Accurate prediction of main engine power is essential for vessel performance optimization, fuel efficiency, and compliance with emission regulations. Conventional machine learning approaches, such as Support Vector Machines, variants of Artificial Neural Networks (ANNs), and tree-based methods like Random Forests, Extra Tree Regressors, and XGBoost, can capture nonlinearities but often struggle to respect the fundamental propeller law relationship between power and speed, resulting in poor extrapolation outside the training envelope. This study introduces a hybrid modeling framework that integrates physics-based knowledge from sea trials with data-driven residual learning. The baseline component, derived from calm-water power curves of the form $P = cV^n$, captures the dominant power-speed dependence, while another, nonlinear, regressor is then trained to predict the residual power, representing deviations caused by environmental and operational conditions. By constraining the machine learning task to residual corrections, the hybrid model simplifies learning, improves generalization, and ensures consistency with the underlying physics. In this study, an XGBoost, a simple Neural Network, and a Physics-Informed Neural Network (PINN) coupled with the baseline component were compared to identical models without the baseline component. Validation on in-service data demonstrates that the hybrid model consistently outperformed a pure data-driven baseline in sparse data regions while maintaining similar performance in populated ones. The proposed framework provides a practical and computationally efficient tool for vessel performance monitoring, with applications in weather routing, trim optimization, and energy efficiency planning.

翻译：主机功率的准确预测对于船舶性能优化、燃油效率及排放法规合规至关重要。传统机器学习方法（如支持向量机、各类人工神经网络变体以及基于树的方法包括随机森林、极限树回归器和XGBoost）虽能捕捉非线性关系，但往往难以遵循功率与航速间基本的螺旋桨定律关系，导致在训练范围外的外推性能较差。本研究提出一种混合建模框架，将基于海试数据的物理知识与数据驱动的残差学习相结合。基准组件源自平静水域功率曲线$P = cV^n$，捕捉主要的功率-航速依赖关系；随后训练非线性回归器预测残差功率，表征由环境与运行条件引起的偏差。通过将机器学习任务约束在残差修正上，混合模型简化了学习过程，提升了泛化能力，并确保与底层物理规律的一致性。本研究比较了XGBoost、简单神经网络及物理信息神经网络与基准组件结合的模型，以及未结合基准组件的相同模型。基于实船数据的验证表明，混合模型在稀疏数据区域持续优于纯数据驱动基准模型，同时在数据密集区域保持相近性能。所提框架为船舶性能监测提供了实用且计算高效的工具，可应用于气象航线规划、纵倾优化与能效管理等领域。