一种Hilbert变换法在非线性系统分析中的应用

Hilbert变换是信号处理领域常用工具之一，将Hilbert变换法改进并应用到信号分解和非线性系统振动分析中。振动信号的多谐波性，使得Hilbert变换法提取信号的瞬时频率和瞬时相角可以通过滤波的方法分离成快变和慢变两部分，从而提取系统的振动分量;通过迭代计算，依次获得振动信号中所有谐波分量;将非线性振动方程用瞬态幅值相关的瞬态参数表示，从而求解系统的频响关系曲线方程。通过相应的数值模拟计算，验证了改进的Hilbert变换法在非线性振动分析的有 效性。

The Modified Method of Hilbert Transform and Application in Nonlinear Vibration Analysis

As one of the important tools in the realm of signal processing, the method of Hilbert transform is modified and it is used in applications to signal decomposition and nonlinear vibration analysis. Due to the characteristic of multi-harmonic component, the instantaneous amplitude and instantaneous frequency of the mechanical signal is decomposed to a slow varying oscillating and a rapidly varying oscillating by a low-pass filtering, and then the largest component of signal is obtained. After several iterations for the Hilbert transform, all the harmonic components of vibration signal are extracted. Then, the nonlinear vibration equations can be transformed to the standard equation with the instantaneous parameters, which are the function of instantaneous amplitude. The amplitude-frequency curve of response of system is obtained. With several numerical simulations, the effectiveness of the Hilbert transform is verified for the application to nonlinear analysis.