基于递归希尔伯特变换的振动信号解调和瞬时频率计算方法

摘要

Accurately extracting instantaneous amplitude and instantaneous frequency is important in structure parametic identification and health monitoring.Hilbert transformation is one of the most commonly used methods for signal demodulation and instantaneous frequency computation.However,it may cause larger errors when vibration signals do not satisfy the conditions of Bedrosian prodact theorem.Aiming at this problem,a recursive Hilbert transformation method was proposed.With this method,a pure frequency modulation signal derived in the previous step was taken as a new signal, it was modulated using Hilbent transformation recursively.The theoretical analysis showed that the recursive HirBert transformation can converge rapidly.The proposed method was compared with Hilbert transformation,the empirical AM-FMdecomposition,and Teager energy method for simulated signal demodulation and instantaneous frequency computation. The results showed that the recursive Hilbert transformation.%精确地提取振动信号的瞬时幅值和瞬时频率对结构的参数识别和健康监测有重要作用。希尔伯特变换是一种常用的信号解调及瞬时频率计算方法，但在信号不满足 Bedrosian 乘积定理的条件时会造成较大误差。针对这一问题，提出了一种递归希尔伯特变换方法，用前一步希尔伯特变换计算出的纯调频信号作为新的信号，递归地使用希尔伯特变换以进行信号解调，理论分析表明递归希尔伯特变换能够快速地收敛。最后采用仿真信号对比了递归希尔伯特变换与单次希尔伯特变换、经验调幅调频分解及 Teager 能量算子法在信号解调及瞬时频率计算中的结果，结果表明了递归希尔伯特变换方法的实用性及精确性。