基于分形盒维数和多重分形的爆破地震波信号分析

英文篇名：Signal analysis for blasting seismic wave based on fractal box-dimension and multi-fractal
中文刊名：振动与冲击
英文刊名：Journal of Vibration and Shock
作者：钟明寿 ; 龙源 ; 谢全民 ; 李兴华
英文作者：ZHONG Ming-shou ; LONG Yuan ; XIE Quan-min ; LI Xing-hua (Engineering Institute of Corps of Engineers ; PLA Univ.of Sci.& Tech. ; Nanjing 210007 ; China)
中文关键词：爆破地震波 ; 分形 ; 盒维数 ; 多重分形 ; 信号分析
英文关键词：blasting seismic wave ; fractal ; box-dimension ; multi-fractal ; signal analysis ; multi-fractal spectrum
出版日期：2010-01-25
机构：解放军理工大学工程兵工程学院;
年：2010
期：01
出版单位：振动与冲击

摘要

为深入研究爆破地震波特性,采用分形盒维数和多重分形理论相结合的数学方法,通过其算法的理论推导和MATLAB软件编程计算得到地震波信号的盒维数值和多重分形谱图,对地震波信号的分形特征进行了分析。研究表明:盒维数D值的大小反映了地震波曲线的复杂程度和频率结构特征,说明盒维数只是对地震波信号整体性的描述;多重分形能够更加精细地描述地震波信号的局部特征,其谱图描述了不同奇异性指数α的概率信息。因此提出使用分形盒维数和多重分形相结合的信号分析方法,获取爆破地震波信号的整体强弱、频谱结构特征和局部的奇异性等重要信息。
In order to study the characteristic of blasting seismic wave,using a method combining fractal box-dimension and multi-fractal theory,the box-dimension and the multifractal spectrum of blasting seismic wave were obtained through theoretic derivation and programrning calculation using MATLAB software.Then,the fractal characteristic of blasting seismic wave was analyzed.The results indicated that the fractal box-dimension reflects the complexity and frequency structure of the seismic signal;the box-dimension describes the seismic signal as a whole;the multifractal can describe the detailed characteristics of the seismic signal;its spectrogram describes the probability information of different singularity indexα;so,the method combining the fractal box-dimension and the multi-fractal can get the strength,the structure of the frequency spectrum and the local singularity characteristic of the blasting seismic wave.

引文

[1]晏俊伟,龙源,等.基于小波包变换的爆破地震波时频特征提取及分析[J].振动与冲击,2007,26(4):25-29.
    [2]章冠人.动力破碎分形和加勒的关系[J].高压物理学报, 1997,11(2):81-84.
    [3]晏俊伟,龙源,等.爆破地震波的分形机制[J].解放军理工大学学报,2008,9(4):367-372.
    [4]Grassberger P.Generalized dimensions of strange attractors [J].Physics Letters A,1983,97:227 -230.
    [5]陈捷,等.基于多重分形的舰船噪声特征提取[J].西北工业大学学报,2000,18(2):241-244.
    [6]余英林,谢胜利,等.信号处理新方法导论[M].北京:清华大学出版社,2004:153-154.
    [7]汪富泉,李后强.小波理论与分形[J].物理,1991,23 (9):539-543.
    [8]娄建武,龙源,等.爆破地震信号的分形盒维数值分析[J].爆炸与冲击,2004,24(4):363-368.
    [9]Maragos Petros,Sun F K.Measuring the fractal dimension of signals:morphological covers an d iterative optimization[J], IEEE Transaction on signal processing.January 1993,41(1 ): 108 - 121.
    [10]Wormel G W,Oppenheim A V.Estimation of fractal signals from noisy measurements using wavelets[J],IEEE transaction on signal processing,1992,40(3 ):611 - 623.
    [11]娄建武,龙源,徐科军,等.爆破地震波信号分形维数计算的矩形盒模型[J].振动与冲击,2005,24(1):81-84.
    [12]Arimitsu T,Arimitsu N.Multifractal analysis of fluid particle accelerations inturbulence[J].Physica D:Nonlinear Phe- nomena,2004,193(1 ):218 - 222.
    [13]孙霞,吴自勤,黄韵,等.分形原理及其应用[M].合肥:中国科学技术大学出版社,2006:68-87.