基于Hilbert变换的结构非线性判断方法

DETECTION OF NONLINEARITY IN STRUCTURES BASED ON HILBERT TRANSFORM

研究了运用Hilbert变换判断系统非线性状态的方法在地震工程中的应用。介绍了运用Hilbert变换判断系统非线性状态的基本理论和非线性程度相对量化指标,在考虑测量噪声影响的情况下,对一个具有Bouc-Wen模型的单自由度非线性结构进行了数值仿真分析。结果表明,随着地震波峰值的增大,结构频率响应函数幅值曲线与相应的Hilbert变换幅值曲线的差异在增大,结构的非线性程度相对量化指标也在增大,说明运用Hilbert变换和非线性程度相对量化指标可以有效地判断结构的非线性状态,为结构的振动控制和健康监测提供一定的参考价值。

The application of the system nonlinearity detection based on Hilbert transform in earthquake engineering is studied. The basic principle of the system nonlinearity detection based on Hilbert transform and the relative quantitative index of the nonlinearity are introduced. Considering the influence of both input and output noises, a single-degree-of-freedom nonlinear structure was analyzed using numerical methods. Results show that with the increase in the peak earthquake acceleration, the difference between the amplitudes of the structure frequency response function and its Hilbert transform increases, and the relative quantitative index of the nonlinearity in the structure also increases. Hilbert transform and the relative quantitative index can detect the nonlinearity in structures and has certain theoretical value in structural control and health monitoring.