Environmentally conditioned paired difference learning with field residual preservation for recovering controlled mooring response parameters from nonstationary buoy observations

Introduction Long-term motion records from aids-to-navigation buoys combine nonstationary environmental responses, mooring-state variations, and positioning errors. These components are difficult to separate when tension measurements and damage labels are unavailable. Methods We propose field-residual-preserving environment-conditioned paired-difference learning. The method first estimates the predictable horizontal response from forward-aligned wind, wave, current, and attitude variables. It then adds controlled response differences to the same measured record and uses matched random-forest models to infer an equivalent response coefficient, a trajectory reference-center offset, and future statistical reference-radius exceedance probabilities. Results During the retrospective later-period evaluation, the random-forest environmental model reduced vector NRMSE by 41.58 % ± 0.13 % relative to a two-dimensional mean baseline. The complete M2 method achieved a joint NMAE of 0.2659 ± 0.0002 , with a paired improvement of 0.0126 (95% interval: [0.0074, 0.0173]) over M0. The reference-center offset vector MAE decreased by approximately 0.371 m, which represents controlled-parameter recovery accuracy. M2-Ridge retained comparable later-period performance, while a causal three-point median filter reduced the 5 m GPS perturbation ratio from 1.273 to 1.154 at the cost of a higher 6h Brier score. Discussion The method establishes a controlled scenario parameter recovery framework for nonstationary buoy observations. Its outputs are limited to equivalent response scaling, trajectory reference-center translation, and statistical reference-radius exceedance within the prescribed scenarios; they do not validate physical damage detection, anchor movement diagnosis, or maintenance decisions.