## 5 Accuracy Verification of Denoising Data  
To verify the accuracy of the denoising algorithm proposed in this paper, ensuring that noise is effectively removed while preserving the main components of the original signal, sensor-acquired signals are directly fused based on variance contribution rates as the control group. For the experimental group, the sensor-acquired signals are first denoised using the proposed method, then fused based on the same variance contribution rates [26; 27]. Both groups are subjected to a spectral analysis to examine the prominent frequencies of the denoised signals. The data fusion method, based on the variance contribution rate of correlation, allocates fusion coefficients according to the importance of the correlation between information, enabling a dynamic fusion of similar data. This approach consolidates multiple similar signals into a single signal. \begin{table}
\begin{tabular}{c c} \hline
**Denoising Methods** & \(d_{nSNR}\) \\ \hline WTD & 6.6242 \\ MVO-VMD-MPE (Discarding Noise IMF) & 3.9179 \\ MVO-VMD-MPE-WTD & 1.14 \\ \hline \end{tabular}
\end{table} 
Table 2: \(d_{nSNR}\) Results for Each Method. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(K\) & \(\alpha\) & **Computation Time (s)** \\ \hline NGO & 12 & 2000 & 1180.2 \\ AOA & 12 & 2000 & 1266.6 \\ MVO & 12 & 2000 & 1113.3 \\ RIME & 12 & 2000 & 1421.1 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of Optimization Algorithms. For the data point \(x_{ij}\) from the (\(j\))-th point of the (\(i\))-th sensor, the equation for the variance contribution rate of these data is  
\[K_{ij}=\frac{\left(x_{ij}-E_{i}\right)^{2}}{m\sigma_{i}^{2}} \tag{18}\]  
Here, \(m\) is the number of data points, \(E\) is the mean of the data sequence, and \(\sigma^{2}\) is the variance of the data sequence. Based on the variance contribution rate of similar signals collected from \(m\) channels at a given time, the allocation coefficient \(K_{ij}\) for any sensor signal \(x_{i}\) is  
\[k_{ij}=\frac{K_{ij}}{\sum_{i=1}^{m}K_{ij}} \tag{19}\]  
Based on the obtained allocation coefficients, the signals collected from \(m\) channels can be fused into a single signal. After fusion, the value (\(x\)) of the (\(j\))-th data point from the (\(x\))-th channel is  
\[x=\sum_{i=1}^{m}k_{ij}x_{ij} \tag{20}\]  
The normalized power spectral density curves for the control group and the experimental group are shown in Figure 8.  
In the evaluation of self-excited vibrations, the dominant frequency has a significant impact on the stability of the system. By comparing the FFT transformations before and after denoising, it can be observed that the noise frequencies have been effectively eliminated, making the dominant frequency more prominent. From the comparison of normalized power spectral density curves before and after denoising, it can be observed that the frequency of peak point 1 is 8.20 Hz and the frequency of peak point 2 is 18.31 Hz. Denoising effectively removes noise and makes the signal peaks more pronounced. To further validate the effectiveness of denoising in preserving key information, a numerical simulation is performed for the measurement with a 20% gate opening. This  
Figure 8: Comparison of normalized power spectral density curves on pre-denoising and post-denoising. simulation demonstrates the validity of the key information from a numerical perspective. The gate-water coupling model is shown in Figure 9.  
Rotational degrees of freedom are applied at the gate lifting lug to simulate the rotational effect of the opening and closing rod bearings. Similarly, rotational degrees of freedom are applied at the hinge plate to simulate the gate's rotation around the lifting lug axis [28; 29]. The water body is modeled using Fluid30 elements, and the gate is modeled with Shell181 shell elements [30; 31; 32; 33].