Hilbert-Huang变换理论及其计算中的问题
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摘要
以地震波的谱分析为例 ,对比分析了Hilbert Huang变换 (HHT)与傅立叶变换的差别 ,结果表明 :HHT是对非平稳时程进行数据分析的有效工具 ,能有效地将各种频率成份以固有模态函数的形式从时程曲线中分离出来 ,但这种固有模态函数与傅立叶变换结果不同 ,而且Hilbert谱是包含时间 -频率 -振幅的三维谱 ;可采用在端点改造一个小波串的方法解决HHT存在的端点飞翼现象 .文中还提出确定是否终止固有模态函数分离过程的一种方法
Hilbert Huang Transform (HHT) method,which includes Huang transform and Hilbert transform,is applied to make spectra analysis of seismic waves.The comparison of HHT and Fourier Transform shows that HHT is an efficient method for analysis of non stationary data.In HHT different intrinsic mode functions (IMF) can be separated by using empirical mode decomposition (EMD),i.e. Huang Transform,from time history.IMF is different from Fourier spectrum,and Hilbert spectrum is a temporal frequency amplitude spectrum which includes three dimensions.The HHT process shows that the suggested method,by improving one short wave series at the end of the time history,can solve the end swing problem.A method to end EMD process is also suggested in this paper.
Hilbert Huang Transform (HHT) method,which includes Huang transform and Hilbert transform,is applied to make spectra analysis of seismic waves.The comparison of HHT and Fourier Transform shows that HHT is an efficient method for analysis of non stationary data.In HHT different intrinsic mode functions (IMF) can be separated by using empirical mode decomposition (EMD),i.e. Huang Transform,from time history.IMF is different from Fourier spectrum,and Hilbert spectrum is a temporal frequency amplitude spectrum which includes three dimensions.The HHT process shows that the suggested method,by improving one short wave series at the end of the time history,can solve the end swing problem.A method to end EMD process is also suggested in this paper.
引文
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[2] ShuoM .HHTanalysisofnear fieldseismicgroundmotions[D].Denver:ColoradoSchoolofMines,2001.
[3] 胡广书.数字信号处理———理论、算法与实现[M ].北京:清华大学出版社,1997.
[4] 张晓哲,罗奇峰.地震加速度波的时-频反应谱分析[J].结构工程师,1999,(增刊):37-42.
[5] deBoorC .Apracticalguidetosplines[M ].NewYork:SpringerVerlag,1978.
[6] SchumakerLL .Splinefunctions:Basictheory[M ].NewYork:Wiley,1981.
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