基于离散频谱分析的自由衰减振动信号的幅值恢复

加矩形窗截断后的自由衰减振动信号可以看成无限长谐波信号与单边指数函数及矩形窗的乘积,从理论上证明了其连续谱峰值点的频率和相位就是信号的实际频率和相位。分析了连续谱的离散频谱幅值误差影响因素,提出一种新的求解幅值恢复系数的方法,该方法根据已估计得到的阻尼、频率和相位重构幅值为给定值的新信号,然后求解加有限长度指数窗幅值恢复系数。当理论频率位于某条离散谱线上,幅值基本无误差。理论分析和仿真表明,采样频率、阻尼和频率误差的变化对幅值分析精度的影响很大,并且是相互作用的,但当理论频率与采样频率之比fn/fs在区间(0.25,0.4)内,且阻尼在区间(0.005,0.02)时,不论频率误差多大,分析精度均很高,幅值误差小于5%。相邻频率成分产生严重模态耦合时,不能使用该方法。

Discrete spectrum analysis for amplitude correction of damped free vibration response

As response signal of damped free vibration could be considered as product of the harmonic wave and the unilateral exponential function and the rectangle window, that the peak frequency and phase are the frequency and phase of the harmonic wave signal is proved theoretically in this paper. The variation of sampling frequency, error of frequency, damping, phase, which affect the precision of the amplitude of discrete spectrum of damped free vibration signal, is analyzed. One presents a new method to obtain the recovery coefficient for amplitude of unilateral finite length exponential window, which reconstructs a new signal with the damping, frequency, phase that have been estimated. Using DFT, one can obtain the coefficient. When the error of the estimated frequency is zero, the error of amplitude is minor. Theory and simulation show the variation of sampling frequency, error of frequency, damping, phase affects the precision of amplitude severely, and the effect of the variation of one parameter is influenced by the others.