用于时变结构模态参数识别的投影估计递推子空间方法

A PROJECTION APPROXIMATION RECURSIVE SUBSPACE METHOD FOR IDENTIFICATION OF MODAL PARAMETERS OF TIME-VARYING STRUCTURES

基于投影估计子空间跟踪算法提出了一种新的可用于时变结构模态参数识别的递推子空间方法。首先利用方阵求逆公式和正交补空间的性质将待跟踪的矩阵变换为一种适合在线跟踪的一阶修改递推格式,然后将奇异值分解转化为无约束优化问题,通过投影估计将目标函数变换为关于新数据的二阶形式,再利用最小二乘法求出系统的特征子空间,最后根据模态分析理论求出时变结构的伪模态参数。使用本文方法辨识一个具有移动质量块机械臂系统的伪模态参数,并将结果与另外两种方法进行比较。理论和仿真结果表明提出的方法具有计算量小、对噪声不敏感等优点。

A novel recursive subspace method is presented for pseudo-modal parameter identification of time-varying structures based on projection approximation subspace tracking algorithm. A first-order update matrix form suitable for on-line tracking is first derived based on matrix inversion and the characteristic of the orthogonal complement space. Then the singular value decomposition is transformed to an unconstrained optimization problem. The objective function is turned into a quadratic form of new data by projection approximation, and the eigensubspace is obtained by least square method. The pseudo-modal parameter of time-varying structure is obtained according to modal analysis theory. The pseudo-modal parameter of a manipulator with moving mass is identified and the results are compared with those of other two methods. The advantages of lower computation complexity and lower sensitivity to the noise are validated.