The applicability of stochastic averaging method to solve the ship rolling response excited by narrow-band waves
In this paper, a single-degree-of-freedom rolling equation under parametric excitation is established. Based on strip theory, the righting arm is calculated by numerical simulation with different roll angles, wave heights, and phase angles of the wave position. Then the least square method is used to obtain an analytical expression of the righting arm. The stochastic averaging method of energy envelope is used to calculate the ship rolling response under random excitation. Compared with the Monte Carlo solution, the accuracy of stochastic averaging method under different sea conditions is evaluated. The results show that with the decreasing of the hydrodynamic damping, the peak factor or the excitation intensity of the considered JONSWAP sea spectrum, the accuracy of the stochastic averaging method increases. As a result, conditions for applicability of the stochastic averaging method of energy envelope for practical engineering problems are given. A very efficient way to analyze the roll response of ships in random seas is when stochastic averaging and Monte Carlo simulations are used hand in hand.
Stochastic averaging method