Risk coupling analysis of ship-source marine pollution accidents based on the N-K model and dynamic Bayesian network

Ship-source marine pollution accidents often occur suddenly and may result in spatially widespread and persistent environmental consequences. Their formation generally involves interactions among human, ship, environmental, and management factors. Based on 537 maritime accidents involving pollution or presenting explicit pollution risks, this study establishes a four-dimensional risk-factor system comprising 11 basic nodes and develops an integrated N-K-DBN framework. First, the N-K model is used to calculate coupling frequencies and coupling intensities for different combinations of risk factors, thereby identifying critical coupling patterns in the formation of pollution risk. Second, coupling intensity is embedded into the state-transition process of a dynamic Bayesian network (DBN) to simulate the propagation, persistence, and amplification of pollution risk across standardized time slices. The results show that action errors, safety awareness, navigational environment, decision errors, and organizational management occur frequently in the sample. Multi-factor coupling intensities generally show stronger statistical dependence than two-factor couplings, with the human-ship-environment-management coupling being the strongest. Dynamic inference indicates that human-environment coupling maintains a high probability of activation across multiple time slices and constitutes an important pathway for pollution risk propagation. Sensitivity analysis identifies organizational management, navigational environment, navigational aids, and action errors as influential in selected pathways, while uncertainty analysis indicates that the ranking of the principal coupling pathways remains stable under transition-probability perturbations. The proposed model provides methodological support for risk warning, key-node identification, and hierarchical prevention and control of ship-source marine pollution accidents.