Elsevier

NDT & E International

Volume 41, Issue 5, July 2008, Pages 382-394
NDT & E International

Application of the wavelet transform and the enhanced Fourier spectrum in the impact echo test

https://doi.org/10.1016/j.ndteint.2008.01.002Get rights and content

Abstract

The objective of this study is to develop a reliable and effective method to analyze the signal of the impact echo test. The impact echo test is a nondestructive testing technique for civil structures. In the test, the surface response of the target structure due to an impact is measured. Then, the Fourier transform is adopted to transform the signal from the time domain to the frequency domain. Owing to the multiple reflections induced by cracks, voids, or other interfaces, peaks will form in the Fourier spectrum. The frequencies of the peaks can then be used to determine the size of the structure or the location of the defect.

Several difficulties are encountered when applying the Fourier transform to impact echo data. Because the impact echo data are non-stationary and contains multiple reflections, ripples and multiple peaks appear in the Fourier spectrum, which may mislead the follow-up diagnosis. Furthermore, the existence of the high-energy surface wave and structural vibrations often complicates the spectrum and makes the data interpretation even more difficult.

To overcome these difficulties, this research adopts the wavelet transform in the analysis of impact echo data. Theoretically, the wavelet transform can avoid ripple and multiple-peak phenomena. Furthermore, the frequency range and time span of surface wave can be observed in the wavelet scalogram. However, the spectral resolution of the wavelet marginal spectrum is inferior to that of the Fourier transform. Therefore, two approaches are proposed in this paper. One is to combine the Fourier spectrum and the wavelet marginal spectrum to determine the precise location of the echo peak. The other is to take the product of the two spectra to establish the enhanced Fourier spectrum. As such, the interference in the Fourier spectrum is suppressed while the peak is enhanced. Numerical and experimental tests were performed to verify the effectiveness and reliability of the proposed approaches.

Introduction

The impact echo method is widely applied in the nondestructive testing of concrete structures. In its early stages of development, the impact echo method was applied primarily to detect internal flaws in concrete plate [1], [2]. Later it was used for the inspection of the flaws in rod structures [3], flaws in concrete panels [4], and the corrosion damage of rebars in concrete [5].

In the impact echo test, a steel ball or a hammer is used to knock at the surface of the specimen. Consequently, stress waves will be generated and propagate in the structure, including the longitudinal wave, the transverse wave, and the surface wave. The surface wave propagates along the surface, while the transverse wave and the longitudinal wave propagate into the interior of the structure. As the bulk wave encounters an interface such as crack or boundary, it will be reflected, refracted, or diffracted. A transducer is placed near the impact point to measure the response of the structure. Then, the received signals are recorded for data analysis.

Since the received signals contain the surface wave and the reflected or diffracted bulk wave, it is difficult to extract useful information directly from the raw data. Therefore, the conventional impact echo method applies the Fourier transform (FT) to the time signal. The idea is as follows: When a wave propagates in a structure, it reflects as it encounters an interface. Then the reflected wave rebounds back to the surface and reflect again into the interior of the structure. The process repeats and multiple reflections occur between the surface and the interface until the wave fades out. The echo of the wave will form a peak in the Fourier spectrum, and its frequency f is related to the depth of the interface D by the following equation [1]:f=Cp2D,where Cp is the velocity of the longitudinal wave. Thus, by locating the peaks in the Fourier spectrum, the size of the structure or the depth of an internal crack can be determined.

The FT has been adopted to detect the size or flaws of concrete structures successfully in numerous cases. However, the interpretation of Fourier spectrum is by no means easy because it contains a lot of interference which is intrinsic in the impact echo spectrum.

The FT theory is built on the assumption of a stationary signal. However, the impact response of a structure is not stationary, and its frequency content varies with time. Hence, interference appears in the spectrum, such as ripples and multiple peaks. Furthermore, the existence of the high-energy surface wave and structural vibrations often complicates the spectrum and makes the data interpretation even more difficult.

To deal with the aforementioned difficulties, several time–frequency analyses were proposed for use in the impact echo test, for example, the wavelet transform (WT), the short-time Fourier transform (STFT), and the Hilbert–Huang transform (HHT). Abraham et al. [6] proposed a windowed FT for the detection of voids in a concrete block. Kim and Kim [7] used WT to find the position of an opening crack in a rod-liked structure. Chiang and Cheng [8] employed WT to inspect steel tubes and PVC tubes. Shokouhi et al. [9] used STFT and WT in the size detection of concrete block. Algernon and Wiggenhauser [10] compared the performance of STFT, WT and HHT in the measurement of structural dimension. Different from the aforementioned papers, in which data interpretation was performed in the time–frequency plane, the marginal spectra were used to determine the depth of structural members. The time–frequency analyses were also adopted in the evaluation of structures using other nondestructive tests [11], [12], [13], [14], [15], [16].

This paper studies in depth the application of WT in the impact echo test of concrete structures with internal cracks. The results of FT and WT will be compared and discussed. Based on the investigation, a better data processing approach for the impact echo test will be devised.

Section snippets

Fourier transform

The FT of a signal x(t) and its inverse transform are as follows:X(f)=-+x(t)e-2iπftdtx(t)=-+X(f)e2iπftdf.

The above equations imply the signal x(t) is expanded in terms of the harmonic function e2iπft from t=−∞ to +∞, and X(f) represents the magnitude of the component with frequency f. It is seen that the signal is transformed completely from the time domain to the frequency domain. Hence, X(f) contains no information on the temporal variation of the frequency content.

FT has two drawbacks

Numerical simulation

This study adopted the finite element code LS-Dyna970 [24] to simulate the response of concrete specimens due to the impact of a steel ball. It is also used to perform modal analysis to find the natural frequencies of the specimens.

Two concrete specimens with internal cracks are considered in the numerical examples. The mass density, Young's modulus, Poisson's ratio, and the longitudinal wave speed of the concrete are 2300 kg/m3, 33.1 GPa, 0.2, and 4000 m/s, respectively. The dimensions of the

Model tests

Model tests were carried out to illustrate the signal processing methods proposed in this study. The compressive strength of the concrete is 30 MPa, the water cement ratio is 0.6, and the concrete mix design is as follows: cement, 392 kg/m3; sand, 752 kg/m3; gravel, 915 kg/m3; additives, 0.98 kg/m3; water, 235 kg/m3. The longitudinal wave velocities of models 1 and 2 are 3890 and 3900 m/s, respectively.

The experiments were conducted on two concrete specimens. The dimensions of the concrete specimens,

Conclusion

This paper applies the WT in the analysis of the response signal received in the impact echo test. The WT was first compared with the conventional FT theoretically. Then, numerical simulation and model tests were conducted to check the performance of these transforms.

From the numerical examples and model tests, it is seen that surface wave, ripples, and multiple peaks complicate the Fourier spectrum and jeopardize the diagnosis of structures. The WT, on the other hand, is free from such

Acknowledgment

This work was supported by the National Science Council, Republic of China under grant NSC 90-2211-E-002-079.

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