白噪声海浪激励下船舶非线性横摇运动的概率分析(英文)  

Probability Analysis of Ship Nonlinear Roll-Motion Excited by White Noise

作　　者：谷家扬[1] 

机构地区：[1]江苏科技大学船舶与海洋工程学院,江苏镇江212003

出　　处：《船舶力学》2006年第3期17-25,共9页Journal of Ship Mechanics

摘　　要：应用求解FPK方程近似解的一种新理论研究白噪声激励下船舶非线性横摇运动的联合概率密度函数及稳定期望穿阈率。船舶随机横摇运动微分方程考虑到阻尼力与恢复力的非线性。新理论基于减少FPK方程的误差以获得参数化的联合概率密度函数。应用本理论易得一维积分表达的系统响应的概率特性,如联合概率密度函数及稳定期望穿阈率。近似解与精确解的比较结果表明:新理论在研究白噪声激励下船舶非线性横摇运动是非常有效的。The stationary probability density function （PDF） and the stationary mean out-crossing rate （MOR） of the response of ship nonlinear roll-motion subjected to additive stochastic white noise excitation are examined by a new approximate method in this paper. The method is based on finding the best probability density function from a parameterized class of trial non-Gaussian PDF by minimizing the weighted norm of the Fokker-Planck-Kolmogorov （FPK） equation error. The ship rolling motion is described by a nonlinear random differential equation that includes a nonlinear damping moment and restoring moment. The proposed procedure yields simple expression in terms of one dimensional integral for determining desired probability characteristics of the system response, such as moments and mean out-crossing rate. Comparison results are given to show the effectiveness of the method in the study of randomly excited nonlinear ship roll motion.

关 键 词：FPK方程 白噪声 联合概率密度函数 稳定期望穿阈率 非线性横摇运动 

分 类 号：U661.32[交通运输工程—船舶及航道工程]