识别时变结构模态参数的改进子空间方法

给出了基于整体数据子空间方法的改进算法,原方法对噪声的影响极为敏感,基于原方法的关键是计算一个与原系统的广义能观阵的特征值相同的矩阵的基本事实,将求矩阵的过程转化为最小二乘的问题,然后用广义能观阵替换输出矩阵,对数据进行滤波,从而有效地降低了算法对噪声敏感性,但同时增加了计算量。利用奇异向量矩阵的正交性,将最小二乘问题中求矩阵伪逆的过程简化为求该矩阵的转置,从而降低了计算量,改进后的算法能够在提高算法对噪声的敏感性的同时降低计算量。最后利用改进后的方法辨识出一个两自由度弹簧质量块模型在三种不同的刚度变化形式下的伪模态参数,并通过与使用原方法所得的结果比较,验证了以上结论。

Improved Subspace Method with Application in Linear Time-Varying Structural Modal Parameter Identification

An improved subspace method using ensemble response sequence was developed. The original method can identify the pseudo-modal parameter of time-varying structure efficiently, but is sensitive to the noise severely. Considering that the key of this method is to find a matrix whose eigenvalues are the same to the system matrix, the process of finding this matrix was converted to a Least Square (LS) problem. Using generalized observability instead of the output matrix ,an improved method was obtained, where the sensitivity to noise was abated,but the computational complexity increased. The orthogonality of the left singular matrix was once considered, the process of computing the pseudo-inverse of the matrix in LS problem was simplified into finding the transposed itself to greatly reduce the computational complexity. The improved method was verified via identifying pseudo-modal parameters of a 2DOF spring-mass model with three kinds of time-varying stiffness.