction of the blasting vibration signal at the tunnel portal.