Construction of Typical Sailing Conditions for Harbor Tugs Based on WOA-K-Means++ Clustering and Hidden Markov Models

The global shipping industry faces severe carbon emission challenges. Harbor tugs, as significant contributors to port emissions, require improved energy efficiency. However, their sailing conditions are complex and dynamic, making temporal feature characterization difficult with traditional static or simplistic clustering methods. To address this, this study proposes a novel method for constructing typical sailing conditions by integrating an enhanced clustering approach with Hidden Markov Models (HMM). First, kinematic segments are extracted from processed ship speed data, and key features are selected and reduced via Principal Component Analysis (PCA). Subsequently, an improved clustering model combining the Whale Optimization Algorithm (WOA) and K-means++ is developed to categorize segments into six distinct condition types. These clustered states then serve as the hidden states of an HMM, whose learned transition matrix synthesizes a 3600 s typical sailing condition profile. The constructed profile is validated through multi-dimensional comparison with original data, demonstrating high fidelity in statistical characteristics, temporal properties, and distribution similarity. The results confirm that the proposed method can accurately replicate the operational patterns of harbor tugs. This study provides a reliable data foundation for the energy efficiency assessment and optimization of harbor tugs and offers a new methodological perspective for constructing operational profiles for ships and other mobile machinery.