A Novel Method of Bolt Detection Based on Variational Modal Decomposition

1 ） The project w as supported by F undamental Sc ience on Radioac tive Geology and Exploration T echnology L aboratory （ RGET1502 ） 2 ） E-m ai l ： renqw@hhu.edu.cn 2017 Conference of Theoretical and App lied Mechanics in Jiangsu, CTAMJS 2017 A Novel Method of Bolt Detec tion Based on Variational Modal Decomposition 1 Juncai Xu a,b , Qingwen Ren a,2) a Hohai University, Nanjing 210098, China b Fundamental Science on Radioactive Geology and Exploration Technology Laboratory, East China Institute of Technology ， Nanchang, Jiangxi ,330013,China Abstract The pull test is a destructive de tection method, an d it can’t m easure the actual length of the bolt. A s such, ultrasonic echo is one of the most important non-destructi ve testing methods for bolt quality detec tion. In this paper, the variance modal decomposition (VMD) method is introduced int o the bolt det ection signal analysis. Based on the morphological filtering and the VMD method, the VMD combined morphological filtering princip le (MF) is establis hed into the bolt detection signal analysis method (MF-VMD). MF-VMD was used in or de r to analyze the simulation’s vibration signal and the actual bolt det ection signal. Th e results showed that th e MF-V MD is able to effectively sep arate the intrins ic mode function, even when under the background of strong interference. Compared with the conv entional VMD method, the proposed method is able to remo ve the noi se interference. The intrinsic mode func tion o f the field detection signal can be effectively ident ified by the r eflection of the signal at the bottom of the bolt. Keywords: bolt detection, variational modal decomposition, morphological filtering, in trinsic mode function. 1. Introduction The bolt anch oring system is a hidden engin eering process and is s ubject to g eological cond itions, construction t echnology and ot her environm ental aspects [1]. As such, it is d ifficu lt to find hidde n problems. The a coustic method is one of most im portant non-destructiv e testing meth ods used for b olt detection in civil engine ering[2-4]. In order to obtain an ef fective signal, m any data process ing methods, such as the Short-time Fourier transform, Gabor transform , W igner-V ille transform and wavelet transform, are proposed[5-7]. W avelet transform has been adopted in m any studies [8, 9]. However , the effec t of wavelet transform is often limited by the selection of the w avelet bases an d the decomposed layers. The em pirical mode decomposition (EMD) ca n adaptively select the substrate according to the chara cteristics of the signal in multi-resolution, bu t it also avoids the selection of the w avelet basis[10, 1 1]. Nonethel ess, EMD has the modal aliasing problem when processing the data. The ensemble em pirical mode decomposition (EE MD) was also pr oposed for solving the modal aliasing probl em that is pr esent on EM D[12]. However , because t his method adds a dif ferent white noise, it m ay produce a false pa ttern after the de composition, whic h may cause error s[13]. In recent years, the variational modal dec ompos ition ( VMD) method has b een proposed[14]. This method transform s an input signal into s everal dif f erent constra int problems by W iener filtering and Hilbert transform . It iterates the cen ter frequenc y of each com ponent and the bandwidth in order t o achieve the adap tive decom position of the signal. The results show tha t the method is superior to the traditional EMD method[15]. Based on the VMD the ory , the VMD method is intr oduced into the bolt detec tion signal analysis. W e combined the principle of morphological filtering w ith VMD and proposed m orphological filterin g VMD (MF-VMD), and est ablished the MF-VMD analysis method. The MF-VMD is used to simulate the vibration signal, as well as the actual Bolt detection signal processing in order to c heck its eff ect. 2. Theory and methodology 2.1. Morpho logical Filter Pr inciple Morphologica l filtering is a chieved throu gh the segm enting elem ent moving in a signal to extract the signal’ s information, maintain ing the det ails of the sign al and removing the purpose of the noise interference. Morpho logical filtering is generally achi eved by expans ion, corrosion, op ening and closi ng operations. Assum ing that one vibr ation s ( n ) has N number of sam pling points, then the se gmenting element g ( m ) ， m =0,1,… ,M-1, and the expansi on and corrosion o perations with s ( n ) to g ( m ) can be defined as follows:           min m s gn s n m g m    (1)           max m s gn s n m g m    (2) Opening and closi ng operations with s ( n ) to g ( m ) can be defined as follows:         sg n s g g n    (3)       sg n s g g n    (4) In practical applica tions, the open-cl osed and the c losed-and-open com bined morpholog ical filters are constructed th rough the use of the cascade form , which is used for noise reduction of the vibration signal. The expression is as follows:     /2 MMC s s g g s g g     (5) The effec t of the morpholog ical filtering not only depends on the sele cted morphologic al operation, but it’ s also related to the structural elements that are used. The vi bration signal is f iltered by the linear structure’ s elements, as well as t he correlation betwee n the acoustic signa l before and after the filtering is chosen as the criter io n of the selection width value in the research . 2.2. VMD Principle VMD is a variational prob lem. In order to minim i ze the sum of the estim ated bandwidths of each mode, we assum ed that each m ode has a finite b andwi dth with dif ferent central frequencies . As a result, the alternating direction m ultiplier metho d was adopted in order to consta ntly updat e the mode an d its central frequency , with the mode bein g gradually dem odulated to its corresponding baseba nd. Then, the final mode and t he corresponding center frequency wer e extracted. Assuming that a signal 0 S is decomposed into N intrinsic mode function (IMF), then the corresponding variation al problem's solution can be expressed as follo ws: 1) The Hilbert transform of each IMF component is used to obtain the analytic signal   k j tu t t       (6) 2) The center frequency is estimated with the obtained analytic si gnal and the spectrum of e ach analytical signal is transformed into the baseband with a fr equency shift   k jt k j tu t e t            (7) 3) The 2 L norm of the demodulated signal is calculated, and the bandwidth of each mode is estimated. The variational problem is expressed as fo llows:       2 , min .. k kk jt tk uw k k k j tu t e t st u f t                            (8) 4) For the mentioned v ariational problem, the quadratic penalty function and the Lagrange multiplier can be used in order to t ransform t he problem into an unconstraine d problem form,            2 2 2 2 ,, , k jt kk t k k kk kk j Lu t ut e t f tu t t f t u t                      (9) wher e  is the penalty factor, and   t  is the Lagrange multiplier. Finally , the m ultiplier alternate directi on algorithm is used in order to solve th e unconstrained variational probl em of equation ( 9), and then the IMF can be obtai ned. 3. Simulation Signal Analysis The anchor’s anchoring det ection signal is regarded as a vibrati on signal. The singular poi nt of th e vibration signal is usu ally used to iden tify the anchor ing quality mark of the bolt. One simulation sign al was adopted in order to check th e ability of the iden tifying abnormality of the VMD and the stud y recognition of the VMD and MF-VMD for the vibration signal in an environment with strong noise. 3.1. The VMD decom position of Simulat ion Signal One simulation signal s ( t ) has a singular point and two frequenc ies, 10kHz and 2 0kHz. There are singular points at 0.8ms and at 1.2ms (Fig. 1).      sin 20000 , 0 ms 0.8 sin 40000 , 0 .8 ms 1.2 sin 20000 , 1.2 ms 2 tt m s st t t m s tt m s             (10) Fig.1. Simulation signal s ( t ) The simulation test signal s ( t ) in Fig. 1 is decomposed by the VMD method . The result of t he decomposition is s hown in Fig.2. Fig.2. The decomposition result of VMD (a)IMF1 (b)IMF2 Based on Fig.2, IMF1 and IMF2 can both be com pletely obtaine d from signal s ( t ) and i t can display two kinds of vibrat ion. T he instantaneous f requency spec trum is shown in Fig. 3. Fig.3. Instantaneous frequency with VMD As can be seen in Fig.3, t he two kinds of freque ncies, 10kHz an d 20kHz, appe ar in the signal. The singularity poi nts are at 0.8ms and at 1.2m s. Thus , VMD is able to decompose the dif ferent m odes from the signal when there are no noise interferences 3.2. Simulatio n Signal under N oise Interfer ences In the studied vibration signal decompositi on with VMD , s ( t ) in Fig.1 was a dded with no ise when SNR=5dB. The simulation si gnal s n ( t ) that contains the noise interference is shown in Fig.4. Fig.4. s n ( t ) containing the noise interference W e use the VMD t o decompo se s n ( t ). The dif ferent IMF can be obtained with VMD. The results ar e shown in Fig.5. Fig.5. Decomposit ion results of VMD (a) IMF1(b ) IMF2 (c) IMF3 (d ) IMF4 (e) IMF5 Based on Fig.5, IMF1 has a sm all difference with the original signal s ( t ). H owever , IMF2~5 are noise. VMD i s unable to d ecompose the dif ferent m odes from s n ( t ), as there are two ty pes of mode signal mixing in IMF1. T he Hilbert insta ntaneous frequency com es from VMD in Fig.6. Fig.6. Hilbert instantaneous frequency As can be seen i n Fig.6, the ins tantaneous frequency is continuous fr om the VMD m ethod. There are no significant singularities in the instantaneous frequency , so the vibration signal has obvious interference. MF-VMD was also adopted in order to decom pose s n ( t ). The IMFs of s n ( t ) can be obtai ned, as is shown in Fig.7. Fig.7. MF-VMD d ecomposition results (a) IMF1 (b)I MF2 (c)IMF3 (d)IMF4 (e)IMF5 As is shown in Fi g.7, we are a ble to find tha t IMF1, IMF4 and IMF5 are the residual noise s ignals, and the IMF2, IMF3 are the two different m odes of s (t), and correspond to IM F1 and IMF2 in Fig.2. The IMF was taken from the Hilbert transform ation; the Hilbert ins tantaneous spectrum is shown in Fig.8. Fig.8. Hilbert instantaneous frequency As can be seen from the spectr um in Fig.8, the instantaneous frequency with the MF-VMD decomposition h as some obvious s ingularities at b oth frequencies of 10 kHz and 20 kHz. T he random interference signal is well suppressed w hen compared wit h the spectrum in Fig. 6. T he frequency strength’ s display is s ignificantly hi gher than the frequency stren gth that is seen in Figure 6. In a strong noise backgroun d, MF-VMD has good recogni tion of the singul ar point of the vi bration sig nal. 4. Bolt Anchoring Detection Signal Analysis T aking the hi gh-slope bolt anch oring testing site i n Y unnan expressway in Ch ina as an exam ple, the instrument used is the AGI-MG bolt quality d etector (Fig. 9). Th e sampling par ameter is 1.05kHz, t he sampling num ber is 980, and the sam pling interval is 4.0us. The coll ected vibration sig nal is shown in Fig.10. Fig.9. Bolt anchoring testing site (a) Detection apparatus (b) T esting site Fig.10. bolt anchoring detection signal It is dif ficult to directly determine the b ottom of the bolt ref lection signal i n Fig.10. As such, we adopted MF-VMD in order to decom pose the signa l. Th e decomposition res ult is shown i n Fig.1 1. Fig.11. Decomposition results with MF-VMD ( a) IMF1 (b) IMF2 (c) IMF3 According to Fig. 1 1, three IMFs were obtained by MF-VMD. There is one obvious reflect ion signal from the bolt bottom at 1.0ms in IMF1. As the b olt length is 3, and the velocity of the wave in the bolt is 6000m/s, t hen the reflection si gnal should be a t 1.0ms. Thus, the proposed m ethod is able to decompose th e reflection signa l of the bolt b ottom and determ ine the reflection t ime. 5. Conclusions Based on t he VMD principle, the VMD theory was introduced into th e detection signal analysis of bolt anchorin g. W ith the c ombination of MF and VMD, we propos ed the MF-VMD method t o analyze the bolt de tection sign al. Based on the analys is of the sim ulation signal, as well as t he field appl ication, we are able to draw some conclusions, w hich are the follow ing: 1 ） VMD is able to dec ompose the dif ferent m odes from the vibratio n signal. However , VMD can’ t properly decom pose the IMFs from vibration when there is strong noise interferenc e. 2 ） MF-VMD is able to properly decom pose the IMFs from vibration sig nal, even when u nder strong noise interference and reduce t he ef fect of noise. 3 ） MF-VMD is able to properly d ecompose the bolt detection signal int o the IMFs, and the reflection signal from the bott om of the bolt ca n also be identifie d in IMF . Acknowledgments This research was funded by the Open Research Fund of the Fund amental Science on Radioactive Geology an d Exploratio n Technolo gy Laboratory (Grant No.R GET1502) an d A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutio ns (Grant No.3014-SYS14 01). References [1] Shuan-Cheng G U, Zhang J, Zhang S, et al. Influence Analys is of Anchoring Defects on Bolt Pull-out Load[J] . Safety in Coal Mines. 2013. [2] Beard M D, Lowe M J S. Non-destructive testing of rock bo lts using guided ultrasonic waves[ J]. I nternational Journal of Ro ck Mechanics & Mining Sciences. 2003, 40(4): 527- 536. [3] W ang G , Li B. Research on Non-destructive T esting T echni ques of Bolt[J]. Chinese Journal of Engineering Geophysics. 2009. [4] Y ue X H, Liu M G , Qi L I. Develop ment of Bolt ’ s T esting T echnique[J]. Soil Engineering & Foundation. 2005. [5] Lee I M, Han S I, Kim H J, et al. 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