Complexity Research of Nondestructive Testing Signals of Bolt Anchor System Based on Multiscale Entropy

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1 Complexity Research of Nondestructive Testing Signals of Bolt Anchor System Based on Multiscale Entropy Zhang Lei 1,2, Li Qiang 1, Mao Xian-biao 2,Chen Zhan-qing 2,3, Lu Ai-hong 2 1 State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou,Jiangsu ,China; 2 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu ,China; 3 School of Science, China University of Mining and Technology, Xuzhou, Jiangsu ,China. Abstract We set up the finite element models of bolt anchor system to study anchoring quality detection of bolt anchor system by using an acoustic method. On this basis, we studied the propagation of stress wave in the case of the increasement of the number of with the fixed defect size in the anchor system. We analyzed the numerical simulation signal using multiscale entropy (MSE) method, then we found that the complexity of reflected signal of defective anchor system is higher than the defectless one. In order to describe the deviation degree between the signals of defective and defectless anchor sytem quantitatively, we defined a parameter named pseudo residual sum of squares (PRSS). By calculating,we found that the more the amounts of the were, the larger the value of PRSS. We further found that the complexity of reflected signals has certain relations with the defect types. The existence of increase the complexity of the reflected signal.this shows that the anchor quality of bolt anchor system can be evaluated effectively by using the MSE method. Keywords - bolt anchor system; finite element model; stress wave; defect; multiscale entropy; complexity I. INTRODUCTION As a kind of very important technology in geotechnical and geological engineering, the technology of bolt anchoring is widely used all over the world. The working condition of the bolt anchor is closely related to the safety of the whole project, and how to make a quick and effective nondestructive testing for the construction quality of the bolt anchor is a hot spot in current research[1-3]. At present, the widely used NDT method is the stress wave reflection. This method is that, by using the hammer to stimulate a pulse at the exposed end of bolt anchor, when the sound pulse spreads along the longitudinal direction of the bolt, a reflection signal will be produced at the defect, which will be received by the sensor installed at exposed end of bolt anchor, so the anchoring quality will be evaluated [4-5]. People have put forward a variety of signal analysis methods to process the stress wave reflection signal, and Fourier transformation, wavelet transformation and so on are commonly used. However, because the above methods need to select basis functions, which makes the analysis of reflection signal has some subjectivity, diversity of analytical results influences the accurate evaluation of non-destructive testing signal of the quality of bolt anchor. Therefore, it is necessary to find out a signal analysis method, which is of good anti-noise performance, of strong adaptability and easy to operate, to carry out an objective and accurate analysis for the non-destructive testing signal of the quality of bolt anchor[6-8]. Aimed at above issues,we introduce Multiscale Entropy (MSF) into the analysis for the non-destructive testing signal of the quality of bolt anchor. First proposed by Costa et al [9-10], the MSE method was initially used for measuring the complexity of physiological time series in different time scales. Because the MSE method has the advantages of small amount of required data, strong anti-interference and antinoise abilities and no need to select the basis function, people begin to apply it to the analysis of nondestructive testing signal. Zheng Jinde [11] et al apply MSE to the signal fault characteristics extraction of rotor system, to achieve the fault diagnosis by analyzing the characteristics of rotor radial displacement signal. Zhang Long [12] et al input the MSE as the proper vector into the fuzzy neural network to identify the bearing fault types, which gets better recognition effect. In this article, we first establish the finite element model of the anchor system and use ANSYS/LSDYNA software to simulate the propagation process of stress wave under the circumstance of limited defect size and increasing in defect numbers of anchorage system. Multi scale entropy of reflection signal is calculated with the MSE method. The results show that the existence of defect increases the complexity of the reflected signals and there is a certain correspondence between the complexity of the reflected signals and the defect types. This shows that the multi-scale entropy method provides an effective means to reveal the DOI /IJSSST.a.16.3B ISSN: x online, print

2 effect of on the complexity of the stress wave reflection signal in the anchor system. II. MULTI SCALE ENTROPY METHOD Multi scale entropy method can be used to quantify the amount of information contained in the signal at multiple scales. In short, multi-scale entropy method is divided into two steps: first, the original signal is discreted and a number of data series containing possible values are transformed to symbol sequences containing fewer and non identical values, which is a process of "coarse graining". Each group of coarse graining can obtain dynamic behavior characteristics of the system at a given time scale, so the effect of dynamic noise and measurement noise can be reduced. Second, by calculating the entropy of all samples of coarse time series, the amount of information contained in the signal is quantified. Finally, the corresponding relation curve of the entropy and scale is drawn up, and with the curve, the complexity of the signal is analyzed. Specific algorithms as follows[13-15]: for the length L of non destructive testing signal of anchorage quality of bolt anchor x,,,, 1 xi xl, it is constructed as coarse ( ) time series y by defining the scale factor τ, defined as: j ( ) 1 L yj xi, 1 j (1) τ i ( j 1) 1 τ Thus the length of each coarse-grained time series is N=L/τ. When τ=1, it its the original signal. The schematic diagram of coarse granulation processes during τ=2 and τ=3 is shown in Figure 1. For each set of coarse time series, the sample entropy SampEn(τ,m,r)is calculated. In it, m is the embedding dimension of reconstructed phase space in coarse time series and r is the similarity coefficient. Sample entropy calculates the m dimension's negative natural pair value of conditional probability of maintaining similarity when the sequence with similarity adds one dimension. While the multiscale entropy is defined as a set of sample entropy of time series at multiple scales. Multiscale entropy can measure the complexity degree and the probability of generating a new model in dimension changes of the nondestructive testing signal of the anchorage quality of bolt anchor at different scales. The greater the probability of generating a new mode is, the higher the complexity of the signal is and the greater the multi-scale entropy. If the multi-scale entropy increases monotonically with the scale factor increasing, it indicates that the structure of the signal is relatively complex, which contains more information at multiple scales. According to this characteristic, the complexities of the two signals are compared by using multi scale entropy: If above most scales, the multiscale entropy of one signal is higher than that of another, which means the complexity of the former is higher than that of the latter. III. THE MODEL AND PARAMETERS OF BOLT ANCHORAGE SYSTEM Figure 1. Coarse graining method for time series (a. Structure model,b. geometric parameter) Figure 2. Model and geometric parameters of anchor system (Unit: cm) TABLE I MATERIAL PROPERTIES Elastic modulus/gpadensity /kg m -3 Poisson ratio Bolt Anchor agent Surrounding Rock Normal constraint is imposed both at the bottom and around the surrounding rock and the no reflection boundary is set, which will weaken the influence of boundary reflection wave on simulation results. Half sine signal is used as pumping signal, which, in the form of force loading, acts on a circular area with a radius of 0.5cm that takes the center of exposed end of anchor bolt as the center of the circle. Acceleration signal of the circle center node of the exposed end face of anchor bolt is taken as the research object. IV. RESEARCH CONTENTS AND RESULTS ANALYSIS A. Defect Length 2cm The total length of anchorage section is 30cm, the initial end of the first defect is 10cm and the length of the defect is 2cm, as shown in Figure 3 (b). All the distances between adjacent are 2cm, as shown in Figure 3 (c) - (f). The number of increased from 1 to 5, and the defect location distribution is shown in Figure 3 (b) - (f). The DOI /IJSSST.a.16.3B ISSN: x online, print

3 reflection signal obtained from the numerical simulation is shown in figure 4. (a. zero defect; b. one defect; c. two ; d. three ; e. four ; f. five ) Figure 3. Location distribution of 2cm defect (a. zero defect; b. one defect vs. zero defect; c. two vs. zero defect; d. three vs. zero defect; e. four vs zero defect; f. five vs. zero defect) Figure 4. Comparison of 2cm defect and zero defect nondestructive testing signals The reflected signals in cases of and defect free before 0.7ms is coincident. Therefore, we only give the reflection signals after 0.7ms. As seen from Figure 4, there are both obvious valley values in 0.75ms, which are corresponding to the reflection signals of anchoring start end. After the first wave trough position between ms, the reflected signals of defect and non defect appear differences in amplitude and phase. When the number of is small, the differences of the two curves are mainly reflected in the amplitude (Fig. 4 (b)). With the increase of the number of, the differences between the two curves in the phase are more and more significant. In order to describe the difference between the two qualitatively, we calculate the multiscale entropy of the above signals, as shown in figure 5. (a. zero defect; b. one defect vs. zero defect; c. two vs. zero defect; d. three vs. zero defect; e. four vs zero defect; f. five vs. zero defect) Figure 5. Comparison of MSE curves of 2cm defect and zero defect nondestructive testing signals We find that when the numbers of are one, three and four, the sample entropy of reflected signals on 18 scales is larger than that of the defect free. The sample entropy of two-defect reflected signals on 16 scales is larger than that of the defect free. The sample entropy of five-defect reflected signals on 19 scales is larger than that of the defect free. This means that all the multiscale entropies of reflected signals in anchor system are higher on most scales than those of defect free. In order to make further research on the influence of defect number change to the differences between the entropy curves with and no defect, with reference to the definition of the sum of squares of residuals in Mathematics, pseudo residual sum of squares (PRSS) is introduced, which is defined as the reflected signals of defective and non defective anchorage system and the square of the difference of sample entropy at each scale. It can be used to describe the deviation degree of the entropy curve of the reflected signal of the defect anchoring system, compared with that of the reflected signal of the no defect anchoring system. Its expression is: 20 2 PRSS ( Sd τ So τ) (2) τ 1 In the expression, Sd is the sample entropy of reflection signal of defective anchoring system on the γ scale, and So is that of defect free anchorage system on the γ scale. Table 2 shows the PRSS values of the five types of. As can be seen from table 2, PRSS values is increasing in turn, which shows that the more the are, or the higher the defect degree is, the more significant the differences between the two entropy curves are. Influence of defect number changes to PRSS is clearly reflected in Figure 6. When the number of increases from one to four, the slope of PRSS curve is small and PRSS value increases slowly. When the number of reaches 5, the PRSS value increases rapidly, and the total length of the defect reaches 10cm, which accounts for 1/3 of the total length of the anchoring part.this shows that when the number of is low, the multiscale entropy curve of reflected signal of defective anchorage system gradually deviates from the no defect one, which means complexity increases slowly. And when the number of increases and its total length reaches 1/3 DOI /IJSSST.a.16.3B ISSN: x online, print

4 of the total length of the anchorage, the two entropy curves will have large deviations, which means that the complexity of the defective anchorage system increases rapidly. TABLE II PRSS PARAMETER OF 2CM DEFECT MODEL Types PRSS One defect Two Three Four Five Size 2cm (a. zero defect; b. one defect; c. two ; d. three ; e. four ; f. five ) Figure 7. Location distribution of 3cm defect Figure 6. The variation curve between PRSS and defect types of 2cm defect model B. Defect Length 3cm In order to study the influence of the defect length under the condition of multiple to the anchoring complexity, in the following we change the defect length to 3cm, with the total length of the anchoring part is still 30cm, as shown in Figure7 (a).the distance between the start end of the first defect and the anchor start end is 5cm (FIG.7 (b)), and the distance between any two is 2cm. The number of increased from 1 to 5, as shown in Figure 7 (b) - (f). When the defect length 3cm, we obtain the reflected signal as shown in figure 8. Likewise, Figure 8 only shows the waveform after 0.7ms. An obvious valley value appears at 0.75ms, corresponding to the reflection signal of anchoring start end. After the first wave trough position between ms, the reflected signals of defect and non defect appear differences in amplitude and phase. Different from the defect condition of 2cm in 4.1 section, when the defect number of 3cm defect situation is low, the differences between the two curves in the phase is very obvious. This may be due to the defect in large size and the defect location is nearer to the the anchor start end than the case of 2cm. With the increase of the defect numbers, the differences between the two curves become more and more obvious, which illustrates influence of the changes of defect numbers on reflected signal is very large. Multiscale entropy calculation of the signal, as shown in figure 9. (a. zero defect; b. one defect vs. zero defect; c. two vs. zero defect; d. three vs. zero defect; e. four vs zero defect; f. five vs. zero defect) Figure 8. Comparison of 3cm defect and zero defect nondestructive testing signals (a. zero defect; b. one defect vs. zero defect; c. two vs. zero defect; d. three vs. zero defect; e. four vs zero defect; f. five vs. zero defect) Figure 9. Fig. Comparison of MSE curves of 3cm defect and zero defect nondestructive testing signals TABLE III PRSS PARAMETER OF 3CM DEFECT MODEL Types One defect Two Three Four Five PRSS Size 3cm DOI /IJSSST.a.16.3B ISSN: x online, print

5 Figure 10. The variation curve between PRSS and defect types of 3cm defect model As can be seen from Figure 9, multiscale entropy of reflection signal of defective anchor system is larger than that of the defect free anchorage system on most scales. Among them, the sample entropies of reflected signal with four and five are larger than that of the defect free on 17 scales. The sample entropies of reflected signal with one and three are larger than that of the defect free on 16 scales. The sample entropy of reflected signal with one defect is larger than that of the defect free on 12 scales. This shows that the complexity of the reflected signal of the defective anchorage system is higher than that of the no defect. In order to describe the difference between the entropy change curves of defective and non defective with the defect number changes quantitatively, we make further calculation of the PRSS values of the above five cases, and the results are in Table 3. From table 3, we can see with the increase of the defect number, the PRSS values increase in turn. This shows that the bigger the defect number is, or the higher the defect degree is, the differences of two entropy curves are more obvious. The relationship between PRSS and the number of is reflected in figure 10. It can be seen that when the defect number increases from 1 to 3, the slope of PRSS curve is small. That means PRSS values increase relatively slowly. When the number of increases from 3 to 4, the PRSs value increases rapidly, and now the total length of the defect is up to 12cm, more than one-third of the total length of the anchoring portion. When the number of increases from 4 to 5, the PRSS value increase, although smaller than the process from 3 to 4, is bigger than that of the first two processes (from 1 to 2, from 2 to 3). This shows that in case of fewer, when the defect number increases, the multiscale entropy curve of reflected signal of defective anchorage system gradually deviates from the no defect one, that is, the complexity increases relatively slowly. And when the defect number increase continuously and makes the defect length close to 1/3 of the total length of the anchorage, there will be a greater deviation between the two entropy curves. It shows that the complexity of the reflected signal of the defective anchorage system is increasing rapidly. V. CONCLUSION In this article, we first establish the finite element model of anchor system, then with the general explicit nonlinear dynamic analysis program ANSYS / LS-DYNA carry out the finite element modeling of propagation process of stress wave under the circumstance that the defect size of anchorage system is limited and the defect number increases.we use multi-scale entropy method to research the complexity of the reflection signal of the anchorage system and get the conclusion as follows: (1) One can obtain characteristics of large signal scale through the process of coarse grain of reflection signal, so the effect of noise will be reduced. One can compare the differences of amplitude and phase by statistical methods on multiple scales, and further enlarge the difference, which makes the minute differences between the signals is revealed. (2) Multiscale entropies of reflection signal of defective anchor system are all larger than that of no defect, which means the complexity of the reflection signal of a defective anchor system is high. (3) Inputting pseudo residual sum of squares and parameters, the calculation shows that with the increase of the number of, PRSS value also increases gradually. That is, the multiscale entropy curve of reflection signal of defective anchor system deviates gradually from that of no defect. When the total length of the defect is close to 1/3 of the total length of the anchorage, the increase of the defect number will cause the slope of the PRSS curve to become larger and increase rapidly. The above research results show that using multi scale entropy method to research on the complexity of the reflection signal of the bolt anchorage system can reflect the effect of the defect to the stress wave reflection signal more intuitively. Thus, we can make the evaluation of anchorage quality of anchor system more objective and reliable. Thereby, we can provide some reference for the methods of evaluating the quality of anchor bolt. ACKNOWLEDGMENTS This work was supported by Project supported by the Special Funds of the National Natural Science Foundation of China (Grant No ) and general projects of National Natural Science of China(Grant No ) and the State Key Development Program for Basic Research of China (Grant No. 2013CB227900) REFERENCE [1] ZHU Ziqiang, HE Xianqi. Research On Nondestructive Detection Technique Of Full- Grouted Bolt. Chinese Journal Of Engineering Geophysics, vol.2, No.5, pp , [2] ZHANG Shengli, ZHANG Changsuo, WANG Yintao. Analysis of Nondestructive Detection Method of Bolt Anchoring Quality. Safety In Coal Mines, vol.45, No.5, pp , [3] ZHAO Shouyang, TAN Kaiyan. Discussion on nondestructive detection-measurement for anchor bars. Hubei Water Power, vol.1, pp.33-36, [4] WANG Meng, LI Yi, DONG Jia. 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