Ship operational data driven fuel efficiency assessment for shaft generator using input convex neural network

This study develops a data-driven yet physically consistent framework to quantify the real-world fuel efficiency of a PTO-mode shaft generator (S/G) using high-resolution operational data from an 86k CBM LPG carrier. To capture the nonlinear and load-dependent interactions between propulsion and electric power generation, an Input Convex Neural Network (ICNN) is trained under convexity and monotonicity constraints in the S/G power ratio, ensuring both accurate prediction and physically reliable response shapes. Compared with conventional machine-learning models (MLP, gradient boosting, random forest), the ICNN achieves comparable predictive accuracy while eliminating the shape violations frequently observed in unconstrained models. Model performance remains high for both laden and ballast operations (R² = 0.88 – 0.94; RMSE ≈ 1 – 3 g/kWh). On-manifold partial dependence analysis reveals distinct operational patterns: in laden voyages, fuel savings emerge primarily above ∼ 60 % S/G power ratio, reaching ∼3.8 g/kWh at full utilization, whereas in ballast voyages savings increase monotonically across the entire range, peaking at ∼1.65 g/kWh. These behaviors align with main engine BSFC maps and reflect condition-dependent trade-offs between propulsion loading and auxiliary generator displacement. The proposed framework provides actionable guidelines, maximizing S/G use in ballast runs and selectively increasing it in laden runs, and offers a robust foundation for AI-assisted energy-management systems that optimize fuel economy under realistic operating constraints.