The Time-frequency Domain Analysis and Image Method of The Impact Echo Method
Date Issued
2006
Date
2006
Author(s)
Yeh, Po-Liang
DOI
zh-TW
Abstract
The impact echo method is widely used in the nondestructive inspection of concrete structures. In the test, an impact is applied on the surface of the concrete structure, and the surface response of the concrete due to the impact is measured and recorded. Then, the Fourier transform is adopted to transform the response from the time domain to the frequency domain. Since interfaces, cracks, or voids will induce multiple reflections and peaks will form in the Fourier spectrum. Hence, the spectrum will reveal the size of the structure or the location of the defect.
The theory of Fourier transform is built on the hypothetical assumption of stationary signal. Unfortunately, the impact response of a structure is by no means stationary, and its frequency content varies with time. To take the non-stationary nature of impact signal into account, two time-frequency domain analyses are studied in this research, namely, the short-time Fourier transform and the wavelet transform.
To examine the effect of various signal processing methods, several concrete models with imbedded cracks were molded. Finite element models were also constructed to simulate the model tests. The simulation parameters were selected such that the numerical results agreed with the experimental data. The simulation and experiment results were then used to verify and compare the methods proposed in this study.
Through theoretical analysis and case study, it is found that the Fourier transform has the best frequency resolution. However, its spectrum possesses multiple peaks and ripples. Such phenomena complicate the diagnosis. The short-time Fourier transform can avoid the ripples, but multiple peaks still exist. The wavelet transform, on the other hand, has neither interferences. The Fourier transform and short-time Fourier transform has fixed frequency resolution, but the frequency resolution of the wavelet transform deteriorates as the frequency increases. Fortunately, this property complies with the need of the impact echo method. Another advantage of the time-frequency analysis is that one can directly detect the surface wave and the modal vibration from the spectrogram of the short-time Fourier transform and the scalogram of the wavelet transform. Since the surface wave and the modal vibration are usually very high in energy, they often cause trouble when deciphering the signals.
Although the marginal spectrum of the wavelet transform contains least interference among the three methods and is easy to identify the peak due to the multiple reflections of interface in the concrete, the peak is not as sharp as in the Fourier spectrum. Hence, it is suggested that one first identify the peak in the wavelet spectrum, find the corresponding peak in the Fourier spectrum, and then determine the frequency of the peak using the Fourier spectrum.
In order to provide the engineers with a more direct way of detecting the defects in the structure, several imaging methods are developed in this research. The two-dimensional imaging methods adopt the concepts of the B-scan and C-scan in the ultrasonic detection. In the spectral B-scan method, a series of impact echo tests are performed along a line and represent the spectral amplitude of the signals by color scale. Then, an image is constructed using the spectra of the tests with the test position as the horizontal axis and the frequency as the vertical axis. The B-scan image provides the defect information on the vertical section under the test line. The C-scan spectral method, on the other hand, constructs an image for a horizontal section. In the C-scan method, the impact echo tests are performed on an area on the concrete surface. Then, select the depth of the horizontal section to be inspected, and determine the corresponding frequency for the depth. Finally, a spectral image is constructed for the horizontal section by representing the spectral amplitude by color scale.
This research also proposes two three-dimensional imaging methods. Similar to the C-scan method, the impact echo tests are performed on an area on the concrete surface. Then, the surface rendering and volume rendering techniques are applied to the spectra of the signals to construct the three-dimensional image of the concrete interior. It is found in the research that the volume rendering method is more stable and is less sensitive to the signal noise. However, the surface rendering method can better exhibit the details of the internal defect. Therefore, one may utilize the volume rendering image to get a rough image of the concrete interior. Then, use the surface rendering method to observe the details.
Both numerical simulations and experimental results are used to verify the proposed imaging methods. Three spectra are adopted to construct the images, namely, the Fourier spectrum, the wavelet spectrum, and the product of the two spectra. It is found that image of the product spectrum yields the best results. With the numerical signals, all imaging methods can depict the crack locations effectively. In processing the experimental data, the quality of the images is deteriorated by the existence of the noise, especially the surface rendering method. However, the cracks can still be detected. The imaging methods have difficulty in describing shallow cracks, because the energy of flexural vibration is very strong. In that situation, one may determine the location of the shallow crack by observing the bottom reflection.
Subjects
非破壞檢測
敲擊回音
有限元素
時頻分析
小波
影像
三維
NDT
Impact echo
Finite element method
Time-frequency analysis
Wavelet
Image
3D
Type
thesis