爆破振动信号时频特征的三维分形特性研究
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摘要
为进一步研究爆破振动信号能量特征,基于小波包变换方法对爆破振动信号时频能量特征进行分析。在二维矩形盒维数模型的基础上建立了计算三维曲面分形盒维数模型,并计算得到实测爆破振动信号时频能量谱的三维分形盒维数D3d=2.148 8。该分形维数满足空间分形条件22d之间的数值关系,表明计算空间分形曲面分维数的常规假设D3d=D2d+1并非严格成立。研究表明,所提出的长方体覆盖空间曲面的分形维数计算方法可行、有效,为进一步研究爆破振动信号特征、控制爆破地震效应提供了新的研究思路。
To further study the characteristics of blast vibration signals,time-frequency energy characteristics of blast vibration signals were analyzed,taking advantage of wavelet packet transform.The three-dimensional fractal surface box dimension model was established based on two-dimensional rectangular box covering method.By analyzing the measured blasting vibration signal data,the fractal dimension of the three-dimensional time-frequency energy spectrum D3d is 2.1488,which meets the condition of space fractal dimension 23,and verifies that the time-frequency energy spectra of blasting vibration signals have 3D fractal characteristics.By studying the relationship between the three-dimensional fractal surface and two-dimensional box dimension of its section,the assumption of D3d=D2d+1 for traditional 3D surface fractal dimension calculation method does not hold true exactly.The study indicates,3D cuboids' covering surface calculation method for fractal dimension is feasible and effective,which provides a new idea for further study of blast vibration characteristics and the control blasting seismic effect.
To further study the characteristics of blast vibration signals,time-frequency energy characteristics of blast vibration signals were analyzed,taking advantage of wavelet packet transform.The three-dimensional fractal surface box dimension model was established based on two-dimensional rectangular box covering method.By analyzing the measured blasting vibration signal data,the fractal dimension of the three-dimensional time-frequency energy spectrum D3d is 2.1488,which meets the condition of space fractal dimension 2
引文
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[2]史秀志,薛剑光,陈寿如.爆破振动特征参量的粗糙集模糊神经网络预测[J].振动与冲击,2009,28(7):73-76.
[3]谢全民,龙源,钟明寿.基于小波、小波包两种方法的爆破振动信号对比分析[J].工程爆破,2009,15(1):5-9.
[4]张济中.分形[M].北京:清华大学出版社,1995.
[5]谢和平.分形应用中的数学基础与方法[M].北京:科学出版社,1997.
[6]杨军,金乾坤,黄凤雷.岩石爆破理论模型及数值计算[M].北京:科学出版社,1999.
[7]娄建武,龙源,徐全军.爆破地震信号的分形盒维数值分析[J].爆炸与冲击,2004,24(4):363-369.
[8]娄建武,龙源,徐全军.爆破地震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.
[9]龙源,晏俊伟,娄建武.基于分形理论的爆破地震信号盒维数研究[J].科技导报,2007,25(18):27-31.
[10]晏俊伟,龙源,唐献述.矿冶工程,基于分形盒维数的爆破震动信号研究[J].矿冶工程,2007,27(1):13-16.
[11]史秀志,薛剑光,陈寿如.爆破振动信号双线性变换的二次型时频分析[J].振动与冲击,2008,27(12):131-134.
[12]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社,1998.
[13]飞思科技产品研发中心编著.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005.
[14]金以文,鲁世杰.分形几何原理及其应用[M].杭州:浙江大学出版社,1998.
[15]Fractal analysis of the three-dimensional fracture surfaces inmaterials by the box-counting method[J].Journal ofmaterials science letters,2003,22:1279-1281.
[16]李成贵,董申.三维表面形貌的分形维数计算方法[J].航空精密制造技术,2000,36(4):36-40.
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