Trajectory prediction of cylinders freely dropped into water in two dimensions based on state space model

Abstract

Experiments show that the behavior of dropped cylindrical objects may be stochastic if small disturbances exist at the initial moment. An envelope of various trajectories can be obtained from experimental tests. In addition, numerical results also indicate that small changes of initial states, e.g., drop angle, rolling frequency, and the selection of drag coefficient, affect the trajectory greatly. If the initial state follows the Gaussian distribution,it can be considered as a nonlinear prediction problem. Then the Unscented Transformation (UT) method, as a deterministic sampling method, can be used to predict the trajectory. In this paper, we firstly present a systematic formulation of the cylinder's three-degree-of-freedom (3DOF) of motions as a state space model. Secondly, the UT method and the interval estimation method are employed to solve this prediction problem. Finally, the predicted trajectories will be compared with the experimental data. Meanwhile, two performance parameters are first proposed to evaluate the accuracy of predicted trajectory. Both parameters can be directly applied to the salvage and recovery of dropped objects in the offshore operations. In addition, the numerical results also show that the UT method is an efficient way to predict the trajectory of cylinders freely dropped into water. • The state space model of a dropped cylinder has been successfully constructed in this paper. • The trajectory of a dropped cylinder is considered as the stochastic process due to the uncertainty at the initial moment. • The Unscented Transformation (UT) method is employed to solve the nonlinear trajectory prediction. • Two performance measures R A and R L have been first proposed to evaluate the accuracy of numerical trajectory prediction, in order to meet the requirement from the offshore engineering industry.