# Adjustment Algorithm for Free Station Control Network of Ultra-Large Deepwater Jacket
## 3 Results and Discussion
### Comparison of Different Adjustment Schemes
#### 3.2.3 Adjustment Results via the Proposed Method  
Firstly, the classical free network adjustment is carried out with the same starting data as that of the first phase to obtain the results of the coordinates of each control point and their differences from those of the first phase, which are listed in Table 4. It can be seen that the results are similar to those of Table 2, and the deviations of the points except S7 and S8 are large, with the smallest S5 being 9.8 mm, the largest S6 reaching 16.3 mm, and the mean value being 11.6 mm. Then, the coordinate similarity transformation is carried out using the common points in Tables 1 and 4. The unit-weighted RMSE is 3.3 mm after the transformation. The residuals of each point are shown in Table 5, in which Vx and Vy denote the residuals in the x and y directions, respectively, and \(Vp=\sqrt{Vx^{2}+Vy^{2}}\) denotes the point position deviation. Since the coordinate similarity transformation can absorb the rigid part of the deformation between the two control networks, the residual distribution after the coordinate transformation can effectively reflect the consistency of the deformation of each point. The maximum value of the point deviations is 7.7 mm, the minimum value is 1.5 mm, and the mean value is 3.5 mm, which is one order of magnitude lower than that of Table 4. Taking the value of two times the unit-weight RMSE of the coordinate similarity transformation as the tolerance, the control points whose point deviation is less than this value are regarded as stable points. Otherwise, they are considered to be unstable points. In this example, the tolerance is 6.6 mm, so all control points except S7 in Table 5 can be regarded as quasi-stable points. Figure 7 shows the position deviations after applying multiple schemes for the classical free network adjustment and coordinate similarity transformation, which constrains the initial coordinates of S8 and the initial azimuths of different sides (denoted by S8-S#). It can be seen that the point deviations and unit-weight RMSE of each scheme show good consistency. This shows one of the significant advantages of this method over \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Point Name** & **x (m)** & **y (m)** & **dx (cm)** & **dy (cm)** & **dp (cm)** & **mdp (cm)** \\ \hline S1 & 553.905 & 1090.552 & \(-1.0\) & 0.4 & \(1.1\) & 0.2 \\ S3 & 600.749 & 759.512 & 0.5 & 0.9 & \(1.0\) & 0.2 \\ S4 & 679.342 & 748.656 & 0.6 & 0.9 & \(1.1\) & 0.4 \\ S5 & 661.111 & 898.161 & \(-0.4\) & 0.9 & \(1.0\) & 0.3 \\ S6 & 655.606 & 1095.415 & \(-1.2\) & 1.1 & \(1.6\) & 0.3 \\ S7 & 500.000 & 1074.988 & 0.0 & 0.2 & \(0.2\) & 0.2 \\ S8 & 500.000 & 800.000 & 0.0 & 0.0 & \(0.0\) & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Classical free network adjustment coordinates of the second phase and their comparison with the first phase. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Point Name** & **Vx (mm)** & **Vy (mm)** & **Vp (mm)** & **m0 (mm)** \\ \hline S1 & 1.5 & 0.3 & 1.5 & 3.3 \\ S3 & \(-0.8\) & \(-2.0\) & 2.2 & 3.3 \\ S4 & \(-1.6\) & 1.1 & 1.9 & 3.3 \\ S5 & 2.7 & 0.0 & 2.7 & 3.3 \\ S6 & 3.0 & \(-2.8\) & 4.1 & 3.3 \\ S7 & \(-7.7\) & 0.3 & 7.7 & 3.3 \\ S8 & 2.9 & 3.0 & 4.2 & 3.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Residuals of two phases of coordinate similarity transformations. traditional methods--no matter how the starting data are selected, the final result will not be significantly different. Finally, the quasi-stable adjustment is carried out, and the coordinates of each point after adjustment and the difference between them and the first adjustment result are listed in Table 6. It can be seen that the point deviation of S7 after adjustment reaches 1.1 cm and exceeds twice its mdp (\(2\times 0.3=0.6\) cm). In contrast, the deviations of the rest of the points do not exceed 3 mm, and these values are also less than twice their RMSE, indicating a significant inconsistent deformation of S7 compared to the other points.