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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。
In recent years, the least square (LS) identification method in frequency domain has drawn much attention in modal analysis, especially in aircraft chatter modal analysis due to its small amount of computation and high recognition accuracy. In practice, in order to improve the identification accuracy, the over-fitting method is often used to identify the system. However, excessive model orders may introduce extra mathematical poles, resulting in the appearance of false modal in the steady-state diagram and thus the real modal Recognize. Therefore, in view of the multi-input multi-output system identification problem, this paper studies the different influence of two typical parameters on the least-squares identification method in frequency domain. The theoretical analysis and mathematical derivation are used to explain the stability between the constraints and the false mathematical pole Relationship. The results show that choosing appropriate constraints helps to distinguish between real and false modalities is the key to obtaining a clear and steady state graph. Finally, the simulation results and flutter measured data verify the conclusion of this paper.