多输入多输出频域模态识别算法的探讨

在应用多输入多输出频域正交多项式方法进行模态参数识别时，发现其存在一些不完善之处：１）识别振型需对重根单根情况分别作出判断和计算；２）在分析频带内系统存在重根重数与输入个数相同时，理论上振型无法识别，实际应用时识别结果有较大误差。对此进行了深入探讨，从理论上论证了出现上述问题的原因：识别过程中对矩阵进行奇异值分解，在存在重数与输入个数相同的重根时，此矩阵数值小，信噪比低，因此识别精度差。针对这些问题，对原算法进行了修正，使振型识别精度得到提高。算例与试验验证证明了所做的讨论和修正是正确的、有效的。

Study of multiple input multiple output frequency domain parameter estimation method

Some shortcomings exist in the multiple input multiple output frequency domain orthogonal polynomial parameter estimation method: (1) It uses different methods to calculate modal vectors according to whether the corresponding pole is a single root or repeated roots. (2) If the system has repeated roots which multiplicity is equal to the number of input in the selected frequency band, it is impossible to identify modal vectors in theory and will introduce great errors in practice. This paper discusses the problem. In the estimation, a singular value decomposition of a certain matrix is performed to calculate the modal vectors. But when repeated roots which multiplicity is equal to the number of input exist, all the elements of this matrix are very small and the signal to noise ratio is low and the result is inaccurate. Under these discussions, this paper revises the original algorithm to improve the estimation. A theoretical example and an experiment prove the correctness and the effectiveness of the discussion and revision.