Time-evolving graph-based approach for multi-ship encounter analysis: Insights into ship behavior across different scenario complexity levels

Maritime traffic management confronts significant challenges in understanding multi-ship encounter dynamics, particularly in busy waterways. Despite extensive research, the intricate ship behavior patterns and traffic complexity remain insufficiently explored. This study proposes an innovative time-evolving graph-based approach to systematically decompose and analyze multi-ship encounters. Firstly, we employ classical collision risk indicators—Distance to Closest Point of Approach (DCPA), Time to Closest Point of Approach (TCPA), and Relative Distance (RD)—to detect all ship pairs exhibiting encounter relationships. Subsequently, a novel Find-Verify-and-Fix (FVF)-based clustering algorithm is designed to transform sequential two-ship encounters into multi-ship scenarios, capturing the dynamics of ship interactions and their spatiotemporal interference characteristics through evolutionary topology graphs. Furthermore, we integrate a matrix energy model from graph theory with an improved k-means clustering method to assess the complexity level of multi-ship encounters, facilitating an in-depth examination of the key factors contributing to high complexity. Finally, a detailed correlation analysis is conducted to explore the relationship between ship behavior patterns and different complexity levels of encounter scenarios. Experimental analysis using Automatic Identification System (AIS) data from Ningbo-Zhoushan Port reveals critical insights into maritime traffic dynamics. Results demonstrate that factors such as the number of ships and changes in ship topology over time significantly influence traffic complexity. Key findings highlight that in multi-ship encounter scenarios, ships collectively exhibit a relatively conservative behavior pattern, maintaining both a constant speed and steady course. As scenario complexity increases, ships demonstrate adaptive behaviors—notably reduced average speeds and increased turning frequencies, with a particular tendency towards starboard turns. These results will assist traffic management authorities in providing a scientific basis for decision-making, thereby optimizing navigational safety policies.