基于Morlet小波变换的结构密集模态参数识别

Modal identification of closely spaced modes based on Morlet wavelet transform

为了解决结构密集模态识别精度不高的问题,提出了基于Morlet小波变换进行结构模态参数识别的一套方法流程.首先,从公式推导的角度对结构模态混叠的机理进行研究分析,明确和量化了密集模态的定义,提出了结构模态密集度指标——相邻模态的频率比,以此判定应用Morlet小波变换进行模态识别的有效性.其次,针对边端效应和噪声污染的不利影响,改进了小波变换识别结构模态参数的方法,并提出了最优小波中心频率的选取方法.理论研究结果表明,当相邻模态的频率比值一定时,随着阻尼比以及相邻模态阻尼比差值的增加,模态混叠的严重程度也增加.数值仿真算例结果表明,这种改进的模态识别方法可有效地识别结构的模态参数,且能够获得较高的参数识别精度.

In order to improve the precision of the modal parameter identification of closely spaced modes, an identification method and procedure based on Motet wavelet transform is proposed. First- ly, the mechanism of modal overlap is studied through formula derivation. The concept of closely spaced modes is defined and quantified with an index, the frequency ratio of two adjacent modes, toassess the validity of modal identification by Morlet wavelet transform. Secondly, in order to limit the edge effect and noise pollution, the modal identification method using continuous wavelet trans- form is modified, and then an interactive algorithm for the center frequency of the mother wavelet isproposed. The theoretical results show that at the fixed frequency ratio of two adjacent modes, the severity of modal overlap is greater with the increase of the damping ratios and the difference be- tween the damping ratios of the adjacent modes. The results of the numerical simulation exampleshow that the modified modal identification method can effectively identify modal parameters of structures and the identification precision is high.