基于HHT方法的时变多自由度系统的参数识别

Identifying the parameters of multi-freedom degree systems with time varying using Hlbert-Huang transform

将HHT(Hilbert-Huang transform)方法与数学规划方法相结合,用于时变多自由度系统的参数识别.把响应信号如加速度信号通过一个窗函数,得到要研究的某阶模态成分,然后通过经验模态分解(EMD)把通过窗函数的信号分解成各个本征模函数(IMF),对分解出来的IMF进行希尔伯特变换得到该阶模态的瞬时频率,以待识别的刚度或质量参数作为设计变量,极小化计算得到的频率与瞬时频率之差的平方和.对应该平方和最小的刚度或质量值即为选定时刻识别得到的刚度或质量参数值,并进行了数值仿真.

In combination with mathematical programming, Hilbert-Huang transform （HHT） was used in multi-freedom degree system （MFDS） to identify the system parameters. A responding signal, for example acceleration signal, was passed through a window function to obtain a responding signal that was to be analyzed. The signals passing through the window faction was decomposed into each intrinsic mode function （IMF） by empirical mode decomposition （EMD）. Theoretically, first IMF was regarded as the signal responding to that order and was further analyzed by hilbert-huang transform （HHT） to get the instantaneous frequency under that mode. The stiffness or mass parameters at given time were selected to be design variables and identified by minimizing the summation of the square of errors between the instantaneous frequencies and computed frequencies.