TOFD (time of flight diffraction) is a kind of weld defect detection technology by using ultrasonic diffraction wave signal. Because the diffraction intensity is far less than ultrasonic echo wave intensity, thus, the noise contained in TOFD signal is fairly large, and the formed image is not clear enough. Therefore, it is difficult to determine the size of defects accurately. In this paper, a method of noise reduction of TOFD signal and improving the resolution of the image are discussed based on the combination of wavelet thresholding and image registration. Wavelet multiresolution analysis method is adopted and the A-scan signal is decomposed into different frequency components. We propose a new threshold function to process the wavelet coefficients, which guarantees to denoise while preserving the useful information as much as possible. Setting up the ultrasonic TOFD inspection system and the image data with randomly distributed noise can be obtained via fine shake of the probes during testing. Then, image registration based on maximum correlation and blending is adopted to eliminate the noise in further step. The result shows that the proposed method can achieve denoising, together with resolution enhancement.
Ultrasonic time of flight diffraction defect inspection was introduced by Silk [
This paper discusses a concept of multiframe model and adopts multiple TOFD images, in the sense of the combination of wavelet transform and image registration, SNR and the quality of the image can be enhanced by blending the denoised images together. The remaining of this paper is arranged as follows: in Section
Ultrasonic TOFD inspection is a kind of defect-testing technique using ultrasonic diffraction signal. Figure
Ultrasonic TOFD inspection schematic diagram.
The inspection system shown in Figure
In the testing procedure of TOFD system, in order to solve the problem of difficult recognition of echo wave, longitudinal wave can be adopted but not lateral wave. The calculation result of the depth of the defect is unique via longitudinal wave and its speed in different modes of the wave have different speeds in the same specimen, and the fastest one is the longitudinal wave. In the propagation of the wave in steel, the speed of the longitudinal wave is twice as much as the lateral wave. Consequently, the earliest received signal is the longitudinal wave. Ultrasonic TOFD inspection can be proceeded by A-scan, and the B- or D-scan signal can be synthesized by A-scan signal. B-scan and D-scan signal is 2D image and is generated if the probe pair is moved parallel and perpendicular to the middle line of the weld, respectively. The weakness of the diffracted wave and the inhomogeneity of specimen structure makes the observed signal always contains lots of noise. For the convenience of observation of the diffracted wave signal, it is necessary for the system to be operated under the high-gain mode. As a result, the useful signal and the noise are enhanced together; thus, the formed TOFD image is always with low SNR.
According to the theory of wavelet analysis proposed by Mallat [
In order to achieve the restored signal with much less noise than before, we combine the high-frequency components after processing and the retained low-frequency components together. Thresholding is one of the most widely used methods to compress the noise in high-frequency components, including hard thresholding and soft thresholding. In the procedure of hard thresholding, the discontinuity at critical points can lead to bell effect; moreover, the pixel value ranges between two critical points are all substituted to 0, which makes the image information lost severely and results to the loss of image fidelity. Soft thresholding is more flexible compared to hard thresholding. However, the soft thresholding could not give an optimum value for the calibration of the higher coefficients, and the smoothness of the soft thresholding always reduces the resolution and the definition of images.
In order to overcome the shortcomings in classic threshold functions, the variance of the noise signal should be estimated based on Bayesian statistics before adopting thresholding on the wavelet coefficients. Assuming that the wavelet coefficient in high-frequency components yields to Gaussian distribution, thus the posterior probability can be presented as follows:
The Bayesian mean square error (
The Bayesian posterior variance can be calculated when
According to the characteristics of the ultrasonic TOFD data, a new threshold function with the adaptivity to noise is established based on the estimated noise variance to compress the wavelet coefficients. This threshold value for thresholding is as follows:
In the condition of the above threshold functions, we give a new self-adaptive thresholding to compress the wavelet coefficients. The wavelet coefficients can be processed as follows and some thresholding curves including the classic thresholding and the proposed one are shown in Figure
Thresholding curves. Dotted line, asterisk line, dash line, and solid line denote soft thresholding, hard thresholding, semisoft thresholding, and the proposed thresholding, respectively.
Ultrasonic TOFD inspection system usually samples one image to determine the size and the depth of the defect quantitatively, and the TOFD images are easy to be contaminated by noise in this procedure. Actually, it is easy to find from multiple TOFD images that the noise is randomly distributed in each image; in addition, each image is obtained with small displacement. Therefore, we adopt image registration and blending them together to eliminate the displacement and the stochastic noise. In order to sample the TOFD signal with higher stochasticity, the initial position of probes should be finely tuned each time. Then, the TOFD images with small random displacement can be obtained. Adopting image registration to modify the displacement in each image and the noise can be reduced via blending the registered images together. Thereafter, the quality of TOFD images can be improved.
Figure
The noise distribution in different TOFD images. (a) Original image. (b) The other original image with small displacement of probe during data sampling. (c) and (d) are the zoomed in images of the part framed with white box in (a) and (b), respectively.
In order to eliminate the error lead by the probe displacement in TOFD images, we select one of the TOFD images as the template image or reference image, and the others are the images needed to be registered or the floating image. The error between
The whole experiment system consists of establishing TOFD weld defect inspection system, data sampling, and forming a series of TOFD images. Firstly, we adopt wavelet transform on the raw data for denoising; then, image registration is adopted on the denoised data; lastly, we superimpose all the registered images together to form one new image. The experiment part is realized via TOFD inspection system and data processing. The experiment system is composed of ultrasonic TOFD probes, a scanning device, and specimen with one or more cracks inside. In this paper, we use austenitic steel as the specimen. There are 5 cracks inside the specimen. The size of the specimen is 400 × 400 × 30 mm, and we use standard DDENV583-6:2000 probes; the central frequency is 5 MHz, the refracted angle is 30°, and the size of the wafer is 6 mm. The gain of the test signal is 63 dB–67 dB. The sampling frequency is 100 MHz, the refracted angle is 45°, the central moment of the probes is 99 mm, the filter frequency is 5 MHz, and water is used as coupling.
In the proceeding of experiment, transmitter and receiver keep a certain distance, and the probe pair moved along the middle line of the weld. The A-scan data is being generated while scanning, adjusting the initial position of the probes before scanning each time; then, the TOFD images with stochastic displacement are obtained. Especially, owing to the randomly setting of the probes’ position, the correlation of the noise in each image is rather low.
Before image registration, we adopt two modes of wavelet transform on the original TOFD data: 1D wavelet transform and 2D wavelet transform. The result of wavelet transform is evaluated by SNR presented in (
Figure
The processed result of A-scan signal by wavelet thresholding. (a) Original signal. (b) The result via soft thresholding. (c) The result via proposed thresholding method.
The new image is formed by the composition of multiple denoised A-scan signal, as shown in Figure
The denoised image via our proposed method. (a) Original TOFD image. (b) Denoised image via soft thresholding. (c) Denoised image via proposed thresholding. The zoomed in image is shown on the right side.
Figure
Multiple TOFD images blending result. (a) Original image. (b) Five superimposed images. (c) 60 superimposed images. (d) Five superimposed registered images obtained via soft thresholding. (e) 60 superimposed registered images obtained via soft thresholding. (f) Five superimposed registered images obtained via our proposed method blending result. (g) 60 superimposed registered images obtained via our proposed method.
Figures
The curve of SNR with respect to the number of superimposed images among different methods.
The bar chart of SNR by using different methods.
This paper discusses a repeated ultrasonic TOFD inspection method. In so doing, the TOFD A-scan and B-/D-scan signal are characterized with high stochasticity via the random adjustment of the probe pair before each sampling. The average effect impairs the noise to a rather low level via blending all the images together. In order to improve the SNR and the definition of the TOFD images in further step, we adopt 1D wavelet transform and the proposed thresholding method to enhance the SNR of the A-scan signal, which is 39 dB. The denoised TOFD image is composed of multiple denoised A-scan signal. In order to eliminate the displacement among the TOFD images derived from the adjustment of probes, image registration based on maximum correlation is used, thereafter, blending the registered images together. The result shows that SNR got another improvement, from 16.3 dB to 23.5 dB. The method discussed in this paper is aiming at enhancing the SNR and definition of TOFD images. Indeed, only 10 images are needed to complete the whole image quality enhancement procedure. The method is quite simple and efficient, and it is possible to be applied in timing process in industrial field.
The authors declare that they have no conflicts of interest.
This work was supported by National Nature Science Foundation of China (Grant no. 61471304), and the authors wish to acknowledge them for their support. The authors also thank Southwest Jiaotong University NDT Research Center and Olympus NDT Joint Laboratory of Nondestructive Testing for their kind support in the experiment.