Practical method for evaluating wind influence on autonomous ship operations

Abstract

The autonomous operations of marine vehicles have recently attracted significant attention. In particular, automation of harbor operations, such as autonomous docking or berthing, is a challenging target. In low-speed harbor operations, the external disturbance of wind is a non-negligible factor. Therefore, the stochastic behavior of gusty wind should be considered in numerical simulations. This study presents a practical computational scheme for generating random wind velocity fields. In the proposed method, the von Kármán’s spectrum [1] and Hino’s wind speed spectrum [2] were fitted by a degree of freedom (1DoF) filter driven by the Wiener process. The corresponding Itô’s equation had the form of the Ornstein–Uhlenbeck process. By employing the analytical solution of the Ornstein–Uhlenbeck process, the wind process was successfully generated without time series repetition. Furthermore, the wind speed and direction processes were also generated from the measured drift and diffusion terms. The spectra of these numerical results are consistent with the observed spectra.

Appendix

In some studies, e.g., [5, 33], forces and moment acting on hull due to wind can be estimated using Fujiwara’s regression formulae [34]

$$\begin{aligned} \begin{aligned} X_{A}&= (1/2)\rho _{A}U_{A}^{2}A_{T}\cdot C_{X} \\ Y_{A}&= (1/2)\rho _{A}U_{A}^{2}A_{L}\cdot C_{Y} \\ N_{A}&= (1/2)\rho _{A}U_{A}^{2}A_{L}L_{OA}\cdot C_{N} , \end{aligned} \end{aligned}$$

(31)

where

$$\begin{aligned} \begin{aligned} C_{X} = &X_{0}+X_{1} \cos (2\pi - \gamma _{A})+X_{3} \cos 3 (2\pi - \gamma _{A}) \\&+X_{5} \cos 5 (2\pi - \gamma _{A}) \\ C_{Y} = &Y_{1} \sin (2\pi - \gamma _{A})+Y_{3} \sin 3 (2\pi - \gamma _{A}) \\&+Y_{5} \sin 5 (2\pi - \gamma _{A}) \\ C_{N} = &N_{1} \sin (2\pi - \gamma _{A})+N_{2} \sin 2 (2\pi - \gamma _{A}) \\&+N_{3} \sin 3 (2\pi - \gamma _{A}) . \end{aligned} \end{aligned}$$

(32)

Here, $X_{A}$ is the surge directional wind force; $Y_{A}$ is the sway directional wind force; $N_{A}$ is the yaw directional wind moment; $\rho _{A}$ is the density of air; $A_{T},\ A_{L}$, and $L_{OA}$ are the transverse projected area, lateral projected area, and the overall length of the ship, respectively. $X_{i}, \ Y_{i}$, and $N_{i}$ are the coefficients in the regression formulae [34]. These parameters can be estimated only from the geometric parameters of the ship.