基于密度峰值聚类算法的模态参数识别

稀疏成分分析是解决欠定盲源分离问题的一种有效方法，其主要分为两步：计算振型矩阵和重构单模态信号。在计算振型矩阵时，针对无法预知源信号数量和高阶振动模态混叠的问题，本文利用一种基于密度峰值聚类算法识别模态振型。相比于传统的聚类算法，该方法具有以下特点：1利用决策图直观地选出聚类中心和聚类数目；2算法可以自动分离噪声点，对噪声不敏感。在重构单模态信号时，利用可以快速重构稀疏信号的SL-0算法，重构出单模态时频域信号，提取出各阶模态频率。最后，通过振动结构仿真算例验证了该方法的有效性。
Abstract：The sparse component analysis is an efficient approach to handle the underdetermined blind source separation,which contains two steps: calculating the mixing matrix and second,reconstructing the sources.In the paper,the modal shapes were calculated by using the Density Peaks Clustering Algorithm to deal with the cases that the number of sources cannot be known a priori and high order modes are overlapped with each other.Compared to the traditional clustering algorithms,it has two advantages: determining the centers of clusters according to the decision graphs directly and being insensitive to noises.The SL0 algorithm a sparse recovery algorithm,was used to reconstruct the sources.Then the frequency of each mode was identified from the sources in time-frequency domain.The effectiveness of the proposed method was validated via adopting a six degree-of-freedom vibration system as a simulation example.