## 4 Engineering Applications  
### Vibration Signal Noise Reduction  
The Xiali tunnel is one of the key control projects of the Ji-Xin expressway in the Henan province, with a total length of 1020 m. The bedrock in the tunnel site is exposed and the stratigraphic lithology indicates the presence of medium-strong weathered limestone. The portal section of the Xiali tunnel is a steep slope, which is affected by combined joints, and the slope stability is poor. The blasting of the shallow buried section of the tunnel portal will cause great vibrations to the overlying slope. Smooth blasting was used to excavate the tunnel on site. Detonator delays in the blasting have six sections, Ms1-Ms11. Due to the joint development of the surrounding rock and slope in the tunnel portal, the displacement and blasting vibration were monitored during the construction process. The blasting vibration of the tunnel portal is monitored by the vibration meter. Set the sampling frequency to 4000 Hz and the time to 1 s. A typical signal is selected for noise reduction, and the blasting vibration time history curve is shown in Figure 2. The Y axis represents particle vibration velocity, which is directly obtained by the sensors [20]. According to Figure 2, blasting vibration monitoring sensors are usually arranged on rock outcrop in the shallow buried section of a tunnel portal. The blasting vibration propagation is affected by a complex rock and soil layer structure, and the measured signal has a large amount of noise, which has a greater impact on signal feature identification. Therefore, the WOA was used to optimize the VMD parameters [\(K\), \(\alpha\)], set the population size as 50, the maximum number of iterations as 30, the iteration range of \(K\) as [2; 15], and the iteration range of \(\alpha\) as [1000, 10,000]. After 30 iterations, the minimum envelope entropy of the fifth iteration is 1.045, and the output optimal parameters are [\(K\), \(\alpha\)] = (8, 5600). The IMF component and its center frequency of signal VMD decomposition were obtained, and the vibration energy and percentage of the original signal and each IMF component were calculated. The results are shown in Figure 3 and Table 1.  
Figure 2: Blasting seismic wave signal (s1). According to Figure 3 and Table 1, eight IMF components are obtained from WOA-VMD decomposition, and the center frequencies of IMF1-IMF8 gradually increase. The vibration amplitude and energy of IMF4-IMF8 are low, accounting for less than 1% of the total energy. The center frequency of IMF5-IMF8 is above 900 Hz, which is obviously higher than the frequency of the general blasting vibration signal. Therefore, it can be basically judged that IMF4-IMF8 may be high-frequency noise. In order to accurately identify the noise components, the mean MPE values of different scales of each IMF were calculated. The trial calculation determined the embedding dimension \(m=6\), the delay \(\tau=1\), and the scale factor \(s=5\), and the mean MPE was obtained as shown in Table 2.  
According to the literature [21], the MPE threshold of the blasting vibration signal is 0.6, so IMF4-IMF8 is determined as signal noise. After removing IMF4-IMF8 and reconstructing other IMFs, the blasting vibration signal after noise reduction is obtained, as shown in Figure 4.  
The noise reduction process shows that the WOA algorithm can adaptively obtain the VMD decomposition results and avoid the calculation error caused by human factors. Comparing Figures 2 and 5, it can be seen that the waveform of the denoised signal is basically the same as that of the original signal, the noise is significantly eliminated, and the impact on the peak vibration velocity is small.