1. School of Civil Engineering and Architecture, Changsha University of Science & Technology. Changsha 410114；
2. Construction science research institute of fujian province，Fuzhou 350000
When use wavelet basis to analyze blast vibration signal, the wavelet basis is mainly selected from MATLAB wavelet toolbox at present. During wavelet analysis, there are many questions such as the blindness, limitation and low efficiency in selecting or constructing wavelet basis. This paper has proposed a wavelet construction method for blast vibration signal analysis (short for BWBV method), according to an improved biorthogonal wavelet construction method and characteristics of blast vibration sub-signal. And a new wavelet basis (short for MB4.2 wavelet) has been constructed and used in numerical simulation signal and tested signal analysis, the results of which have been compared with those of pattern adapted wavelet and Db6 wavelet. The analysis results show that BWBV method has good application effect, the MB4.2 wavelet, constructed by BWBV method, has better accuracy, more stability and higher resolution than pattern adapted wavelet and Db6 wavelet in identification of the delay interval of millisecond blast. Compared with the pattern adapted wavelet construction method, the BMBV method need not construct new wavelet basis for each millisecond blast vibration signals, which can improve the Application efficiency of wavelet analysis.
凌同华1，刘浩然1，张 亮1，谷淡平1，吴联迎2. 双正交小波基构造法及其在爆破振动信号分析中的应用[J]. 振动与冲击, 2018, 37(11): 273-280.
LING Tonghua1，LIU Haoran1，ZHANG Liang1，GU Danping1，WU Lianying2. The improved biorthogonal wavelet construction method and its application in blast vibration signal analysis. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(11): 273-280.
[1] ZHONG Guo-sheng，LI Jiang，ZHAO Kui. Structural safety criteria for blasting vibration based on wavelet packet energy spectra[J]. International Journal of Mining Science and Technology，2011，21(1)：35–40.
[2] 张胜，凌同华，刘浩然，等. 模式自适应小波时能密度法及其在微差爆破震动信号分析中的应用[J]. 煤炭学报，2014，39(10)：2007–2013.
ZHANG Sheng，LING Tong-hua，LIU Hao-ran，et al. Pattern adapted wavelet time-energy density method and its application in millisecond blast vibration signal analysis[J]. Journal of China Coal Society，2014，39(10)：2007–2013.
[3] 李夕兵，凌同华. 单段与多段微差爆破地震的反应谱特征分析[J]. 岩石力学与工程学报， 2005，24(14)：2409–2413.
LI Xi-bing， LING Tong-hua， Response spectrum analysis of ground vibration induced by single deck and multi-deck blasting[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(14)：2409–2413.
[4] 朱权洁，姜福兴，于正兴，等. 爆破震动与岩石破裂微震信号能量分布特征研究[J]. 岩石力学与工程学报，2012，31(4)：723–730.
ZHU Quan-jie，JIANG Fu-xing，YU Zheng-xing，et al. Study on energy distribution characters about blasting vibration and rock fracture microseismic signal[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(4)：723–730.
[5] LING Tong-hua，ZHANG Sheng，CHEN Qian-qian，et al. Wavelet basis construction method based on separation blast vibration signal[J]. Journal of Central South University，2015，22(7)：2809–2815.
[6] 单仁亮, 白瑶, 宋永威,等. 冻结立井模型爆破振动信号的小波包分析[J]. 煤炭学报, 2016, 41(8):1923-1932.
SHAN Ren-liang, BAI Yao, SONG Yong-wei,et al. Wavelet packet analysis of blast vibration signals of freezing shaft model[J]. JOURNAL OF CHINA COAL SOCIETY, 2016, 41(8): 1923-1932.
[7] 凌同华，张胜，陈倩倩，等. 模式自适应小波构造与添加及其在爆破振动信号分析中的应用[J]. 振动与冲击，2014，33(12)：53–57+120.
LING Tong-hua，ZHANG Sheng，CHEN Qian-qian，et al. Pattern adapted wavelet construction and addition and its application in blast vibration signal analysis[J]. Journal of Vibration and Shock，2014，33(12)：53–57+120.
[8] 粟涓，董新汉. 双正交小波滤波器簇代数结构及构造[J]. 数学年刊A辑(中文版)，2014，35A(04)：451–462.
SU Juan，DONG Xin-han. Algebraic structure and construction of bi-orthogonal filter banks [J]. Chinese Annals of Mathematics，Series A，2014，(04)：451–462.
[9] 成礼智，王红霞，罗永. 小波的理论与应用[M]. 北京：科学出版社，2004：103–131.
CHENG Li-zhi，WANG Hong-xia， LUO Yong. Wavelet theory and its applications[M]. Beijing：CSPM，2004：103–131.
[10] COHEN A，DAUBECHIES I，FEAUVEAU J C. Biorthogonal bases of compactly supported wavelets[J]. Communications on Pure and Applied Mathematics，1992，41(5)：909–996.
[11] 成谢锋，张正. 一种双正交心音小波的构造方法[J]. 物理学报，2013，62(16)：168701-168701.
CHENG Xie-feng，ZHANG Zheng. A construction method of biorthogonal heart sound wavelet[J]. ACTA Physica Sinica，2013，62(16)：168701-168701.
[12] TAY D B H，KINGSBURY N G. Flexible design of multidimensional perfect reconstruction FIR 2-band filters using transformations of variables[J]. IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society，1993，2(4)：466–480.
[13] 陈勇，王国秋. 4-带紧支对称小波框架的构造[J]. 系统科学与数学，2014，34(6)：718–723.
CHEN Yong，WANG Guo-qiu. Construction of 4-band compactly supported symmetric wavelet frame[J]. J. Sys. Sci. & Math. Scis.，2014，34(6)：718–723.
[14] TAY D B H. Rationalizing the coefficients of popular biorthogonal wavelet filters[J]. IEEE Transactions on Circuits & Systems for Video Technology，2000，10(6)：998–1005.
[15] 牟力, 陈召曦. 重力资料多尺度分析最优小波基的选择[J]. 物探与化探, 2015, 39(5):1013-1019.
Mou Li, Chen Zhao-xi. The optimal choice of wavelet bases in gravity data multi-scale analysis［J］. Geophysical and Geochemical Exploration, 2015, 39( 5): 1013–1019
[16] LIBAL U，SPYRA K. Wavelet based shock wave and muzzle blast classification for different supersonic projectiles[J]. Expert Systems with Applications，2014，41(11)：5097–5104.
[17] 张华，陈小宏，杨海燕. 地震信号去噪的最优小波基选取方法[J]. 石油地球物理勘探，2011，46(1)：70–75.
ZHANG Hua，CHEN Xiao-hong，YANG Hai-yan. Optimistic wavelet basis selection in seismic signal noise elimination[J]. OGP，2011，46(1)：70–75.
[18] Xu H, Sun S Z, Gui Z，et al. Detection of sub-seismic fault footprint from signal-to-noise ratio based on wavelet modulus maximum in the tight reservoir[J]. Journal of Applied Geophysics，2015,114(4)：259-262.
[19] ZHENG Zu-duo，WASHINGTON S. On selecting an optimal wavelet for detecting singularities in traffic and vehicular data[J]. Transportation Research Part C Emerging Technologies，2012，25(8)：18–33.
