## 4 Case Study
### Principal Components Analysis Based on Mechanism and Knowledge  
During the construction, mud formation is influenced by many factors such as soil type, mechanical parameters and rotation speed of the cutter, traverse speed of the dredger, dredge pump parameters, and so on. To monitor and control the dredging process, up to 255 specific real-time sensors were arranged to collect the operational data [27]. Figure 4 shows some of the related monitoring parameters and relationship in automatic control system. As shown in Figure 4, some of the parameters are control variables, while some of them are only display variables that make the data visualization. Soil property is an important factor affecting the construction process and efficiency of cutter suction dredgers. For different solidity and water-solubility, the mud concentration is limited by cutting performance and silt mixing. The cutter structure, pipeline diameter, and the motor power of pumps are all specific variables (constant), which were demonstrated according to the demand for rated productivity at the beginning of the design. However, the cutter speed, trolley trip, cutter ladder movement, and dredge pump rotation are all control variables that can be adjusted during the operation process in specific construction. When digging hard soil, the dredging depth should be reduced while enhancing the cutter speed to prevent the formation of large diameter mud balls and pipe blocking. When the dredging soil is sediment or silt, the pump velocity should be appropriately increased to reduce the mud concentration and avoid sedimentation or clogging in the pipeline. According to the actual sensor system of cutter suction dredger \"Chang Shi 10\", we firstly select 20 variables from the initial operational dataset as shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Unit** \\ \hline S\({}_{8}\) & Angle of the cutter ladder & \\ S\({}_{9}\) & Depth of the dredging & m \\ S\({}_{12}\) & Rotation speed of the submersible pump & rpm \\ S\({}_{13}\) & Rotation speed of the cutter & rpm \\ S\({}_{20}\) & Flow & m\({}^{3}\)/h \\ S\({}_{23}\) & Soil density & kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial variables from the operational dataset. Figure 4: The monitoring parameters related to dredging process and productivity. Traditionally, the instantaneous productivity of the cutter suction dredger is the product of the flow and mud concentration. \[P=C_{m}\cdot Q=C_{m}\cdot(v\cdot\pi r^{2}) \tag{39}\]  
where \(C_{m}(\%)\) represent the mud concentration; \(Q\) is the flow amount per hour; and \(v\) is the flow rate. As shown in Table 1, we choose \(\mathbf{S_{21}}\) (mud concentration) as the target variable. In actual dredging construction process, the change of flow rate in the sludge pipeline is one of the important factors affecting the flow. Thus, we delete the redundant variable \(\mathrm{S_{20}}\) flow in the first step. Meanwhile, the mud concentration is determined by the density of soil, water, and mud. \[C_{m}=\frac{\gamma_{m}-\gamma_{w}}{\gamma_{s}-\gamma_{w}} \tag{40}\]  
where \(\gamma_{m}\) is the mud density; \(\gamma_{w}\) is the water density; and \(\gamma_{s}\) is the soil density. Then we drop three redundant variables \(\mathrm{S_{223}}\), \(\mathrm{S_{23}}\), and \(\mathrm{S_{164}}\) in the second step. For the study period in this case, the ship works with just No.1 dredge pump. Thus, the variables related to No.2 dredge pump are non-meaningful to the productivity. Namely, \(\mathrm{S_{101}}\) and \(\mathrm{S_{200}}\) are dropped according to human analysis and finally we obtain the related variable set as:  
\[X^{\prime}=\left\{S_{8},S_{182},S_{108},S_{13},S_{9},S_{201},S_{12},S_{198},S_ {100},S_{199},S_{165},S_{79},S_{80},S_{21}\right\} \tag{41}\]  
As described in Section 3.1, the selected variables \(\mathbf{X}^{\prime}\) dataset based on human experience will be processed by PCA in this section.