## 3 MS Monitoring System for the Spillway Tunnel
### MS Signal Noise Reduction  
The monitoring system often works in a pretty noisy environment, and the signals picked up by each channel contain a lot of external noises, which seriously interfere with the subsequent research work such as P-wave and S-wave first-arrival pickup, source localization, and source mechanism interpretation. Therefore, it is necessary to reduce noises in MS signals. This paper provides complementary ensemble empirical mode decomposition (CEEMD), compressed sensing (CS), and soft thresholding (ST) methods for reducing noises in MS signals. Generally, the steps are as follows:  
First, the CEEMD method was adopted to decompose MS signals containing noises into multiple intrinsic mode function (IMF) components by frequency from high to low and to perform cross-correlation analysis on each IMF component and the original signals, thus identifying the boundary IMF between noises and signals. Next, the IMF components containing noises were decomposed into sparse signals using the discrete wavelet transform (DWT) and reconstructed using the CS method, so that the reconstruction coefficient \(\theta\) was obtained. Then, soft thresholding was performed to filter \(\theta\) values, thus filtering out the sparsity coefficients corresponding to most of the noises. Finally, the IMF components with noise reduction were reconstructed using the inverse discrete wavelet transform (IDWT) and recombined with the remaining IMF components to achieve the effective noise reduction in MS signals.  
In this paper, three groups of MS signals containing noises were randomly selected from the monitoring data for analysis. To facilitate calculation and comparison, the main MS signals were intercepted from each group of 30,000 sampling points. In particular, the MS signals were intercepted from sampling points No. 8000-18000. Therefore, the signals at each group of 10,000 sampling points had the same wavelength, and the fast Fourier transform (FFT) could be used for time and frequency analysis, which could judge the noise reduction effect of MS signals more intuitively. The methods in this paper were adopted to reduce noises from the three groups of MS signal waveforms. Figure 5 shows the waveforms and time-frequency spectra before and after noise reduction. Moreover, the signal-to-noise ratio (SNR), information standard deviation (SD), and correlation coefficient (CC) of the original signals and signals after noise reduction were calculated, and the calculation results are listed in Table 1. Figure 5 shows that the three groups of original MS signals all contained a lot of random noises. Although the distribution of the dominant spectrum in these signals could be seen from the time-frequency spectrum, it was not obvious due to the interference from noise, which would cause interference to the MS monitoring at a later stage. After noise reduction was made as described in this paper, the MS signal waveform and time-frequency spectrums were clearer, and the dominant spectrum was more obvious. Table 1 shows that the SNRs of the original signals are all 0 dB, and the SNRs after noise reduction are up to 24.325 dB, that the standard deviations of the signals are all small, indicating a small deviation of the original signals from the signals after noise reduction, and that the correlation coefficients of the original signals and the signals with noise reduction are all close to 1, indicating remarkably similar waveforms between the original signals and the signals with noise reduction.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **B\_SNR** & **A\_SNR** & **SD** & **CC** \\ \hline Signal A & 0 & 24.325 & 0.004 & 0.954 \\ Signal B & 0 & 20.442 & 0.003 & 0.941 \\ Signal C & 0 & 21.904 & 0.003 & 0.935 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Analysis of the noise reduction effect for MS signals.