传统观点认为阻尼识别方法受截断误差影响；增加采样长度，即增加采样点数，提高频率分辨率，可以减少误差，形成了采样时间长（即采样点数多）阻尼识别误差小的观点。但实际采样信号中包含噪声，对采样信号进行傅里叶变换时，噪声信号随阻尼信号一同被积分。将振动衰减信号作傅里叶变换，得出当采样时间超过4.6/n（n为阻尼值）时振动衰减信号频谱幅值与采样点数呈反比关系；对噪声使用统计分析，噪声频谱实际发生值不是期望值，而是主要在期望值与三倍标准差之间浮动，将噪声信号作积分推导得出噪声频谱幅值与采样点数的开方值呈反比关系。得出采样时间过长时，噪声信号将掩盖振动衰减信号，导致阻尼识别误差变大，通过计算推导得出了采样点数临界值的计算公式。运用仿真算例与悬臂梁敲击实验进行了验证。
Abstract
Conventional view holds that the damping identification method is influenced by truncation error, increasing the number of sampling points and improving the frequency resolution can reduce errors,forming a view that the more the sampling points, the smaller the damping identification error.But, the actual sampling signal usually contains noise, when the Fourier transform is applied on the sampling signal, the noise signal is also integrated together with the damping signal.It is found doing the Fourier transform on a vibration attenuation signal with the sampling time over 4.6/n(n is damping value), the amplitude of the vibration attenuation signal is inversely proportional to the number of sampling points.When using the statistical analysis on a noise signal, the actual occurrence value of the noise spectrum is not the expected value but mainly fluctuates between the expected value and the tripple of standard deviation.Through the inner product operation of the noise signal, it is shown the noise spectrum amplitude is inversely proportional to the square root of the sampling points.When the sampling time is too long, the noise signal will cover the vibration attenuation signal, which results in a larger damping identification error.Through calculations, the formula of sampling threshold was derived and verified by simulation examples and cantilever beam experiments.
关键词
采样点数 /
傅里叶变换 /
噪声 /
频谱 /
阻尼
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Key words
sampling points /
Fourier transform /
noise /
frequency spectrum /
damping ratio
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