基于Hilbert-Huang变换与理想带通滤波器的系统识别

System Identification Based on HHT and Ideal Band-Pass Filter

针对经验模态分解存在模态混叠现象,提出基于Hilbert-Huang变换与理想带通滤波器的系统识别方法。该方法利用傅里叶变换得到结构加速度响应频响函数,粗略估计固有频率范围,通过半功率带宽法设计理想带通滤波器,定量化确定通带带宽,使信号在经过滤波器后频域内零相移,同时不改变其幅值谱。结构响应通过指定频带的理想带通滤波器产生若干窄带信号,利用经验模态分解获取结构模态响应,经Hilbert变换构造模态响应解析信号,并通过线性最小二乘拟合提取结构模态参数与物理参数。结果表明:半功率带宽法可实现带通滤波器频带的定量化设计,理想带通滤波器的零相移特点较好契合Hilbert-Huang变换用于系统识别的要求,两者结合可有效地解决模态混叠现象,减少虚假模态,大大提高结构系统识别精度。

Aiming at the mode mixing problem in the sifting process of empirical mode decomposition (EMD), a new approach for system identification (SI) based on Hilbert-Huang transform (HHT) and ideal band-pass filter was proposed. First, using Fourier transform, a rough estimation of the natural frequency was obtained from the frequency response function. Then, an ideal band-pass filter was designed, with passband determined through the half-power bandwidth method. The filter provides zero phase shift within the passband, and at the same time does not change amplitude spectra. The original response was filtered into a series of narrow band signals through designed filters. Further, narrow band signals were decomposed into modal responses using EMD. The Hilbert transform was applied to each modal response to construct the analytical signal. Finally, the least-square fitting was proposed to identify structural modal and physical parameters. Results show that the half power bandwidth method can realize the quantitative design of the passband. Zero phase shift characteristics of the ideal band-pass filter can better meet the requirements of HHT used in the SI. The combination of the two methods can effectively solve the mode mix problem, eliminate the false modal components and greatly improve SI accuracy. © 2016, Editorial Department of JVMD. All right reserved.