A Hybrid Theil–Hoover Entropy Model for Navigational Disorder and Collision Risk Assessment: A Case Study of Ningbo Zhoushan Port

This paper introduces a hybrid entropy-based model that combines the Theil and Hoover indices to quantify navigational disorder as a meso-scale indicator for comparative screening of navigational order and relative collision-risk exposure in maritime traffic systems. It is not intended to predict collision probability at the encounter level, and its collision-risk interpretation requires independent validation against accident, near-miss, or conflict data. Although traditional information entropy methods are useful for measuring overall uncertainty, they provide limited insight into differences in the distributional characteristics of vessel trajectories. Drawing on concepts from information theory and spatial econometrics, this study proposes a dual-index framework that combines a normalised entropy-based measure with an absolute-deviation measure of course distributions. When the number of angular bins is fixed, the Theil index is a linear transformation of Shannon entropy, i.e., T = lnn − H; it therefore does not provide independent information beyond entropy. The Hoover index, by contrast, measures cumulative absolute deviation from a uniform distribution and can respond differently to distributions with similar entropy values. Using AIS data from Ningbo–Zhoushan Port, the results show that the hybrid model is broadly consistent with conventional information entropy in high- and low-disorder areas while providing complementary information for medium-disorder and structurally complex areas. A composite Navigational Disorder Score (DNS) is constructed using the entropy weight method, providing a unified and interpretable metric for comparative screening of navigational order across waterway legs. The DNS combines a normalised entropy-based component with an absolute-deviation component, rather than combining two mathematically independent entropy measures. The proposed framework offers a complementary meso-scale diagnostic tool for assessing navigational order and improving the interpretability of statistical assessments in complex maritime traffic systems.