Stochastic inversion for the roll gyradius second moment mass property in ships at full-scale and model-scale

In current Naval Architecture practice, employing static considerations is an important and necessary step in assessing ship stability and seakeeping properties (e.g. inclining experiments, load line regulations, range of stability calculations). However, damaged vessels and vessels operating in heavy weather or in conditions where topside icing is a concern may require an additional assessment of stability that considers dynamic effects. Within such contexts, the actual (i.e. current) second moment properties of the vessel mass become very important in the associated equations of motion for a given ship. One such critical second mass moment property is the roll gyradius, as it is closely related to the occurrence of capsizing. The present paper furnishes a means for reckoning the actual roll gyradius of a given ship operating within a seaway. The approach hinges on the formulation and solution of a stochastic inverse problem that leverages existing seakeeping software against the shipboard inertial measurement unit (IMU) telemetry. The method is demonstrated at full-scale and validated at model scale.