Physics-constrained probabilistic inversion of sinker position for navigation buoy maintenance

Moored navigation buoys work under combined wind, wave, current, and tide loads, but maintenance depends on the seabed sinker and the watch-circle boundary, which are rarely observed continuously. This study aims to infer sinker position and watch-circle behaviour from routine buoy trajectories and environmental records. A physics-constrained probabilistic inversion framework is proposed for this purpose. The method combines local coordinate reconstruction, a dominant wind–wave–current load surrogate, alternating anchor–radius updates, and a heteroscedastic Gaussian process to model condition-dependent uncertainty. Long-term records from multifunctional buoy No. 304 in Qingdao Port are assessed by leave-one-month-out cross-validation. Relative to the unconstrained Data-driven HGP, PRHI-GP reduces monthly anchor drift from 0.862 m to 0.631 m and improves axis consistency from 0.587 to 0.644, while maintaining Coverage95 of 0.995, NLL of 2.903, and radius RMSE of 3.984 m. When wind speed exceeds 9 m/s, Coverage95 remains 0.973, and the mean and maximum restoration vectors are 0.573 m and 0.920 m. These results indicate that the proposed framework yields a more stable maintenance-oriented interpretation than the corresponding model without the physical load constraint, while keeping acceptable predictive accuracy. It can support restoration planning, risk ranking, and routine buoy maintenance.