基于自迭代主元抽取的工作模态参数识别

摘要

针对传统批处理主成分分析工作模态参数识别中存在的矩阵奇异值或特征值分解病态问题,本文提出了一种基于自迭代主元抽取的工作模态参数识别方法.与传统批处理主成分分析通过矩阵分解一次获得所有主成分不同,该方法通过自迭代逐一抽取主成分从而实现主要贡献工作模态的逐一识别.理论分析表明,该方法的时间复杂度和空间复杂度比传统批处理主成分分析工作模态参数识别方法更低.在简支梁仿真数据集上的识别结果表明,自迭代主元抽取算法可以从平稳随机响应信号中有效地识别出线性时不变结构的主要贡献模态振型和固有频率,在响应测点和采样时间较多时其时间开销较传统方法也更小.%Aiming at singular value of matrix decomposition and ill-posed problems in traditional batch processing principal component analysis (PCA) based operational modal analysis (OMA),an operational modal identification method based on self-iterative principal component extraction is proposed.Different from traditional batch processing PCA,which obtains all principal components by matrix decomposition one time,the proposed method can realize the identification of main contribution operational modals by self-iterative principal component extraction one by one.Theoretical analysis shows its lower time and spatial complexity than traditional batch processing PCA based OMA.The simulation results on simple beam datasets show that the self-iterative principal component extraction algorithm can identify effectively main contribution modals and natural frequency of linear time invariant structure from smooth and random response signals.And it has smaller time cost in the case of more response points and more sampling time in contrast with traditional methods.