Calculation of Ship Rolling Capsizing Probability by Path Integral Solution

Abstract

Abstract: By analyzing nonlinear rolling motion of the ship, a nonlinear differential equation of ship rolling motion was established. The two-dimensional FokkerPlanck equation in time domain was solved by using the path integral solution (PIS) and the transition probability density of the ship rolling was obtained. The distribution of the first passage time was achieved by first passage theory. Some examples were presented and the influences of the magnitude of external excitation, the rolling damping and the nonlinear restoring moment on the transition probability density of the ship rolling and the first passage time were analyzed. The results show that the method is available to predict the distribution of the first passage time and provides valuable reference to the ship design and the safe standards.

Key words: ship capsizing, nonlinear rolling, FokkerPlanck equation, path integral solution(PIS), first passage

CLC Number:

U 661.32

CHAI Wei, FAN Ju, ZHU Ren-Chuan, HUANG Xiang-Lu, MIAO Guo-Ping. Calculation of Ship Rolling Capsizing Probability by Path Integral Solution[J]. Journal of Shanghai Jiaotong University, 2013, 47(02): 317-322.

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