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Localization of defects in steam generator tubes using a multi-coil eddy current probe dedicated to high speed inspection
NDT&E International 35 (2002) 53±59
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Localization of defects in steam generator tubes using a multi-coil eddy current probe dedicated to high speed inspection P.-Y. Joubert*, Y. Le Bihan, D. Placko Laboratoire d'Electricite Signaux et Robotique, Ecole Normale SupeÂrieure de Cachan, 61 avenue du PreÂsident Wilson, 94235 Cachan Cedex, France Received 8 January 2001; revised 27 March 2001; accepted 12 April 2001
Abstract Steam generator (SG) tubing of pressurized water reactor in nuclear plants must be rapidly and accurately checked in order to detect defects in their early stages. In this paper, the authors present a multi-coil eddy current (EC) probe allowing both high speed inspection and circumferential localization of defects in the tube wall. A method of multi-coil EC signal processing, based on a continuous wavelet transform combined with a maximum likelihood diagnosis, is elaborated in order to enhance the detection performances and to provide automatic localization of defects. The inspection of SG tube samples shows good localization performances for defects as small as 10% deep, 15 mm long and 100 mm wide outer diameter notches, of both circumferential and axial orientations. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Steam generator tube; Defect localization; Eddy currents; Continuous wavelet transform; Maximum likelihood
1. Introduction The steam generator (SG) tubing of the pressurized water reactors (PWR) in nuclear power plants is routinely inspected to guarantee the safety of operations. Defects occurring in the SG tubes should be detected in their early stages so that proper remedial measures can be taken in time. The eddy current (EC) technique is widely applied to in-service inspection because of its ease of operation [1]. It is mostly performed with axial bobbin coil probes allowing high speed inspection. These probes are used in both absolute and differential modes. The absolute mode measurement is used to detect gradually varying defects, such as wall thinning resulting from corrosive wastage or tube to tube fretting [2]. Conversely, the differential mode measurement is sensitive to defects inducing abrupt variations (AV) of the tube properties, such as fatigue cracks or pitting corrosion, while resistant to anomalous effects, such as probe wobble or gradual variations of the tube wall. However, the axial probe sensitivity towards small circumferential defects is poor and no circumferential localization of defects is possible. These limitations are critical for the detection and characterization of AVs, and * Corresponding author. Tel.: 133-1-47-40-55-90; fax: 133-1-47-40-2199. E-mail address: [email protected] (P.-Y. Joubert).
therefore, pancake coil probes are used (in absolute or differential mode) as expertise tools in addition to standard axial probe inspection. These probes provide spatial localization thanks to a mechanical rotation. However, the use of such probes is very time-consuming and their spatial positioning is quite inaccurate [3]. To overcome the disadvantages encountered using conventional probes, the authors present a patented multi-coil probe [4], combining high speed inspection with a capability of circumferential localization. The probe shows separate emission and reception functions. It consists of an excitation device and a pickup coil set dedicated to the detection of AVs. In this study, it is implemented for the testing of different tube samples showing calibrated defects. The signals delivered by the pickup coil set are then processed in order to enhance the detection of small defects and to provide automatic positional information in the form of a binary map. The processing consists in a wavelet analysis combined with a maximum likelihood diagnosis. This paper focuses on the proposed probe and on the processing of the EC signals delivered by the pickup coil set. 2. Multi-coil probe and measurement data 2.1. Probe structure and principle of operation
0963-8695/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0963-869 5(01)00026-3
The structure of the probe derives from a conventional
54
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59 Bobbin coils
Iexc
P.C.
V2 V1 Tube
Demux 16 to 1
SG tube Sample
Pickup coil set
ei
Fig. 1. Multi-coil EC probe scanning SG tube.
axial probe (Fig. 1), for which the two axial bobbin coils are fed in phase. Therefore, conventional EC signals can be obtained through the measurement of the voltages induced across the two bobbin coils [2], V1 (absolute measurement) and V1 ±V2 (differential measurement), as shown in Fig. 1. The originality of the probe lies in an additional pickup coil set. The pickup coils are equidistantly distributed around the circumference of a disk placed between the two bobbin coils, each pickup coil facing the tube wall as shown in Fig. 1. The bobbin coils are used as an excitation device, and the pickup coil set is used to sample the radial component of the magnetic ®eld along the circumference of the tube wall. In absence of variation of the tube wall properties, the radial component of the magnetic ®eld is null on the median plane situated between the two bobbin coils, thus no electromotive force (EMF) is induced across the pickup coils. On the contrary, any AV in the tube wall causes a local unbalance of the magnetic ®eld distribution depending on the relative position of the excitation coils to the AV. The unbalance induces the apparition of a non-zero EMF ei across the pickup coils (Fig. 1) situated in the vicinity of the AV. As the probe scans the tube, the simultaneous measurement of the EMF across all the pickup coils provides EC signals which can be represented in the form of a 2D map providing positional information about the AVs. The EC signals relative to the AVs are called AV signatures in the following. 2.2. Probe prototype and experimental set-up A probe prototype was designed for the inspection of the SG tubes of 900 MW PWR. These tubes are made of Inconel 600, a nickel based alloy featuring a 10 6 S/m electrical conductivity and a 1.01 relative permeability. The tubes have a 22.22 mm outside diameter (OD) and a wall thickness of 1.27 mm. The probe features a 16 pickup coil set, providing a 22.58 circumferential sampling step of the magnetic ®eld. The pickup coils are 86 turns wound coils of 1 mm mean diameter and 1.4 mm length. The probe was implemented in the laboratory for the testing of calibrated SG tube samples thanks to a computer controlled data acquisition system organized as depicted in Fig. 2. Feeding the two excitation bobbin coils in phase with an excitation current Iexc (Fig. 1), the EC signals are obtained through a 16 to 1 demultiplexer board thanks to the measurement of the trans-impedance ei /Iexc by the means
Robot
Probe holder
Impedance gain/phase analyser HP 4194A
Fig. 2. Schematic of the acquisition system.
of a 4194A impedance analyser (Fig. 2). The probe is moved into the tested tube sample by the means of a single axis robot, providing a 1 mm axial sampling step. 2.3. Measurement data First evaluation of the probe was performed on four tube samples t1±t4, containing calibrated notches obtained by electrical discharge machining. All the notches are 15 mm long and 100 mm wide. They are inside diameter (ID) or OD notches with different depths and orientations as described in Table 1. Circumferentially oriented notches constitute the worst case for detection with the given excitation device (axial bobbin coils) because of the circumferential ¯ow of the EC in the tube wall. The testing of the tube samples was performed at a 240 kHz excitation frequency, which is the analysis frequency dedicated to 900 MW PWR tube testing [5]. Indeed, this frequency is chosen for phase shift difference between ID and OD events of 908, which eases the distinction between inner and outer defects, considering the real and imaginary parts of the complex EC signals provided by the probe. For tube samples t1±t4, the complex EC signals obtained with the pickup coil set are shown in Figs. 3±6, respectively. According to the chosen frequency and phase shift reference, OD events are mainly observable on the real part of the EC signals, and ID events on the imaginary part. The probe being sensitive to AVs, only the extremities of the notches are observable in the case of axially oriented notches. For the four tube samples, the deepest ID or OD notches (40±100%) are clearly visible and well localized in both axial and circumferential directions. However, the smallest notches (10 and 20% deep) are hardly
Table 1 Tubes samples and calibrated notches Tube samples
Calibrated notches
t1 t2 t3 t4
OD, circumferential 100, 60, 40, 20 and 10% deep ID, circumferential 60, 40, 20 and 10% deep OD, axial 60, 40, 20 and 10% deep ID, axial 100, 60, 40, 20 and 10% deep
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
55
Circumference 0-360˚
60% OD
100% 20% OD OD
10% OD
Axial position (mm)
Length : 270mm
40% OD
50
50
50
100
100
100
150
150
150
200
200
200
250
250
250
5
10
15
5
10
15
5
10
15
N˚ of pick up coil
a)
b) real part
c) imag. part
d)
Fig. 3. Tube sample t1 (circumferential OD notches): (a) notch positions, (b,c) raw complex EC signal maps and (d) notch localization.
3. Enhancement of EC signals using continuous wavelet transform
observable, especially in the case of circumferential notches. This is due mainly to the fabrication process of the tube (pilgering) which creates inner deformations in the tube wall, inducing high magnitude noise (pilgering noise) [5], which particularly affects the imaginary part of the EC signals. Therefore, a signal processing is necessary to enhance the detection and localization of the smallest defects.
As shown in the raw EC signals (Figs. 3±6), the pilgering noise mainly induces low spatial frequency signals. On the contrary, AVs, such as notches, induce signatures with high spatial frequency contents. It seems therefore natural to turn to time/frequency, that is to say space/spatial-frequency,
Circumference 0-360˚
60% ID
20% ID
10% ID
Axial position (mm)
Length : 270mm
40% ID
50
50
50
100
100
100
150
150
150
200
200
200
250
250
250
5
10
15
5
10
15
5
10
15
N˚ of pick up coil
a)
b) real part
c) imag. part
d)
Fig. 4. Tube sample t2 (circumferential ID notches): (a) notch positions (b,c) raw complex EC signal maps, and (d) notch localization.
56
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
Circumference 0-360˚
50
50
50
100
100
100
150
150
150
200
200
200
250
250
250
60% OD
20% OD
Axial position (mm)
Length : 270mm
40% OD
10% OD
5
10
15
5
10
15
5
10
15
N˚ of pick up coil
a)
b) real part
c) imag. part
d)
Fig. 5. Tube sample t3 (axial OD notches): (a) notch positions (b,c) raw complex EC signal maps, and (d) notch localization.
functions c a;b x according to Eq. (1): Z1 1 p s xc a;b x dx Ws a; b
processing to highlight the AV signatures. Among the existing techniques, the continuous wavelet transform (CWT) is particularly well suited to the analysis of AVs [6], especially in the case of tube testing [7,8]. Let us consider the EC signal s x provided by a pickup coil. The CWT of s x consists in the projection of s x on a set of analysing
21
where a denotes the scale parameter (or dilatation parameter) and b denotes the spatial shift parameter [9].
Circumference 0-360˚
50
50
50
100
100
100
150
150
150
200
200
200
250
250
250
100% ID
60% ID
Axial position (mm)
Length : 270mm
10% ID
20% ID 40% ID
5
10
15
5
10
15
5
10
15
N˚ of pick up coil
a)
b) real part
1
c) imag. part
d)
Fig. 6. Tube sample t4 (axial ID notches): (a) notch positions (b,c) raw complex EC signal maps, and (d) notch localization.
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59 x 10
mainly horizontal pattern. In order to quantify the noise in¯uence at each scale of the CWT, we de®ne a signal to noise ratio (SNR) per scale as given below: X uWd a; bu2 kn b 3 SNR a X 2 k uWn a; bu d
-3
5
60% ID
real part
0
40% ID
60% ID
20% ID
40% ID
10% ID
20% ID
10% ID
-5 0
50
100
150
200
250
Axial position (mm) x 10
-3
5
60% ID
imaginary part
20% ID
40% ID
10% ID
b
0
-5 0
50
100
150
200
250
Axial position (mm)
Fig. 7. One pickup coil raw complex EC signal (tube t2).
The whole set of these functions (wavelets) is generated from a mother wavelet c x according to Eq. (2): 1 x2b c a;b x p c 2 a a The wavelet set features imply a particular space/ frequency localization of the wavelet transformed signal. This localization is optimized with Morlet wavelets because of their gaussian envelope [10]. The energy density 2 uWs a; bu , called scalogram [9], exhibits a good spatial localization (and poor frequency localization) in the high spatial frequencies (low scales) and a good frequency localization (and poor spatial localization) in the low spatial frequencies (high scales). Consequently, a good spatial localization of the AV signature is provided in the high frequency contents of the scalogram. As an illustration, let us consider the EC signal obtained by a single pickup coil facing the notches while scanning the tube sample t2 (Fig. 7). The corresponding scalogram was computed and is shown in Fig. 8. Four vertical patterns appear clearly in the high frequency contents of the scalogram (low scales) with good spatial resolution and correspond to the positions of the AVs (four circumferential ID notches). On the contrary, the low spatial frequency contents (high scales) correspond mainly to the pilgering noise and exhibit a 500
where Wn a; b is the CWT of the noise n provided by experimental measurements in sound tube samples, and Wd a; b is the CWT of the defect signature d provided by ®nite element (FE) computations which was carried out to build a defect signature database [11]. The parameters kd and kn, respectively, denote the sample number of d and n used for calculation. As an example, the SNR is calculated for a 10% ID notch and is represented vs. scale in Fig. 9. The SNR exhibits a maximum value at scale a 5 of the CWT. The result of the scale a 5 CWT of the EC signal shown in Fig. 7 is presented in Fig. 10, and show the enhancement of the four ID notch signatures (apart from the edge effects due to the truncation of the EC signals). Similar results are obtained for the other considered AVs, i.e. for the ID and OD notches of both orientations. Therefore, this single scale is selected to facilitate the detection of AVs. The CWT is applied to the EC signals provided by the 16 pickup coils in what follows. 4. Defect detection and localization using maximum likelihood decision 4.1. Defect detection principle The detection of defects is based on a maximum likelihood decision, applied to the CWT at scale a 5 of the EC signal s. The problem lies in the estimation of the binary diagnosis parameter u which equals 0 when no defect is present, and which equals 1 when a defect is present. The maximum likelihood decision lies in the evaluation of the likelihood function L(u ) de®ned as [12]: L u f Suu
4
2 60% ID
40% ID
20% ID
10% ID
30
400
20
2,5
3,33
200
5
100
10
SNR(a) (dB)
10
300
scales
Spatial frequenciesy (m-1)
57
0 -10
a=5
-20
Frequency (m-1)
-30
0 0
50
100
150
200
250
Axial position (mm) Fig. 8. Scalogram of the EC signals shown in Fig. 7.
-40
20
500
400
300
200
100
200
2
2,5
3,33
5
10
Scale
Fig. 9. SNR vs. scale of the WT (for a 10% IN).
0 20
200
58
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
Fig. 10. Modulus of the CWT at scale a 5 of the EC signal shown in Fig. 7.
where S {uWs 5; bu2 } is a data vector constituted of k consecutive samples of uWs 5; bu2 , where k is the sample number constituting the spatial support of the AV signature along the axial direction, and f Suu is the probability distribution function of S given u . De®ning the likelihood ratio as follows, LR
L 1 L 0
5
the detection is expressed by the following decision rule:
u 1 if LR $ 1 presence of defect
6
4.3. Defect localization The detection rule given in Eq. (6), using Eqs. (9) and (10) allows one to de®ne defective areas. In each defective area, the most likely position of the AVs corresponds to the LR local maxima. Therefore, the determination of the AV position in the defective area was achieved thanks to the modi®ed decision rule, which reads as follows:
u 1 if LR $ 1 and LR is a local maximum u 0 in other cases
11
u 0 if LR , 1 absence of defect 5. Application to defect localization in notched tube samples
4.2. Determination of the likelihood function Let us de®ne n as the measurement data in absence of defect, and N {uWn 5; bu2 } the noise vector constituted of 2 k consecutive samples of uWn 5; bu . The distribution func2 tion of uWn 5; bu can be approximated with the x -squared distribution of 2 degrees of freedom x 2(2) as follows[13]: ! a auWn 5; bu2 2 fn uWn 5; bu exp 2 7 2 2 where a is a ranging parameter depending on the amplitude 2 of uWn 5; bu . Assuming the independence of the samples of N, the distribution function of N is given by k a a sum N fN N exp 2 8 2 2 where sum(N) denotes the summation of the k elements of N. In the absence of defect S N; therefore the likelihood L(0) is expressed by L 0 f Su0 fN S
9
On the contrary, in the presence of defect, the signal is 2 expressed by S N 1 D; where D {uWd 5; bu } stands for the CWT signature vector relative to the defect d to be detected. Then, the likelihood L 1 is given by L 1 f Su1 fN S 2 D
10
The localization method was implemented to the testing of the tube samples. Considering the fact that the worst case of AV localization corresponds to a 10% OD circumferential notch, we assigned to D the 10% OD circumferential notch signature provided by FE computation and CWT. Since the other considered AVs show similar signatures with greater SNR, they should be therefore easier to localize. The likelihood ratio was calculated thanks to Eqs. (9) and (10), and the decision rule thanks to Eq. (11). The AV localization results are shown in Figs. 3c±6c in the form of binary maps where white coloured pixels correspond to u 0 (no AV) and black pixels for u 1 (presence of AV). For the considered tube samples, all the notches were properly detected and localized without false alarm. The obtained localization error is less than 5 mm in the axial direction and 22.58 in the circumferential direction. In the case of axially oriented notches, only the extremities of the actual defects are localized (Figs. 5c and 6c.). This can lead to confusion between one axial defect and two short circumferential defects. However, this ambiguity can be overcome thanks to the EC signals provided by the bobbin coils used in absolute measurement mode (see Section 2.1). In the case of circumferential notches (Figs. 3c and 4c), the obtained AV localization results correspond to the actual shape and position of the notches. The smallest notch (10% OD notch, Fig. 3c.) is localized with a lower
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
circumferential resolution because of the poor SNR of the corresponding signature. 6. Conclusion In the presented work, a multi-coil EC probe was designed and implemented for the inspection of PWR SG tubing. This probe combines high speed inspection with a capability of circumferential localization of defects inducing AV in the tube wall properties. A processing of the multi-coil EC signals, based on a CWT combined with a maximum likelihood diagnosis, was proposed in order to enhance the sensitivity towards small defects and to provide automatic defect localization. The inspection of SG tube samples containing calibrated notches shows 5 mm/22.58 spatial localization performances for defects of size down to 10% deep, 15 mm long and 100 mm wide notches. The circumferential localization of the defects could be increased with the number of pickup coils, and a 32 pickup coil prototype is under fabrication. The proposed localization method gives positional and extent information about the defects. The method could be extended to a defect classi®cation thanks to the numerical or experimental elaboration of an enlarged defect signature database. Acknowledgements This work was supported by Framatome (France). The authors thank M.M.E. Savin, B. Sartre and L. Legrandjacques from the Framatome technical centre, for assistance.
59
References [1] Birring AS. Selection of NDT techniques for inspection of heat exchanger tubing. Proceedings of the ASNT International Conference on Petroleum Industry Inspection, Houston, TX: ASNT, 1999. p. 1±14. [2] Sullivan SP, Smith SP, Sharp FL. Simultaneous absolute and differential operation of eddy current bobbin probes for heat exchange tube inspection. Mat Eval 2000;58(5):634±8. [3] Sollier T, Schepens H, Benoist B, Reuchet J. First evaluation of the Set (rotating excitation) EC probe designed for fast SG tubing inspection. Proceedings of the 7th European Conference on Nondestructive Testing, Copenhagen, Denmark: ECNDT, 1998. p. 1339±46. [4] Dehan C, Joubert PY, Miller D, Placko D, Savin E. Sonde aÁ courants de Foucault pour le controÃle non destructif de la paroi d'un tube et proceÂde de traitement des signaux de la sonde, 1999. World patent WO9904253. [5] Benoist B, Gaillard P, Pigeon M, Morizet-Mahoudeaux P. Expert system for the characterisation of defect signal in steam generator tubes. Engng Appl Artif Intell 1995;8(3):309±18. [6] Chabert M, Tourneret JY, Castanie F. Additive and multiplicative jump detection using continuous wavelet transform, Proceedings of the ICASSP'96. Atlanta, GA: IEEE, 1996. p. 3002±5. [7] Chen G, Yamaguchi A, Miya K. Signal processing for defects from composite eddy current signals. Insight 1997;39(11):785±9. [8] Chuang SF, Basart J, Moulder J. The application of wavelets and fuzzy logic to eddy current ¯aw detection in steam generator tubes. QNDE 1998;17:775±81. [9] Mallat S. A wavelet tour of signal processing. New York: Academic Press, 1998. [10] Flandrin P. Temps/freÂquence. Paris: HermeÁs, 1993. [11] Joubert PY. Contribution to the design of an eddy current sensor and to the corresponding signal processing for the NDT of steam generator tubes. PhD Thesis. Universite de Paris XI, 1999. [12] Rao CR. Linear statistical inference and its applications. New York: Wiley, 1965. [13] Grimmett GR, Stirzaker DR. Probability and random process. Oxford: Oxford University Press, 1992.
www.elsevier.com/locate/ndteint
Localization of defects in steam generator tubes using a multi-coil eddy current probe dedicated to high speed inspection P.-Y. Joubert*, Y. Le Bihan, D. Placko Laboratoire d'Electricite Signaux et Robotique, Ecole Normale SupeÂrieure de Cachan, 61 avenue du PreÂsident Wilson, 94235 Cachan Cedex, France Received 8 January 2001; revised 27 March 2001; accepted 12 April 2001
Abstract Steam generator (SG) tubing of pressurized water reactor in nuclear plants must be rapidly and accurately checked in order to detect defects in their early stages. In this paper, the authors present a multi-coil eddy current (EC) probe allowing both high speed inspection and circumferential localization of defects in the tube wall. A method of multi-coil EC signal processing, based on a continuous wavelet transform combined with a maximum likelihood diagnosis, is elaborated in order to enhance the detection performances and to provide automatic localization of defects. The inspection of SG tube samples shows good localization performances for defects as small as 10% deep, 15 mm long and 100 mm wide outer diameter notches, of both circumferential and axial orientations. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Steam generator tube; Defect localization; Eddy currents; Continuous wavelet transform; Maximum likelihood
1. Introduction The steam generator (SG) tubing of the pressurized water reactors (PWR) in nuclear power plants is routinely inspected to guarantee the safety of operations. Defects occurring in the SG tubes should be detected in their early stages so that proper remedial measures can be taken in time. The eddy current (EC) technique is widely applied to in-service inspection because of its ease of operation [1]. It is mostly performed with axial bobbin coil probes allowing high speed inspection. These probes are used in both absolute and differential modes. The absolute mode measurement is used to detect gradually varying defects, such as wall thinning resulting from corrosive wastage or tube to tube fretting [2]. Conversely, the differential mode measurement is sensitive to defects inducing abrupt variations (AV) of the tube properties, such as fatigue cracks or pitting corrosion, while resistant to anomalous effects, such as probe wobble or gradual variations of the tube wall. However, the axial probe sensitivity towards small circumferential defects is poor and no circumferential localization of defects is possible. These limitations are critical for the detection and characterization of AVs, and * Corresponding author. Tel.: 133-1-47-40-55-90; fax: 133-1-47-40-2199. E-mail address: [email protected] (P.-Y. Joubert).
therefore, pancake coil probes are used (in absolute or differential mode) as expertise tools in addition to standard axial probe inspection. These probes provide spatial localization thanks to a mechanical rotation. However, the use of such probes is very time-consuming and their spatial positioning is quite inaccurate [3]. To overcome the disadvantages encountered using conventional probes, the authors present a patented multi-coil probe [4], combining high speed inspection with a capability of circumferential localization. The probe shows separate emission and reception functions. It consists of an excitation device and a pickup coil set dedicated to the detection of AVs. In this study, it is implemented for the testing of different tube samples showing calibrated defects. The signals delivered by the pickup coil set are then processed in order to enhance the detection of small defects and to provide automatic positional information in the form of a binary map. The processing consists in a wavelet analysis combined with a maximum likelihood diagnosis. This paper focuses on the proposed probe and on the processing of the EC signals delivered by the pickup coil set. 2. Multi-coil probe and measurement data 2.1. Probe structure and principle of operation
0963-8695/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0963-869 5(01)00026-3
The structure of the probe derives from a conventional
54
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59 Bobbin coils
Iexc
P.C.
V2 V1 Tube
Demux 16 to 1
SG tube Sample
Pickup coil set
ei
Fig. 1. Multi-coil EC probe scanning SG tube.
axial probe (Fig. 1), for which the two axial bobbin coils are fed in phase. Therefore, conventional EC signals can be obtained through the measurement of the voltages induced across the two bobbin coils [2], V1 (absolute measurement) and V1 ±V2 (differential measurement), as shown in Fig. 1. The originality of the probe lies in an additional pickup coil set. The pickup coils are equidistantly distributed around the circumference of a disk placed between the two bobbin coils, each pickup coil facing the tube wall as shown in Fig. 1. The bobbin coils are used as an excitation device, and the pickup coil set is used to sample the radial component of the magnetic ®eld along the circumference of the tube wall. In absence of variation of the tube wall properties, the radial component of the magnetic ®eld is null on the median plane situated between the two bobbin coils, thus no electromotive force (EMF) is induced across the pickup coils. On the contrary, any AV in the tube wall causes a local unbalance of the magnetic ®eld distribution depending on the relative position of the excitation coils to the AV. The unbalance induces the apparition of a non-zero EMF ei across the pickup coils (Fig. 1) situated in the vicinity of the AV. As the probe scans the tube, the simultaneous measurement of the EMF across all the pickup coils provides EC signals which can be represented in the form of a 2D map providing positional information about the AVs. The EC signals relative to the AVs are called AV signatures in the following. 2.2. Probe prototype and experimental set-up A probe prototype was designed for the inspection of the SG tubes of 900 MW PWR. These tubes are made of Inconel 600, a nickel based alloy featuring a 10 6 S/m electrical conductivity and a 1.01 relative permeability. The tubes have a 22.22 mm outside diameter (OD) and a wall thickness of 1.27 mm. The probe features a 16 pickup coil set, providing a 22.58 circumferential sampling step of the magnetic ®eld. The pickup coils are 86 turns wound coils of 1 mm mean diameter and 1.4 mm length. The probe was implemented in the laboratory for the testing of calibrated SG tube samples thanks to a computer controlled data acquisition system organized as depicted in Fig. 2. Feeding the two excitation bobbin coils in phase with an excitation current Iexc (Fig. 1), the EC signals are obtained through a 16 to 1 demultiplexer board thanks to the measurement of the trans-impedance ei /Iexc by the means
Robot
Probe holder
Impedance gain/phase analyser HP 4194A
Fig. 2. Schematic of the acquisition system.
of a 4194A impedance analyser (Fig. 2). The probe is moved into the tested tube sample by the means of a single axis robot, providing a 1 mm axial sampling step. 2.3. Measurement data First evaluation of the probe was performed on four tube samples t1±t4, containing calibrated notches obtained by electrical discharge machining. All the notches are 15 mm long and 100 mm wide. They are inside diameter (ID) or OD notches with different depths and orientations as described in Table 1. Circumferentially oriented notches constitute the worst case for detection with the given excitation device (axial bobbin coils) because of the circumferential ¯ow of the EC in the tube wall. The testing of the tube samples was performed at a 240 kHz excitation frequency, which is the analysis frequency dedicated to 900 MW PWR tube testing [5]. Indeed, this frequency is chosen for phase shift difference between ID and OD events of 908, which eases the distinction between inner and outer defects, considering the real and imaginary parts of the complex EC signals provided by the probe. For tube samples t1±t4, the complex EC signals obtained with the pickup coil set are shown in Figs. 3±6, respectively. According to the chosen frequency and phase shift reference, OD events are mainly observable on the real part of the EC signals, and ID events on the imaginary part. The probe being sensitive to AVs, only the extremities of the notches are observable in the case of axially oriented notches. For the four tube samples, the deepest ID or OD notches (40±100%) are clearly visible and well localized in both axial and circumferential directions. However, the smallest notches (10 and 20% deep) are hardly
Table 1 Tubes samples and calibrated notches Tube samples
Calibrated notches
t1 t2 t3 t4
OD, circumferential 100, 60, 40, 20 and 10% deep ID, circumferential 60, 40, 20 and 10% deep OD, axial 60, 40, 20 and 10% deep ID, axial 100, 60, 40, 20 and 10% deep
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
55
Circumference 0-360˚
60% OD
100% 20% OD OD
10% OD
Axial position (mm)
Length : 270mm
40% OD
50
50
50
100
100
100
150
150
150
200
200
200
250
250
250
5
10
15
5
10
15
5
10
15
N˚ of pick up coil
a)
b) real part
c) imag. part
d)
Fig. 3. Tube sample t1 (circumferential OD notches): (a) notch positions, (b,c) raw complex EC signal maps and (d) notch localization.
3. Enhancement of EC signals using continuous wavelet transform
observable, especially in the case of circumferential notches. This is due mainly to the fabrication process of the tube (pilgering) which creates inner deformations in the tube wall, inducing high magnitude noise (pilgering noise) [5], which particularly affects the imaginary part of the EC signals. Therefore, a signal processing is necessary to enhance the detection and localization of the smallest defects.
As shown in the raw EC signals (Figs. 3±6), the pilgering noise mainly induces low spatial frequency signals. On the contrary, AVs, such as notches, induce signatures with high spatial frequency contents. It seems therefore natural to turn to time/frequency, that is to say space/spatial-frequency,
Circumference 0-360˚
60% ID
20% ID
10% ID
Axial position (mm)
Length : 270mm
40% ID
50
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250
250
5
10
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5
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5
10
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N˚ of pick up coil
a)
b) real part
c) imag. part
d)
Fig. 4. Tube sample t2 (circumferential ID notches): (a) notch positions (b,c) raw complex EC signal maps, and (d) notch localization.
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P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
Circumference 0-360˚
50
50
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60% OD
20% OD
Axial position (mm)
Length : 270mm
40% OD
10% OD
5
10
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5
10
15
5
10
15
N˚ of pick up coil
a)
b) real part
c) imag. part
d)
Fig. 5. Tube sample t3 (axial OD notches): (a) notch positions (b,c) raw complex EC signal maps, and (d) notch localization.
functions c a;b x according to Eq. (1): Z1 1 p s xc a;b x dx Ws a; b
processing to highlight the AV signatures. Among the existing techniques, the continuous wavelet transform (CWT) is particularly well suited to the analysis of AVs [6], especially in the case of tube testing [7,8]. Let us consider the EC signal s x provided by a pickup coil. The CWT of s x consists in the projection of s x on a set of analysing
21
where a denotes the scale parameter (or dilatation parameter) and b denotes the spatial shift parameter [9].
Circumference 0-360˚
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Axial position (mm)
Length : 270mm
10% ID
20% ID 40% ID
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5
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15
N˚ of pick up coil
a)
b) real part
1
c) imag. part
d)
Fig. 6. Tube sample t4 (axial ID notches): (a) notch positions (b,c) raw complex EC signal maps, and (d) notch localization.
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59 x 10
mainly horizontal pattern. In order to quantify the noise in¯uence at each scale of the CWT, we de®ne a signal to noise ratio (SNR) per scale as given below: X uWd a; bu2 kn b 3 SNR a X 2 k uWn a; bu d
-3
5
60% ID
real part
0
40% ID
60% ID
20% ID
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10% ID
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5
60% ID
imaginary part
20% ID
40% ID
10% ID
b
0
-5 0
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Axial position (mm)
Fig. 7. One pickup coil raw complex EC signal (tube t2).
The whole set of these functions (wavelets) is generated from a mother wavelet c x according to Eq. (2): 1 x2b c a;b x p c 2 a a The wavelet set features imply a particular space/ frequency localization of the wavelet transformed signal. This localization is optimized with Morlet wavelets because of their gaussian envelope [10]. The energy density 2 uWs a; bu , called scalogram [9], exhibits a good spatial localization (and poor frequency localization) in the high spatial frequencies (low scales) and a good frequency localization (and poor spatial localization) in the low spatial frequencies (high scales). Consequently, a good spatial localization of the AV signature is provided in the high frequency contents of the scalogram. As an illustration, let us consider the EC signal obtained by a single pickup coil facing the notches while scanning the tube sample t2 (Fig. 7). The corresponding scalogram was computed and is shown in Fig. 8. Four vertical patterns appear clearly in the high frequency contents of the scalogram (low scales) with good spatial resolution and correspond to the positions of the AVs (four circumferential ID notches). On the contrary, the low spatial frequency contents (high scales) correspond mainly to the pilgering noise and exhibit a 500
where Wn a; b is the CWT of the noise n provided by experimental measurements in sound tube samples, and Wd a; b is the CWT of the defect signature d provided by ®nite element (FE) computations which was carried out to build a defect signature database [11]. The parameters kd and kn, respectively, denote the sample number of d and n used for calculation. As an example, the SNR is calculated for a 10% ID notch and is represented vs. scale in Fig. 9. The SNR exhibits a maximum value at scale a 5 of the CWT. The result of the scale a 5 CWT of the EC signal shown in Fig. 7 is presented in Fig. 10, and show the enhancement of the four ID notch signatures (apart from the edge effects due to the truncation of the EC signals). Similar results are obtained for the other considered AVs, i.e. for the ID and OD notches of both orientations. Therefore, this single scale is selected to facilitate the detection of AVs. The CWT is applied to the EC signals provided by the 16 pickup coils in what follows. 4. Defect detection and localization using maximum likelihood decision 4.1. Defect detection principle The detection of defects is based on a maximum likelihood decision, applied to the CWT at scale a 5 of the EC signal s. The problem lies in the estimation of the binary diagnosis parameter u which equals 0 when no defect is present, and which equals 1 when a defect is present. The maximum likelihood decision lies in the evaluation of the likelihood function L(u ) de®ned as [12]: L u f Suu
4
2 60% ID
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10% ID
30
400
20
2,5
3,33
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5
100
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SNR(a) (dB)
10
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scales
Spatial frequenciesy (m-1)
57
0 -10
a=5
-20
Frequency (m-1)
-30
0 0
50
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Axial position (mm) Fig. 8. Scalogram of the EC signals shown in Fig. 7.
-40
20
500
400
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2
2,5
3,33
5
10
Scale
Fig. 9. SNR vs. scale of the WT (for a 10% IN).
0 20
200
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P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
Fig. 10. Modulus of the CWT at scale a 5 of the EC signal shown in Fig. 7.
where S {uWs 5; bu2 } is a data vector constituted of k consecutive samples of uWs 5; bu2 , where k is the sample number constituting the spatial support of the AV signature along the axial direction, and f Suu is the probability distribution function of S given u . De®ning the likelihood ratio as follows, LR
L 1 L 0
5
the detection is expressed by the following decision rule:
u 1 if LR $ 1 presence of defect
6
4.3. Defect localization The detection rule given in Eq. (6), using Eqs. (9) and (10) allows one to de®ne defective areas. In each defective area, the most likely position of the AVs corresponds to the LR local maxima. Therefore, the determination of the AV position in the defective area was achieved thanks to the modi®ed decision rule, which reads as follows:
u 1 if LR $ 1 and LR is a local maximum u 0 in other cases
11
u 0 if LR , 1 absence of defect 5. Application to defect localization in notched tube samples
4.2. Determination of the likelihood function Let us de®ne n as the measurement data in absence of defect, and N {uWn 5; bu2 } the noise vector constituted of 2 k consecutive samples of uWn 5; bu . The distribution func2 tion of uWn 5; bu can be approximated with the x -squared distribution of 2 degrees of freedom x 2(2) as follows[13]: ! a auWn 5; bu2 2 fn uWn 5; bu exp 2 7 2 2 where a is a ranging parameter depending on the amplitude 2 of uWn 5; bu . Assuming the independence of the samples of N, the distribution function of N is given by k a a sum N fN N exp 2 8 2 2 where sum(N) denotes the summation of the k elements of N. In the absence of defect S N; therefore the likelihood L(0) is expressed by L 0 f Su0 fN S
9
On the contrary, in the presence of defect, the signal is 2 expressed by S N 1 D; where D {uWd 5; bu } stands for the CWT signature vector relative to the defect d to be detected. Then, the likelihood L 1 is given by L 1 f Su1 fN S 2 D
10
The localization method was implemented to the testing of the tube samples. Considering the fact that the worst case of AV localization corresponds to a 10% OD circumferential notch, we assigned to D the 10% OD circumferential notch signature provided by FE computation and CWT. Since the other considered AVs show similar signatures with greater SNR, they should be therefore easier to localize. The likelihood ratio was calculated thanks to Eqs. (9) and (10), and the decision rule thanks to Eq. (11). The AV localization results are shown in Figs. 3c±6c in the form of binary maps where white coloured pixels correspond to u 0 (no AV) and black pixels for u 1 (presence of AV). For the considered tube samples, all the notches were properly detected and localized without false alarm. The obtained localization error is less than 5 mm in the axial direction and 22.58 in the circumferential direction. In the case of axially oriented notches, only the extremities of the actual defects are localized (Figs. 5c and 6c.). This can lead to confusion between one axial defect and two short circumferential defects. However, this ambiguity can be overcome thanks to the EC signals provided by the bobbin coils used in absolute measurement mode (see Section 2.1). In the case of circumferential notches (Figs. 3c and 4c), the obtained AV localization results correspond to the actual shape and position of the notches. The smallest notch (10% OD notch, Fig. 3c.) is localized with a lower
P.-Y. Joubert et al. / NDT&E International 35 (2002) 53±59
circumferential resolution because of the poor SNR of the corresponding signature. 6. Conclusion In the presented work, a multi-coil EC probe was designed and implemented for the inspection of PWR SG tubing. This probe combines high speed inspection with a capability of circumferential localization of defects inducing AV in the tube wall properties. A processing of the multi-coil EC signals, based on a CWT combined with a maximum likelihood diagnosis, was proposed in order to enhance the sensitivity towards small defects and to provide automatic defect localization. The inspection of SG tube samples containing calibrated notches shows 5 mm/22.58 spatial localization performances for defects of size down to 10% deep, 15 mm long and 100 mm wide notches. The circumferential localization of the defects could be increased with the number of pickup coils, and a 32 pickup coil prototype is under fabrication. The proposed localization method gives positional and extent information about the defects. The method could be extended to a defect classi®cation thanks to the numerical or experimental elaboration of an enlarged defect signature database. Acknowledgements This work was supported by Framatome (France). The authors thank M.M.E. Savin, B. Sartre and L. Legrandjacques from the Framatome technical centre, for assistance.
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References [1] Birring AS. Selection of NDT techniques for inspection of heat exchanger tubing. Proceedings of the ASNT International Conference on Petroleum Industry Inspection, Houston, TX: ASNT, 1999. p. 1±14. [2] Sullivan SP, Smith SP, Sharp FL. Simultaneous absolute and differential operation of eddy current bobbin probes for heat exchange tube inspection. Mat Eval 2000;58(5):634±8. [3] Sollier T, Schepens H, Benoist B, Reuchet J. First evaluation of the Set (rotating excitation) EC probe designed for fast SG tubing inspection. Proceedings of the 7th European Conference on Nondestructive Testing, Copenhagen, Denmark: ECNDT, 1998. p. 1339±46. [4] Dehan C, Joubert PY, Miller D, Placko D, Savin E. Sonde aÁ courants de Foucault pour le controÃle non destructif de la paroi d'un tube et proceÂde de traitement des signaux de la sonde, 1999. World patent WO9904253. [5] Benoist B, Gaillard P, Pigeon M, Morizet-Mahoudeaux P. Expert system for the characterisation of defect signal in steam generator tubes. Engng Appl Artif Intell 1995;8(3):309±18. [6] Chabert M, Tourneret JY, Castanie F. Additive and multiplicative jump detection using continuous wavelet transform, Proceedings of the ICASSP'96. Atlanta, GA: IEEE, 1996. p. 3002±5. [7] Chen G, Yamaguchi A, Miya K. Signal processing for defects from composite eddy current signals. Insight 1997;39(11):785±9. [8] Chuang SF, Basart J, Moulder J. The application of wavelets and fuzzy logic to eddy current ¯aw detection in steam generator tubes. QNDE 1998;17:775±81. [9] Mallat S. A wavelet tour of signal processing. New York: Academic Press, 1998. [10] Flandrin P. Temps/freÂquence. Paris: HermeÁs, 1993. [11] Joubert PY. Contribution to the design of an eddy current sensor and to the corresponding signal processing for the NDT of steam generator tubes. PhD Thesis. Universite de Paris XI, 1999. [12] Rao CR. Linear statistical inference and its applications. New York: Wiley, 1965. [13] Grimmett GR, Stirzaker DR. Probability and random process. Oxford: Oxford University Press, 1992.