Global behavior monitoring of underwater lines using generalized coordinate based polynomial equations and sensor fusion

A line-monitoring methodology employing cubic polynomial equations and sensor fusion has been developed to evaluate the global behavior and stress distribution of underwater lines. The approach integrates generalized coordinates with a single global coordinate framework to efficiently and conveniently capture the behavior of geometrically complex lines. The system requires input data including displacements and curvatures at both ends and inclinations along the line, which serve as boundary conditions for the polynomial equations. Using the computed global displacements, other stress-related variables, such as tensile, bending, and nominal stresses, can subsequently be estimated. To validate the proposed methodology, two numerical case studies—a submerged inclined tunnel and a lazy-wave riser—were conducted. Results indicate that the global behavior of the underwater lines is accurately recovered when a sufficient number of sensors are employed although its accuracy can be diminished with less number of sensors. Stress estimation demonstrated higher precision in the submerged inclined tunnel compared to the lazy-wave riser due to the latter's pronounced initial curvature and sharp transitions near the touchdown zones.