基于小波变换和奇异值分解的模态参数识别方法

Modal Parameters Identification Method Based on Wavelet Transform and Singular Value Decomposition

提出了一种新的基于小波变换和奇异值分解相结合的结构模态参数识别方法.该方法首先对环境激励下的结构加速度响应信号进行互协方差分析,得到时域互协方差响应,通过小波变换将互协方差响应转换到时频域中得到信号的时频系数并沿每一个尺度点提取协方差响应的小波系数阵,然后对提取的小波系数阵进行奇异值分解得到奇异值和奇异向量,最后从重组的奇异值和奇异向量中识别出结构的模态参数.文章对提出的方法进行了理论证明,通过三自由度系统的数值算例验证了该方法的可行性,表明与直接小波变换方法相比,其识别结果精度更高.

A novel modal parameters identification method based on wavelet transform and singular value decomposition is proposed. Assuming that the structural system is timeinvariant and the ambient excitations are white noise, the covariance response of structural accelerations were calculated from response data measured at multiple locations of the structure; and wavelet transform was imposed to obtain the wavelet coefficient matrix of the covariance response. Then the singular value decomposition was adopted to decompose the wavelet coefficient matrix at each wavelet scale, and the modal parameters could be identified exactly from the singular value and singular vector. The formulations of the proposed method were derived and the method was verified by numerical simulation using 3 DOF structure. The results show that the method can be used to identify the modal parameters of multi-degree of freedom structure and the accuracy is better than that using a conventional wavelet transform method.