基于正交化HHT和随机相位模拟非平稳随机过程  

Simulation of nonstationary stochastic processes based on orthogonal Hilbert-Huang transform and random phase approach

作　　者：胡灿阳[1,2] 陈清军[2] 祁冰 徐庆阳[1] 

机构地区：[1]南京审计学院江苏省公共工程审计重点实验室,南京210029 [2]同济大学土木工程防灾国家重点实验室,上海200092 [3]河南省建筑科学研究院有限公司,郑州450053

出　　处：《振动与冲击》2012年第14期102-106,共5页Journal of Vibration and Shock

基　　金：科技部国家重点实验室基础研究资助项目(SLDRCE08-B-03);江苏省高校自然科学研究项目(10KJB560003);江苏省自然科学基金项目(BK2011693)

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 was then defined as the Hilbert spectrum of the peocess and on OHHT, the average of the Hilbert spectra over all samples 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.

关 键 词：非平稳随机过程 正交HHT Hilbert谱 随机相位角 

分 类 号：P315.9[天文地球—地震学]