利用主成分分析的模态参数识别

Modal Parameter Identification with Principal Component Analysis

针对运行模态分析和独立成分分析技术不完善、可能会识别出虚假模态等缺点,提出一种新的利用主成分分析进行模态参数识别的方法。基本思想是找出模态振型与线性混叠矩阵之间及各阶模态响应与主成分之间的对应关系,并将模态参数识别问题转化为结构响应数据的主成分分解问题。不同状态下梁的仿真结果表明,仅以系统结构的时域响应数据为对象,利用含观测噪声基于主元抽取的主成分分析算法,就可以识别响应中占主要贡献的各阶模态振型和固有频率,且适用于不同边界条件、载荷类型及加载位置,对高斯测量噪声也不敏感,可应用于独立模态控制方法中被控系统的辨识与建模、最优控制点选择、作动器安装位置和控制频率确定以及减振效果预估。

A novel modal parameter identification method based on principal component analysis is proposed to improve the operational modal analysis and the independent component analysis,and to decrease the possibility of identifying false modal.The essentiality is to find the relationship between modal shape and linear compound matrix and the relationship between modal responses and principal components.The modal parameter identification is then changed into principal component decomposition.Numerical simulations of two beams with different state show that the new principal component extraction based method is insensitive to Gauss measurement noise,and enables to identify dominant modal shapes and natural frequencies only using vibration time-domain response signals of a structure with measurement noise in despite of system boundary,load type,and load position.The proposed method can be applied to independent modal control method in terms of system recognition and modeling,selection of optimal control point,mounting position of actuator,determination of control frequency,and estimation of active vibration suppression.