Advances in Materials Science and Engineering

Volume 2018, Article ID 7872036, 11 pages

https://doi.org/10.1155/2018/7872036

## Application of Wavelet and EEMD Joint Denoising in Nonlinear Ultrasonic Testing of Concrete

^{1}Key Laboratory of Hydraulic and Waterway Engineering of Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, China^{2}Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China

Correspondence should be addressed to Kui Wang; moc.361@kwiuhna

Received 15 September 2017; Revised 20 March 2018; Accepted 16 April 2018; Published 16 May 2018

Academic Editor: Santiago Garcia-Granda

Copyright © 2018 Zhichao Nie 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 health state of concrete is deteriorating during its service. Nonlinear ultrasonic detection based on the amplitude of the fundamental and the second harmonic is considered to be a powerful tool for the discovery of the microcrack in concrete. However, the research on processing the nonlinear ultrasonic signal is still insufficient. In order to highlight the real frequency domain components in the nonlinear ultrasonic signal, wavelet and ensemble empirical mode decomposition (EEMD) were joined to denoise the numerical and measured signal. The optimal wavelet base and the decomposition level were determined by the signal-to-noise ratios (SNRs). Then, the wavelet threshold denoising signal was decomposed by EEMD, omitting the high-frequency components and ultimately achieving the desired denoising effect. The denoising result of the test signals demonstrates that this method is effective in denoising the details of the ultrasonic signal and improving the reliability and adaptability of the nonlinear ultrasonic testing. In this experiment, the concrete with the microcrack was tested by linear and nonlinear ultrasonic methods. Based on the variation regularity of the nonlinear ultrasonic coefficient and velocity , we can conclude that the nonlinear ultrasonic parameter is more sensitive to the microcrack in concrete than the traditional wave velocity . The nonlinear ultrasonic testing can be an important supplement to the current nondestructive testing technique of the concrete.

#### 1. Introduction

Nonlinear ultrasonic technique has been considered as a promising method for detecting the microdamage of materials [1]. Lissenden’s research shows that when single-frequency ultrasonic waves pass through the damaged area of the medium, the tensile-compression asymmetry, shear-normal coupling, and deformation-induced compression asymmetry are the reasons for the generation of high-order harmonics [2]. At present, the research on the nonlinear ultrasonic technique is mainly focused on the following aspects: (1) Experimental study on dislocation slip damage for metal material (microscale) [3, 4]. (2) Experimental and numerical simulation study on closed crack damage for metal or nonmetallic materials (mesoscale) [5–7]. (3) Exploration of the generation and propagation mechanism of nonlinear ultrasound [8–10]. However, the amplitude of higher order harmonic in signals tends to be smaller and differ by one to two orders from the fundamental. Therefore, it is difficult to accurately measure the amplitude of the high-order harmonic in the experiment, and an effective signal processing method is needed.

Wavelet-based denoising and compression have been widely used in engineering, biology, and so on. Staszewski compared the wavelet compression effects of the periodic, continuous nonstationary and transient nonstationary vibration signals, providing data compression selecting basis for different types of signals [11]. In addition, the wavelet transform also has the ability to recognize the damage of the material or structure. Using orthogonal wavelet transform and setting the appropriate threshold value, the reflected wave features caused by defect can be effectively displayed [12]. Another important application of the wavelet-based technique is signal denoising. The combined denoising method based on wavelet entropy was proposed by Hou and Gui, which processes the high-frequency wavelet decomposition coefficients with wavelet entropy thresholds under different scales [13]. Cunha et al. determined the wavelet functions based on the SNR computed from the wavelet coefficients, and the wavelet decomposition level was chosen according to the energy spectral density principle [14]. The proposed method provides a new thought and approach for the selection of wavelet basis and decomposition layer in wavelet denoising.

Unlike the wavelet transform, the empirical mode decomposition (EMD) can be decomposed adaptively according to the trend of the signals. Wu and Huang added the Gaussian white noise to the original signal to supplement the missing frequency components and obtained desired decomposition results [15]. A major application of EEMD is to extract intrinsic mode functions (IMFs) from the vibration signals to identify the mechanical faults. Žvokelj et al. proposed the EEMD-based multiscale ICA (EEMDMSICA) method. The rotating machinery vibration signals are analyzed by this method, and the bearing fault can be detected [16]. In addition, Ridder et al. compared the SNR acquired by EEMD, wavelet, and FIR denoising and considered the wavelet denoising method is the best [17]. Wei et al. denoised the IMF components using criteria, singular value decomposition, and SG filtering. The superiority of this method was verified by processing the simulated and experimental data [18].

In order to accurately extract the amplitude of the fundamental and the second harmonic, this paper uses wavelet and EEMD joint method to denoise the numerical signal containing higher order harmonics, which tend to be more effective than a single step denoising. Then, the nonlinear ultrasonic experiment was carried out. And the wavelet and EEMD joint denoising method was applied to the experimental signal, gaining the correlation between the cracked angle and nonlinear coefficient .

#### 2. Denoising Method

##### 2.1. Wavelet Threshold Denoising Theory

Wavelet theory originated in the late 19th century and has been widely applied in various fields. Wavelet threshold denoising is one of the important applications of the wavelet theory proposed by Donoho and Johnstone. The main idea is comparing each level of wavelet coefficients with the selected threshold. When the wavelet coefficient is greater than the selected threshold, it is completely preserved or shrunk. These wavelet coefficients are considered as the original components of the signal. Otherwise, the wavelet coefficients are zero setting. Then, the detail and approximation coefficients are reconstructed, and the wavelet threshold denoising is accomplished [19].

The traditional hard and soft threshold functions are shown in the following equations:where is the detail coefficient, is the detail coefficient after denoising, is the wavelet threshold, and is the symbolic function. According to (1) and (2), there are smoothness and continuity problems when denoising by the hard threshold function. When using the soft threshold function, it is very likely to lose important information in the original signal. In order to preserve the frequency domain characteristics of the ultrasonic signal as much as possible, this paper uses the hard threshold method. If the wavelet coefficients are greater than the selected threshold, keep them intact, otherwise 0. In addition, the smoothness problem caused by the hard threshold method will be solved in the next step of EEMD.

The threshold selection rule is based on Stein’s unbiased risk estimation:where is the standard deviation of the noise signal and is the risk function.

The unbiased risk threshold method needs to find the wavelet coefficient corresponding to the minimum risk value, and then the threshold value is calculated according to it. Although the thresholds determined by this way are conservative and may result in incomplete noise removal, it is easier to separate useful weak components from noise when the high-frequency bands are confusing with noise.

Nonlinear ultrasonic testing requires using high-frequency information of the signal. However, the high-frequency band of the signal is more susceptible to noise pollution than low-frequency components. In view of the characteristics of the nonlinear ultrasonic experimental signal, it is appropriate to determine the threshold value by Stein’s unbiased risk estimation to eliminate the noise in the high-frequency coefficients.

##### 2.2. EEMD Denoising Method

In order to overcome the illusive components and mode mixing problems existing in EMD, additive Gaussian white noise is added to the original signal to supplement the missing frequency scale of the signal. The specific EEMD decomposition process is as follows [20]:(1)Adding the Gaussian white noise to the original signal and obtaining a new signal :(2)The signal is decomposed by EMD to obtain the intrinsic modal function (IMF) :(3)Adding the Gaussian white noise to the original signal again and repeating the above steps:(4)Due to the entire frequency spectrum of the Gaussian white noise is zero, the time-frequency effect after adding the noise signal can be neglected. Average the superimposed intrinsic modal function:

The noise signal can be decomposed from high frequency to low frequency adaptively by the EEMD method. By ignoring the high-order IMFs and reconstructing the remaining IMFs, the denoising signals are obtained.

##### 2.3. Wavelet and EEMD Joint Denoising Method

The ultrasonic noise mainly comes from the ultrasonic machine, environment, and crystal scattering of materials, which is usually distributed in the high-frequency field of the received signal. Figure 1 is a flow chart of the denoising method. The appropriate wavelet base and the decomposition layer are selected to denoise the noise signal. Then, the signal is decomposed by EEMD. Because the noise is mainly distributed in the high-frequency range, the high-frequency components imf1∼imfi are discarded and the remaining components are reconstructed [21].