# Adjustment Algorithm for Free Station Control Network of Ultra-Large Deepwater Jacket
## 4 Conclusions  
For the second and consequent phases of a control network, if the first-phase coordinates of two or more control points are constrained to carry out the adjustment, the results would exhibit large differences due to the possible deformation. If there are large relative deformations between the constrained points, each point's adjusted coordinates will be \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Point Name**} & \multirow{2}{*}{**Stable**} & \multirow{2}{*}{**x (m)**} & \multirow{2}{*}{**y (m)**} & \multicolumn{4}{c}{**Difference**} & \multirow{2}{*}{**mdp (cm)**} \\ \cline{5-6}  & & & & **dx (cm)** & & **dy (cm)** & & **dp (cm)** \\ \hline S1 & Y & 553.916 & 1090.547 & 0.2 & \(-0.1\) & 0.2 & 0.2 \\ S3 & Y & 600.744 & 759.505 & 0.0 & 0.2 & 0.2 & 0.2 \\ S4 & Y & 679.337 & 748.646 & 0.2 & \(-0.1\) & 0.2 & 0.2 \\ S5 & Y & 661.113 & 898.152 & \(-0.1\) & 0.0 & 0.1 & 0.2 \\ S6 & Y & 655.617 & 1095.405 & 0.0 & 0.1 & 0.1 & 0.3 \\ S7 & N & 500.010 & 1074.986 & 1.0 & 0. & 1.1 & 0.3 \\ S8 & Y & 499.997 & 799.998 & \(-0.2\) & \(-0.2\) & 0.3 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quasi-stable adjustment coordinates for the second phase and their difference compared to the first-phase results. Figure 7: The point deviations of the proposed adjustment method with different starting data compared to the first phase. affected, leading to incorrect conclusions. The rank-deficient free network adjustment method effectively avoids the adverse effects of improper selection of starting data on adjustment. However, due to the characteristics of the jacket construction site, it is impossible to ensure that the location and number of stations are consistent in each phase relative to those in the first phase. Therefore, the center-of-gravity datum constraints do not apply to free station control networks. The quasi-stable adjustment is based on the rank-deficient free network adjustment while fully considering that some points in the network are stable and some points are unstable, which is more in line with the actual situation and can be applied to the free station control network. However, reasonably identifying the stable points is a major difficulty in the quasi-stable adjustment. According to the special characteristics of the free station control network for deep-water ultra-large jackets, this paper proposes an effective three-step analysis method, i.e., firstly introducing only the necessary starting data to obtain the preliminary solution through the classical free network adjustment, then identifying the stable and unstable points by similarly transforming them with the first-phase coordinates and absorbing the rigid deformation of the two-phase control network, and then finally carrying out the quasi-stable adjustment to solve the coordinates of each point. The stable and unstable points can be identified accurately and efficiently without several adjustment attempts, which is advantageous in terms of accuracy and efficiency compared with the traditional method. The feasibility and accuracy of this methodology are validated through comparative analysis with conventional adjustment results, specifically applied to a real-world case study of ultra-large jacket structures in coastal offshore engineering. Notably, the proposed approach also provides a generalizable framework for various free station-type deformation monitoring scenarios. Conceptualization, D.Z. ; methodology, X.Y. ; software, D.Z. and W.X. ; validation, D.W.; formal analysis, W.S. and H.L. ; investigation, H.W. and W.X. ; resources, H.L. ; data curation J.L. and W.X. ; writing--original draft X.Y., W.S., H.W., Y.W. and D.W.; writing--review and editing, D.Z. and J.L. ; visualization H.W. and H.L. ; supervision, Y.W. ; project administration W.S. ; funding acquisition, D.Z. All authors have read and agreed to the published version of the manuscript. This research received no external funding.