BSAformer-based prediction of marine shaft centerline trajectories with real-vessel validation

Accurate shaft trajectory prediction is crucial for condition-based maintenance of marine propulsion systems. However, nonlinear coupling under sea loads still limits accuracy and speed. Unidirectional data models accumulate long-horizon errors and require substantial computational resources, hindering on-board use. To address these challenges, this work adopts BSAformer, a lightweight Transformer-based architecture, for predicting ship propulsion shaft orbits, serving as the computational backbone that integrates bidirectional spectral attention, reconfigured SPSA, and memory-trimming BASS modules. Bidirectional Sequence Split-and-Aggregate Attention (BSAA) captures both forward and backward frequency-domain dependencies, thereby enhancing the model's robustness to residual non-stationary dynamics and mitigating long-term error propagation. The Sequence Progressive Split-and-Aggregate (SPSA) method separates bearing wear trends from shaft-periodic orbit, s haft-periodic (once-per-revolution) orbit components, thereby enhancing incipient-fault sensitivity. Tests on the public ShaftOrbit-2k set show BSAformer outperforms Informer and Autoformer at every speed: trajectory error below 1.5% at 150 r/min and below 4% at 220 r/min with Hausdorff 0.209 to 0.302 mm. When forecasting up to 720 steps ahead, it reduces dynamic-mode error by 42% compared to the best baseline and achieves an R² of 0.945 on longitudinal vibration displacement, outperforming state-of-the-art methods. The results enable a deployable, low-latency tool for real-time health monitoring and early fault detection of ship propulsion systems.