Forecasting of catamaran roll risk situations in stormy conditions

Abstract

The problem of uncertainty of catamaran behavior during a storm is considered. The main danger of uncertainty lies in the magnitude of the roll by which the catamaran will deviate, since this can lead to adverse consequences with the cargo or the hull of the vessel. The study of this uncertainty is considered from two positions: the study of control actions in the implementation of the worst-case scenarios of unrest at the stage of selecting a control system and online forecasting of roll thresholds. A complex model of catamaran and external disturbances is used. External perturbations are obtained using a formative filter and linear approximation of the Pearson-Moskowitz spectrum, forces and moments. The study of the quality of management is carried out by calculating the most likely trajectories to the specified threshold states and then comparing them with each other. This calculation is performed by solving an optimization problem of the Lagrange-Pontryagin type with an action functional as a criterion and a complex catamaran model and external disturbances as a coupling equation. Using the methods of the theory of large deviations, estimates of the probabilities of movement to threshold values along the most likely trajectories are obtained. Using these estimates and comparing them with the current state of the catamaran made it possible to realize the forecast of risky situations. Examples of trajectories leading to threshold states are given for several cases of wind and heading angles of the vessel obtained with different control circuits. At the same time, it can be seen that depending on the control, fluctuations arise, which must be paid attention to when designing the control. An example of estimating the probability of movement to the threshold state during the rolling of the catamaran is given. The use of threshold state profiles allows not only to obtain useful information in the design of control systems, but also to improve the safety of navigation.