To reduce diagnostic uncertainty in hydraulic systems during vessel operation, this study investigated the correlation between fault features and monitoring parameters. Using monitoring data collected under normal operating conditions as the baseline, the association strength between multi-source monitoring features and ten fault modes was quantified via standardized deviation (Z-scores). On this basis, a hierarchical weight matrix, incorporating correlations between faults and features, devices and features, and subsystems and features, as well as lateral coupling coefficients, was constructed to capture hidden associations among signals, devices, and subsystems. Subsequently, a PGC-LightGBM algorithm was proposed, which embedded prior knowledge from the hierarchical weight matrix into model training through differentiated sample weighting: fault samples exhibiting larger deviations on physically correlated features were assigned higher training weights, thereby enabling multi-level fault diagnosis that accounts for multi-fault coupling and operational interactions across the entire hydraulic system. On a marine hydraulic pump station test bench dataset, the proposed method improved the macro-averaged F1 score from 75.3% to 77.8% under 5-fold stratified cross-validation, and from 63.2% to 68.2% on the independent test set. The fault-class average F1 rose from 59.9% to 65.4%, while the normal-class F1 of the weighted model reached 96.3%, remaining unaffected compared with 95.7% for the standard model. Ablation studies indicated that fault-level physically informed weights were the main contributing factor to the performance improvement, while device-level, subsystem-level, and lateral coupling components provided richer physical interpretability. This study provides an effective reference for reliability analysis and risk prediction in marine hydraulic systems.