·Table of Contents
·Methods and Instrumentation
Experimental Wavelet Analysis and Applications to Ultrasonic Non-destructive EvaluationIk Keun Park, Un Su Park , Hyung Keun Ahn : Research Institute of NDE Technology, Seoul National University of Technology, 172, Gongneung-dong, Nowon-gu, Seoul, 139-743, Korea
Sook In Kwun, Jai Won Byeon, Division of Materials & Engineering, Korea University
Advanced signal analysis which is called "time-frequency analysis (t-f analysis)" provides a new tool for processing transient signals and it can be considered as an alternative to the classical Short-Time Fourier Transform(STFT) for describing the time-frequency evolution of such signals obtained by an ultrasonic pulse-echo method. The utilization of t-f analysis(wavelet transform) is widespread and an attractive signal processing technique for evaluation of material characterization nondestructively. The WT has already been shown as a useful tool for the interpretation and the enhancement of ultrasonic data in the context of NDE. In more conventional ultrasonic nondestructive evaluation(UNDE) work, it clear that the uses of frequency domain and time domain information alone is not adequate for effective NDE. Among all the t-f analysis methods, both Wigner distributions(WD) and WT are the most recent techniques for processing signals with time-varing spectra.[2,3] WD and WT have been considered for use in UNDE. However, the full potential of the t-f analysis in UNDE is yet to be explored.
There have been intense research activity in the application of wavelet transforms in various fields of science and engineering. INOUE et al[5,6] applied the determination of ultrasonic velocity and attenuation by wavelet analysis of echo waveform.
In this paper, the WT theory using the Gabor wavelet is briefly introduced and its application to UNDE is explained. It will be shown that the arrival times of group velocity at each frequency by using the peak of the magnitude of the WT can be extracted. NDE for degraded structural materials used at high temperature by surface SH-wave method which is horizontally polarized shear wave traveling along near surface and subsurface layer is discussed. Two examples of experimental wavelet analysis and applications to UNDE were presented. First, 0.25Cr-1Mo steel used at high temperatures was evaluated by UNDE techniques. wavelet transform is applied to time-frequency analysis of ultrasonic echo waveform obtained by surface SH-wave technique. The Gabor function is adopted the analyzing wavelet. Using the WT, material degradation is to be evaluated through observation of the relation between micro-structural variation of the simulated degradation and surface SH-wave propagation characteristics such as velocity, attenuation coefficient and amplitude spectra etc. In addition, it has verified experimentally the frequency-dependence of ultrasonic group velocity and attenuation coefficient using wavelet analysis.
In the second example, we consider the feasibility of the enhancement of the flaw detection performance(probability of detection; POD, false call probability;FCP) and noise suppression of ultrasonic flaw signal using the WT has been verified experimentally, which results in the enhancement of S/N ratio and the effectiveness of the noise suppression of ultrasonic flaw signal obtained from austenitic stainless steel weld including EDM notch.
where wo and g are positive constants. In this study, we set according to Morlet. If eq (6) is substituted into eq (2), it is understood that the WT using the Gabor wavelet has a similar form to the Fourier transform with Gaussian windowing. Hence we set wo = 2 p such that 1/a takes the same value as the frequency w0/(2 p).
Let us consider two harmonic wave of unit amplitude and different angular frequency w1 and w2 propagating in the x-direction, given by
where k1 and k2 are wave numbers.
If Dw is sufficiently small, the group cg at the angular frequency wc can be defined as
When the Gabor wavelet is adopted as the analyzing wavelet, the magnitude of WT of u(x,t) obtained as
If Dw is sufficiently small such that , we obtain
|Table 1. Chemical composition of 2.25Cr-1Mo steel(wt. %)|
|Time served at 538°C(hr)||Virgin||3,000||12,000||60,000|
|Aging time at 650°C(hr)||0||50||200||1,000|
|Table 2. Accelerated aging time at 650°C for equivalent microstructure served at 538°C|
A schematic of the experimental setup is shown in Fig. 2. A couple of 5 MHz commercial type contact surface SH wave transducers supplied by Japan Probe Co., along with a ultrasonic flaw detector(UDS 15;krautkramer Co.) is used to generate and receive the ultrasonic signals. SHN-40(Nichigou Acetylene Co., Ltd) was used as the couplant for shear wave exclusive use.
Fig 1: Effect of degradation time on the microstructure of 2.25Cr-1Mo steel
The analog signal was digitized using a Lecroy 9374M digital storage oscilloscope(DSO) with a sampling rate of 1GHz. The numerical simulations were performed using the pentium computer and MATLAB software routines. For each specimen, several measurements were made and the average amplitude was used for the calibration. Care was taken to repeat the same coupling condition during each measurement.
To apply the optimal condition of surface SH wave testing, the relation between the transfer efficiency and couplant viscosity, between the transfer efficiency and thickness of couplant, and between the transfer efficiency and surface roughness etc. are considered. Fig. 3 shows the effect of degradation time on ultrasonic time
domain information. The propagation time is measured by pitch-catch method with two surface SH-wave probes. As the degradation time is increasing, ultrasonic propagation time is also an apparent increasing.
|Fig 2: A schematic of the experimental setup|
Fig 3: Effect of degradation time on ultrasonic time domain information
A typical ultrasonic waveform is shown in Fig. 3. Fig. 3 shows the time-frequency distribution of the magnitude of the WT and its contour plot. The absolute value of the WT is plotted in logarithmic scale in Fig. 3(c) as a function of time-shift coefficient and the dilation coefficient. Contour plot of th WT in Fig. 3(b) represents the time-scale representation of the signal in Fig. 3(a). Scale is an attribute of a signal and is inversely proportional to the frequency of the signal. Ultrasonic attenuation and group velocity dependent on frequency are accurately measured using the WT.
Fig 4: (a) Ultrasonic echo waveform
Fig 4: (b) contour plot
Fig 4: (c) wavelet transform
Fig. 5 shows the frequency dependence of attenuation coefficient identified by the WT analysis. Using the time frequency distribution of the magnitude of the WT, analysis of dependency on frequency of group velocity and attenuation can be evaluated. In this experiment, as degradation time increases, attenuation coefficient increases. In the case of this specimen, group velocity isn't greatly dependent on frequency but, in attenuation coefficient, degraded material manifests itself strong dependent on frequency compared with virgin material as shown in Figure 5. It is considered that variation in grain size has a great influence on ultrasonic attenuation as quantity of degradation time increases.
|Fig 5: Frequency dependence of attenuation coefficient identified by the WT analysis|
There have been several investigations into additive noise suppression in signals and images using wavelet transforms[14,15]. De-noising of signals is extremely important in ultrasonic flaw detection, as to correctly identify smaller defects. If the amplitude of the signal from the defect is below the detection threshold, the defect will not be reported. The probability of detection(POD) usually decrease as the defect size decreases, while the probability of false call(PFC) does increase. It is obvious that the threshold level should be set above the noise level and below the signal level, and processing of the signals does increase the POD, without altering or increasing the PFC. For automated inspection systems, it is recommended to set the threshold level about 1.6-2.0 times the mean noise level. This means that the defect signal-to-noise ratio has to be higher than 4.0-6.0 dB. The WT can be used to suppress noise of ultrasonic flaw signals and to enhance flaw detectability. Fig. 6 shows the results of de-noising of ultrasonic flaw signal using the WT obtained from austenite stainless steel weld including EDM notch. The maximum ultrasonic flaw signal is acquired through near side access.
|Fig 6: Results of UT original signal and de-noised signal(EDM notch)|
A commercial 5MHz angle beam transducer is used. Experimental results shows that the WT is capable of flaw echo detection for UNDE application in low signal-to-noise ratio.
This work was supported by Korea Science and Engineering Foundation Grant
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