叶端定时中多重信号分类法的滤波特性研究

Investigation for Filtering Ability of Multiple Signal Classification in Blade Tip Timing

为了揭示多重信号分类法(MUSIC)具有滤除同步频率分量特性的数学机理,基于MUSIC方法中的信号子空间生成过程与主成分分析方法中的主成分生成过程的一致性,对MUSIC滤波特性进行了研究。以正弦信号假设下单频率分量的情况为例,证明了异步频率分量与同步频率分量的信号子空间分别可以用二维直角坐标系和一维坐标轴可视化表示。通过分析导向矢量在信号子空间坐标系中的位置得出,人为设置相位的导向矢量位于同步频率分量的信号子空间之外,从而导致了滤波现象的发生。仿真和实验结果表明:同步频率分量和异步频率分量同时存在于叶片振动信号的非共振区;MUSIC方法能够克服频率混叠且具有滤除同步频率分量的滤波特性;该滤波特性能够被导向矢量与子空间坐标系的相对关系解释。

To reveal the reason why multiple signal classification(MUSIC)can filter out the synchronous frequency components the consistency between signal subspace of MUSIC and principal component of principal component analysis is theoretically investigated.One sinusoidal frequency component case is discussed to verify that the signal subspace of asynchronous frequency component and synchronous frequency component can be visually represented by a 2 D cartesian coordinate and an axis respectively.Analyzing the position of the steering vector in the signal subspace,it is concluded that the artificial steering vector is outside the signal subspace of the synchronous frequency component,which leads to the filtering ability.The simulation and experiment results show that:synchronous frequency components and asynchronous frequency components coexist in the non-resonance region of blade vibration signal;MUSIC can eliminate aliasing andfilter out the synchronous frequency components;the filtering ability can be explained by the relationship between the steering vector and the subspace coordinate.