爆破振动信号的提升小波包分解及能量分布特征
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摘要
针对传统小波包在小波基选取方面与实测爆破振动信号波形匹配欠佳的问题,提出了基于插值细分的二代小波构造方法,并通过引入移频算法,较好地解决了小波包隔点采样导致的频率混叠现象。结合应用实例,对实测信号进行多尺度的提升小波包分解后,得到了爆破振动各个频带的能量分布,总结了爆破振动信号频带能量的分布特征。分析结果表明,提升小波包(SGWP)算法可以真实反映振动信号的能量分布情况,为研究爆破震动效应下的结构安全提供有效的分析手段。
Aimed to the poor match of the traditional wavelet packet transform with the measured blasting vibration signal in the choice of wavelet base,a method was proposed for the construction of second generation wavelets based on interpolation subdivision.And the frequency alias resulted by dot interlaced sampling was overcome by using an algorithm with frequency shift.Through multi-resolution decomposition of measured signals,energy distribution in every frequency band was obtained,by which the distribution features of the blasting seismic signals were analyzed.Analysis results show that the algorithm for the SGWP transform can reflect the energy distribution of the blasting seismic signals and it is an effective approach to estimating the structure safety under blasting vibration conditions.
Aimed to the poor match of the traditional wavelet packet transform with the measured blasting vibration signal in the choice of wavelet base,a method was proposed for the construction of second generation wavelets based on interpolation subdivision.And the frequency alias resulted by dot interlaced sampling was overcome by using an algorithm with frequency shift.Through multi-resolution decomposition of measured signals,energy distribution in every frequency band was obtained,by which the distribution features of the blasting seismic signals were analyzed.Analysis results show that the algorithm for the SGWP transform can reflect the energy distribution of the blasting seismic signals and it is an effective approach to estimating the structure safety under blasting vibration conditions.
引文
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[19]中国生,熊正明.基于小波包能量谱的建(构)筑物爆破地震安全评估[J].岩土力学,2010,31(5):1522-1528.Zhong Guo-sheng,Xiong Zheng-ming.Safety assessment of structure by blasting seism based on wavelet packetenergy spectra[J].Rock and Soil Mechanics,2010,31(5):1522-1528.
[2]晏俊伟,龙源,方向,等.基于小波变换的爆破振动信号能量分布特征分析[J].爆炸与冲击,2007,27(5):405-409.Yan Jun-wei,Long Yuan,Fang Xiang,et al.Analysis on features of energy distribution for blasting seismic wavebased on wavelet transform[J].Explosion and Shock Waves,2007,27(5):405-409.
[3]何军,于亚伦,梁文基.爆破振动信号的小波分析[J].岩土工程学报,1998,20(1):47-50.He Jun,Yu Ya-lun,Liang Wen-ji.Wavelet analysis for blasting seismic signals[J].Chinese Journal of Geotechni-cal Engineering,1998,20(1):47-50.
[4]谢全民,龙源,钟明寿,等.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.Xie Quan-min,Long Yuan,Zhong Ming-shou,et al.Comparative analysis of blasting vibration signal based onwavelet and wavelet packets transform[J].Engineering Blasting,2009,15(1):5-9.
[5]张耀平,曹平,高赛红.爆破振动信号的小波包分解及各频段的能量分布特征[J].金属矿山,2007(11):42-43.Zhang Yao-ping,Cao Ping,Gao Sai-hong.Wavelet packet decomposition of blasting vibration signals and energydistribution characteristics of frequency bands[J].Metal Mine,2007(11):42-43.
[6]张德丰.MATLAB小波分析[M].北京:机械工业出版社,2009.
[7]姜洪开,何正嘉,段晨东,等.基于提升方法的小波构造及早期故障特征提取[J].西安交通大学学报,2005,39(5):494-498.Jiang Hong-kai,He Zheng-jia,Duan Chen-dong,et al.Wavelet construction based on lifting scheme and incipientfault feature extraction[J].Journal of Xi’an Jiaotong University,2005,39(5):494-498.
[8]Sweldens W.The lifting scheme:A construction of second generation wavelet[J].SIAM Journal on MathematicsAnalysis,1997,29(2):511-546.
[9]Claypoole R L,Davis G M,Sweldens W,et al.Nonlinear wavelet transforms for image coding via lifting[J].IEEETransactions on Image Processing,2003,12(12):1449-1458.
[10]Daubechies I,Sweldens W.Factoring wavelet transforms into lifting steps[J].Journal of Fourier Analysis andApplication,1998,4(3):247-269.
[11]段晨东,张建丁.基于第二代小波变换的转子碰摩故障特征提取方法研究[J].机械科学与技术,2006,25(10):1229-1232.Duan Chen-dong,Zhang Jian-ding.Study of the fault feature extraction method for rotor rub-impact based on thesecond generation wavelet transform[J].Mechanical Science and Technology,2006,25(10):1229-1232.
[12]邓建中,刘之行.计算方法[M].2版.西安:西安交通大学出版社,2001.
[13]Sweldens W,Schrder P.Building your own wavelets at home[DB/OL].http://cm.bell-labs.com/who/wim/papes.html/at home,1998-01-05.
[14]Sweldens W.The lifting scheme:A custom-design construction of biorthogonal wavelets[J].Applied and Compu-tational Harmonic Analysis,1996,15(3):186-200.
[15]耿中行,屈梁生.小波包的移频算法与振动信号处理[J].振动工程学报,1996,19(2):145-152.Geng Zhong-xing,Qu Liang-sheng.Frequency shift algorithms of wavelet packet and vibration signal analysis[J].Journal of Vibration Engineering,1996,19(2):145-152.
[16]刘世元,杜润生,杨叔子.小波包改进算法及其在柴油机振动诊断中的应用[J].内燃机学报,2000,18(1):11-16.Liu Shi-yuan,Du Run-sheng,Yang Shu-zi.An improved algorithm for wavelet packets and its applications to vi-bration diagnosis in diesel engines[J].Transaction of CSICE,2000,18(1):11-16.
[17]Alan V O,Ronald W S,John R B.Discrete-time signal processing[M].刘树堂,黄建国,译.西安:西安交通大学出版社,2001:557-582.
[18]周德廉,邵国友.现代测试技术与信号分析[M].徐州:中国矿业大学出版社,2005.
[19]中国生,熊正明.基于小波包能量谱的建(构)筑物爆破地震安全评估[J].岩土力学,2010,31(5):1522-1528.Zhong Guo-sheng,Xiong Zheng-ming.Safety assessment of structure by blasting seism based on wavelet packetenergy spectra[J].Rock and Soil Mechanics,2010,31(5):1522-1528.
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