用Morlet小波变换研究舰船横摇垂荡耦合特性

Using Morlet wavelet transform to analyze dynamical characters of nonlinear ship rolling with heave-roll coupling

本文探索了用小波变换方法对舰船横摇垂荡非线性耦合动力学特性的研究。对于考虑与垂荡二次耦合的舰船横摇方程,用Morlet小波变换分析其摇摆响应动力学特性,研究分析了船舶在几种典型波浪中的状况:稳定区域中的横摇回复和稳态横摇;非稳定区域的横摇发散;以及混沌现象。研究表明,通过小波变换所特有的时频窗,对横摇响应小波变换系数的模和相等信息进行分析,可以获得船舶横摇—垂荡耦合非线性动力学幅值和频率的各种典型特征。

Wavelet transform was explored to investigate the nonlinear dynamical characteristics of ship rolling with heave-roll coupling in this paper.The Morlet wavelet transform was applied to the equations of ship rolling quadratically coupled with heave to analyze the dynamical character of ship roll.And various typical wave situations were considered： a） the restore rolling and the steady status when the wave parameters in stable regions, b） the diverging roll status when wave parameters in unstable regions, and c） the chaotic response of ship rolling.It was shown that by investigating the modulus and phase of the wavelet coefficients of ship roll through the unique time-frequency window of wavelet transform,typical nonlinear characters of the amplitudes and frequencies of ship roll nonlinearly coupling with heave could be obtained distinctly.The research revealed that wavelet transform would be expected a new and powerful ways and means to research the nonlinear behaviors of ship rolling.