Abstract
In this paper, a mathematical model for the rolling motion of ships in random beam seas has been investigated. The ships’ steady-state rolling motion with a nonlinear restoring moment and damping effect is modeled by the nonlinear second-order differential equation. Furthermore, an artificial neural network (NN)-based, backpropagated Levenberg-Marquardt (LM) algorithm is utilized to interpret a numerical solution for the roll angle , velocity , and acceleration of the ship in random beam seas. A reference data set based on numerical examples of the mathematical model for a rolling ship for the LM-NN algorithm is generated by the numerical solver Runge–Kutta method of order 4 (RK-4). The LM-NN algorithm further uses the created data set for the validation, testing, and training of approximate solutions. The outcomes of the design paradigm are compared with those of the homotopy perturbation method (HPM), optimal homotopy analysis method (OHAM), and RK-4. Statistical analyses of the mean square error (MSE), regression, error histograms, proportional performance, and computational complexity further validate the worth of the LM-NN algorithm.
Highlights
Ships experience different motions, including angular and displacement motions, categorized as yaw, pitch, roll, heave, drift, and surge
An approximate solution for each example obtained by the LM-neural network (NN) is compared with those of the homotopy perturbation method (HPM) [19], the Runge–Kutta method (RK-4), and the optimal homotopy analysis method (OHAM) [39], as shown in
This paper analyzes a mathematical model of the rolling motion of ships with nonlinear damping in random beam seas
Summary
Ships experience different motions, including angular and displacement motions, categorized as yaw, pitch, roll, heave, drift, and surge. The stabilization of a ship depends on two methods, namely roll reduction and the modeling or evaluation method of roll performance. In the later part of the mid-18th century, Froude studied a ship’s rolling motion for the first time. Norio Tanaka [1] introduced the empirical and semi-empirical roll damping coefficient for dynamic equations. A simple method was proposed by Himeno [2] for the prediction of the roll damping of ships at forwarding speed. In 2004, Ikeda [3] presented the modified model of roll damping with a steady drift motion
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call