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该文采用Hilbert-Huang变换(HHT)对时变阻尼自由振动系统以及常见的Duffing振动系统和Van der Pol振动系统进行参数识别。首先通过经验模态分解将振动信号分解为自由振动信号和强迫振动信号,通过经验包络法得到分解后信号的振幅包络线和瞬时频率。进而使用瞬时振幅及瞬时频率通过最小二乘法估计得到振动方程的各项参数。与小波识别结果进行对比,数值算例表明Hilbert-Huang变换可以有效地识别时变阻尼自由振动以及Duffing振动系统和Van der Pol振动系统的时变参数并且有较高精度。
In this paper, Hilbert-Huang transform (HHT) is used to identify the parameters of the time-dependent damped free vibration system and the common Duffing vibration system and Van der Pol vibration system. Firstly, the vibration signal is decomposed into free vibration signal and forced vibration signal by empirical mode decomposition. The amplitude envelope and instantaneous frequency of the decomposed signal are obtained by empirical envelope method. Then the instantaneous amplitude and instantaneous frequency are used to estimate the parameters of the vibration equation through the least square method. Compared with the wavelet recognition results, numerical examples show that the Hilbert-Huang transform can effectively identify the time-varying parameters of the time-dependent damping free vibration and the Duffing vibration system and the Van der Pol vibration system with high accuracy.