基于小波变换的时变及典型非线性振动系统识别

摘要

用Morlet小波变换方法对时变振动系统和典型非线性振动系统进行参数识别。首先，通过Morlet小波变换提取振动响应的小波脊线，从而获得瞬时频率和瞬时幅值，然后，通过最小二乘曲线拟合即可估计系统的非线性阻尼和刚度系数。分别以时变阻尼自由振动系统、达芬有阻尼非线性简谐振动系统和范德波尔非线性自由振动系统为例子来说明小波变换方法对识别时变振动系统和非线性振动系统的有效性。%The parameter identifications of time-varying vibration system and typical nonlinear vibration system were conducted by using Morlet wavelet transform method.The wavelet ridge of vibration response was extracted by Morlet wavelet transform,and then the instantaneous frequency and instantaneous amplitude were obtained.The nonlinear damping and stiffness coefficients were estimated by using the least squares curve fitting.The time-varying damping free vibration system,the Duffing damped nonlinear harmonic vibration system,and the Van der Pol nonlinear free vibration system were taken as examples to show the effectiveness of wavelet transform method in identifying time-varying vibration system and nonlinear vibration system.