Eddy Current Techniques in NDE
Lalita Udpa
Nondestructive Evaluation Laboratory
Department of Electrical and Computer Engineering
Michigan
c g State
S e University
U ve s y
East Lansing, MI 48824
WCNDT P
Preconference
f
W
Workshop,
kh
D
Durban,
b
A
April
il 15
15, 2012
Outline




Part I - Physical Principles
Part II – Probes
Part III – Inspection Modes
Part IV - Forward Problem in EC-NDE Finite Element Modeling
 Part V - Inverse Problem in EC-NDE –
Defect Classification/Characterization
 Part VI – Case Study- Eddy current
p
of SG tubes
inspection
Application of Eddy Current NDE
• Eddy current NDE is commonly used in the inspection of
conducting samples
– Measurement of impedance changes in coils in the presence of an
anomaly
l in
i a conducting
d ti specimen
i
• Typical applications
– Steam generator tubing in nuclear power plants
– Aircraft components
• Nuclear
N l P
Power IIndustry
d t
–Inspection of Steam Generator Tubing in
Nuclear Power Plants
Aircraft components
•
•
•
•
Wheels
Rivet Holes
E i
Engines
– Impeller
I
ll bores
b
Fuselage skin
Part I - Physical Principles
Part I - Physical
y
Principles
p
•
Alternating magnetic fields are generated by alternating current
excitation – Maxwell Ampere
p
Law
•
Magnetic field induces currents (eddy currents) in test specimen –
Maxwell Faraday Law
•
Eddy currents establish secondary fields which oppose the primary
fields
•
Changes net flux linkage and hence the impedance of the coil
•
Anomalies in the test specimen affect the induced field, changing the
net impedance of the coil
Changes in the impedance of the
Bprimary
probe coil constitutes the
p
eddy current signal
Bsecondary
Physical
y
Principles
p
•
Test coil characteristics
 Inductive reactance L  2 f L
 Ohmic resistance R
f : excitation frequency
L : self-inductance of the coil
Coil
Eddy Currents
Test Specimen
Eddy
y Current Inspection
p
Significant properties of test specimen
 Electrical conductivity ()
 Dimensions (such as depth of conducting plate)
 Magnetic permeability (µ)
 Material discontinuities (such as cracks or corrosions)
Significant instrument characteristics
 Frequency of current excitation in the probe coil
 Size and shape of the probe coil
 Distance of test coil to the test specimen (lift off)
Transformer Analog
• Transformer
– Two circuits coupled inductively, in which a change of current in
one winding induces an electromotive force (or voltage) in a
second winding
Magnetic Coupling Between Two Coils
Equivalent Electrical Circuit for air core transformer
Eddy
y Current Inspection
p
- Transformer Analog
g
W e two
When
wo coils
co s aree coup
coupled
ed by a magnetic
g e c field,
e d, they
ey aree subject
subjec too
the effects of a mutual inductance.
M 12 
 12
I1

N 212
I1
M 21 
 21
I2

N121
I2
where
h
M 12  M 21
mutual inductance of two coils (henrys)
 12 ( or  21 ) flux linkage created by flux of coil-1 passing through
the interior of coil-2 (reverse vise)
N 1 ( or N 2 )
number
b off turns iin coil-1
il (coil-2)
( il )
I 1 ( or I 1 )
current flow in coil-1 (coil-2)
12 ( or  21 )
mutual
t l flux
fl created
t d by
b currentt in
i coil-1
il 1 andd passing
i
though interior of coil-2 (reverse vise)
Transformer Analog
g (Cont’d.)
(
)
So e of
Some
o magnetic
g e c flux
u lines
es associated
ssoc ed with
w each
e c coil
co do not
o couple
coup e
with both coils, those flux lines are called leakage magnetic flux
lines, and they contribute to self-inductance of the coil.
L1 
 11
I1

N111
I1
L2 
 22
I2

N 222
I2
Transformer Analog
g ((Cont’d.))
Faraday’s law of electromagnetic induction
An electromotive force (emf) is induced within an electric
circuit whenever the magnetic flux linking with the circuit changes,
and it is proportional to the time rate of change of flux linkage.
linkage
d
dI
d
L N
emff 
dt
dt
dt
emf  induced electromotive force (volts);
  total flux linkage (weber - turns);
t  time (seconds);
I  current (amperes);
L  self - inductance (henrys);
  coupled magnetic flux (webers); and
N  number of turns coupled with magnetic flux.
Transformer Analog
• If coil 1 serves as the primary winding, the voltage induced
in coil 2 is
dI1
d12
e2  M 12
 N2
dt
dt
• Likewise,
Likewise if coil 2 is the primary,
primary voltage induced in coil 1
is
dI 2
d21
e1  M 21
 N1
dt
dt
• Since M 12  M 21 ,
e1
N1
 Turns Ratio TR
e2 N 2
• When the secondary is short-circuited,
short-circuited

N1 I1  N 2 I 2
I 2 N1

 TR
I1 N 2
Transformer Action In EC Test Systems
• A practical eddy current test system can be considered
analogous to a transformer
– Excitation coil: Primary
– Test
T object:
bj
One-turn
O
secondary
d
– Properties and dimensions of test object can be reflected in primary
or p
pickup
p coil voltages
g as a consequence
q
of transformer action
• Let I 2 be the current flowing in the test material. Then,
component of primary voltage corresponding to secondary
2
reaction is
 N1 
N1
V1 
I 2 R2    I1 R2
N2
 N2 
• Total voltage across test/probe coil
2


 N1 
dI1
V1   R1    R2  I1  L1
dt
 N2 


Coil Winding Resistance
Self inductance term
Skin Depth
p
For a plane wave incident on an conducting half plane,
The variation of induced current with depth is given by -
J x  J o exp( x  f  )
where
δ
1
πfμσ
is called
skin depth
Factors Affecting Eddy Current
Measurements
• Factors affecting eddy current transducers
– Lift-off: Separation between the coil and the specimen surface
• Impedance of the coil changes as the probe is moved from air till it
touches the material surface – liftoff curve
• Minimized by the use of surface-riding probes or multifrequency
measurements
• Can be used to determine the thickness of non-conducting coatings on
conducting surfaces
– Skin effect
• Eddy currents decay exponentially with depth in the material
• Standard depth of penetration: (depth at which eddy currents become
1/e the surface value)
• This limits the sensitivity of eddy current method to the surface of the
conducting specimen
Part II - Eddyy Current Sensors
Part II - Eddy
y Current Sensors
 Absolute probe
 Differential Bobbin probe
 Plus Point & Array Probe
 Meandering coil
 Eddy Current – Magneto-optic (MOI) sensor
 Eddy Current – Magneto-resistive (MR) sensor
Absolute Probe
• Absolute probe: a single coil is used for impedance
measurements
• Disadvantage
– Detects small changes in impedance, factors such as changes in
coil parameters or lift-off may mask this small signal.
Absolute Probe
Impedance plane trajectory of a coil over a ferromagnetic (or
nonferromagnetic ) specimen with and without a discontinuity
11. C
Coil
il in
i air
i
2. Coil over a nonferromagnetic specimen
containing a discontinuity
3. Coil over a nonferromagnetic specimen
containing no discontinuities
11. C
Coil
il in
i air
i
2. Coil over a ferromagnetic specimen
containing a discontinuity
3. Coil over a ferromagnetic specimen
containing no discontinuities
Differential Bobbin Probe
• Differential bobbin probe
– Two bobbin coils with current in opposite
pp
direction
– Resulting signal is a difference signal from two coils
• Flaw signal is more distinguishable from relatively
constant
t t background
b k
d signal.
i l
Differential Bobbin Probe
Impedance-plane trajectory of a coil over a conducting
nonferromagnetic
f
i test specimen
i
Impedance plane trajectory from a differential bobbin probe over a defect
Bobbin Probe
•
Diff. mode: two identical bobbin coils, with fixed space
– Very sensitive to abrupt anomalies
anomalies, such as pitting corrosion,
corrosion and fretting
wear
– resistant to probe wobble, temperature variations, and gradual variations in
tube’s conductivity, diameter, and ovality
•
Abs. mode: one testing bobbin coil, one shielded ref. coil
– gradually varying wall thinning, which could not be detected by diff. mode
Differential coil
Diff. sig.
Differential mode
FBH, OD
20%-100%
Absolute coil
Ref. coil
Abs. sig.
Axial
Absolute mode
Metallic Shield
ZETEC Bobbin Probes
Bobbin Probe Disadvantages
• Merits:
– inexpensive, fast scanning( typ. up to 1m/s )
– Reliably detect and size volumetric flaws, such as
fretting wear and pitting corrosion
• Disadvantage:
– insensitive to circ. oriented flaws, because induced
eddy current parallel to flaws and not perturbed by the
flaws
– limited sensitivity at expansions, U-bend, and support
plates
– low resolution for flaw location and characterization
Rotating Probe - RPC
•
Components of RPC:
– Typ. 4~8 surface-riding pancake coils placed around the circumference
– Driven motor, rotating circumferentially and moving forward (helical
pattern)
•
Characteristics:
– Capable of both axial and circ
circ. oriented flaws
– Very sensitive to cracking in transition zone
- 3 coils spaced 120 deg. Apart
- Each scan the inner surface of
the tube in a helical path
- multi-freq. : 400, 300, 200 kHz
- C-Scan impedance plot
Circ.
Axial
Rotating Probe - Plus Point
•
•
•
•
•
Twoo orthogonal coils connected in diff.
T
diff
mode crossing at a point
Affect simultaneously by material and
geometric distortion,
distortion such as defects
sensitive with circ. and axial flaws
Rotate and move forward same as RPC
Slow scan speed
Array Probe - X-Probe
- 40 times faster than rotating
probes
b
C01: work both on transmit and receive mode
Make control circuit much complicated
Combined with diff. bobbin coils
X-Probe
Diff Bobbin
Diff.
Planar Coils for Plates
Exciting
E
citing coil: meander coil
Receiving coil: mesh coil
Perpendicular to each o
S Yamada
S.
Yamada, etc.
etc 1995,
1995 Japan and Canada
Planar Coils for Plates
Lock-in Voltmeter output
S
Scan
li
line perpendicular
di l to
t crackk
Scan line parallel to crack
Eddy
y Current – MOI Sensors
Aloha Airlines B-737-200 lost
part of its front fuselage during
a flight in Hawaii, 1985.
Eddy Current Excitation
Magneto-Optic Sensing
Imaging
Operational Principles of MOI
•
Faraday rotation effect (1845)
  KMd
K : Kundt's constant
M : Magnetization vector
d : path length of light
Magneto--Optic Sensors
Magneto
Thin film of Bismuth-doped iron garnet grown on 3” diameter, 0.02” thick
substrate of gadolinium gallium garnet
1 Uniaxial magnetic anisotropy,
1.
anisotropy i.e.
i e they have an ‘easy’
axis of magnetization normal to the sensor surface and a
‘hard’ axis of magnetization in the plane of the sensor.
2. Memory, i.e. if the magnetization along the easy axis is
removed, the film will retain most of the established
magnetization.
3. Large Faraday Rotation, i.e. ~ ± 20,000~30,000
degrees/cm
Eddy Current Induction
Conventional methods rely on coils
Surface to be inspected
Magneto-Optic methods rely on
sheet current induction
Eddy current foil
Surface to be inspected
Magneto--Optic Imaging
Magneto
Schematic of MOI Instrument
LIGHT SOURCE
ANALYZER
POLARIZER
BIAS COIL
SENSOR
LAP JOINT
• Eddy Current Excitation - f ~ 100Hz-100kHz
• Magneto-Optic Sensing
• Imaging
INDUCTION FOIL
Multi--Directional (Rotating) Eddy Current
Multi
E i i
Excitation
Linear null
region
MOI image using linear
excitation
Cracks
MOI image using rotating
excitation
Advantages of MOI
•
•
•
•
•
•
•
•
•
NDT systems are evolving towards imaging capability
MOI systems produce real time analog images of inspected part
I
Images
bboth
th surface
f
breaking
b ki andd subsurface
b f
cracks
k
Easy to interpret ( reduces operator fatigue)
Eliminates need for removing paint or decal
Can be used on conducting samples as well as composites by
“tagging” with ferromagnetic particles
Allows rapid inspection of large areas for surface and subsurface
defects
Use is straightforward
g
requiring
q
g minimal trainingg
Output can be readily videotaped
Eddy Current – GMR Sensors
•
•
•
AG
GMR ddevice
i consists
i off two or more llayers off ferromagnetic
f
i material
i l (typically
( i ll
NiFe, CoFe or related transition metal alloy) separated by ultra-thin non-magnetic
metal spacer layers (Cu, Au or Ru).
In the absence of an externally applied field, the magnetic layers alternate in
magnetization, resulting in a high resistance. When a magnetic field is applied, this can
overcome the interlayer coupling and force all of the layers to align with the field and
reduce
d
the
h resistance.
i
Since a magnetic field in either direction will cause alignment of the magnetization, the
resulting R vs. H curve is an even function, symmetric about zero
GMR Sensor
S
•
Giant Magneto-Resistive
Magneto Resistive (GMR)
– Decrease in resistance in presence
of a magnetic field
– Uni-polar
i l sensor
• Needs to be biased to measure
sinusoidal (+,-) fields
• GMR sensor kept in a coil
through which a constant DC
current is passed.
• DC fi
field
ld keeps
k
the
th GMR sensor
biased during operation
Normal
Biased
Operating point
GMR Sensor Calibration and Bias
Source and Sensor Configuration
Uniform linear currents with a single line of symmetry
Alternate Sensors (GMR, MOI)
•Eddy Current Excitation
•Image the magnetic fields associated with the induced currents
Anomaly free region
Defect free rivet region
Rivet with defect
Measurement
Region
T
Tangential
i l flux
fl
Local Normal flux
(Symmetric)
Local Normal flux
(Asymmetric)
GMR Signals
Line of symmetry for placing detector
Results
• Schematic and parameters
Excitation current in y direction
Results
• Finite Element Geometry
Top View
Side
View
30%
% Depth with 3mm square
Results--GMR and EC (z component)
Results
GMR Voltage
EC Induced Voltage
Results--GMR and EC (x component)
Results
GMR Voltage
EC Induced Voltage
Results--GMR and EC (y component)
Results
GMR Voltage
EC Induced Voltage
Part III - Eddyy Current Inspection
p
Modes
Part III - Inspection Methods
•
Si l frequency
Single
f
inspection
i
i
– Single frequency sinusoidal excitation
– Magnitude and phase changes can be used to detect flaws
•
M l if
Multifrequency
inspection
i
i
– Multiple excitation frequencies multiplexed in time
– Used to detect (and locate) flaws throughout the depth of a specimen
– Can
C be
b usedd to
t suppress interfering
i t f i signals
i l that
th t may maskk defects
d f t
•
Pulsed eddy current inspection
– Driving coil excited with a repetitive broadband pulse, such as a square
wave.
– Broad frequency spectrum is produced in one pulse: reflected signal
contains depth information
– Pulse is broadened and delayed as it travels deep into the conducting
material
• Flaws or other anomalies close to the surface will affect the eddy current
response earlier in time than deep flaws
•
Remote Field Eddy Current inspection
– Low frequency excitation
Pulsed Eddy
y Current
1 D
1.
Driving
i i probe
b coil
il excited
it d with
ith a repetitive
titi broadband
b db d pulse,
l
such as a square wave.
2. Broad frequency spectrum is produced in one pulse:
transient/reflected signal contains depth information
3. Pulse is broadened and delayed as it travels deep into the
conducting material
•
Flaws or other anomalies close to the surface will affect the eddy
current response earlier
li iin time
i than
h deep
d
flaws
fl
M i i
Motivation
Multilayer aircraft structure needs accurate characterization of
hidden corrosions and cracks
Pulsed Eddy Current
Pulsed Excitation
Top Layer
Bottom Layer
Typical
yp
Signals
g
A-scan : a transient signal measured under typical test conditions.
Amplitude and the time for zero-crossing is most important features.
Amplitude of voltage measured
by pick-up coil
Difference voltage between measured
signal and reference signal
Typical
yp
Signals
g
C-scan : at a time instance, measured signal from a observation plane
i displayed
is
di l d as image.
i
Amplitude of voltage
Ti for
Time
f zero-crossing
i
Typical
yp
Signals
g
B-scan : Image of a linear cross section of C-scan within a time
period.
i d X-axis
i represents the
h probe
b location,
l
i Y-axis
i represents the
h
time, amplitude of signal is displayed in gray value.
Remote Field Eddy Current Testing
• Originally developed for inspecting tubular structures
• Is sensitive to both ID and OD defects
• The signal is sensed by a pick
pick-up
up coil located in the remote
field region
I di t P
Indirect
Path
th
Direct Path
Remote
Field
Sensor
Indirect Path
Pi Wall
Pipe
W ll
Excitation
Coil
Remote Field Eddy Current Testing
• Direct and indirect
fields interaction
– Direct field energy
d i t in
dominant
i the
th
near field zone
– Indirect field
dominant in the
remote field zone
– In the transitional
zone DF and IF
may cancel out
Remote Field Probe
Receiver
Transmitter
Active or Passive Shield
Test Specimen
IMTT Probe Response
3.0”  3.0”  0.040” Flat-bottom corrosion
0 603” Below Surface
0.603
C
Corrosion
i Si
Size Estimate
E ti t
.
Y. Sun, at al
0.5”  0.5”  0.040” Flat-bottom corrosion
0 603” Below Surface
0.603
C
Corrosion
i Si
Size Estimate
E ti t
Part IV - Forward Modeling
What Simulation Models Can Do
•
•
Simulation Models are useful in
– Solution of forward problem – Predict EC probe signals
– Effect of probe wobble, frequency, sludge characteristics on probe
measurements (POD)
– Visualization of field/flaw interaction
– Optimization of sensor/system design
– Test bed for generating defect signatures
– Useful in Probability of Detection (POD) Models at low cost
– Inverse problem solution (Reverse engineering models for finding root
cause)
Key
ey Advantages
dva ages of
o Simulation
S u a o Model
ode
– Provides an inexpensive and fast method to simulate realistic test and
defect geometries
Part IVIV- Forward Modeling
•
Maxwell's equations:
B
E  
t
B  0
D  
H, E are the magnetic & electric
fi ld strengths
field
t
th
B, D are the magnetic & electric
flux densities
J,  are the current & charge densities
Constitutive relations for linear and isotropic media:
D  E



B  H
is the permittivity
is the permeability
is the conductivity
J  E
Finite Element Modeling -Technical Details
The governing equations for the eddy current
excitation in

terms of the magnetic vector potential A and electrical scalar
potential V

1



(  A )  j ( A  V )  0

  ( j ( A  V ))  0


1
  (  A )  J S

in 1
in 1
in  2
 ,  are the permeability and conductivity of the media.
Finite Element Formulation
Step 1. Mesh generation - Discretize the solution region into
finite elements –
 Nodes are numbered globally and locally.
 A connectivity array is constructed to describe the relationship
between the elements and nodes.
Step 2.
2 Choose shape functions.
functions (hexahedral element)
N i ( , ,  )  (1   i )(1   i )(1   i )
i=1,2, . . ., 8
Finite Element Formulation (continued)
Step 3. Compute stiffness matrix and load vector for each element.
 Notation
8
24
j 1
k 1
A   N j Axj x N j Ayj y  N j Azj z   N k Ake
8
V   N jV je
j 1
N j x

Nk  N j y

N j z
k 3j2
k  3 j 1
k 3j
 Axje
 e
e
Ak   Ayj
 e
 Azj
k  3j 2
k  3 j 1
k  3j
Finite Element Formulation (continued)
24
1
1
{
(


N
)

(


N
)

(
  N i )(  N j )dV } Aej 

i
j
j 1
e


24
8
e
{
j

N

N
dV
}
A

{

N


N
dV
}
V

 i j
i
j
j 
j 1

 e
e
j
e
j 1
1
N i  (   A  n)dS  

 e
24
e
N i  (n
1

  A)dS   N i  J S dV
e
8
e
{
j


N

N
dV
}
A

{


N


N
dV
}
V


k
j
k
j
j 
j 1

 e
i  1,2,  ,24
e
e
j
j 1
N k ( jA  V )  ndS  0
e
e
e
[G ]32
[
A
]

[
Q
]
32
321
321
e
k  1,2,  ,8
Finite Element Formulation (continued)
Step 4. Assemble element matrices to global matrix.
[G ] [ A]  [Q ]
Step 5. Boundary conditions.
 Dirichlet boundary ( A ,
 Neumann boundary (
V)
B , H)
Finite Element Formulation (continued)
Step 6. Solve the matrix equation.
 Direct solver
 Iterative solver ((Transpose
p
Free Q
Quasi-Minimal-Residual method))
Step 7. Calculate other measured quantities.
B   A
- magnetic flux density
J   jA  V
- electric current density
Model Validation
(Palanisamy, 1980)
Resistive
Reactive
Impedance Plane
Comparison of Experimental and Predicted Results for An OD Defect
Model Validation
(Palanisamy, 1980)
Resistive
Impedance Plane
R ti
Reactive
Comparison of Experimental and Predicted Results for a Tube Support
Model Validation
(Palanisamy, 1980)
Modeling
Geometry
Experimental
Comparison of Experimental and Predicted Results for Defects in a support
SGTSIM v1.0 Features - 2008
Predefined geometries ,
Support plate
Tube sheet
Free span
Probe s: Bobbin ( absolute, differential, air core, ferrite core),
Pancake coil
Defects: Rectangular : ID, OD
Experimentally Validated
SGTSIM v 2.0 Features –2009
• Model Enhancements
Probes: + Point Probe
• GUI Enhancements
–
–
–
–
New graphical interface:
2D and 3D surface plot and Lissajous plots
Manual Calibration
D W
Data
Writing
i i formats
f
vertical
horizontal
Simulation
vertical
horizontal
Measured
Real Crack Model - Quantitative Validation –
+ point probe ; 300KHz ; ETSS Data file – Farley
Farley-1
1_25_51
25 51
Experimental signals
Axial Notch Profile from
MET data - mesh
Average error - 5.31%
Simulated signals
Vertical Channel
Average error – 2.17%
Horizontal Chan
Real Crack Model - Experimental Validation –
+ point probe ; 300KHz ; ETSS Data file - TMI-1_91_55
Axial Notch Profile
from MET data
Experimental signals
Average error – 6.28%
Average error – 1.19%
Simulated signals
Vertical Channel
Horizontal Cha
Part V - Inverse Problems in EC NDE
Overall Analysis Procedure
Raw EC data
Preprocessing
Features
Signal Classification
No Degradation
Degradation
Compensation
Defect Characterization
A t
Automated
t d Si
Signall Cl
Classification
ifi ti (ASC)
Raw UT Weld Inspection Signal
Preprocessing
• Noise Filtering
• Invariance
• Feature Extraction
Feature Vector (DWT Coefficients)
Classifier
C
ass e
Training
• Clustering Algorithms
• Neural Networks
Signal Class
Model--based Inversion for Defect
Model
Characterization
Initial
Defect Profile
Forward
Model
Measured
Probe Signal
Predicted
P
edicted
Response
Compare
p
with
desired probe
response
Update the defect
p
profile
Defect
D
f t
Profile
Characterization
Defect Parameterization
y
r
d1
x
d3
d2
z
Characterization
Typical Results
(ii)
(i)
0.25
11.4
11.2
0.2
Objectiv e Function
11
r ( mm)
10.8
10.6
10.4
desired profile
initial guess
: reconstructed profile
10.2
0.1
:
0.05
:
10
9.8
0.15
0
0
1
2
3
z (mm)
4
d1  50%
5
6
0
5
10
Iteration Number
d 2  55%
d 3  60%
15
Characterization
Typical Results
(i)
(ii)
11.4
0.25
11.2
0.2
Objectivve Function
11
r ((mm)
10.8
10.6
10.4
10.2
0.1
: desired profile
0.05
: initial guess
: reconstructed profile
10
9.8
0.15
0
1
2
3
z (mm)
4
d1  50%
5
6
0
0
5
10
Iteration Number
d 2  55%
d 3  45%
15
Characterization
Test Configuration
r
d1 d 2 …
d8
z
Characterization
Typical Results
N=100
Characterization
Typical Results
N=100
Case study: Steam Generator Tube Inspection
Rotating probe coil EC Data
Free Span
Drilled Support
Broached Support
Freespan
U bend
Tube Sheet
Tube Expansion Transition
** Plus Point coil, 300kHz channel
Filtering
g
Noisy Data
After Filtering
Volumetric Indications
8
CWT Analysis
y – RPC Data
The continuous wavelet transform of a signal u(t) is given by
 ( , s ) 



u (t )
1
s
 * ((t   ) / s )dt
where τ and s represents translation and scale of the mother wavelet ψ(t)
Property of wavelets to perform multi-scale analysis is exploited for flaw detection
Flaw
Structure
Noise
8
CWT – Flaw Detection
•
A simple threshold based on statistics of CWT coefficients easily separates out flaw signal
from noise
1D RPC Data
CWT
Potential Flaw Signals
Flaw
Flaw
8
Compensation: Deconvolution
•
•
Objective
Development of deconvolution algorithms for removing the response
of the eddy current probe area from the measurements
– Compensation for the finite dimensions of eddy current probes
•
•
•
•
•
•
Approach
Deconvolution algorithm using Wiener filter
System model (time domain)
y i, j   d i, j   hi, j   ni, j 
where y(i,j) – measured signal
d(i,j
,j) – defect
f footprint
f p
h(i,j) – system impulse response (probe footprint)
n(i,j) – noise
* – convolution
l ti
Compensation
T i l Results
Typical
R lt
2
2
2
4
4
4
6
6
6
8
8
8
10
10
10
12
12
12
14
14
14
16
16
16
18
18
20
20
5
10
15
20
25
30
Measured data
35
18
20
5
10
15
20
25
True Defect image
30
35
5
10
15
20
30
Result of deconvolution
The defect diameter is
• True defect image: 0.06”
• Before deconvolution: 0.1”
• After
Aft deconvolution:
d
l ti
0 061”
0.061”
Transfer function (kernel)
25
35
Defect Characterization
• Determine defect parameters from measurement signal
– Calibration Methods, Neural Networks
6000
4000
2000
0
Mapping
-2000
30
25
20
25
15
20
15
10
10
5
axial
5
0
0
circum
Eddy Current Signal
Defect Profile
Overall Profiling
g Procedure
CALIBRATED DATA
ROI SELECTION
LENGTH ESTIMATION
METHOD 1:
PROFILING USING
CLASSICAL
CALIBRATION
CURVE
METHOD 2:
PROFILING USING
ENHANCED
CALIBRATION
CURVE
METHOD 3:
PROFILING USING
RADIAL BASIS
NEURAL
NETWORK
Length
g estimation
Depth Profiling
radial
di l basis
b i neurall network
t
k method
th d
.
.
.
Axial direction
fi, 300kHz
.
.
.
.
.
.
fi,i 200kHz
.
.
Feature Matrix
Trained RBF
Network
d thi
depth
.
.
.
.
fi, 100kHz
.
.
.
Features from line scans in the
background region were also
used to map to zero depth
Radial Basis Function (rbf
(rbf)) Approach
The input-output transformation equation for the RBFNN can be expressed as
p

 
f ( y )   wi (|| y  ti ||,  i )
i 1
where
= input vector of dimension N,
f( ) = output vector of dimension M,
= ith basis
b i center,
wi = weight vector of dimension corresponding to the ith center and
= radially
di ll symmetric
i basis
b i function
f
i with
i h spreadd σ .
A total of p centers (or nodes in hidden layer) are used in basis function expansion
Feature vector
•
•
•
For 300kHz, 200kHz and 100kHz data, the maximum magnitude and its corresponding phase angle is
computed for each gradation in axial direction of the ROI.
The phase spread
spread. which is an additional feature
feature, defined as the range for as three phase angles
computed per gradation
Seven features are thus obtained per gradation in axial direction
Polar plot of raster in 100kHz, 200kHz, 300kHz channel
90
25
120
60
20
15
150
f1
f2
.
.
.
.
fN
30
10
5
180
0
210

f  100 ,  200 , 300 , m100 m200 m300 100,300
330
240
300
270
300 kHz
200 kHz
100 kHz
9
Radial basis neural network method
1
2
.
.
.
.
N
Length
Estimation
(N Axial scans)
TRAINING MODULE
Nx7
Feature Matrix
Training data MET Result
R
B
F
1
2
.
.
.
M
Length
Estimation
(M Axial scans)
TEST MODULE
Test Data
Feature
Matrix
N
E
T
W
O
R
K
1
2
.
.
.
.
.
.
.
.
.
.
.
.
M
Variation of basic rbf algorithm
g
(rbf2)
(
)
 Three feature vectors corresponding to three spatially contiguous line scans are mapped to depth at center scan
TRAINING MODULE
Training data MET Result
Axial direction
}
fn-1
fn
fn+1
NX21
Feature Matrix
depthn
R
B
F
fn-1
fn
fn+1
Feature vector
TEST MODULE
N
E
T
W
O
R
K
Predicted depth at nth scan
Results 1
D f tL
Defect
Length
th & D
Depth
th profiles
fil
Max % TW
PDA ((%))
Flaw Length
g (in)
( )
Log- Mag
26.00
21.69
0.56
Mag
28.53
22.89
0.52
NN (RBF1)
49.23
32.74
0.52
NN2 (RBF2)
56.80
44.52
0.52
MET
60.00
40.97
0.53
RESULTS - profiling
100
90
80
log-mag
mag
NN
MET
NN2
70
%TW
60
50
40
30
20
10
0
0
0.1
0.2
0.3
0.4
Location
0.5
0.6
0.7
Results 2
D f tL
Defect
Length
th & D
Depth
th profiles
fil
Max % TW
PDA (%)
Flaw Length (in)
Log- Mag
62.00
38.91
0.67
Mag
60.14
39.26
0.67
NN (RBF1)
57.39
33.49
0.69
NN2 (RBF2)
64.17
42.25
0.69
MET
77.00
42.01
0.73
RESULTS - profiling
100
90
80
log-mag
70
mag
NN2
%TW
60
NN
50
MET
40
30
20
10
0
0
0.1
0.2
0.3
0.4
Location
0.5
0.6
0.7
0.8
Results 3
D f tL
Defect
Length
th & D
Depth
th profiles
fil
Max % TW
PDA (%)
Flaw Length (in)
Log- Mag
44.00
43.00
0.13
Mag
46.25
43.07
0.13
NN (RBF1)
34.47
26.68
0.14
NN2 (RBF2)
31.15
26.73
0.14
MET
35.80
24.22
0.11
RESULTS - profiling
100
90
80
log-mag
70
mag
NN2
%TW
60
NN
50
MET
40
30
20
10
0
0
0.02
0.04
0.06
0.08
Location
0.1
0.12
0.14
0.16
Results 4
D f tL
Defect
Length
th & D
Depth
th profiles
fil
Max % TW
PDA (%)
Flaw Length (in)
Log- Mag
22 53
22.53
10 35
10.35
0 94
0.94
Mag
9.00
6.79
0.94
NN (RBF1)
76.85
43.11
0.96
NN2 (RBF2)
64.17
42.25
0.88
MET
77.00
42.01
0.82
RESULTS - profiling
100
90
80
log-mag
70
mag
MET
%TW
60
NN2
50
NN
40
30
20
10
0
0
0.2
0.4
0.6
Location
0.8
1
1.2
Summary
Edd Current
Eddy
C
t - Physical
Ph i l Principles
Pi i l
- Transformer Analogy
- Probe
P b C
Coil
il geometry
t
- Continuous, Pulsed & Remote
excitation
it ti
- Simulation models
- Data
D t Analysis
A l i
- Defect Classification
D f tP
Defect
Profiling
fili
- Application (SG tube Inspection)
Questions?