## 5 Alignment Optimization  
### Response Surfaces of the Dynamic BLINs  
When the raft frame is in the leveled state mentioned above, the alignment calculation can be considered as the straight-line alignment calculation taking the raft frame as benchmark. Based on the numerical model of the elastically supported shafting, the alignment in such condition was calculated, and the results are shown in Table 2.  
Due to the cantilever effect induced by the heavy propeller, the load of the rear stern bearing is very large, as listed in Table 2. Vertical displacement ranges of [\(-3.5\), \(3.5\)] mm for both the rear and front stern bearings, and [\(-2\), \(2\)] mm for the thrust bearing were selected to build the response surfaces between vertical displacements and the BLINs, following the measurement criterion of the equivalent line-surface method. Since the vector with dimension greater than four is a hypercube in spatial coordinates, the built response surfaces are presented in three-dimensional form below. Figure 8 shows the response surfaces between each element in the BLINs matrix and the vertical displacement of the rear stern bearing \(\Delta y_{1}\) and \begin{table}
\begin{tabular}{c c c c} \hline
**Bearing** & **Relative Deflection (mm)** & **Bearing Load (kN)** & **Rotation Angle (Rad)** \\ \hline Rear stern bearing & 0.198 & 17.94 & \(9.79\times 10^{-4}\) \\ Front stern bearing & \(-0.076\) & 7.14 & \(-3.31\times 10^{-4}\) \\ Thrust bearing & \(-0.095\) & 8.31 & \(-2.54\times 10^{-4}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Calculation results of straight-line alignment taking the raft frame as benchmark. Figure 7: Flowchart for building the response surfaces using GPR. \(\Delta y_{2}\). It can be seen that the BLINs change dynamically with the variation of \(\Delta y_{1}\) and \(\Delta y_{2}\). As shown in Figure 8a, when the height of the front stern bearing is fixed, the influence number of the rear stern bearing about itself \(A_{11}\) increases approximately linearly with the elevation of itself. However, when the height of the rear stern bearing is fixed, \(A_{11}\) initially decreases and then increases with the elevation of the front stern bearing. In Figure 8b, the influence number of the front stern bearing about itself \(A_{22}\) is positively correlated with the displacements of two stern bearings. When \(\Delta y_{1}\) and \(\Delta y_{2}\) are more than 3 mm, \(A_{22}\) begins to rise rapidly. In Figure 8c, the influence number of the thrust bearing about itself \(A_{33}\) has a nonlinear relationship with the variation of \(\Delta y_{1}\) and \(\Delta y_{2}\). \(A_{33}\) initially decreases and then increases with the increase in \(\Delta y_{1}\), but first increases and then decreases with the increase in \(\Delta y_{2}\). Combined with the analysis results of the bearing displacement characteristics and the deflection of the raft frame, with the heights of the stern bearings within certain ranges, the shafting is approximately in the straight-line alignment state. The load among the bearings is evenly distributed, and the change in bearing load caused by elastic deformation is mainly concentrated on the rear stern bearing. When the adjacent bearings are continuously elevated or lowered, the raft frame will generate obvious middle arching or subsiding deformation, and the displacement of the thrust bearing Is apparent, to some extent, which will seriously deteriorate its working condition and even cause the bearing to become locked or void. The BLINs of the thrust bearing will significantly increase or decrease, too. Figure 8d-f show the response surfaces between \(A_{12}\), \(A_{13}\), \(A_{23}\) and \(\Delta y_{1}\), \(\Delta y_{2}\). It can be seen that there is a weak coupling between the load of the rear stern bearing and the front stern bearing. When \(\Delta y_{1}\) or \(\Delta y_{2}\) is individually adjusted, \(A_{12}\) exhibits minimal variation characterized by an approximately linear trend.