An adaptive method for channel equalization in MFL inspection

ARTICLE IN PRESS

NDT&E International 40 (2007) 127–139 www.elsevier.com/locate/ndteint

An adaptive method for channel equalization in MFL inspection Yong Zhang, Zhongfu Ye, Xu Xu Institute of Statistical Signal Processing, University of Science and Technology of China, Hefei, Anhui 230027, China Received 17 January 2006; received in revised form 28 July 2006; accepted 6 September 2006 Available online 7 November 2006

Abstract Influenced by the lift-off value between the pipeline and coil sensors, the various properties of electronic component and the different location of coil sensor, the output signal’s amplitude and phase of each channel are different despite the same flaw in magnetic flux leakage (MFL) inspection. The channel-to-channel mismatch may severely degrade the performance of testing equipment and disturb the evaluation of the level of flaw unless some form of compensation is employed. In this paper an adaptive method for channel equalization in MFL inspection is presented by using the finite impulse response filter. Both theoretical analysis and experimental results have shown the effectiveness of the proposed method. r 2006 Published by Elsevier Ltd. Keywords: Magnetic flux leakage; Adaptive equalizer; Channel mismatch

1. Introduction Nondestructive evaluation of the seamless pipeline is most commonly performed by magnetic flux leakage (MFL) techniques [1]. An array of coil (or Hall) sensors is usually installed around the circumference of the pipeline to sense the leakage flux. Influenced by the lift-off value between the pipeline and coil sensors [2], the various properties of electronic component and the different location of coil sensors, the output signal’s amplitude and phase of each channel are different despite to the same flaw. We commonly call it channel-to-channel mismatch. The channel-to-channel mismatch may severely degrade the performance of testing equipment and disturb the evaluation of the level of flaw unless some form of compensation is employed. The conventional methods involving manual analysis are time consuming and the performances are subject to the level of skills and the training of analysts. Adaptive filtering as one of the important signal processing techniques has already been applied to NDT research such as identification [3], inverse modeling, prediction and interference canceling [4,5]. In this paper, Corresponding author. Tel.: +86 5513601314; fax: +86 5513601305.

E-mail address: [email protected] (Y. Zhang). 0963-8695/$ - see front matter r 2006 Published by Elsevier Ltd. doi:10.1016/j.ndteint.2006.09.004

adaptive filtering is introduced into the MFL evaluation of seamless pipeline. An efficient adaptive channel equalization method is proposed. First, the model of the MFL signal processing is set up. Then, the error function of each channel is obtained by comparing with the reference channel and FIR filters are designed by the Least Square error theory. Third, some experiments are conducted to validate the theoretical model. Finally, a realization scheme is given.

2. The model of MFL signal processing The conventional signal-processing diagram of MFL inspection is shown in Fig. 1. There are n+1 channels in the system. All these channels are assumed to be linear ones. We selected one channel as reference and the others are auxiliary channels. cref ðtÞ, ci ðtÞ and C ref ðjoÞ, Ci(jo) (i ¼ 1; 2;    ; n) are inherent time domain impulse response and frequency domain transfer function of the reference channel and auxiliary channels, respectively. Every channel includes coil sensor, amplifier, lowpass filter and A/D converter. The input signal of the reference channel and auxiliary channels is d(t) (signal d(t) will be introduced in Section 4.1). Signal y(t) and xi(t) (i ¼ 1; 2;    ; n) are the output of the reference channel and auxiliary channels,

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

128

… Coil sensor n

Coil sensor

Coil sensor 1

…

Amplifier

Amplifier 1

…

Amplifier n

Lowpass filter

Lowpass filter 1

…

Lowpass filter n

A/D converter

A/D converter 1

…

A/D converter n

MFL signal d(t)

Reference channel y(t)

Auxiliary channel n xn(t) …

Auxiliary channel 1 x1(t)

Fig. 1. The model of MFL signal processing.

...

C1(j)

Cref (j)

Cn (j)

x1(t)

y(t)

xn(t) H1(j)

Href (j)

MFL signal d(t)

...

+

Hn(j)

...

+

sn(t)

s1(t) Fig. 2. Diagram of the adaptive equalizer.

respectively, and satisfied with: xi ðtÞ ¼ dðtÞ  ci ðtÞ;

i ¼ 1; 2; . . . ; n,

yðtÞ ¼ dðtÞ  cref ðtÞ.

ð1Þ

In an ideal condition, all channels in the MFL system should have the same transfer function, which means the output signals of all channels are the same. So, we have yðtÞ ¼ x1 ðtÞ ¼ x2 ðtÞ ¼    ¼ xn ðtÞ.

H ref ðjoÞ is chosen to be an all-pass filter with a linear phase response. This is necessary to ensure that the delay through the reference channel will be the same as the delay through the auxiliary channel. In order to make the two channels output signal equivalent, we get relations as follows: C ref ðjoÞ  H ref ðjoÞ ¼ H i ðjoÞ  C i ðjoÞ;

i ¼ 1; 2; . . . ; n,

(2)

(3)

In fact, due to the lift-off variation of MFL sensors and the various properties of electronic component, each channel in the MFL system has different transfer functions. The mismatch may severely degrade the performance of testing equipment and disturb the evaluation of the level of flaw unless some form of compensation is employed.

The desired equalizer transfer function H i ðjoÞ of the ith channel is given by

3. The model and algorithm of the adaptive equalizer

H i ðjoÞ ¼

FIR equalizing filters are employed in each of the auxiliary channels to ensure the transfer function of each of the n+1 channels well matched. Fig. 2 shows the diagram of the adaptive equalizer. In Fig. 2, the signal s1(t) to the signal sn(t) is the desired post-processed signals.

The transfer function of Nth order FIR filter is expressed as follows:

C ref ðjoÞ  H ref ðjoÞ ¼

DFTðyref Þ . DFTðdÞ

C ref ðjoÞ H ref ðjoÞ; C i ðjoÞ

i ¼ 1; 2; . . . ; n.

(4)

(5)

N

HðjoÞ ¼ S hðkÞ expðjoðk  1ÞÞ. k¼1

(6)

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

The weighting coefficients h are chosen to minimize the vector norm

129

4. Experiment 4.1. The testing condition

M  X  W ðiÞ½aT ðoi Þh  Hðjoi Þ2 .

(7)

i¼1

The N  1 vector a(o) and h are defined by aðoÞ ¼ ½1; ejoD ; . . . ; ejoðN1ÞD T and h ¼ ½h1 ; h2 ; . . . ; hN T . The product aT ðoÞh is the frequency response of the adaptive equalizer. The weights thus chosen will minimize the Least Square error between the desired filter response and the actual response obtained. A diagonal weighting matrix W is a weighting matrix, which is related to the requirement of fitting accuracy in different frequencies. The optimization solution to Eq. (7) is expressed as follows: (8)

Rh ¼ P,

R¼

M X

rkl i ;

k; l ¼ 1; 2; . . . ; N,

i¼1

P¼

M X

rki Hðjoi Þ;

i¼1 joi

ri ¼ e

k ¼ 1; 2; . . . ; N,

.

ð9Þ

Considering Eqs. (1) and (3)–(5), the desired response value H^ i ðmÞ of the equalizer can be calculated at M discrete frequencies by taking the M-point discrete Fourier transform (DFT) of the sampled yref and xi sequences. DFTðyref Þ . H^ i ðmÞ ¼ DFTðxi Þ

(10)

Substitute H^ i ðmÞ with Hi(jo) ( H i ðmÞ ¼

H^ i ðM þ mÞ; H^ i ðmÞ;

 M2 pmo0 0pmp M2

;

The standard pipeline: The diameter, tube wall and length of specimen drill pipeline are 139.7 mm, 10.54 mm and 10 m, respectively. In the middle of the pipeline, along the radial direction, arranged at intervals of 200 mm and along the circumference direction, every 451, we drilled eight + 1.6 mm holes. Magnetization equipment: The magnetization equipment is a set of Helmholtz coils (Helmholtz coils could get a fairly uniform magnetic field by using a pair of circular coils on a common axis with equal currents flowing in the same sense). Its breadth and diameter are 100 and 600 mm. In every coil there are 5000 rounds. Fig. 3 shows the geometry in the 2D-model. The signal sample: There are eight coil sensors surrounding the pipeline’s circumference direction. When the pipeline is inspected through the equipment at a speed of 28 M/s, every artificial hole is situated on the center of the corresponding coil sensor. We set the signal sample rate to be 1000 Hz/s and sampled 64 points. In fact, there is a time delay between the MFL signals of different artificial holes. Considering the inspection speed and the interval between two holes, the time delay is about 0.42 s. For the sake of eliminating the influence of time delay, we selected the peak value of every hole’s MFL signal d(t) as the center. The input signal d(t) of every channel will be approximately equivalent. Based on the aforementioned testing condition, we applied the adaptive equalization algorithm to two sets of experimental (practical) data. They are different only in the magnetization current. The magnetization current of the first experiment is 1.2 A, the other is 1.02 A. In the first

i ¼ 1; 2; . . . ; n,

100mm 230mm

(11)

A

where m is the sample point number in the bandwidth to be equalized. We set the frequency response H ref ðjoÞ as standard; the mismatch characteristic of frequency response H i ðjoÞ is shown in Eq. (12). DðjoÞ ¼

H i ðjoÞ ¼ ½1 þ DHðjoÞ ejDfðoÞ ; H ref ðjoÞ

Define channel amplitude mismatch and phase mismatch: 1=2 Z 1 p 2 DH ¼ DH ðjoÞ do , 2p p   Z 1=2 p ____ 1 Df ¼ Df2 ðjoÞ do . 2p p

500mm

i ¼ 1; 2; . . . ; n. (12)

____

139.7mm



(13)

100mm Φ 1.6mm

Coil sensor

Pipeline wall

10.54mm

DETAIL A

(14) Fig. 3. 2-D model for testing.

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

130

Fig. 4. The reference signal y(t).

Fig. 5. The auxiliary signal x1(t).

experiment, we selected the reference signal y(t) and the auxiliary signal x1(t) for analyzing in detail and gave a quantitative assessment of how well the filtering worked. The order of the adaptive FIR filter has been also discussed, and then we gave the equalization results of other six auxiliary channels using the same process method. In the experiment two, we gave the whole channels equalization results to validate the effectiveness of the proposed method again.

The amplitude mismatch and phase mismatch____ of the first four ____ frequency components descended ____ ____ from DH ¼ 0:253 and Df ¼ 3:794 to DH  0 and Df  0 . The whole amplitude mismatch DHðoÞ and phase mismatch DjðoÞare compared in Figs. 7 and 8. The desired weighting coefficient h^ of the FIR filter is inverse FFT of H^ i ðmÞ, which can be calculated from Eq. (10) and is shown in Fig. 9. Fig. 10 shows the weighting coefficients h of the FIR filter when N ¼ 32 and 45. From Figs. 9 and 10 we know that the coefficient is not convergence to zero, which means that in order to get the best result the order of the FIR filter should set to be 64 in this paper. Using the same processing method, we got the equalization results of other six channels’ data. The original signals and post-processed signals are shown in the first column and the third column in Fig. 11, respectively. The original signals and post-processed signals are shown in the first column and the third column in Fig. 11, respectively. The second column shows the detail of the original signal, and

4.2. Experiment 1 The magnetization current is 1.2 A. The reference signal y(t) and auxiliary signal x1(t) are shown in Figs. 4 and 5. The parameters of equalizer are: BD ¼ 1, m ¼ M ¼ 64, the frequency band of equalization B ¼ 500 Hz, and we ignored the imaginary part of the result (the value of imaginary part far less than the value of real part). Fig. 6 shows the equalization result.

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 8. Phase mismatch comparison.

Fig. 6. The post-processed signal s1(t).

Fig. 9. The desired weighting coefficients.

Fig. 7. Amplitude mismatch comparison.

Fig. 10. The weighting coefficients in different orders.

131

ARTICLE IN PRESS 132

Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 11. The whole equalization effectiveness (the magnetization current is 1.2 A). (a) The equalization effectiveness of the second auxiliary channel, (b) the equalization effectiveness of the third auxiliary channel, (c) the equalization effectiveness of the fourth auxiliary channel, (d) the equalization effectiveness of the fifth auxiliary channel, (e) the equalization effectiveness of the sixth auxiliary channel, (f) the equalization effectiveness of the seventh auxiliary channel.

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 11. (Continued)

133

ARTICLE IN PRESS 134

Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 11. (Continued)

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

135

Fig. 12. The whole equalization effectiveness (the magnetization current is 1.02 A). (a) The signal of the reference channel, (b) the equalization effectiveness of the first auxiliary channel, (c) the equalization effectiveness of the second auxiliary channel, (d) the equalization effectiveness of the third auxiliary channel, (e) the equalization effectiveness of the fourth auxiliary channel, (f) the equalization effectiveness of the fifth auxiliary channel, (g) the equalization effectiveness of the sixth auxiliary channel, (h) the equalization effectiveness of the seventh auxiliary channel.

ARTICLE IN PRESS 136

Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 12. (Continued)

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 12. (Continued)

137

ARTICLE IN PRESS 138

Y. Zhang et al. / NDT&E International 40 (2007) 127–139

Fig. 12. (Continued)

ARTICLE IN PRESS Y. Zhang et al. / NDT&E International 40 (2007) 127–139

the fourth column shows the detail of the post-processed signal. 4.3. Experiment 2 The magnetization current is selected to be 1.02 A. The factor of the order of channel amplitude mismatch and phase mismatch is 104, which is sufficient for MFL inspection. The arrangement of Fig. 12 is the same as Fig. 11. 5. Conclusions 1. The channel-to-channel mismatch may severely degrade the performance of testing equipment and disturb the evaluation the level of the flaw. By using the adaptive channel equalizer we could reduce these influences. Both theoretical analysis and experimental results have shown the effectiveness of the proposed method. 2. The frequency of the MFL signal centralizes within 100 Hz, which is shown in Fig. 6. In order to shorten computing time, we could decrease the sample rate from 1000 to 500 Hz/s.

139

3. In practical inspections, the transfer function is calculated offline and stored in memory. At the beginning of the inspection, auxiliary channels have a corresponding time delay. The 64 sampled data were input to data buffer storage and multiplied by the transfer function and output repeated periodically.

References [1] Afzal M, Polikar R, Udpa L, Udpa S. Adaptive noise cancellation schemes for magnetic flux leakage signals obtained from gas pipeline inspection. Proceedings 2001 IEEE international conference on acoustics, speech, and signal processing 2001;6: 3389–92. [2] Katoh M, Masumoto N, Nishio K, Yamaguchi T. Modeling of the yoke-magnetization in MFL-testing by finite elements. NDT&E Int 2003;36:479–86. [3] Dadic´ M, Vasic´ D, Bilas V. A system identification approach to the modelling of pulsed eddy-current systems. NDT&E Int 2005;38: 107–11. [4] Zhang Y, Ye Z, Zhang L. Correlation canceling principle used in pipeline head inspection. NDT&E Int 2006;39:253–7. [5] Haykin S. Adaptive filter theory, third ed. Englewood Cliffs, NJ: Prentice-Hall; 1996. p. 18–9.