The rational placement of pollutant monitoring sensors has long been a prominent research focus in ocean environment science. Our method integrates an incremental Proper Orthogonal Decomposition with a mobility-constrained sensor selection strategy, enabling efficient monitoring and dynamic adaptation to spatio-temporal field changes. At each time step, the position of the sensors is updated based on the incoming measurements to minimize the reconstruction error while adhering to movement constraints. This online approach considers the need for mobility distance, making it suitable for long-term deployments in resource-limited scenarios. The proposed framework is validated in three scenarios: a linear advection–diffusion system with multiple moving pollution sources, the distribution of particulate matter with an aerodynamic diameter smaller than 2.5 μm (PM2.5) across the United States, and scalar transport in flows past side-by-side cylinder arrays in the ocean. The results demonstrate that the method achieves high reconstruction accuracy with significantly fewer sensors. This study conducts a comparative analysis of three typical mobility constraints and their respective effects on reconstruction accuracy. In addition, the proposed localized sensor mobility strategy effectively tracks evolving plume structures and maintains a low approximation error, providing a generalizable solution for sparse monitoring of the marine environment.

Ship safety assessment must accommodate aleatory variability, epistemic incompleteness, and heterogeneous representations of uncertainty. This study develops a generalized probability theory (GPT) as an extended probabilistic framework that interfaces with classical probability, fuzzy theory, grey system theory, and Dempster-Shafer (D-S) evidence theory while preserving their distinct semantics. Generalized random numbers (GRNs) represent information at different levels of precision; the degree of overlap (DOO) characterizes shared information structures; and the residual event W retains probability mass outside the currently identified factor set. Generalized total probability and generalized Bayesian inference enable forward propagation and backward diagnostic updating, respectively. Using multi-factor coupling data from complex waters, the framework distinguishes empirical co-occurrence from information overlap, corrects double counting among coupled factors, and supports higher-order propagation and posterior updating. The case study is limited to real-valued coupling data. Within this validation boundary, the generalized probability theory provides a consistent and interpretable interface for uncertainty representation and probabilistic inference in ship safety assessment.