## 4 Establishment of a Prediction Model for Dual-Mode Shield Tunneling Parameters
### Data Preprocessing
#### 4.2.3 Data Denoising  
After removing outliers, the data exhibits inevitable fluctuations that can impact the modeling process and even the calculation results. These anomalous fluctuation data in the tunneling parameter sequence are called noise data. This phenomenon is particularly pronounced in geological environments with complex and variable conditions, rendering the temporal parameter data more unstable. [PERSON] et al. [28] pointed out that denoising tunneling parameters can reduce the spatial variability of these parameters, making it easier for machine learning algorithms to learn the patterns in data changes. An improved mean filtering algorithm is employed to denoise the tunneling parameters to mitigate these irregular variations. The formula for the original mean filtering algorithm is as follows, assuming a non-stationary data set of total length N. To eliminate noise, a window size of \(2\text{n}+1\) (<N) is set, and as the window slides forward, the average of every \(2\text{n}+1\) adjacent data \(\overline{y}_{k}\) is taken to represent the measurement result of the midpoint data. This method effectively eliminates noise. \[\overline{y}_{k}=\frac{1}{2n+1}\!\!\!\!\sum_{i=-n}^{2\text{n}+1}\!\!\!\!y_{k+i}, \tag{9}\]  
There is significant data fluctuation with sudden rises and falls throughout the shield tunneling process, accompanied by changes in the soft and hard composite strata. An improved mean denoising algorithm is proposed to mitigate the impact of significant differences in window values on denoising effectiveness. In each forward-sliding window process, the data within the window is sorted, and the maximum value \(y_{kmax}\) and the  
Figure 5: Outlier tag. minimum number \(y_{\text{\emph{kmin}}}\) are excluded. The mean of the remaining data is then calculated to represent the measurement result. The formula for the improved algorithm is as follows:  
\[\overline{y}_{k}=\frac{1}{2n-1}(\sum_{i=-n}^{2n+1}y_{k+i}-y_{\text{\emph{kmax}}} -y_{\text{\emph{kmin}}}), \tag{10}\]  
In order to assess the denoising effect, this paper selects two evaluation metrics: Signal-to-Noise Ratio (SNR) and Peak Signal-to-Noise Ratio (PSNR). Signal-to-Noise Ratio (SNR): It evaluates signal strength and noise level ratio. Peak Signal-to-Noise Ratio (PSNR): It evaluates the ratio between the maximum possible signal and noise power. Excellent _SNR_ and _PSNR_ depend on the specific application scenarios and requirements. The metrics only need to reach a certain level, and in the context of denoising the same data, higher _SNR_ and _PSNR_ indicate better denoising effects. The formulas for calculating both metrics are as follows:  
\[SNR=10*\lg\left(\frac{\sum p^{2}}{\sum(p-q)^{2}}\right), \tag{11}\]  
\[PSNR=10*\lg\left(\frac{p_{\text{max}}^{2}}{\frac{1}{n}*\sum(p-q)^{2}}\right), \tag{12}\]  
where \(p\) represents the original data, \(q\) is the filtered data, and \(p_{max}\) denotes the maximum signal value. In the engineering calculations, considering that the data processing is conducted in a ring-by-ring manner, with varying lengths of the excavation parameter sequences for each ring, a sliding window of size 11 is chosen after multiple tests. Here, the denoising effect after handling outliers is presented. Table 2 compares the evaluation metric values before and after algorithm improvement, while Figure 6 illustrates the denoising effect achieved via the improved mean filtering algorithm. Figure 6: Comparison of variation amplitude of data values before and after denoising. The improved algorithm enhances the denoising effect on the cutterhead rotation and tunneling speed. The SNR for the cutterhead rotation and tunneling speed increased by 0.58 and 0.12, respectively, while the PSNR increased by 0.58 and 0.13, respectively. The SNR for tunneling speed and cutterhead torque is below 20, indicating a relatively low signal-to-noise ratio.