环境激励下基于小波变换和奇异值分解的结构模态参数识别  

Structural modal parameter identification using wavelet transform and singular value decomposition under ambient excitation

作　　者：闵志华[1] 孙利民[1] 孙智[1] 淡丹辉[1] 

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《振动工程学报》2009年第2期142-149,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金重点资助项目(50538020);国家科技部973项目(2002CB412709);上海市科委"登山计划"项目(062112007);土木工程防灾国家重点实验室团队重点课题(ZD-08-05)

摘　　要：采用小波变换和奇异值分解相结合的方法对环境激励下结构的模态参数进行识别。首先对环境激励下的时不变结构的加速度响应进行协方差分析得到时域协方差响应,利用小波变换将协方差响应转换到时/频域中,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,最后从重构的奇异值和奇异向量中识别出结构的模态参数。文章通过3自由度系统数值算例分析了该方法的抗噪性能,结果表明该方法具有很好的抗噪能力,在15 dB噪声干扰下能够稳定和准确地识别出结构的模态参数,且比直接用小波变换方法识别的结果更准确;并通过东海大桥主航道斜拉桥模态参数识别的例子进一步验证该方法的实际应用可行性。Structural modal parameters were identified using the method of wavelet transform and singular value decomposition under ambient excitation. Assuming that the structural system was time-invariant and the ambient excitations were 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. A numerical example of three-degree-of-freedom structure was used to analysis the noise resistance of the method. Results show that the method does not seen to be affected at the presence of 15 dB measurement noise and at same time the accuracy was better than that using a conventional wavelet transform method. Finally the result of a cable-stayed bridge validated the method.

关 键 词：模态参数识别 小波变换 奇异值分解 抗噪性 

分 类 号：TB123[理学—工程力学] TU317[理学—力学]