基于HHT方法的时变多自由度系统的参数识别
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摘要
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.
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.
引文
[1]钟佑明,秦树人,汤宝平.Hilbert-Huang变换中的理论研究[J].振动与冲击,2002,21(4):637-640.
[2]Huang N E,Shen Z,Long S R,et al.The empiricalmode decomposition and Hilbert spectrumfor nonlin-ear and non-stationary ti me series analysis[J].Pro-ceedings of the Royal Society of London,Series A.1998,454:903-995.
[3]公茂盛,谢礼立.HHT方法在地震工程中的应用之初步探讨[J].世界地震工程,2003,19(3):39-43.
[4]陈隽,徐幼麟.HHT方法在结构模态参数识别中的应用[J].振动工程学报,2003,16(13):383-397.
[5]Yang J N,Lei Y,Pan S W.Systemidentification oflinear structures based on Hilbert-Huang spectral a-nalysis.Part 1:Normal modes[J].Earthquake Engi-neering and Structural Dynamics,2003,32(9):1 443-1 467.
[6]张郁山,梁建文,胡聿贤.应用HHT方法识别刚度渐变的线性SDOF体系的动力特性[J].自然科学进展,2005,5(15):597-603.
[7]Yang J N,Lei Y,Lin S.Hilbert-Huang based ap-proach for structural damage detection[J].Earth-quake Engineering and Structural Dynamics.2004,130(1):85-95.
[8]Xu Y L,Chen J.Structural damage detection usingempirical mode decomposition:experi mental investi-gation[J].Journal of Engineering Mechanics,2004,130(11):1 279-1 287.
[9]唐友刚.高等结构动力学[M].天津:天津大学出版社,2002.
[2]Huang N E,Shen Z,Long S R,et al.The empiricalmode decomposition and Hilbert spectrumfor nonlin-ear and non-stationary ti me series analysis[J].Pro-ceedings of the Royal Society of London,Series A.1998,454:903-995.
[3]公茂盛,谢礼立.HHT方法在地震工程中的应用之初步探讨[J].世界地震工程,2003,19(3):39-43.
[4]陈隽,徐幼麟.HHT方法在结构模态参数识别中的应用[J].振动工程学报,2003,16(13):383-397.
[5]Yang J N,Lei Y,Pan S W.Systemidentification oflinear structures based on Hilbert-Huang spectral a-nalysis.Part 1:Normal modes[J].Earthquake Engi-neering and Structural Dynamics,2003,32(9):1 443-1 467.
[6]张郁山,梁建文,胡聿贤.应用HHT方法识别刚度渐变的线性SDOF体系的动力特性[J].自然科学进展,2005,5(15):597-603.
[7]Yang J N,Lei Y,Lin S.Hilbert-Huang based ap-proach for structural damage detection[J].Earth-quake Engineering and Structural Dynamics.2004,130(1):85-95.
[8]Xu Y L,Chen J.Structural damage detection usingempirical mode decomposition:experi mental investi-gation[J].Journal of Engineering Mechanics,2004,130(11):1 279-1 287.
[9]唐友刚.高等结构动力学[M].天津:天津大学出版社,2002.
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