Shock and Vibration

Volume 2018 (2018), Article ID 1590983, 10 pages

https://doi.org/10.1155/2018/1590983

## Bolt Detection Signal Analysis Method Based on ICEEMD

^{1}College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China^{2}Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing, China^{3}Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA

Correspondence should be addressed to Zhan Zhang; moc.qq@uhh_gnahznahz

Received 23 September 2017; Revised 9 January 2018; Accepted 28 February 2018; Published 18 April 2018

Academic Editor: Carlo Trigona

Copyright © 2018 Chunhui Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The construction quality of the bolt is directly related to the safety of the project, and, as such, it must be tested. In this paper, the improved complete ensemble empirical mode decomposition (ICEEMD) method is introduced to the bolt detection signal analysis. The ICEEMD is used in order to decompose the anchor detection signal according to the approximate entropy of each intrinsic mode function (IMF). The noise of the IMFs is eliminated by the wavelet soft threshold denoising technique. Based on the approximate entropy and the wavelet denoising principle, the ICEEMD-De anchor signal analysis method is proposed. From the analysis of the vibration analog signal, as well as the bolt detection signal, the result shows that the ICEEMD-De method is capable of correctly separating the different IMFs under noisy conditions and also that the IMF can effectively identify the reflection signal of the end of the bolt.

#### 1. Introduction

The bolt anchoring system is subject to the geological conditions and the construction technology effect. If there are any hidden dangers that have not been detected, then it will cause engineering accidents and serious economic losses. Therefore, the construction 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 anchor’s anchoring quality is mainly based on the drawing test [1–3]. However, this method will cause damage to the anchoring system. The method is also not suitable for large-scale detection and cannot be fully reflected [4–6].

The detection method for the quality of the anchor will be gradually replaced by the use of nondestructive testing methods, such as the acoustic wave method [7–10]. This method is established based on the mathematical model of the one-dimensional elastic rod [8, 11, 12]. The assumption is that the longitudinal wave wavelength that is generated by the exciting force is much larger than that of the bolt radius, so the transverse displacement of the system can be neglected. By solving the longitudinal one-dimensional wave equation, the dynamic response of the bolt system is obtained.

The low-end reflection signal of the bolt can be easily disturbed during the process of bolt detection; it is difficult to directly obtain the reflected wave arrival time. In order to obtain the effective signal, many data processing methods, such as the short-time Fourier transform, the Gabor transform, the Wigner-Ville transform, and the wavelet transform, are proposed. Wavelet transform is the most used signal analysis method among them [13–17]. However, the effect of the wavelet transform is often limited by the wavelet base, as well as the number of decomposed layers.

The empirical mode decomposition (EMD) can adaptively select the substrate according to the characteristics of the signal for the multiresolution analysis of the signal, which will overcome the wavelet base selection problem [18–20]. The decomposition is based on the local timescale of the data. There have been many applications about EMD processing detection signal [21–24]. However, the EMD encounters some modal aliasing problems during the processing procedure [25–27]. The ensemble empirical mode decomposition (EEMD) overcomes the modal aliasing problem that is inherent of the EMD, but due to the addition of different white noise, the decomposition may produce a false mode, which can also cause errors. The reconstructed signal still includes residual noise, and different realizations of signal and noise may produce different modes [28–30]. Complete EEMD (CEEMD) has been successfully applied to seismic signal analysis. Li et al. used CEEMD to obtain an exact reconstruction of the original signal and a better spectral separation of the modes with synthetic and real seismic data [31]. However, the CEEMD cannot be proven, and the final averaging problem remains unsolved since different noisy copies of the signal can produce a different number of modes [32]. In recent years, the improved complete EEMD (ICEEMD) has been proposed by adding adaptive white noise to the signal and by redefining the calculations of the local mean for each model [29, 32–35]. The result shows that the method is superior to the traditional method. Although EMD is more adaptive and more efficient, the EEMD outperforms EMD in causing less mode mixing [36]. The CEEMD outperforms EMD in causing less mode mixing and EEMD in better reconstruction performance [37]. The ICEEMD, as illustrated in the paper, outperforms CEEMD in being more physical meaningful and less number of components.

Based on the mentioned research, the ICEEMD method is introduced into the bolt detection signal analysis in this paper. However, the actual signal of bolt detection is under noise interference. The processing signal under noise is critical problem with ICEEMD for bolt detection. By combining the approximate entropy and the wavelet denoising principle, the ICEEMD-De was established based on the ICEEMD. Then, the ICEEMD-de was used to process the simulation vibration signal and the actual bolt detection signal.

#### 2. Theory and Methodology

Based on the ICEEMD anchor detection signal analysis method, the ICEEMD-De integrates ICEEMD, the approximate entropy, and wavelet denoising. The three methods are introduced in the section.

##### 2.1. ICEEMD 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 the local mean of each modal. Assuming the anchor detection signal* s*, then the decomposition process of the ICEEMD is as follows.

The signal is added to the M group Gaussian white noise in order to generate a new signal* s*^{i}.* s*^{i} can be expressed aswhere () is one group of Gaussian white noise, , is the* k*th residue, takes 0.2.

The* k*th mode can be obtained by EMD. We can obtain the mean of the* k*th mode and have where is the operator of mean.

* s*^{i} is decomposed by using EMD. We obtain 1th residue and 1st IMF . We have

We take 2nd residue, , as the local mean of . The 2nd IMF is

For any and th IMF , the expression is as follows:

Go to step ; we obtain all of the IMF.

##### 2.2. Approximate Entropy

All of the IMF approximate entropy can be expressed as . Then the calculation procedure is as follows.

Take* k*th IMF as the time series of points and define it as

Compute the binary distance matrix of the time series:where*a* is threshold ( = 0.1~0.2) [38].

Compute the ratio of and to number for matrix element less than and as follows:

Compute of the nature logarithm, and get the average of of the nature logarithm. Then the approximate entropy of the th IMF is as follows:

The wavelet denoise is performed with the approximate entropy of the IMF that is greater than the threshold.

##### 2.3. Wavelet Denoise

The wavelet denoise is achieved based on a critical threshold. The main steps of its denoise principle are as follows.

Select the appropriate wavelet base and the number of decomposition layers. We take the wavelet transform with the noise signal and obtain its wavelet coefficients :where is the low-pass filter,* G *is the high-pass filter,* v *is for the scale factor, and is the wavelet coefficient.

Select the appropriate threshold function to process the wavelet coefficients and get the estimation wavelet coefficients :where* λ* is threshold, , is the mean square error of the signal, and

*N*is the sampling point number.

Use the estimation wavelet coefficients and get the reconstruct signal :where is reconstruct low-pass filter and is reconstruct high-pass filter.

Based on ICEEMD, the approximate entropy, and wavelet denoising theory, we proposed ICEEMD-De method. The method is divided into five steps to implement processing vibrational signal. The ICEEMD-De analysis process is shown in Figure 1. At first step, we sample the anchoring detection signal and take sampling signal for analysis. Then the sampling signal is decomposed with ICEEMD method. Each IMF of the signal can be obtained. At third step, we solve the approximate entropy of each IMF based on approximate entropy theory. At fourth step, the method takes the approximate entropy as the condition of whether the IMF is denoised. When approximate entropy of the IMF is higher than threshold, the wavelet denoising was processed. Finally, by means of the wavelet soft threshold denoising technique, the noise in the intrinsic mode function (IMF) is eliminated. The original signal components are retained in maximum with ICEEMD-De.