基于正交化HHT和随机相位模拟非平稳随机过程
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摘要
模拟非平稳随机过程已经成为工程中经常遇到的情况,使非平稳过程的大量模拟样本具有相同的统计特性并不容易。基于样本记录正交HHT变换的Hilbert谱提出了非平稳随机过程的模拟方法。首先,利用正交化方法对IMF分量进行处理,避免了传统EMD分解造成的能量泄漏。第二步,把样本的Hilbert谱均值作为随机过程的目标Hilbert谱,通过引入随机相位进行非平稳随机过程的仿真,并且给出了随机过程的统计特性函数。通过对低频地震动记录和高频地铁振动记录的模拟算例表明,模拟的非平稳过程样本与原记录在时频分布上非常接近,具有相同的统计特性。
A new method was proposed for the simulation of nonstationary random processes based on the Hilbert spectra from the orthogonal Hilbert-Huang transform(OHHT) of observed samples.An orthogonal approach was introduced to deal with IMF,and the result shows that the orthogonal HHT is a universal method which can avoid the leakage of energy comparing with conventional HHT.Based on OHHT,the average of the Hilbert spectra over all samples was then defined as the Hilbert spectrum of the peocess and used as the target spectrum in the simulation of the process.The statistic characteristic fuction of stochastic process was given out.The simulation of earthquake ground motion with low frequency characteristics and the simulation of subwary vibration with high frequency characteristics were carried out.The time histories,Fourier magnitude spectra and response spectra of samples are in good agreement with those of the records.Samples and records of the process are of the same statistic characteristics.
A new method was proposed for the simulation of nonstationary random processes based on the Hilbert spectra from the orthogonal Hilbert-Huang transform(OHHT) of observed samples.An orthogonal approach was introduced to deal with IMF,and the result shows that the orthogonal HHT is a universal method which can avoid the leakage of energy comparing with conventional HHT.Based on OHHT,the average of the Hilbert spectra over all samples was then defined as the Hilbert spectrum of the peocess and used as the target spectrum in the simulation of the process.The statistic characteristic fuction of stochastic process was given out.The simulation of earthquake ground motion with low frequency characteristics and the simulation of subwary vibration with high frequency characteristics were carried out.The time histories,Fourier magnitude spectra and response spectra of samples are in good agreement with those of the records.Samples and records of the process are of the same statistic characteristics.
引文
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[12]Husid R L.Analisis de terremotos:analisis general[J].Revista del ID1EM,Santiago Chile,1969,8(1):21-42.
[2]李锦华,李春祥,申建红.非平稳脉动风速的数值模拟[J].振动与冲击,2009,28(1):18-23.
[3]Yeh C H,Wen Y K.Model of nonstationary earthquakeground motion and application[C].Proceedings of Fourth U.S.National Conference on Earthquake Engineering,1990,1:505-514.
[4]Liang J,Chaudhuri S R,Shinozuka M.Simulation of non-stationary stochastic processes by spectral representation[J].J.Engrg Mech,ASCE,2007,133(6):616-627.
[5]王国林,胡蛟,钱金戈,等.路面对汽车非平稳激励的时域仿真及小波分析[J].振动与冲击,2010,29(7):28-32.
[6]朱昱,冯启民.地震加速度相位差谱分布的数字特征[J].地震工程与工程振动,1993,13(2):30-37.
[7]大崎顺彦著,吕敏申,谢礼立,译.地震动的谱分析入门[M].北京:地震出版社,1980.
[8]金星,廖振鹏.地震动相位特性的研究[J].地震工程与工程振动,1993,13(1):7-13.
[9]Huang N E,Shen Z,Long S R,et al.The empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysis[J].Proc.R.Soc.Lond.A,1998,454:903-995.
[10]胡灿阳,陈清军.非平稳地震地面运动局部谱密度正交化HHT估计[J].同济大学学报(自然科学版),2008,36(9):1164-1169.
[11]楼梦麟,黄天立.正交化经验模式分解方法[J].同济大学学报(自然科学版),2007,35(3):293-298.
[12]Husid R L.Analisis de terremotos:analisis general[J].Revista del ID1EM,Santiago Chile,1969,8(1):21-42.
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