A quantitative assessment framework for ship collision risk: Integrating spatiotemporal urgency analysis

Ship collision risk assessment is essential for maritime safety, guiding timely and accurate evasive actions. Traditional models often fail to capture key factors such as dynamic vessel motion and relative positioning. This study proposes a novel spatiotemporal framework for collision risk quantification. Spatial urgency is assessed using a Quaternion Ship Domain (QSD), where the dynamic rate of change in overlapping areas—computed via the Monte Carlo method—reflects spatial collision risk. Meanwhile, temporal urgency is captured through a newly defined Minimum Safe Distance Urgency (MSDU), which evaluates how the actual distance between vessels compares to a simulated minimum safe threshold under various encounter geometries. By integrating these two indicators, the study establishes a multidimensional Collision Risk Index (CRI) optimized via ridge regression. Three classic encounter scenarios—crossing, head-on, and overtaking—are simulated to validate the model. Results show that the proposed method detects risk trends more accurately and promptly than traditional DCPA, TCPA, or static ship domain approaches. The framework enhances situational awareness and offers practical value for real-time navigation and decision-making under urgent maritime conditions. • A novel ship collision risk assessment model is developed by integrating spatial and temporal urgency indicators derived from vessel encounter geometry. • The Quaternion Ship Domain (QSD) combined with Monte Carlo simulation is used to dynamically quantify the rate of change of overlapping areas between vessels. • A Minimum Safe Distance Urgency (MSDU) metric is proposed to capture collision risk trends under various heading angle and relative bearing conditions. • A Collision Risk Index (CRI) is constructed by fusing QSD-based and MSDU-based indicators, with weight coefficients optimized via ridge regression. • The proposed model demonstrates higher sensitivity and accuracy than traditional DCPA/TCPA and static domain methods in simulated crossing, head-on, and overtaking scenarios.