自适应主元分析的线性时变结构工作模态参数在线识别

发布时间：2018-06-26 03:58

  本文选题：线性时变结构 + 工作模态参数识别　； 参考：《华侨大学》2016年硕士论文

【摘要】：线性时变结构的工作模态参数识别在振动控制和故障诊断等领域具有重要的理论意义和工程应用价值。本文基于线性时变结构的“时间冻结”和“瞬态”表示,提出了自适应主元分析的线性时变结构工作模态参数在线识别方法,并进行了理论推导和数值仿真验证。主要工作如下:(1)从基本主成分分析(PCA)算法出发,建立其与线性时不变结构位移响应的模态坐标表示之间的对应关系,阐述了基于PCA工作模态参数识别方法各参数物理意义及适用条件,通过数值仿真验证了该方法在线性时不变结构工作模态参数识别中的效果。(2)基于“短时时不变”思想,将基于PCA的线性时不变结构工作模态参数识别方法与滑动窗技术结合,提出了滑动窗主元分析的线性时变结构工作模态参数识别方法。在选取合适大小的数据窗后,该方法能有效识别线性时变结构的瞬态模态频率和模态振型。在此基础上,将该方法与自相关矩阵递推、特征值特征向量递推技术相结合,分别提出滑动窗自相关矩阵在线递推和滑动窗特征值特征向量在线递推的主元分析算法。通过理论分析和数值仿真验证,基于滑动窗特征值特征向量递推的主元分析算法较滑动窗自相关矩阵递推的主元分析算法具有更低的时间复杂度、空间复杂度和数值稳定性。(3)基于“遗忘因子加权”思想,将基于PCA的线性时不变结构工作模态参数识别方法与“加权遗忘技术”结合,提出带遗忘因子加权的主元分析的线性时变结构工作模态参数识别方法。在选取合适大小的遗忘因子后,该方法能有效识别线性时变结构的瞬态模态频率和模态振型。在此基础上,将该方法与自相关矩阵递推、特征值特征向量递推技术相结合,分别提出带遗忘因子加权的自相关矩阵在线递推和带遗忘因子加权的特征值特征向量在线递推主元分析算法。通过理论分析和数值仿真验证,基于带遗忘因子加权的特征值特征向量递推主元分析算法较带遗忘因子加权的自相关矩阵递推主元分析算法具有更低的时间复杂度、空间复杂度和数值稳定性。
[Abstract]:The identification of working modal parameters of linear time-varying structures has important theoretical significance and engineering application value in the fields of vibration control and fault diagnosis. Based on the "time freeze" and "transient" representations of linear time-varying structures, an adaptive principal component analysis method for on-line identification of operating modal parameters of linear time-varying structures is proposed, and theoretical derivation and numerical simulation are carried out. The main work is as follows: (1) based on the basic principal component analysis (PCA) algorithm, the corresponding relationship between the principal component analysis (PCA) algorithm and the modal coordinate representation of the displacement response of the linear time-invariant structure is established. The physical meaning and applicable conditions of each parameter of the working modal parameter identification method based on PCA are expounded. The effectiveness of the method in identifying the operating modal parameters of linear time-invariant structures is verified by numerical simulation. (2) based on the idea of "short time invariance", Based on PCA and sliding window technique, a method for identifying the working modal parameters of linear time-invariant structures based on principal component analysis with sliding windows is proposed. The method can effectively identify the transient modal frequencies and modal modes of linear time-varying structures by selecting suitable data windows. On this basis, the method is combined with autocorrelation matrix recursion and eigenvalue eigenvector recursion technology, and the principal component analysis algorithm of sliding window autocorrelation matrix online recursion and sliding window eigenvalue eigenvector online recursion are presented respectively. Through theoretical analysis and numerical simulation, it is proved that the principal component analysis algorithm based on eigenvector recursion of sliding window has lower time complexity than that of sliding window autocorrelation matrix recursive principal component analysis algorithm. Space complexity and numerical stability. (3) based on the idea of "forgetting factor weighting", the paper combines the PCA based identification method of linear time-invariant structure working modal parameters with the "weighted forgetting technique". A method for identifying the working modal parameters of linear time-varying structures based on principal component analysis with forgetting factor weighted is presented. The method can effectively identify the transient modal frequencies and modal modes of linear time-varying structures by selecting appropriate forgetting factors. On this basis, the method is combined with the recursive technique of autocorrelation matrix and eigenvalue eigenvector. An online recursive principal component analysis algorithm with forgetting factor weighted autocorrelation matrix and eigenvalue eigenvector with forgetting factor weighting is proposed respectively. The theoretical analysis and numerical simulation show that the eigenvalue eigenvector recursive principal component analysis algorithm with forgetting factor weighting has lower time complexity than the autocorrelation matrix recursive principal component analysis algorithm with forgetting factor weighting. Space complexity and numerical stability.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TB535
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本文编号：2068978