## 4 Case Study
### Principal Components Analysis Based on Mechanism and Knowledge
In addition, the contribution result is shown in Figure 5.  
It is obvious that the top 10 principal components can represent more than 97% of the overall data. For the top two principal components, the dataset can be plot as Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Unit** \\ \hline \(\mathrm{S_{79}}\) & Distance of the swing movement & m \\ \(\mathrm{S_{80}}\) & Angle of the swing & \\ \(\mathrm{S_{100}}\) & Rotation speed of the No.1 dredge pump & rpm \\ \(\mathrm{S_{101}}\) & Rotation speed of the No.2 dredge pump & rpm \\ \(\mathrm{S_{108}}\) & Power of the cutter & kw \\ \(\mathrm{S_{164}}\) & Mud density & kg/m\({}^{3}\) \\ \(\mathrm{S_{165}}\) & Flow rate & m/s \\ \(\mathrm{S_{182}}\) & Trolley trip & m \\ \(\mathrm{S_{198}}\) & Discharge pressure of the submersible pump & kPa \\ \(\mathrm{S_{199}}\) & Discharge pressure of the No.1 dredge pump & kPa \\ \(\mathrm{S_{200}}\) & Discharge pressure of the No.2 dredge pump & kPa \\ \(\mathrm{S_{201}}\) & Vacuum & kPa \\ \(\mathrm{S_{223}}\) & Water density & kg/m\({}^{3}\) \\ \(\mathbf{S_{21}}\) & **Mud concentration** & **\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._From the scatter plot of dataset in 2D figure, the correlation of the variables related to target S\({}_{21}\) can be set as shown in Equation (28):  
\[X^{\prime\prime}=\{S_{8},S_{182},S_{108},S_{13},S_{9},S_{201},S_{12},S_{198},S_{1 00},S_{199},S_{165},S_{79},S_{80}\} \tag{42}\]  
The most positively relevant variables to target can be further determined by the correlation matrix, as shown in Figure 7.  
As the correlation matrix shows, the correlation between S\({}_{21}\) and S\({}_{199}\) is 0.48677, which means the discharge pressure of No.1 dredge pump affects the concentration most. It is consistent with the practical production. Pressure will influence the mud and water proportion that is pumped into pipeline. The variable S\({}_{165}\) shows a correlation of 0.34628, which is also mentioned by other researchers [5,27]. The flow rate may determine the mud sedimentation during pipeline transportation. Furthermore, the vacuum correlation is 0.34152, since the vacuum gauge is installed on the upper part of the cutter, which is sensitive to the change of the mud concentration in the pipeline. Additionally, the angle of cutter ladder, the depth of dredging, and the trolley trip are all factors that affect the mud formation by operation controllers. However, for the discharge of the submersible pump, it is just the indirect factor to display the vacuum condition. Figure 5: The percentage of explained variance for principal components. Figure 6: Scatter plot of the dataset after PCA. Meanwhile, it is indicated in the correlation matrix that there are five negative variables to the target. Thus, we obtain the final variables set most positively relevant to the target S\({}_{21}\) as:  
\[X^{**}=\{S_{182},S_{108},S_{8},S_{9},S_{201},S_{198},S_{100},S_{199},S_{165}\} \tag{43}\]  
In general, the mud concentration is mainly inter-influenced by the dredge pump pressure, flow rate, vacuum, cutter ladder angle, dredging depth, and trolley trip.