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Enhancing ultrasonic time-of-flight diffraction measurement through an adaptive deconvolution method
Ultrasonics 96 (2019) 175–180
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Enhancing ultrasonic time-of-flight diffraction measurement through an adaptive deconvolution method
T
⁎
Jian Chen, Eryong Wu , Haiteng Wu, Hongming Zhou, Keji Yang The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Time-of-flight diffraction Sub-band signals Wiener filtering and spectral extrapolation Adaptive deconvolution
Deconvolution is generally applied to improve the temporal resolution of ultrasonic signals. However, using this process in the time-of-flight diffraction (TOFD) measurement of small and shallow defects is challenging because TOFD signals are dispersive in space–frequency distribution. Particularly, determining the reference signal for deconvolution remains a critical barrier. To this end, an adaptive deconvolution method is proposed in this study. Using wavelet transform, we firstly decompose the TOFD signals into sub-band signals to standardise the space–frequency distribution. Then, sub-band signals with strong coherences are adaptively selected on the basis of coherence coefficient metric. Upon the opted sub-band signals, a lateral wave can be readily used as the reference signal, and TOFD signals can be reconstructed with established Wiener filtering and spectral extrapolation methods. The feasibility of the proposed method is validated with the TOFD measurement of a small side-drilled hole near the surface. Results show that the proposed method effectively separates overlapping TOFD signals and improves the axial resolution of a TOFD image.
1. Introduction Weldments are ubiquitous and play a significant role in various applications (e.g., airplanes, power plants, nuclear reactors and civil infrastructures). Thus, weldments are often subject to thorough inspection, evaluation and monitoring for quality and safety. Despite the considerable attention during design and fabrication, weldments are still prone to fail at weld-affected zones and thus show poor performance. Most failures are attributed to improper welding processes, residual stresses and operating parameters [1]. One of the routine methods for minimising failure is non-destructive testing (NDT), which ensures that welded regions are defect-free. Several NDT methods have been used [2–7], including ultrasonic time-of-flight diffraction (TOFD) technique, which has attracted increasing interest in recent years because of its radiation safety, high accuracy, fast speed and low cost and because it has considerably outperformed its radiographic counterpart. Although significant success has been achieved in ultrasonic TOFD testing, several challenges remain, especially in the inspection of small defects at shallow depths, which are commonly formed in welded components. Specifically, ultrasonic TOFD signals overlap with one another, causing difficulties in extracting useful information, especially time-of-flight. For this case, improving the temporal resolution of ultrasonic TOFD measurement is highly desired. Generally, the temporal
⁎
resolution of ultrasonic signals can be improved with deconvolution methods, which are either direct [8–12] and iterative [13–15]. For iterative deconvolution, Mor et al. [14] proposed a support matching pursuit concept for effectively separating two overlapping ultrasonic signals. However, this algorithm demands a complete set of dictionary atoms as a prerequisite. To address this problem, Demirli et al. [15] used a parametric mathematical model to describe the ultrasonic echoes, upon which the reference signal for deconvolution can be determined via maximum likelihood estimation. The iterative deconvolution method can generate higher resolution and better image contrast than its direct counterpart. However, these methods suffer low computation efficiency and poor real-time performance, hampering their widespread application in the industrial field. On the contrary, direct deconvolution can readily mitigate these limitations and is thus more popular in real-time applications. Thus, several algorithms have been employed for the direct deconvolution, such as Wiener filtering [8,9], wavelet analysis [10] and autoregressive (AR) spectral extrapolation [11]. However, these methods cannot be applied directly in ultrasonic TOFD measurements because, as discussed hereafter, TOFD signals are dispersive in space–frequency distribution. Consequently, determining the reference signal for deconvolution is difficult as diffracted waves may be retrieved from different paths, and no one-size-fits-all reference signal exists.
Corresponding author. E-mail address: [email protected] (E. Wu).
https://doi.org/10.1016/j.ultras.2019.01.009 Received 8 November 2018; Received in revised form 27 January 2019; Accepted 28 January 2019 Available online 29 January 2019 0041-624X/ © 2019 Elsevier B.V. All rights reserved.
Ultrasonics 96 (2019) 175–180
J. Chen et al.
Fig. 1. Schematic illustration of ultrasonic TOFD measurement.
Fig. 2. Space-frequency distribution of the probing beam in TOFD measurement.
Fig. 4. Flowchart of the proposed adaptive deconvolution method.
Fig. 5. Experimental setup for TOFD measurement.
To solve this problem, we propose an adaptive deconvolution method based on wavelet sub-band Wiener filtering and spectral extrapolation to separate overlapping TOFD signals. The raw signals are firstly wavelet-transformed into sub-bands, which are uniform in space–frequency distribution. Then, the sub-band signals with strong causalities are adaptively selected according to their metric of coherence coefficients. Any one of these strongly coherent signals can serve as the reference signal for deconvolution as they have the similar
Fig. 3. (a) Measured ultrasonic TOFD signals and (b) their space-frequency distributions.
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Fig. 6. The geometry of the specimen.
waveform and spectrum. Finally, TOFD signals are reconstructed by applying Wiener filtering and spectral extrapolation. The proposed approach can enhance the temporal resolutions of TOFD signals, and thus the merged waves can be effectively separated to screen out small and shallow defects. The axial resolution of a TOFD image can also be enhanced by assembling deconvolved A-scan traces. The rest of this paper is organised as follows: In Section 2, the space–frequency characteristic of ultrasonic TOFD signals is discussed, and the implementation of adaptive deconvolution method is presented. In Section 3, the experiment conducted on ultrasonic TOFD measurement to validate the feasibility of the proposed method is presented. The conclusion is provided in Section 4.
Fig. 8. The coherence coefficient (a) between sub-band LW and TDWs and that (b) between TDWs and BE at scale 39.
Fig. 7. (a) Measured TOFD signals from the SDH, and that reconstructed with (b) proposed method, (c) conventional method. 177
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nearly all the frequency components. The spectra of the TDWs depend on their propagation paths, which are between those of the LW and BE. Under this condition, conventional deconvolution methods are ineffective for the TOFD measurement of small defects in a shallow depth as neither the measured reference signal nor the TOFD signal itself can work properly.
Table 1 Location and size of the SDH.
Reference Measured Error
Depth of upper tip
Depth of lower tip
Defect size
7 mm 7.325 mm 4.64%
9 mm 9.379 mm 4.21%
2 mm 2.054 mm 2.7%
2.2. Adaptive deconvolution method 2. Theory The deconvolution method based on Wiener filtering and spectral extrapolations has proven its capability in separating overlapping waves [18]. However, such method only works well when the ultrasonic wave does not change during propagation. Apparently, it cannot be employed directly in TOFD measurements. To address this issue, we develop an adaptive algorithm to deconvolve the TOFD signals by combining wavelet transform and conventional Wiener filtering and spectral extrapolation. Thus, the first step is to standardise the space–frequency distribution of the TOFD signals. Thus, we decompose them into their subbands using wavelet transform:
2.1. Space-frequency distribution of ultrasonic TOFD signals The principle of the conventional TOFD technique is depicted in Fig. 1 [16,17]. The transmitter transducer launches an ultrasonic wave into the specimen via a coupling wedge. The lateral wave (LW), the tipdiffracted waves (TDWs) and the backwall echo (BE) are then excited and detected by a receiver. The depth and size of the defect can be derived based on the time-of-flight between the LW and the top TDW and between two TDWs, respectively. For the TOFD measurement, the emission beam generally features a widespread angle, which can be evaluated by
γ=
sin−1 (Cl F / fD)
WTy (a, b) = < y (t ), φa, b (t ) > =
(1)
1 a
+∞
∫−∞
t − b⎞ y (t ) φ∗ ⎛ dt ⎝ a ⎠
(2)
where y(t) denotes the TOFD signal; φ(t) and WTy (a,b) are the wavelet function and coefficients, respectively; parameters a and b are the wavelet scale and time shift, respectively and * represents a conjugate transpose. By changing the wavelet scale, the TOFD signals can be decomposed into a set of narrow-band signals, which alleviate the space–frequency dispersion considerably. As discussed, the reference signal is crucial to the separation and restoration of overlapping signals. However, its determination remains a critical barrier. To overcome this problem, we select sub-band signals with strong coherence because coherent signals are more alike in time and frequency domains. Any one of the coherent signals can serve as the reference signal. Thus, we use the coherence coefficient as the coherence metric.
where f and D are the central frequency and aperture size of the transmitter transducer, respectively; Cl is the acoustic velocity of longitudinal wave and F is the spread factor. Eq. (1) shows that the beam spread is frequency-dependent. As a qualitative illustration, we use a ray-trace model to investigate the space–frequency distribution of the TOFD waves. According to Snell’s law and Eq. (1), the spread angle is between [− sin−1 (CL sin(θp + γ )/ Cp) , sin−1 (CL sin(θp + γ )/ Cp) ], where θp is the incident angle and Cp and CL are the acoustic velocities of the longitudinal wave in the wedge and specimen, respectively. For clarity, the space–frequency distribution of the emission beam in a steel block is illustrated in Fig. 2. Here, the central frequency and aperture size of the transmitter transducer are 5 MHz and 6 mm, respectively. A plastic wedge, with an incident angle of 30°, is used. The figure shows that the low-frequency components have a large coverage, whereas the high-frequency components concentrate towards the acoustic axis. Thus, the TOFD signals, and thus the waveform, may vary in frequency as the defects can be arbitrarily located. For further confirmation, the space–frequency distribution of the measured TOFD signals is shown in Fig. 3. As predicted, the LW has a low central frequency as it is confined to the surface. On the contrary, the BE retains
C (ω) =
|Sxy (ω)|2 Sxx (ω) Syy (ω)
(3)
where Sxy (ω) is the cross-power spectra density and Sxx (ω) and Syy (ω) are the autospectral densities. Through Eq. (3), the coherence coefficients of the sub-band TOFD signals can be calculated at each scale. Then, the strongly coherent sub-band signals used for reconstruction can be adaptively selected by pre-setting a threshold. For convenience,
Fig. 9. (a) Measured TOFD image of the SDH, and that reconstructed with (b) proposed method, (c) conventional method. 178
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results are comparable with the reference values, and the relative errors are less than 5%, thereby providing a direct evidence that the proposed method can effectively deal with the TOFD measurement of small and shallow defects. Moreover, the signal-to-noise ratio (SNR) is also markedly increased. The figures indicate that the normalised amplitude of the LW using the proposed approach is nearly twice that obtained through conventional deconvolution. This is expected as more energy can be restored with the appropriate reference signal. This improvement is crucial to TOFD measurements in attenuative materials. Similarly, the proposed method can be applied to the TOFD image [Fig. 9(a)] by decomposing the image into a sequence of A-scan traces and then processing them individually. Based on this idea, the reconstructed TOFD image is illustrated in Fig. 9(b). Similarly, the deconvolved image using the conventional method is also shown in Fig. 9(c). The figures show that both deconvolution methods can improve temporal resolution and SNR and achieve a higher axial resolution than the raw image. Nevertheless, the proposed approach exhibits a better performance than the conventional one, which has a larger margin between the TOFD waves. Meanwhile, Fig. 9(b) shows that the edges are sharper, and the waveforms are narrower when the proposed approach is used, indicating that the proposed method can detect smaller defects at a shallower depth than the conventional method. However, the TOFD waves are acquired in the far-field region. According to the Rayleigh criterion, the detectable defect depth and size are limited to 0.61 λ where λ is the wavelength. As mentioned, the central frequency of the TOFD waves is ∼2 MHz when they are confined to the subsurface area. Thus, the wavelength is ∼2.95 mm with the CL being 5900 m/s. Accordingly, the proposed approach becomes unsuitable when either the defect depth or the defect size is smaller than 1.8 mm.
the LW is chosen as the reference signal in the following content. After the sub-band TOFD and reference signals are determined, Wiener filtering is applied to reconstruct the TOFD signal:
H ̂ (ω) =
Y (ω) X ∗ (ω) |X (ω)|2 + Q 2
(4)
where Y (ω) and X (ω) are the Fourier transforms of y(t) and x(t), respectively; Q is the noise-desensitising factor, which is set to Q = |X (ω)|max /10 with |X (ω)|max being the maximum amplitude [11]. The reconstructed signal with Wiener filtering is a narrowband. Thus, an AR model is employed to extrapolate the reconstructed signal: ⌢
⌢
H (ω) =
⎧ − ∑ip= 1 αib H (ω + iωs / N ), ⌢ ⎨− ∑ p α f H (ω − iωs / N ), i=1 i ⎩
0 ⩽ ω < ω1 ω2 < ω ⩽ ωs /2
(5)
ω1 and ω2 are the lower and upper bounds of the reconstructed sub-band signal; N is the number of sampling points with a sampling frequency of ωs ; αi f and αib are the forward and backward coefficients derived from the Burg method, respectively; and p is the order of the AR model. Finally, the extrapolated results are converted into time-domain signals by performing inverse Fourier transform. To summarise, the flowchart of the proposed adaptive deconvolution method is illustrated in Fig. 4. 3. Experiment As a proof-of-concept demonstration, the TOFD measurement of a small side-drilled hole (SDH) at a shallow depth is determined. Fig. 5 shows the experimental setup, which consists of a transducer pair (I5P6NF, Doppler Electronic Technologies, China), a pulser/receiver, a scanning stage, and a data acquisition system. The pulser/receiver is used for the emission, collection and preamplification of the ultrasonic signals, which are then sent to the computer for further analysis. The specimen is obtained from a steel block. The geometry is depicted in Fig. 6. The diameter and depth of the SDH are 2 and 8 mm, respectively. According to the specimen thickness, the transducers are separated by 65 mm. The scanning step for B-scan imaging is set to 0.5 mm. The testing process complies with the ASTM E2373-04 standards [19]. The raw ultrasonic TOFD signals are shown in Fig. 7(a). As expected, the LW and TDWs overlap with each other (blue dash rectangle) because of the small size and shallow depth of the SDH. The respective waves cannot be recognised as the signals are merged. Consequently, the defect size and location cannot be measured accurately. Then, we apply the proposed deconvolution method to the measured TOFD signals. To accommodate the Gaussian modulated pulse excitation, we adopt the Gaussian wavelet for the sub-band decomposition. Then, the coherence coefficients between the sub-band signals are calculated starting from scale 1 until they exceeded the threshold. Here, the coherence threshold is set to 0.8. Accordingly, the sub-band signals at scale 39 are selected, and their coherence coefficients are shown in Fig. 8. As expected, the coherent spectra are approximately 2 MHz, and this result confirms our assertion that the diverse spacefrequency distribution of TOFD signals is diverse. Thereafter, the subband TOFD signals are further processed with Wiener filtering and AR spectral extrapolation with a model order of (p = ) 16 [11]. For comparison, the reconstructed TOFD signals are shown in Fig. 7(b). As expected, the waveforms narrow, and the transition zones between the overlapping signals are deterministic, with which each TOFD wave can be confidently identified. For reference, the signals reconstructed with the conventional deconvolution method using Wiener filtering and spectral extrapolation are also shown in Fig. 7(c). Although the overlapping signals become less distorted, they remain merged and inseparable. For the quantitative evaluation of the proposed method, SDH size and depth are extracted. The results are listed in Table 1. The measured
4. Conclusions In this study, we propose an adaptive deconvolution method to accommodate the space-frequency dispersive characteristic of ultrasonic TOFD signals. The proposed method combines the wavelet decomposition and the well-established Wiener filtering and spectral extrapolation. The signals used for reconstruction and the reference signal for deconvolution are adaptively selected on the basis of the coherences of the TOFD signals, which are characterised by the coherence coefficient. The feasibility of the proposed method is validated by performing experiments on a small and shallow SDH. The results show that the overlapping TOFD waves can be effectively separated with deterministic transitions. The measured defect size and location coincide well with their actual values, with errors of less than 5%. Furthermore, after applying the proposed method to a TOFD image, we confirm that the axial resolution can be readily improved. Notably, a homogeneous specimen with a regularly shaped defect is used for the proof-of-concept demonstration. However, the applications in practical scenarios may be more complicated. Therefore, we will focus on the quantitation of irregular defects, such as cracks and notches, in future studies and consider material properties. Acknowledgment This work is supported by the National Natural Science Foundation of China project (Nos. 51675480 and 61401392). References [1] T.L. Teng, C. Fung, P. Chang, Effect of weld geometry and residual stresses on fatigue in butt-welded joints, Int. J. Press. Vessels Pip. 79 (2002) 467–482. [2] H.G. Brokmeier, Non-destructive evaluation of strain-stress and texture in materials science by neutrons and hard X-rays, Procedia Eng. 10 (2011) 1657–1662. [3] J. Schlichting, S. Brauser, L.A. Pepke, Ch. Maierhofer, M. Rethmeier, M. Kreutzbruck, Thermographic testing of spot welds, NDT&E Int. 48 (2012) 23–29. [4] G. Almeida, J. Gonzalez, L. Rosado, P. Vilaca, Telmo G. Santos, Advances in NDT
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[12] B. Shakibi, F. Honarvar, M.D.C. Moles, et al., Resolution enhancement of ultrasonic defect signals for crack sizing, NDT and E Int. 52 (2012) 37–50. [13] S. Mallat, Z. Zhang, Matching pursuit with time-frequency dictionaries, IEEE Trans. Signal Process. 41 (12) (1993) 3397–3415. [14] E. Mor, A. Azoulay, M. Aladjem, A matching pursuit method for approximating overlapping ultrasonic echoes, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 (9) (2010) 1996–2004. [15] R. Demirli, J. Saniie, Model-based estimation pursuit for sparse decomposition of ultrasonic echoes, IET Signal Proc. 6 (4) (2012) 313–325. [16] The British TOFD standard BS 7706, 5, 1993. [17] T. Mihara, Y. Otsuka, H. Cho, K. Yamanaka, Time-of-flight diffraction measurement using laser ultrasound, Exp. Mech. 46 (2006) 561–567. [18] J. Chen, X. Bai, K. Yang, B. Ju, An ultrasonic methodology for determining the mechanical and geometrical properties of a thin layer using a deconvolution technique, Ultrasonics 53 (7) (2013) 1377–1383. [19] ASTM -04, Standard Practice for Use of the Ultrasonic Time of Flight Diffraction (TOFD) Technique, ASTM International, 2004.
and materials characterization by eddy currents, Procedia CIRP 7 (2013) 359–364. [5] Z. Fan, A.F. Mark, M.J.S. Lowe, P.J. Withers, Nonintrusive estimation of anisotropic stiffness maps of heterogeneous steel welds for the improvement of ultrasonic array inspection, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62 (2015) 1530–1543. [6] J. Rao, M. Ratassepp, Z. Fan, Limited-view ultrasonic guided wave tomography using an adaptive regularization method, J. Appl. Phys. 120 (19) (2016) 194902. [7] M. Felice, Z. Fan, Sizing of flaws using ultrasonic bulk wave testing: a review, Ultrasonics 88 (2018) 26–42. [8] N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary time Series vol. 2, MIT Press, Cambridge, MA, 1949. [9] K. Jhang, H. Jang, B. Park, et al., Wavelet analysis based deconvolution to improve the resolution of scanning acoustic microscope images for the inspection of thin die layer in semiconductor, NDT and E Int. 35 (8) (2002) 549–557. [10] A. Abbate, J. Koay, J. Frankel, et al., Signal detection and noise suppression using a wavelet transform signal processor: application to ultrasonic flaw detection, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 14 (1) (1997) 4–25. [11] F. Honarvar, H. Sheikhzadeh, M. Moles, Improving the time-resolution and signalto-noise ratio of ultrasonic NDE signal, Ultrasonics 41 (9) (2004) 755–763.
180
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Enhancing ultrasonic time-of-flight diffraction measurement through an adaptive deconvolution method
T
⁎
Jian Chen, Eryong Wu , Haiteng Wu, Hongming Zhou, Keji Yang The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Time-of-flight diffraction Sub-band signals Wiener filtering and spectral extrapolation Adaptive deconvolution
Deconvolution is generally applied to improve the temporal resolution of ultrasonic signals. However, using this process in the time-of-flight diffraction (TOFD) measurement of small and shallow defects is challenging because TOFD signals are dispersive in space–frequency distribution. Particularly, determining the reference signal for deconvolution remains a critical barrier. To this end, an adaptive deconvolution method is proposed in this study. Using wavelet transform, we firstly decompose the TOFD signals into sub-band signals to standardise the space–frequency distribution. Then, sub-band signals with strong coherences are adaptively selected on the basis of coherence coefficient metric. Upon the opted sub-band signals, a lateral wave can be readily used as the reference signal, and TOFD signals can be reconstructed with established Wiener filtering and spectral extrapolation methods. The feasibility of the proposed method is validated with the TOFD measurement of a small side-drilled hole near the surface. Results show that the proposed method effectively separates overlapping TOFD signals and improves the axial resolution of a TOFD image.
1. Introduction Weldments are ubiquitous and play a significant role in various applications (e.g., airplanes, power plants, nuclear reactors and civil infrastructures). Thus, weldments are often subject to thorough inspection, evaluation and monitoring for quality and safety. Despite the considerable attention during design and fabrication, weldments are still prone to fail at weld-affected zones and thus show poor performance. Most failures are attributed to improper welding processes, residual stresses and operating parameters [1]. One of the routine methods for minimising failure is non-destructive testing (NDT), which ensures that welded regions are defect-free. Several NDT methods have been used [2–7], including ultrasonic time-of-flight diffraction (TOFD) technique, which has attracted increasing interest in recent years because of its radiation safety, high accuracy, fast speed and low cost and because it has considerably outperformed its radiographic counterpart. Although significant success has been achieved in ultrasonic TOFD testing, several challenges remain, especially in the inspection of small defects at shallow depths, which are commonly formed in welded components. Specifically, ultrasonic TOFD signals overlap with one another, causing difficulties in extracting useful information, especially time-of-flight. For this case, improving the temporal resolution of ultrasonic TOFD measurement is highly desired. Generally, the temporal
⁎
resolution of ultrasonic signals can be improved with deconvolution methods, which are either direct [8–12] and iterative [13–15]. For iterative deconvolution, Mor et al. [14] proposed a support matching pursuit concept for effectively separating two overlapping ultrasonic signals. However, this algorithm demands a complete set of dictionary atoms as a prerequisite. To address this problem, Demirli et al. [15] used a parametric mathematical model to describe the ultrasonic echoes, upon which the reference signal for deconvolution can be determined via maximum likelihood estimation. The iterative deconvolution method can generate higher resolution and better image contrast than its direct counterpart. However, these methods suffer low computation efficiency and poor real-time performance, hampering their widespread application in the industrial field. On the contrary, direct deconvolution can readily mitigate these limitations and is thus more popular in real-time applications. Thus, several algorithms have been employed for the direct deconvolution, such as Wiener filtering [8,9], wavelet analysis [10] and autoregressive (AR) spectral extrapolation [11]. However, these methods cannot be applied directly in ultrasonic TOFD measurements because, as discussed hereafter, TOFD signals are dispersive in space–frequency distribution. Consequently, determining the reference signal for deconvolution is difficult as diffracted waves may be retrieved from different paths, and no one-size-fits-all reference signal exists.
Corresponding author. E-mail address: [email protected] (E. Wu).
https://doi.org/10.1016/j.ultras.2019.01.009 Received 8 November 2018; Received in revised form 27 January 2019; Accepted 28 January 2019 Available online 29 January 2019 0041-624X/ © 2019 Elsevier B.V. All rights reserved.
Ultrasonics 96 (2019) 175–180
J. Chen et al.
Fig. 1. Schematic illustration of ultrasonic TOFD measurement.
Fig. 2. Space-frequency distribution of the probing beam in TOFD measurement.
Fig. 4. Flowchart of the proposed adaptive deconvolution method.
Fig. 5. Experimental setup for TOFD measurement.
To solve this problem, we propose an adaptive deconvolution method based on wavelet sub-band Wiener filtering and spectral extrapolation to separate overlapping TOFD signals. The raw signals are firstly wavelet-transformed into sub-bands, which are uniform in space–frequency distribution. Then, the sub-band signals with strong causalities are adaptively selected according to their metric of coherence coefficients. Any one of these strongly coherent signals can serve as the reference signal for deconvolution as they have the similar
Fig. 3. (a) Measured ultrasonic TOFD signals and (b) their space-frequency distributions.
176
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J. Chen et al.
Fig. 6. The geometry of the specimen.
waveform and spectrum. Finally, TOFD signals are reconstructed by applying Wiener filtering and spectral extrapolation. The proposed approach can enhance the temporal resolutions of TOFD signals, and thus the merged waves can be effectively separated to screen out small and shallow defects. The axial resolution of a TOFD image can also be enhanced by assembling deconvolved A-scan traces. The rest of this paper is organised as follows: In Section 2, the space–frequency characteristic of ultrasonic TOFD signals is discussed, and the implementation of adaptive deconvolution method is presented. In Section 3, the experiment conducted on ultrasonic TOFD measurement to validate the feasibility of the proposed method is presented. The conclusion is provided in Section 4.
Fig. 8. The coherence coefficient (a) between sub-band LW and TDWs and that (b) between TDWs and BE at scale 39.
Fig. 7. (a) Measured TOFD signals from the SDH, and that reconstructed with (b) proposed method, (c) conventional method. 177
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nearly all the frequency components. The spectra of the TDWs depend on their propagation paths, which are between those of the LW and BE. Under this condition, conventional deconvolution methods are ineffective for the TOFD measurement of small defects in a shallow depth as neither the measured reference signal nor the TOFD signal itself can work properly.
Table 1 Location and size of the SDH.
Reference Measured Error
Depth of upper tip
Depth of lower tip
Defect size
7 mm 7.325 mm 4.64%
9 mm 9.379 mm 4.21%
2 mm 2.054 mm 2.7%
2.2. Adaptive deconvolution method 2. Theory The deconvolution method based on Wiener filtering and spectral extrapolations has proven its capability in separating overlapping waves [18]. However, such method only works well when the ultrasonic wave does not change during propagation. Apparently, it cannot be employed directly in TOFD measurements. To address this issue, we develop an adaptive algorithm to deconvolve the TOFD signals by combining wavelet transform and conventional Wiener filtering and spectral extrapolation. Thus, the first step is to standardise the space–frequency distribution of the TOFD signals. Thus, we decompose them into their subbands using wavelet transform:
2.1. Space-frequency distribution of ultrasonic TOFD signals The principle of the conventional TOFD technique is depicted in Fig. 1 [16,17]. The transmitter transducer launches an ultrasonic wave into the specimen via a coupling wedge. The lateral wave (LW), the tipdiffracted waves (TDWs) and the backwall echo (BE) are then excited and detected by a receiver. The depth and size of the defect can be derived based on the time-of-flight between the LW and the top TDW and between two TDWs, respectively. For the TOFD measurement, the emission beam generally features a widespread angle, which can be evaluated by
γ=
sin−1 (Cl F / fD)
WTy (a, b) = < y (t ), φa, b (t ) > =
(1)
1 a
+∞
∫−∞
t − b⎞ y (t ) φ∗ ⎛ dt ⎝ a ⎠
(2)
where y(t) denotes the TOFD signal; φ(t) and WTy (a,b) are the wavelet function and coefficients, respectively; parameters a and b are the wavelet scale and time shift, respectively and * represents a conjugate transpose. By changing the wavelet scale, the TOFD signals can be decomposed into a set of narrow-band signals, which alleviate the space–frequency dispersion considerably. As discussed, the reference signal is crucial to the separation and restoration of overlapping signals. However, its determination remains a critical barrier. To overcome this problem, we select sub-band signals with strong coherence because coherent signals are more alike in time and frequency domains. Any one of the coherent signals can serve as the reference signal. Thus, we use the coherence coefficient as the coherence metric.
where f and D are the central frequency and aperture size of the transmitter transducer, respectively; Cl is the acoustic velocity of longitudinal wave and F is the spread factor. Eq. (1) shows that the beam spread is frequency-dependent. As a qualitative illustration, we use a ray-trace model to investigate the space–frequency distribution of the TOFD waves. According to Snell’s law and Eq. (1), the spread angle is between [− sin−1 (CL sin(θp + γ )/ Cp) , sin−1 (CL sin(θp + γ )/ Cp) ], where θp is the incident angle and Cp and CL are the acoustic velocities of the longitudinal wave in the wedge and specimen, respectively. For clarity, the space–frequency distribution of the emission beam in a steel block is illustrated in Fig. 2. Here, the central frequency and aperture size of the transmitter transducer are 5 MHz and 6 mm, respectively. A plastic wedge, with an incident angle of 30°, is used. The figure shows that the low-frequency components have a large coverage, whereas the high-frequency components concentrate towards the acoustic axis. Thus, the TOFD signals, and thus the waveform, may vary in frequency as the defects can be arbitrarily located. For further confirmation, the space–frequency distribution of the measured TOFD signals is shown in Fig. 3. As predicted, the LW has a low central frequency as it is confined to the surface. On the contrary, the BE retains
C (ω) =
|Sxy (ω)|2 Sxx (ω) Syy (ω)
(3)
where Sxy (ω) is the cross-power spectra density and Sxx (ω) and Syy (ω) are the autospectral densities. Through Eq. (3), the coherence coefficients of the sub-band TOFD signals can be calculated at each scale. Then, the strongly coherent sub-band signals used for reconstruction can be adaptively selected by pre-setting a threshold. For convenience,
Fig. 9. (a) Measured TOFD image of the SDH, and that reconstructed with (b) proposed method, (c) conventional method. 178
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results are comparable with the reference values, and the relative errors are less than 5%, thereby providing a direct evidence that the proposed method can effectively deal with the TOFD measurement of small and shallow defects. Moreover, the signal-to-noise ratio (SNR) is also markedly increased. The figures indicate that the normalised amplitude of the LW using the proposed approach is nearly twice that obtained through conventional deconvolution. This is expected as more energy can be restored with the appropriate reference signal. This improvement is crucial to TOFD measurements in attenuative materials. Similarly, the proposed method can be applied to the TOFD image [Fig. 9(a)] by decomposing the image into a sequence of A-scan traces and then processing them individually. Based on this idea, the reconstructed TOFD image is illustrated in Fig. 9(b). Similarly, the deconvolved image using the conventional method is also shown in Fig. 9(c). The figures show that both deconvolution methods can improve temporal resolution and SNR and achieve a higher axial resolution than the raw image. Nevertheless, the proposed approach exhibits a better performance than the conventional one, which has a larger margin between the TOFD waves. Meanwhile, Fig. 9(b) shows that the edges are sharper, and the waveforms are narrower when the proposed approach is used, indicating that the proposed method can detect smaller defects at a shallower depth than the conventional method. However, the TOFD waves are acquired in the far-field region. According to the Rayleigh criterion, the detectable defect depth and size are limited to 0.61 λ where λ is the wavelength. As mentioned, the central frequency of the TOFD waves is ∼2 MHz when they are confined to the subsurface area. Thus, the wavelength is ∼2.95 mm with the CL being 5900 m/s. Accordingly, the proposed approach becomes unsuitable when either the defect depth or the defect size is smaller than 1.8 mm.
the LW is chosen as the reference signal in the following content. After the sub-band TOFD and reference signals are determined, Wiener filtering is applied to reconstruct the TOFD signal:
H ̂ (ω) =
Y (ω) X ∗ (ω) |X (ω)|2 + Q 2
(4)
where Y (ω) and X (ω) are the Fourier transforms of y(t) and x(t), respectively; Q is the noise-desensitising factor, which is set to Q = |X (ω)|max /10 with |X (ω)|max being the maximum amplitude [11]. The reconstructed signal with Wiener filtering is a narrowband. Thus, an AR model is employed to extrapolate the reconstructed signal: ⌢
⌢
H (ω) =
⎧ − ∑ip= 1 αib H (ω + iωs / N ), ⌢ ⎨− ∑ p α f H (ω − iωs / N ), i=1 i ⎩
0 ⩽ ω < ω1 ω2 < ω ⩽ ωs /2
(5)
ω1 and ω2 are the lower and upper bounds of the reconstructed sub-band signal; N is the number of sampling points with a sampling frequency of ωs ; αi f and αib are the forward and backward coefficients derived from the Burg method, respectively; and p is the order of the AR model. Finally, the extrapolated results are converted into time-domain signals by performing inverse Fourier transform. To summarise, the flowchart of the proposed adaptive deconvolution method is illustrated in Fig. 4. 3. Experiment As a proof-of-concept demonstration, the TOFD measurement of a small side-drilled hole (SDH) at a shallow depth is determined. Fig. 5 shows the experimental setup, which consists of a transducer pair (I5P6NF, Doppler Electronic Technologies, China), a pulser/receiver, a scanning stage, and a data acquisition system. The pulser/receiver is used for the emission, collection and preamplification of the ultrasonic signals, which are then sent to the computer for further analysis. The specimen is obtained from a steel block. The geometry is depicted in Fig. 6. The diameter and depth of the SDH are 2 and 8 mm, respectively. According to the specimen thickness, the transducers are separated by 65 mm. The scanning step for B-scan imaging is set to 0.5 mm. The testing process complies with the ASTM E2373-04 standards [19]. The raw ultrasonic TOFD signals are shown in Fig. 7(a). As expected, the LW and TDWs overlap with each other (blue dash rectangle) because of the small size and shallow depth of the SDH. The respective waves cannot be recognised as the signals are merged. Consequently, the defect size and location cannot be measured accurately. Then, we apply the proposed deconvolution method to the measured TOFD signals. To accommodate the Gaussian modulated pulse excitation, we adopt the Gaussian wavelet for the sub-band decomposition. Then, the coherence coefficients between the sub-band signals are calculated starting from scale 1 until they exceeded the threshold. Here, the coherence threshold is set to 0.8. Accordingly, the sub-band signals at scale 39 are selected, and their coherence coefficients are shown in Fig. 8. As expected, the coherent spectra are approximately 2 MHz, and this result confirms our assertion that the diverse spacefrequency distribution of TOFD signals is diverse. Thereafter, the subband TOFD signals are further processed with Wiener filtering and AR spectral extrapolation with a model order of (p = ) 16 [11]. For comparison, the reconstructed TOFD signals are shown in Fig. 7(b). As expected, the waveforms narrow, and the transition zones between the overlapping signals are deterministic, with which each TOFD wave can be confidently identified. For reference, the signals reconstructed with the conventional deconvolution method using Wiener filtering and spectral extrapolation are also shown in Fig. 7(c). Although the overlapping signals become less distorted, they remain merged and inseparable. For the quantitative evaluation of the proposed method, SDH size and depth are extracted. The results are listed in Table 1. The measured
4. Conclusions In this study, we propose an adaptive deconvolution method to accommodate the space-frequency dispersive characteristic of ultrasonic TOFD signals. The proposed method combines the wavelet decomposition and the well-established Wiener filtering and spectral extrapolation. The signals used for reconstruction and the reference signal for deconvolution are adaptively selected on the basis of the coherences of the TOFD signals, which are characterised by the coherence coefficient. The feasibility of the proposed method is validated by performing experiments on a small and shallow SDH. The results show that the overlapping TOFD waves can be effectively separated with deterministic transitions. The measured defect size and location coincide well with their actual values, with errors of less than 5%. Furthermore, after applying the proposed method to a TOFD image, we confirm that the axial resolution can be readily improved. Notably, a homogeneous specimen with a regularly shaped defect is used for the proof-of-concept demonstration. However, the applications in practical scenarios may be more complicated. Therefore, we will focus on the quantitation of irregular defects, such as cracks and notches, in future studies and consider material properties. Acknowledgment This work is supported by the National Natural Science Foundation of China project (Nos. 51675480 and 61401392). References [1] T.L. Teng, C. Fung, P. Chang, Effect of weld geometry and residual stresses on fatigue in butt-welded joints, Int. J. Press. Vessels Pip. 79 (2002) 467–482. [2] H.G. Brokmeier, Non-destructive evaluation of strain-stress and texture in materials science by neutrons and hard X-rays, Procedia Eng. 10 (2011) 1657–1662. [3] J. Schlichting, S. Brauser, L.A. Pepke, Ch. Maierhofer, M. Rethmeier, M. Kreutzbruck, Thermographic testing of spot welds, NDT&E Int. 48 (2012) 23–29. [4] G. Almeida, J. Gonzalez, L. Rosado, P. Vilaca, Telmo G. Santos, Advances in NDT
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