频域最小二乘辨识方法的参数约束条件选取

 近年来,频域最小二乘(LS)辨识方法因其较小的计算量和较高的辨识精度,在模态分析尤其是飞机颤振模态分析中得到了广泛关注。在实际应用中为提高辨识精度,通常采用过拟合方法进行系统辨识,然而过高的模型阶次会引入多余的数学极点,导致稳态图中虚假模态的出现,进而影响真实模态的识别。为此,针对多输入多输出系统辨识问题,研究了两种典型参数约束条件对频域最小二乘辨识方法的不同影响,通过理论分析和数学推导解释了约束条件和虚假数学极点稳定性之间的关系。研究结果表明:适当选取约束条件有助于区分真实和虚假模态,是获得清晰稳态图的关键。最后,采用仿真算例和颤振实测数据验证了本文的结论。

On the Choice of Parameter Constraint for Frequency-domain Least Squares Identification

In recent years, the frequency-domain least squares (LS) identification, because of its less computation and higher identification precision, has received considerable attentions in the field of modal analysis, especially the aircraft flutter modal analysis. In the practical application, the over-fitting method is usually used for system identification to improve identification precision. However, higher model order will introduce extra mathematical poles and lead to spurious mode in stabilization diagram. This seriously effects the identification of true (physical) mode. For this reason, two typical parameter constraints are investigated for multiple-input and multi-output system LS identification. Theoretical analysis and mathematical derivation are given to explain the relation between parameter constraint and stability of mathematical poles. The work of this paper shows that the right constraint choice is helpful to distinguish the true and spurious modes, which is the key to obtain a clear stabilization diagram. Finally, a numerical simulation and real flutter test measurements are used to validate the conclusions drawn from the paper.