单段爆破振动信号频带能量分布特征的小波包分析

1、振动与冲击第26卷第5期JOURNAL OF V I B RATI O N AND SHOCKVol . 26No . 52007单段爆破振动信号频带能量分布特征的小波包分析凌同华1, 2, 李夕兵2(1. 长沙理工大学桥梁与结构工程学院, 长沙410076; 2. 中南大学资源与安全工程学院, 长沙410083爆破振动分析是研究爆破振动危害控制的基础, 也是控制爆破振动危害的前提。根据爆破振动信号具有摘要短时非平稳的特点, 利用小波包分析技术对满足分析要求的单段微差爆破振动信号的能量分布特征进行研究。首先, 简略地介绍了小波变换与小波包分析的特点。其次, 基于MAT LAB 对单段爆破振动信

2、号进行小波包分析, 得到了爆破振动信号在不同频带上的能量分布图。最后, 总结了单段爆破振动信号频带能量的分布特征。结果表明, 在单段爆破中, 爆破震动信号成分主要以中高频(39Hz 156Hz 为主, 低频成分(39Hz 以下 所占比例极少。关键词:爆破振动, 能量分布, 小波包分析, 非平稳信号, 单段爆破中图分类号:O382; T D235. 1文献标识码:A爆破振动分析是研究爆破振动危害控制的基础, 也1是控制爆破振动危害的前提。以往分析和处理爆破2-4振动信号最常用也是最主要的方法是Fourier 分析从众多爆破振动实地监测资料看, 时短、突变快等特点, 5-7展, 人们研究它时, (

3、伪平稳 问题近年来, 随着科学技术的发展和进步特别是新的数学工具的出现, 信号的时频表示法已广泛应用于工程技术领域, 用小波变换处理非平稳8-9随机信号已激起了人们很高的热忱。但用小波变换处理爆破振动信号还处于起步阶段, 许多研究者正对此10-12做一些有益的尝试和探索。本文针对爆破振动信号的特征, 对单段爆破振动信号进行小波包分析, 指出了单段爆破振动信号能量分布的特征, 为综合研究爆破地震效应特别是振动速度-频率相关安全准则提供了一种有效的分析技术。1小波包分解与爆破震动信号的能量111小波包分析及其特点12345678注:表中S S S “粗糙”和“细节”两部分。细节”部分为信号的高“粗

4、糙”和“细节”从小波分解的结构可以看出, 小波变换的频率分辨率随频率升高而降低。小波包分解则不然, 它不仅对低频部分进行分解, 而且对高频部分实施分解。小波包分解能根据信号特征和分析要求自适应地选择相应频带与信号频谱相匹配。小波包分解具有严密的数学理论和数值计算法, 是一种5-7比小波分解更为精细的分解方法。112爆破震动信号小波包分解将爆破震动信号进行小波包分解时, 分解的层数取决于具体信号及采用的爆破震动分析仪的工作频带而定。本文中所采用的爆破震动分析仪的最小工作频率为5Hz, 由于爆破震动信号的频率一般在200Hz 以6下, 根据采样定理, 信号的采样频率设为2500Hz, 则其奈奎斯特

5、(Nyquist 频率为1250Hz 。因此, 可以将分析信号分解到第8层, 对应的最低频带为0Hz -4. 883Hz 。根据小波包算法, 其对信号分解后各层重构信号的频带范围见表1。S S 表1小波包分解系数重构信号各层频带范围0-6250-312. 50-156. 250-78. 1250-39. 0630-19. 5310-9. 7660-4. 883S i , j 表示第i 层第625-1250937. 5-12501093. 75-12501171. 875-12501210. 937-12501230. 469-12501240. 234-12501245. 117-125031

6、2. 5-625625-937. 5156. 25-312. 5312. 5-468. 7578. 125-156. 25156. 25-234. 3751093. 75-1171. 87539. 063-78. 12578. 125-117. 1881171. 875-1210. 93719. 531-39. 06339. 063-58. 5941210. 937-1230. 4699. 766-19. 53119. 531-29. 2971230. 469-1240. 2344. 883-9. 7669. 766-14. 6491240. 234-1245. 117i -1j 个小波包分解

7、系数重构信号, j =0, 1, 2, , 2, i =1, 2, 3 n基金项目:国家自然科学基金资助项目(50678028 和中国博士后基金资助项目(2004036430 收稿日期:2006-11-13修改稿收到日期:2006-12-12第一作者凌同华男, 硕士, 副教授, 1960年9月生42振动与冲击2007年第26 卷113各频带的能量表征将被分析信号分解到第8层, 设S 8, j 对应的能量为E 8, j , 则有6, 10m为分析单段爆破震动信号频带能量分布的特征,在某地下矿进行了单段爆破震动测试, 其测试点的爆破条件见表2, 相应的速度-时程曲线见图1 。E 8, j =|S

8、8, j (t |d t =|x j , k |k =122(1式中:x j , k (j =0, 1, 2, 2-1, k =1, 2, m , m 为信号的离散采样点数 表示重构信号S 8, j 的离散点的幅值。设被分析信号的总能量为E 0, 则有:28-18E 0=Ej =08, j(2各频带的能量占被分析信号总能量的比例为:E j =8E 8, j E 0×100%(3式中j =0, 1, 22-1这样, 由式(1 、式(2 、式(3 可以得到信号经小波包分解后不同频带的能量, 从而可以找出爆破振动信号在传播过程中能量的变化规律。图1竖向振动速度时程曲线2211爆破振动测试表

9、2信号DD -1DD -2测点到爆心距离/m6678段药量/kg718孔数12212单段爆破震动信号频带能量分布的小波包分析用db8作为小波基函数对图1所示爆破震动信号分别进行深度为8层的小波包分析, 根据式(1 、式(2 、式(3 编制计算程序, 运行后得到各频带的能量分布图, 见图2。为便于比较, 将各信号不同频带能量占该信号总能量的百分比统计于表3。表3单段爆破震动信号的频带能量分布百分比统计频带/Hz04. 8834. 8839. 7669. 76614. 64814. 64819. 5319. 5324. 41424. 41429. 29729. 29734. 1834. 1839.

10、 06339. 06343. 94543. 94548. 82848. 82853. 71153. 71158. 59458. 59463. 47763. 47768. 35968. 35973. 24273. 24278. 12578. 12583. 00883. 00887. 89187. 89192. 77392. 77397. 657信号DD -10. 0030. 0020. 0133E -040. 9920. 7590. 0360. 1950. 7780. 6232. 3013. 9610. 4340. 4651. 6443. 8000. 3660. 0150. 4290. 382D

11、D -20. 0030. 0030. 0120. 0010. 6670. 9190. 0270. 1624. 5972. 5770. 2441. 8161. 5462. 3022. 3131. 3570. 9810. 4660. 0210. 068DD -30. 0036E -040. 0220. 0060. 7010. 2630. 0290. 0558. 5556. 0080. 6577. 5190. 7891. 8612. 4110. 5140. 1350. 2130. 9820. 164频带/Hz102. 107. 112. 117. 122. 126. 131. 136. 141. 1

12、46. 151. 156. 161. 166. 170. 175. 180. 185. 190. 195. 54-107. 4242112. 3030117. 1919122. 0707126. 9595131. 8484136. 7272141. 6060146. 4848151. 3737156. 2525161. 1313166. 0202170. 9090175. 7878180. 6666185. 5555190. 4343195. 3131200. 20信号DD -14. 6592. 3151. 2017. 33513. 0108. 1041. 02714. 56010. 1301

13、0. 4503. 5860. 0130. 0040. 0040. 0050. 0170. 0140. 0120. 0179E -04DD -26. 3870. 0430. 5862. 1844. 3902. 7326. 5431. 30312. 83016. 02012. 5108E -050. 0034E -040. 0020. 0030. 0010. 0107E -040. 039DD -30. 1040. 5811. 3431. 9912. 54019. 32019. 7602. 5210. 7936. 56011. 3209E -040. 0013E -045E -040. 0070.

14、 0060. 0120. 0040. 019 第5期凌同华等: 单段爆破振动信号频带能量分布特征的小波包分析43明爆破震动信号的主震频带比较宽, 主震频带又可以分成多个子震频带。同时表明, 工程结构是一个包含众多子结构的系统, 各子结构的固有特性各不相同, 因而其爆破震动具有多模态、多震型的特点。3结论1 单段爆破震动信号成分主要以中高频(39Hz 156Hz 为主, 低频(39Hz 以下 成分所占比例极少。2 受爆破地震波干涉效应的影响, 段药量低的爆破震动峰值段完全可能超过段药量高的爆破震动峰值。3 单段爆破震动信号的优势频率较高, 其主震频带较宽, 并可以被分成多个子震频带。图2单段爆破

15、震动信号的频带能量分布参考文献1李洪涛, 舒大强. J .武38(1 :7982. 2, , J ., 1996, 16(1 :6167. , 龚敏, 于亚伦. 爆破振动频率预测及其回归分析J .辽宁工程技术大学学报, 2005, 24(2 :187189. 4M a Guowei, Hao Hong, Zhou Yingxin . A ssess ment of struc 2ture damage t o blasting induced J .Engineering Structures,2000, (22 :13781389.5Charles K Chui . An intr oduc

16、ti on t o waveletsM.Ne w York:Academ ic Press, I nc . 1992:297333.6胡昌华, 张军波. 基于MAT LAB 的系统分析与设计小213单段爆破震动信号频带能量分布特征从图2、表3可以看出, 单段爆破震动信号的频带能量分布呈现出以下特征:1 从图3-2可以看出, 量虽然分布很广泛(0Hz 1 要位于中高频(39Hz 3以看出, 三条信号在分比分别为:2%、1. 1. 1%。表明在单段爆破中, 爆破震动信号成分主要以中高频为主, 低频成分所占比例极少。显然, 由于工程结构体的自振频率往往较低, 这有利于受控对象的安全。2 从图2还可以

17、看出, 虽然DD -3和DD -2的段药量分别为DD -1的3倍和2. 6倍, 但其相应的能量峰值(其实质为质点震动速度 不存在类似的比例关系, 甚至出现了DD -3的能量峰值还略小于DD -1的能量峰值的现象。表明在工程爆破中, 同段次药包(装药 爆破时, 各药包产生的地震波存在干涉效应, 从而出现了段药量高的爆破震动峰值反而低于段药量低的震动峰值的现象。3 从图2和表3中都可以看出, 虽然单段爆破震动信号的能量主要集中于中高频, 但在中高频段其能量分布也极不均匀, 出现了为数不少的“子中心”。这些“子中心”构成了爆破震动信号不同的主震频带, 表波分析M.西安:西安电子科技大学, 2000:

18、265266.7王宏禹. 非平稳随机信号分析与处理M.北京:国防工业出版社, 1999:1220. 8李友荣, 曾法力, 吕勇等. 小波包分析在齿轮故障诊断中的应用J .振动与冲击, 2005, 24(5 :101103. 9郭亚, 应怀樵, 武颖奎. 小波在频率发生较小变化识别中的应用研究J .振动与冲击, 2005, 24(5 :99100.10林大超, 施惠基, 白春华等. 爆炸地震效应的时频分析J .爆炸与冲击, 2003, 23(1 :3136.11凌同华, 李夕兵. 用时-能密度法确定微差爆破中的实际延迟时间J .岩石力学与工程学报, 2004, 23(13 :22662270.1

19、2凌同华. 爆破震动效应及其灾害的主动控制D .长沙:中南大学, 2004.Vol . 26No . 52007JOURNAL OF V I B RATI O N AND S HOCK 151M Fs fr om mode confusing I .Key words:I M F (intrinsic mode functi on , fast band 2pass filtering, analytic signal, H ilbert s pectrumA NO NL I NEAR V I SCO 2HY PERELAST I C CO NST I TUT I VE MOD EL BASE

20、D O N Y EO H STRA I N ENERGY FUNCT I O N W I TH I TS APPL I CAT I O N TO I M PACT S I M ULAT I O NZHOU X iang 2rong , WAN G Q iang , WAN G B ao 2zhen112(11ShanghaiM arine Equi pment Research I nstitute, Shanghai 200031, China; 21C AS Key Laborat ory of MechanicalBehavi or and Design of Materials, Un

21、iversity of Science and Technol ogy of China, Hefei 230026, China Abstract According t o the viscoelastic 2hyperelastic theory And the visco 2hyperelastic model p r oposed by L. M. Yang etc, a ne w nonlinear visco 2hyperelastic constitutive model (VHC M based on Yeoh strain energy functi on is p r o

22、posed t o describe m iddle 2high strain rate effects of incomp ressible rubber . The ne w VHC M is composed of only one variable 2the fist invariant of the left Cauchy 2Green def or mati on tens or B , which si m p lifies the Yang s VHC M. A user material subr ou 2tine (ABAQUS/VUMAT of the ne w VHC

23、M is als o comp iled t o si m ulate i m pact res pads and rubber shock abs orbers . The good agree ment bet w een experi m ent results and ones w VHC M is effective and feasible in the cases of m iddle 2high strain rates of rubber .Key words:rubber, Yeoh, strain rate, 2model, ABAQUS/VUMAT,i m pactA

24、M ETHOD W AY BARR I ER CRASH ACC I D ENT RECO NSTRUCT I O NSHEN J ie , J I N X ian 2long11, 2, CHEN J ian 2guo3(11H igh Perf or mance Computing Center, Shanghai J iaot ong University (SJT U , Shanghai 200030, China;21State Key Laborat ory of V ibrati on, Shock &Noise, S JT U, Shanghai 200030, Ch

25、ina;31I nstitute of Forensic Sciences, M inistry of Justice, Shanghai 200063, China Abstract A ne w method of car 2high way barrier crash accident reconstructi on is p resented based on CRASH3da m 2age algorith m. Because the stiffness of a barrier is easy t o obtain, the stiffness coefficients of a

26、 vehicle deter m ined by this method is based on residual crush and the vel ocity before i m pact is calculated with change of kinetic energy . A ls o, a de 2tailed FE model of a typ ical ty pe of high way guardrail is established . U sing this model, the dyna m ic characteristics of this guardrail

27、under vehicle i m pact are investigated . It s f ound that the nor mal contact f orce bet w een the vehicle and the barrier can be a linear functi on of the residual crush in most conditi ons, but the linear relati on for the tangential f orce can only be satisfied in s ome conditi ons . Finally, th

28、e above 2menti oned method is app lied t o a real 2world accident . Compared with PC 2CRASH, this method is p r oved t o be feasible f or accident reconstructi on .Key words:accident reconstructi on, computer si m ulati on, high way barrierFEATURES O F ENERGY D I STR I BUT I O N O F S I NGL E D ECK

29、BLASTV IBRAT I O N S I GNAL S W I TH W AVEL ET PACKET ANALY S I SL I N G Tong 2hua1, 2, L I X i 2bing2(11School of B ridge and Structural Engineering, Changsha University of Science and Technol ogy, Changsha 410083, China; 21School of Res ources and Safety Engineering, Central South University, Chan

30、gsha 410083, China Abstract B last vibrati on analysis is a f oundati on for studying contr ol of blast vibrati on da mage and p r ovides a p re 2requisite t o contr olling blast vibrati on . Based on the characteristic of a short 2ti m e non 2stati onary random signal, the feature of energy distrib

31、uti on of a single deck blast vibrati on signal is investigated by means of wavelet packet method . Firstly, the152JOURNAL OF V I B RATI O N AND SHOCK Vol . 26No . 5 2007characteristics of wavelet transfor mati on and wavelet packet analysis are intr oduced briefly . Secondly, three single deckblast

32、 vibrati on signals are analyzed by wavelet packet based on s oft w are MAT LAB , and change of energy distributi on curves at different frequency bands are obtained . Finally, the change la w of energy distributi on of single deck blast vibra 2ti on signals is analyzed . The results show that the d

33、o m inant frequency compone m s of single deck blast vibrati on signals are concentrated at the higher frequency band (39Hz 2156Hz and the rati o of the energy of l ow frequency components (less than 39Hz t o the t otal energy is l ower .Key words:blast vibrati on, energy distributi on, wavelet pack

34、et analysis, non 2stati onary random signal, single deck blastSTUDY O N M UL T I 2D I M ENS I O NAL V IBRAT I O N TRANS M ISS I O N PERFO R M ANCE BASED O N V I BRAT I O N POW ER FLOW CALCULAT I O NW ITH NO RTO N EQU I VAL ENT S Y STE MHAN X u, G UO Yong 2jin, ZHU P ing, YU Ha i 2(School of Mechanic

35、al Engineering, Shanghai J iaot ong Shanghai China Abstract Structural vibrati on trans m issi on is of energy trans m issi on . Power fl ow method ex p lains mechanis m of vibrati on trans m on It is increasingly used in structural vibrati on contr ol . the po wer fl ow calculati syste m has an adv

36、antage of being easily integrated with finite ele ment m ment, thus p r oviding an effective way t o evaluate vibrati on perf or m 2ance of real and . The power fl o w calculati on method based on Nort on equivalent syste m is used t o analyze the multi 2di m onal vibrati on trans m issi on perfor m

37、ance of a typ ical is olati on syste m here . Thr ough comparing the power fl ow of each vibrati on di m ensi on, it is f ound that the flexibility of the receiving structure is a maj or fact or contr olling the vibrati on trans m issi on perf or mance . Then, t w o measures including thickening p l

38、ates and using ribs are used t o strengthen the receiving structure . It is shown that using ribs is better . Not only better effect of vibrati on reducti on is ob 2tained, it is als o p r op iti ous t o structural lightening . The power fl o w calculati on method based on Nort on equivalent syste m is de monstrated t o be an effective way t o analyze multi 2di m ensi ona