Abstract: To solve the problem of low accuracy and poor robustness of underdetermined operational mode parameters identification methods based on sparse component analysis and orthogonal basis compressed sensing,a method based on adaptive dictionary compressed sensing was proposed.In this method,the adaptive dictionary compressed sensing was used to reconstruct the modal coordinate response on the basis of modal shape estimation.The training samples of dictionary learning were constructed by filtering separation method under the framework of compressed sensing.The dictionary learning method based on K-means Singular Value Decomposition (K-SVD) and the hierarchical coupling dictionary training strategy was used to generate the adaptive dictionary,and the unsupervised dictionary learning was realized.The Orthogonal Matching Pursuit (OMP) algorithm was used to obtain the sparse coefficient components and recover the source signal to reconstruct modal coordinate response.Under the framework of compression sensing,the adaptive dictionary obtained by the K-SVD algorithm was better than the orthogonal basis such as Fourier basis or discrete cosine basis in sparse representation of signal decomposition.The identification results of underdetermined operational mode parameter identification under 5-degree-of-freedom simulation dataset showed that the proposed method had better recognition accuracy and robustness than the methods such as sparse component analysis and orthogonal basis compression sensing.

Key words: operating modal analysis, underdetermined, compressed sensing, adaptive dictionary, filter separation

摘要： 针对基于稀疏成分分析和正交基压缩感知的欠定工作模态参数识别方法准确率低、鲁棒性差的问题,提出一种基于自适应字典压缩感知的欠定工作模态参数识别方法。所提方法在模态振型估计的基础上利用自适应字典压缩感知重构模态坐标响应。在压缩感知框架下,首先,所提方法利用滤波分离的方法构造字典学习的训练样本;然后,使用基于K均值奇异值分解的字典学习方法和层次耦合字典训练策略生成自适应字典,实现了无监督的字典学习;最后,利用正交匹配追踪算法得到稀疏系数分量,进而恢复源信号重构模态坐标响应。在压缩感知框架下,所提方法利用K均值奇异值分解算法学习得到的自适应字典,对于信号的分解比傅里叶基或离散余弦基等正交基具有更强的稀疏表示能力。在5自由度的仿真数据集下的欠定工作模态参数识别的结果表明,所提方法比稀疏成分分析、正交基压缩感知等方法具有更好的识别精度和鲁棒性。

关键词: 工作模态分析, 欠定, 压缩感知, 自适应字典, 滤波分离