Bolt Detection Signal Analysis Method Based on ICEEMD

Bolt Detection Signal Analysis Method Bas ed on ICEEMD Chunhui Guo 1 ,2 , Zhan Zhang 1* , Xin Xi e 3 , Zhengy u Y ang 3 1. ! College of W ater Con servanc y and Hydropower Engine ering , Hohai Unive rsity , Nanjin g , China 2. ! Key Labora tory of Hydr auli c and W aterway Engi neeri ng of the Mini stry of Educati on, Chong qing Jiaotong University , China 3. Depart ment of El ectr ical and Compute r Engi neer ing, North easte rn Uni vers ity , Bost on, US A * Correspo nding author E- mail: 337221231 @qq .co m , zhanzhang_hhu@ qq.com , xie.x@husky .neu.edu , yang.zhe@ husky .neu.edu Abstract: The construction quality of the bolt is directly related to the safety of the project , and as s uch, it must be tested . I n this paper, the improved c omplete e nsemble e mpirical m ode d ecomposition ( IC EEMD ) method i s intro duced to the bolt detection signal analysis . The ICEEMD is used in order to decompose the anchor detection signal according to the approxim ate entropy of each i n trinsic mode fun ction ( IMF ) . The noise of the IMFs is eliminated by the wavelet soft threshold de - noising technique . B ased on the approximate entropy , and the wavelet de - noising principle , the ICEEMD - De anch or signal analysis method is proposed. F rom the analysis of the vibration analog signal , as well as the bolt detection signal, the result shows th at the ICEEM D - De method is capable of correctl y separat ing the different IM Fs under noisy condition s , and also that the IMF can effectively identify the reflection signal of the end of the bo lt. Keywords ： bolt anchorage , a pproximate entropy , intrin sic mode functio n , wavelet de - noise, CEEMD 1. Introduction The bolt anchori ng system is subject to the geologica l conditions and the c onstruction technolo gy effect . If there are any hid den dange rs th at haven ’ t b een detect ed , then it will cause engineeri ng accidents and serious economic losses. Therefore, the con struction quality of the bolt anchorage must be checked , so as to ensure the safety of the project. During the early stage, the detection of the an chor’s anchoring qu ality is mainly based on the drawi ng tes t [1-3] . However, th is method wi ll cause damage to the an choring system. The method is al so not suitable for large - scale detection and can ’t be fully reflect ed [4-6] . T he detection method for the quality of the an chor will be gradually replaced by the use of non - destructive testing methods, such as the acous tic wav e meth od [7-10] . This method is e stablish ed based on the m athematica l mo del of the one - dimensional elastic rod [11-13] . The assumption is that the longitu dinal wave wavelength that is generat ed by the exciting force is much larg er than that of the bolt radius, so the transverse displacem ent of the system can be neglected. By solving the longitudinal one - dimensional wave equation , t he dynamic response of the bolt syst em is obtained. The low - end reflection signal of the bolt can be easily disturbed during the process of bolt detection ; i t is difficult to directly obta in the reflecte d wave a rrival time. I n order to obtain the effective sig nal, many data processing methods, such as the short - time Fourier transform , the G abor transform , th e Wigner -V ille transform , the wa velet trans form and so on, are proposed. W avelet transform is the most used signal analysis method among them [14-18] . Howeve r, the effect o f the wavele t transform is o ften limited b y the wave let base, as well as the number of decomposed layers. The empirical m ode decomposition ( EM D ) can adaptively select the substrate according to the characteristics of the signal for the mu lti - resolution analysis of the signal, which will overcome the wavelet base selection problem [19-21] . The decompositi on is based on the local timescale of the data . The re hav e been many appl icati ons abou t EMD proces sing det ecti on signa l [22-25] . However, the EMD encounters some modal aliasing problems during the processing procedure [26-28] . The E nsemble empiri cal mode decomposi tion ( EEMD ) overcomes the modal alias ing problem that’s inh erent of the EMD, but due to the addition o f different white noise, the decomposition may produce a false mode , w hich can also cause errors. The reconstructed sig nal still includes residual noise, and different realizations of s ignal and no ise may p roduce different modes [29-31] . C omplete EE MD (CE EMD) has b een succes sfully applied to seismic signal analysis. Han et al. used CEEMD to obtain an exact reconstruct ion of the origina l signal and a better spectral separation of the modes with synthetic and real seismic data [32] . However, the CEEMD cannot be proven, and the final averaging problem remains unsolved since different noisy cop ies of the signal can produce a different number of modes [33] . In recent years, the impro ved com plete E EMD ( ICEEMD) has been proposed by adding adaptive white noise to the signal and by redefining the calculations of the local mean for each model [33-37] . Th e result show s that the method is superior to the traditional metho d. A lthoug h EM D is m ore adaptive and more efficient [38, 39] , the E EMD outperform s EMD in ca using les s mode mixing [40, 41] . The CEEMD outperfo rms EMD in causin g less mode mi xing and EEMD in be tter re constru ction pe rformance [42, 43] . T he ICEEMD, as illustrated in the paper, outper form s CE EMD in bein g m ore p hysical meaningful and less numb er of compo nents [44] . Based on the mentio ned research, the ICEEM D m ethod is introduce d into the bolt dete ction signal an alysis in this paper . However , the actua l signal of bolt detection is un der noise interference . T he process ing signal und er noise is critical pro blem with IC EEMD for bolt detection. By c ombining th e approxima te entropy and the wav elet de - noising principle, the ICEEM D - De was established based on the ICEEMD. Then , the ICEE MD - de was used to proc ess the simulation vibration s ignal and the a ctual bolt dete ction signal. 2. Theory and Methodol ogy Based on th e ICEEM D anch or detection sign al analys is me thod, the ICEEM D - De in tegrate s ICEEM D, the approximate en tropy and wavelet de - noising . The three methods are introduced in the section. 2.1 . ICEEM D Principle The ICEEMD method is able to effectively prevent the occurrence of false IMF by adding the adaptive white noise to the signal and by redefining th e local mean of each m odal. Assum ing the ancho r detection sig nal s , then th e decom position process of the I CEEMD is as follo ws: 1 ） The signal s is adde d to the M group G aussian w hite noise in order to g enerate a new signal s i . s i can be expressed as: ii k ss w b =+ (1) w here w i ( i =1,2, … ,M ) is one group of G aussian wh ite no ise, ( ) 0 kk std r be = ， r k is the k - th residue ， e 0 takes 0.2 . 2 ） The k - th mode can be obtained by EMD. W e can obtain the mean of the k - th mo de and have: ( ) ( ) ii i k Es s M s = - (2) where is the operato r of mean . 3 ） s i is decom posed by using EM D. W e obtain 1 - th res idue r 1 and 1 - st IMF d 1 . We h a v e ： ( ) 1 i rM s = (3) 11 ds r = - (4) 4 ） W e take 2 - nd residue , r 2, as the local mean of ( ) 11 2 i rE w b + . The 2 - nd IMF d 2 is: ( ) ( ) 21 1 2 i rM r E w b =+ (5) 21 2 dr r = - (6) 5 ） For any r k , and k - th IMF d k , the expres sion is as follow s ： ( ) ( ) 11 i kk k k rM r E w b -- =+ (7) 1 kk k dr r - = - (8) Go to ste p 3), we obtain all of the IMF . 2.2 . A pproximate E ntropy All of the IMF a pproximate e ntropy can be expressed as { } { } 12 ,, , k AA A A = ! . The n the calculation procedure A k is as follows : 1 ） Ta k e k - th IMF as the time s eries of n points and define it as: { } { } 12 ,z , , n Zz z = ! (9) 2 ） Compute the bi nary dist ance mat rix B of the time series: 11 11 1 21 22 2 12 n n nn n n bb b bb b B bb b éù êú êú = êú êú ëû ! ! "" " ! ( 10 ) where 1, 0, 1 , ij ij ij zz a b zz a ì - < ï = í -³ ï î , a is thres hold ( a =0.1~0.2) [45] . 3 ） Compute th e rat io of n + m +1and n - m +2 to number fo r B matri x el ement le ss than a 2 i C and 3 i C is as follo wing: ( )( ) 2 11 ,1 , 2 , , 1 ii j ij Cb b j n ++ = Ç = - å ! ( 11 ) ( )( ) ( )( ) 3 11 2 2 ,1 , 2 , , 2 ii j ij i j Cb b b j n ++ + + = Ç Ç = - å ! ( 12 ) 4 ） Compute the i C of the nature logarithm, and get the average of the i C of the nature logarithm . Then the approximate entropy of the k - th IMF A k is as follows : 1 2 1 1 1 1 nm i i InC nm - + = F = - + å ( 13 ) 1 3 2 1 1 2 nm i i InC nm - + = F = - + å ( 14 ) 12 k A = F - F ( 15 ) 5 ） The wavele t de - noise is performed with the approximate entropy of the IMF th at is greater than the thre shold. 2.3 . Wa v e l e t D e - noise The wavelet de - nois e is achiev ed based on a critical threshold . T he main steps of its de - noise principle ar e as follows: 1 ） Select the appropriat e wavelet base and the number of decomposition layers . W e take the wavele t t ransf orm wit h th e noi se s ignal s and obtain its wavelet coef ficients w j ： 1 0 jj v D Hv - = ( 16 ) 1 0 jj wD G v - = ( 17 ) W here H is the low - pass filter , G is the high - pass filter , v is for the sc ale factor , and w is the wavele t co ef fic ient . 2 ） S elect the appropriate threshold function to process the wavelet c oef ficient s w j and get the estimation wavelet coef ficients ˆ j w : ( ) ( ) ˆ sgn , ˆ 0, jj j j jj ww w w ww ll l ì = - ³ ï í = £ ï î ( 18 ) w here l is threshold , =2 l o g N ls , s is the mean square error of the signal, N is the sampling point number . 3 ） use the esti mation wavelet coef ficients ˆ j w and get the reconstruct sig nal ˆ v 11 ˆ ˆ jj j vH U w G U v -- =+ ! ! ( 19 ) where H ! is reconstruc t low - pass filter , G ! is reconstruc t high - pass filter . Based on ICEEM D, the approximate entropy an d wavelet de - noising theory , w e prop osed ICEEM D - De method. The method is divide d five steps to implement proce ssing vibr ational signal. T he ICEEMD - De analysis process is shown in Figur e 1. At first step , we sample the anc horin g detection signal and take sampling signal for analysis. Then the sampling signal is decomposed with ICEEMD m ethod . Each IMFs of the signal can be obtai ned. At third step, we solve the approximate entropy of each IMF based on approximate entropy theory . At four th step, t he method takes the approxim ate entropy as the condition of whether the IMF is de - noised. Whe n approximate entropy of the IMF above threshold, the IM F need take w avelet de - nosed. Finally , by means of the wavelet soft threshol d de - noising technique, the noise in the intrinsic mode function (IMF) is eliminate d . T he ori ginal signal components are retained in maximum with ICEEMD - De. I n p u t a n c h o r i n g d e t e c t i o n s i g n a l Input anchoring detection signal I C E E M D d e c o m p o s i t i o n ICEEMD decomposition S o l u t i o n o f e a c h I M F a p p r o x i m a t e e n t r o p y Solution of each IMF approximate entropy I M F w a v e l e t d e - n o i s e w h e n a p p r o x i m a t e e n t r o p y a b o v e t h r e s h o l d IMF wavelet de-noise when approximate entropy above threshold d e - n o i s e d e a c h I M F de-noised each IMF ! Fig.1. Anc horin g det ecti on s ignal ana lysi s fl owchar t using ICEEMD - De . 3. Vi b r a t i o n Simulation Si gnal Analysis Focusing on the analysis of the anc hor detection sig nal, one vibration simulation signal is considered , a nd the signa l is decomp osed by means of ICEE MD. The IC EEMD m ethod is used in order to analy ze the signal under the no ise interferenc e condition . T he noise sig nal is directly decomposed by the ICEE MD, ICE EMD decompos ition after the wavelet de - noising and ICEEM D - De for study ing proce ssin g ef fect . 3.1. Vi b r a t i o n S i g n a l D e c o m p o s e w i t h ICEE MD The s upposed vibration simulation signal s is com posed of the s 1 and s 2 two sine fu nction (Fig.2.). The expression is as follow s : ( ) 1 sin 20 st p = ( 20 ) ( ) 2 0.4 sin 100 0.15 0.25 0 tw h e n t s other p ì´ £ £ = í î ( 21 ) 12 ss s =+ ( 22 ) Fig.2. Vi b r a t i o n s i m u l a t i o n s y n t h e t i c s i g n a l . The simulation synthetic signal in Fig.2 is decomposed with the IC EEMD . The an alysis results in Fig.3 show : Fig . 3. IM F and spectrum after the decomp osition of the vibration signal with ICEE MD: Fig.3 (a) (c) (e) (g)IMF1 ~ IMF4 . Fig3. (b) (d) (f) ( h) IMF4 spect rum . Accord ing to Fig. 3, the ICEEM D deco mposes the s signal into four different IM Fs, where the latter tw o ch aracteristic modu li cor respond to s 2 and s 1, re spectively , with the correspond ing frequencies of the IMF being clearly seen in regards to the sp ectrum. Fig 3 (b) (d) shows the frequency o f both s 2 and s 1 , which are 10 0Hz a nd 20H z, respe ctively . Fig 3 (b) (d) shows that the IMF1 and th e IMF2 are m ainly high frequen cy noise signals. 3.2. Vi b r a t i o n S i g n a l M o d e D ecom position under Noise Condition with ICEEMD Fig. 4. Vi b r a t i o n s i g n a l u n d e r n o i s e c o n d i t i o n . The random signal is added to the source signal in Fig. 2 . W e take SNR= 5dB a s example for the analysis. The signal at 5dB is analyzed by means of IC EEMD and IC EEMD - De. The results are shown in Fig.5 and Fig.6. Fig . 5. The IMF and spectrum which the vibration signal after th e decompositio n with ICE EMD: Fig.5 (a ) (c) (e) (g) is IMF1 ~ IM F4 and Fig.5 (b) (d) (f) ( h) is IMF1~IM F4 spectrum . Accord ing to Fig. 5, the IMF 1 and IMF 2 , wh ich were decomposed by ICEEM D, are still d ominated by th e rand om n oise signal , while the IMF 3 and 4 corresponding s1 and s2 are doped with a la r ge nu mber of r andom i nter fere nce componen ts. Fig.6. The IMF and spectr um which t he vibr ation signal after the d ecomposit ion wit h ICEEMD - De: Fig.5 (a ) (c) (e) (g) is IMF1 ~ IMF4 and Fig .5 (b) (d) (f ) (h) is IMF1~IMF4 spec trum . From Fig . 6, it can be seen that a large number of random noise interference in IM F1,2 has removed, an d the IMF3 ,4 ’ s corresponding s1, s2 , had components of the interference significantly suppressed. The de - no is e signal can be clearly distinguished between the s1 , s2 frequ ency of 100Hz and 20Hz . In order to fu rther study the effect of the proposed method on the de - noising of the vibration signal, the de - noising ef fect of t he wavelet and the ICEEM D - De met hod on the s signal i s compared. Fig. 7 shows the error of t he vibration signal aft er the treatment. Fig 7. De - noisi ng error li ne with Wa v e l e t a n d I C E E M D - De . In F ig . 7, Error1 is the noise error , Error2 is the error after the ICEEM D de - noising and Error3 is the error after the wavele t de - noising. F rom Fig.7 , it can be se en that both methods are able to significantly redu ce th e noise interference. Based on the gene ral trend of the error line , the proposed method results in the error li ne ’ s frequency being higher , but with the error size being lower than the wave let de - noising. In the signa l de - noising analysis, the signal - to - noise ratio ( SNR ) and the root - mean - square deviation （ RMSE ） are used in order to measure the d e - noising effect of the signal, which is defined as follows : ( ) 2 2 11 ˆ 10 lg / NN ii ii SNR X X X == ìü = - íý îþ åå ( 23 ) ( ) 2 1 ˆ N ii n XX RMSE N = - = å ( 24 ) Accord ing to the formulas ( 23 ) ( 24 ) , tw o different metho ds can be c alculated in order to de - noise the ef fect of the index. The inde x is shown in Ta b l e 1 . Ta b l e .1. ICEEM D de - noising performance index Index Original signal ICEEMD Wa v e l e t SNR (dB) 5.000 13.741 11 . 1 7 9 RMSE 0.41 1 0.151 0.201 From T able 1, we can see that both metho ds are able to greatly improve the SNR of the original signal, which is consistent with the results that are shown in Fig 7 . Th e pr oposed meth od improve s the SNR of the original signal by 2.7 times, while the W avelet method increases the SNR of the original signal 2.2 times . T he proposed method’ s RMSE is smalle r than that of the W avelet metho d. Th eref ore, the ICEEMD - De de - noising ef fect is superior to that of the W a velet de - noising metho d. 4 . Analysis of Bolt Detection Signals Ta k i n g t h e h i g h - slope ancho r grouting test of Y unnan - highway as an example, the instrument is the LX - 10 bolt, the sam pling frequency is 10498Hz, the sampling poin t is 980 and the sam pling interval is 4.0 µ s (Fig .8) . T he collected vibration si gnal is shown belo w in Fig 9. Fig . 8. B olt detection testing instrument and site Fig .9. B olt detect ion signal in actual engineer ing The an chor detection signals in Fig. 9 are decomposed by the ICEEM D meth od and ICEEM D - De, res pecti vely . The results are s hown in Fig. 10 and Fig . 1 1 . !!!!!!!!! ! (a ) De t ec ti on in st ru m en t (b ) T es ting s it e ! ! F ig . 10 . The IMF which the vibr ation si gnal afte r the decomposi tion with ICEEMD: Fig . 10 (a) ~ (f) show IMF 1 ~ 6 Signal decomposed wi th ICEEMD. Accord ing to Fig. 10 , th e IMF 1 that is present in the high frequency noise signal, and the frequency of the IM F1 ~ 6 v ibra tion modes gradually increase . In the m odal IMF2, it is o bvious that the noise signa l c an be seen . A t 1.1ms , in the backgro und of the bottom of the anchor reflection , the signal can be identified ; however , the char acteristics are n ot clear enou gh. F ig .1 1. ! The IMF which the vibrati on signal after the decomposition with ICEEM D - De: (a)~ (f) shows t IMF1 ~ 6 which is t he si gnal decomposed with ICEEMD - De. Accord ing to Fig. 1 1 , the noise sig nal in ea ch of the modes is obv iously su ppressed, with the frequency o f the IMF 1 ~ 6 , the vibration modes gradually decrease , and the re flection sig nal of th e bottom of the bolt bec omes clear at 1.1ms in the mod al IMF2 . Fig .1 2 s hows the initial re flection at 1.1ms in Zoo m mo de , and noise interference sign al was signi fica ntly suppresse d . As such, the de- noising effect is obvious. Fig . 12. ICEEM D IMF2v s. ICEEMD - De IMF2 5. Conclusions Based on the princ iple of the ICEEM D decompo sition, the general approximation entropy and wavelet de - noising, the ICE EMD method is introduced into the b olt detection sig nal analysis. T he anchor detecti on signal is decomposed by means of us ing the ICEEMD , while th e approximate entropy is reg arded as the cond ition for whether or not the IMF is de - noising. U sing the wavelet soft thr eshol d de - noisi ng technique to eliminate the noise in th e IMF , t he ICEEM D - De anchor signal analysis method is proposed. Based on the usage of the ICEEM D - De to analyze the vibration’ s analog signal and the anchor detection signal, the follow ing con clusions have been drawn: 1) The ICEEMD method can ef fectively sepa rate the vi bration modal si gnals to IMF . 2) The ICEEM D - De method can ef fect ively remove the interf erenc e in the vibratio n detection si gnal, and the de - noising ef fect is superior to that of the trad itional W avelet m ethod. 3) The ICEE MD method is ab le to separate each IMF from the bolt detectio n sign a l , and the IMF can effectively identify the bo lt ’ s end reflection time . 4) In the analysis of the bolt detection signal, the ICE EMD - De is more ef fective at suppressi ng of the interferenc e than the ICEEM D is . However , ICEEMD - De combi ne ICEEMD and wavelet de - noise tech nology . The metho d ha s m any analysis step s. S o the com putatio nal cost of the method is higher than traditional method. Acknowledgments This research was funded by the Open Research Fund of Key Labora tory of Hydrau lic and Wa t e r w a y E n g i n e e r i n g o f t h e M i n i s t r y o f E d u c a t i o n (G rant No. ! SLK2017A02 ) and A P r o j e c t Funded by the Priority Academic Program Development of Jiangsu H igher Education Institutions (Grant N o.3014 - SYS1401). The author wish to thank the Su Jiankun from Y u nnan A erospace Engineeri ng G eophysic al Limited by Share Ltd for providing the GPR practical detection data used in this study . References [1] Stimpson B. A sim ple rock bo lt pull - out test device for teaching purposes[J]. International Journal of Rock Mechanics & Mining Scie nces & Geomechanics Abstracts . 1984, 21(4): 217 -2 18. [2] Shuan - Cheng G U, Zhang J, Zhang S, et al. Influence A nalysi s of Anchoring Defects on Bolt Pull - out Load[J]. Safety in Coal Mines. 2013. [3] Ivanovi ć A , Starkey A, Ne ilson R D, et al. 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