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DEFECT PROFILING IN STEAM GENERATOR TUBES USING
MULTl-FREQUENCY EDDY CURRENT INSPECTION

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Uduebho Oseghale Olumese

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DEFECT PROFILING IN STEAM GENERATOR TUBES USING
MULTI-FREQUENCY EDDY CURRENT INSPECTION

By

Uduebho Oseghale Olumese

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Electrical & Computer Engineering
2007

ABSTRACT

DEFECT PROFILING IN STEAM GENERATOR TUBES USING
MULTI-FREQUENCY EDDY CURRENT INSPECTION

By

Uduebho Oseghale Olumese

Multi-frequency eddy current technique is one of the widely used Non-destructive
evaluation techniques for steam generator tube inspection in nuclear power industry. The
multi-frequency technique for depth proﬁling is essentially a multi-dimensional data
fusion scheme which tends to mitigate the effect of error-prone single-dimension eddy
current features due to noise and improves defect identiﬁcation, classiﬁcation and
characterization of the eddy current data. In this research, the performance of traditional
defect characterization algorithms are investigated alongside a novel defect depth
proﬁling procedure using a radial basis function neural network by employing the
following two step approach

0 The length of the defect is estimated by setting an adaptive threshold on the
magnitude distribution in the region of interest engulﬁng potential defects.
0 The inversion of the signal features in the defect region to predict a depth proﬁle.

The vehicle for this inversion is the radial basis function neural network.

The thesis also discusses noise removal in eddy current data and their limitations when

deployed for depth proﬁling purposes.

DEDICATION

This thesis is dedicated to God Almighty through Whom all things are possible.

iii

ACKNOWLEDGEMENTS

I would like to gratefully acknowledge the enthusiastic supervision and academic
mentoring of Dr. Lalita Udpa during this work. You gave wings to my dreams. I also
thank Dr. Ramuhalli Pradeep for the technical discussions he provided and Ameet Joshi
who contributed to the development of the algorithms in this research work. I also wish to
express my gratitude to Mr James Benson at the Electric Power Research Institute for his
support. The testing and validation of the algorithms was performed by Steve Brown to

whom I am grateful.

Finally, I am forever indebted to my parents and Onome Ewere, my ﬁancee, for
their understanding, endless patience and encouragement when it was most required. I am

also grateful to Napoleon Iﬁe and my siblings for their support.

iv

STATEMENT OF AUTHENTICATION

The work presented in this thesis is, to the best of my knowledge and belief,
original, except as acknowledged in the text. I hereby declare that I have not submitted

this material, either in whole or in part, for a degree at this or any other institution.

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

TABLE OF CONTENTS

LIST OF TABLES ........................................................................... x
LIST OF FIGURES ......................................................................... xi
KEY TO ABBREVIATIONS AND SYMBOLS ........................................ xv

CHAPTER 1: INTRODUCTION TO NONDESTRUCTIVE EVALUATION

1.1 INTRODUCTION ..................................................................... 1
1.2 TYPICAL METHODS FOR NONDESTRUCTIV E TESTING ............... 2
1.2.1 Ultrasonic NDT ............................................................ 3
1.2.2 Radiographic NDE ....................................................... 5
1.2.3 Electromagnetic NDT .................................................. 5
1.3 Eddy Current Inspection of Heat Exchange Tubes in Nuclear Power Plants . .. 6
1.4 Scope of Thesis ................................................................................ 7
CHAPTER 2
2.1 Principles of Eddy Current Testing and Its Application in Steam Generator Tube
Inspection .................................................................................. 9
2.2 Eddy Current Transducers ............................................................... 11
2.3 Multi-frequency Eddy Current Signals ................................................. 12
2.3.1 Skin Effect .................................................................... 12
2.3.2 Eddy Current Testing Probes .................................................. 13

CHAPTER 3: EDDY CURRENT PROBE DATA ANALYSIS

3.1 Introduction ...................................... , ........................................... 16
3.1. 1 Signal Preprocessing .......................................................... 16
3.1.1.2 Synchronization ....................................................... 18

3.1.1.3 Tube Support Segmentation ................................... 22

3.1.1.4 Tube Support Suppression ....................................... 24

3.2 Band-Pass Filtering, Adaptive Thresholding and ROI Detection ................... 25
3.3 Classiﬁcation ................................................................................... 31
3.4 Defect Characterization ................................................................... 32

3.4.] Calibration Curve ...................................................... 33
3.4.2. Enhanced Calibration Curve ....................................... 36
3.4.3 Iterative Numerical Modeling ....................................... 37

CHAPTER 4: ARTIFICIAL NEURAL NETWORKS

4.1 A Little Biology ........................................................................... 38
4.2 Artiﬁcial Neural Network ............................................................... 40
4.3 Neurons .................................................................................... 41
4.4 Layers ....................................................................................... 41
4.5 Radial Functions ........................................................................ 42
4.6 Radial Basis Function Neural Networks ............................................... 43
4.7 Depth Proﬁling Using RBFNN ......................................................... 45
4.7.1 Length Estimation ................................................................... 45
4.7.2 Depth Proﬁling .................................................................. 49
4.8 Training the Network ................................................................. 49
4.9 Training Parameters of RBFNN ...................................................... 52
4.9.1 Selection of Centers of Basis Functions (ti) .......................................... 53
4.9.2 Selection of Spreads or Radii of the Centers (0;) ................................... 53
4.9.3 Computation of Weights (wi) .......................................................... 55

CHAPTER 5: EXPERIMENTAL ANALYSIS AND RESULTS

5.1 Introduction .................................................................................. 56
5.2 Experimental Methodology ............................................................... 57
5.3 Uncorrelated Noise Removal in Eddy Current Data .................................. 71
CHAPTER 6: CONCLUSION AND SUMMARY ........................................... 78
BIBLIOGRAPHY .............................................................................. 81

vii

LIST OF TABLES

Table 1.1 NDE Classiﬁcation System ......................................................... 2

viii

LIST OF FIGURES

Figure 1.1 Non-Destructive Evaluation System .......................................... 1
Figure 1.2 Non-Destructive Evaluation System ............................................ 7
Figure 2.1 Principles of Eddy Current Testing ............................................. 10

Figure 2.2 Impedance plane trajectory of a coil over a non-ferromagnetic specimen 10
Figure 2.3 Differential and absolute outputs ............................................. 12
Figure 2.4 Tube inspection using the rotating probe coil ............................... 15

Figure 2.5 Typical trigger channel signal alongside signals from pancake and plus point

coils ............................................................................................. 15
Figure 3.1 Schematic of Eddy Current Data Analysis .................................. 18
Figure 3.2 Coil conﬁgurations for trigger signal acquisition ........................... 19
Figure 3.3 (Leﬁ) One-dimensional eddy current signal. (Right) Eddy current data

representation in two-dimension after synchronization ................................. 19

Figure 3.4 Impedance plane representation showing phase characteristics of 100% TW

and 80% TW notch depth .................................................................. 21
Figure 3.5 TSP Segmentation ............................................................... 24
Figure 3.6 TSP Suppression ................................................................ 25
Figure 3.7a Ideal Band Pass Filter ......................................................... 26
Figure 3.7b Band pass ﬁltering in the two-dimensional frequency domain ......... 27

Figure 3.8 TTS suppression using band pass ﬁltering for a tube containing a
circumferential defect along the edge of the TTS ......................................... 29

Figure 3.9 Thresholding algorithm performance for the tube shown in +Pt circumferential
300 kHz ....................................................................................... 30

ix

Figure 3.10a ROI detection using region based adaptive thresholding algorithm 30

Figure 3.1% ROI classiﬁcation for axial ﬂaw indications and noise using rule-bases 31

Figure 3.12 Calibration standard curves (a) Phase (b) Magnitude . .. 34, 35
Fi g 3.13 Magnitude calibration curve using equation .................................... 36
Figure 3.14 Iterative inversion method for solving inverse problems .................. 37
Figure 4.1 The neuron ....................................................................... 39
Figure 4.2 Synaptic connections with a neuron ......................................... 39
Figure 4.3 A simple neural network showing connected nodes .......................... 41
Figure 4.4 Gaussian with c = 0 and r = 1 ................................................... 42

Figure 4.5 Calibrated ﬂaw magnitude distribution (in volts) showing base-line and peak
voltage inside region of interest ............................................................ 46

Figure 4.6 Empirical relationships between optimum thresholds and ratio of peak to base

line voltages in ROI ............................................................................ 47
Figure 4.7 Length estimation scheme ...................................................... 48
Figure 4.8 Effect of varying ROI size on length estimation using twice the standard
deviation in ROI as threshold ............................................................... 49
Figure 4.9 Effect of varying ROI size on length estimation using proposed length
estimation scheme ............................................................................. 50
Figure 4.10 ROI showing arbitrary feature vector structure ............................ 51
Figure 4.11 Original and modiﬁed MET result ............................................. 53
Figure 5.1 Schematic of the overall approach using RBFNN ......................... 58
Figure 5.2 Scatter plot of magnitude vs. depth for training sample at 300 kHz ...... 60
Figure 5.3 Scatter plot of phase vs. depth for training sample at 300 kHz ............ 61
Figure 5.4 Scatter plot of magnitude vs. depth for training sample at 200 kHz ...... 61
Figure 5.5 Scatter plot of phase vs. depth for training sample at 200 kHz ............ 62

Figure 5.6 Scatter plot of magnitude vs. depth for training sample at 100 kHz ...... 62
Figure 5.7 Scatter plot of phase vs. depth for training sample at 100 kHz ............ 63

Figure 5.8 (a - f) Comparison of metallographic ﬂaw proﬁles with proﬁles generated by
different algorithms ..................................................................... 63-67

Figure 5.9 Top Left: two-dimensional representation of calibrated eddy current data
signal with arrow pointing to sample training ﬂaw indication. Top Right: Metallographic
(MET) results plotted against neural network estimated depth proﬁle. Bottom Left:
Structural Proﬁler showing Burst Effective Length and Depth of MET (in red). Bottom
Right: Structural Proﬁler showing Burst Effective Length and Depth of Estimated proﬁle
(in red) ........................................................................................ 68

Figure 5.10 Top Left: two-dimensional representation of calibrated eddy current data
signal with arrow pointing to sample training ﬂaw indication. Top Right: Metallographic
(MET) results plotted against neural network estimated depth proﬁle. Bottom Left:
Structural Proﬁler showing Burst Effective Length and Depth of MET (in red). Bottom
Right: Structural Proﬁler showing Burst Effective Length and Depth of Estimated proﬁle
(in red) ...................................................................................... 69

Figure 5.11 Top Left: two-dimensional representation of calibrated eddy current data
signal with arrow pointing to sample training ﬂaw indication. Top Right: Metallographic
(MET) results plotted against neural network estimated depth proﬁle. Bottom Left:
Structural Proﬁler showing Burst Effective Length and Depth of MET (in red). Bottom
Right: Structural Proﬁler showing Burst Effective Length and Depth of Estimated proﬁle

(in red) ..................................................................................... 70
Figure 5.12(a) MET- Estimated Burst Effective Depth Correlation Statistics 71
Figure 5.12(b) MET- Estimated Burst Effective Length Correlation Statistics 71
Figure 5.13(a) Performance statistics of RBF results on test data ..................... 72

Figure 5.13(b) Performance statistics of enhanced magnitude calibration curve results
on test data ..................................................................................... 72

Figure 5.14 Magnitude values for noisy ROI in 300 kHz channel. (b) Filtered version.
.............................................................................................. 73 — 74

Figure 5.14(a) Top Left: Noisy ROI, Top Right: Corresponding depth proﬁle vs. MET
Bottom Leﬁ: Filtered ROI, Bottom Right: Estimated depth proﬁle versus MET

xi

Figure 5.15(b) Top Left: Noisy ROI, Top Right: Corresponding depth proﬁle vs. MET
Bottom Left: Filtered ROI, Bottom Right: Estimated depth proﬁle versus MET

Figure 5.16 shows calibrated ROI’s corrupted with zero mean noise having different
levels of standard deviations (STD) ........................................................ 77

Figure 5.16 Plot of magnitude values for each circumferential line scan in ROI for
various noise standard deviations .......................................................... 77

Figure 5.17 Plot of phase values for each circumferential line scan in ROI for various
noise standard deviations ................................................................... 78

Figure 5.18 Depth proﬁles of MET against estimated after introducing noise of known
variance ....................................................................................... 79

** Some images in this thesis are presented in color

xii

KEY TO ABBREVIATIONS AND SYMBOLS

ROI — Region of interest

MET - Metallographic Depth Proﬁle

NDE - Non-Destructive Evaluation

ETSS — Examination Technique Speciﬁcation Sheet
A - Difference operator

xiii

CHAPTER 1 Introduction to Nondestructive Evaluation

1.1 INTRODUCTION

Non-Destructive Testing (NDT) is deﬁned as the structural assessment of an
object, material or system without damaging its future utility. In other words, NDT is
carried out in such a way as to preserve the specimen’s structural integrity. In a general
NDT system, an energy source is used to probe the test object with an aim to measure the
interaction of the energy with the test object using a receiving transducer [3]. The
measured signal contains information about structural ﬂaws in the object. The sigma] thus
collected undergoes a series of sigral processing stages that boost the sigial to noise ratio
for accurate ﬂaw detection while minimizing false alarm. Subsequently, classiﬁcation

algorithms are employed for ﬂaw characterization purposes.

 

 

Excitation Loaﬁomshapeﬁze
Source of defect

 

Signal Inversion

    

 

W“ Input Transducer “ V

Structural

Sam le with
p Mechanics

Defects/corrosion

Model

: Signal / Image . 1
Processing

Figure 1.1 Non-Destructive Evaluation System

 

 

 

 

 

1.2 Typical Methods for Nondestructive Testing

The National Materials Advisory Board (NMAB) Ad Hoc Committee on

Nondestructive Evaluation adopted a system [1, 2] that classiﬁes nondestructive methods

into six major categories: visual, penetrating radiation, magretic-electrical, mechanical

vibration, thermal and chemical-electrochemical. A version of the taxonomy of

inspection methods is presented in Table 1.1, with additional categories included to cover

new methods [13].

Table 1.1 NDE Classiﬁcation System

 

Basic cmggoria

Objectives

 

Mechanical and optical

color, cracks, dimensions, ﬁlm thickness, reﬂectivity, strain
distribution and magritude, surface ﬁnish, surface ﬂaws,
through-cracks

 

Penetrating radiation

cracks, density and chemistry variations, elemental distribution,
foreign objects, inclusions, micro-porosity, misalignment,
missing parts, segregation, service degadation, shrinkage,
thickness, voids

 

Electromagretic
electronic

and

alloy content, anisotropy, cavities, cold work, local strain,
hardness, composition, contamination, corrosion, cracks, crack
depth, crystal structure, electrical and thermal conductivities,
ﬂakes, heat treatment, hot tears, inclusions, ion concentrations,
laps, lattice strain, layer thickness, moisture content,
polarization, seams, segregation, shrinkage, state of cure, tensile
strength, thickness, disbands

 

Sonic and ultrasonic

crack initiation and propagation, cracks, voids, damping factor,
degree of cure, deg'ee of impregration, degree of sintering,
delarninations, density, dimensions, elastic moduli, grain size,
inclusions, mechanical degradation, misalignment, porosity,
radiation degradation, structure of composites, surface stress,
tensile, shear and compressive strength, disbonds, wear

 

Thermal and infrared

bonding, composition, emissivity, heat contours, plating
thickness, porosity, reﬂectivity, stress, thermal conductivity,
thickness, voids

 

 

Chemical and analytical

 

alloy identiﬁcation, composition, cracks, elemental analysis and
distribution, grain size, inclusions, macrostructure, porosity,
segregation, surface anomalies

 

 

Table 1.1 continued

 

Auxiliary Categories Objectives

 

Image generation dimensional variations, dynamic performance, anomaly
characterization and deﬁnition, anomaly distribution, anomaly
propagation, magetic ﬁeld conﬁgurations

 

 

Signal image analysis data selection, processing and display, anomaly mapping,
correlation and identiﬁcation, image enhancement, separation of
multiple variables, signature analysis

 

 

The ﬁrst six categories involve basic physical processes that require transfer of
energy to the object being tested. The auxillary category includes processes that provide
for transfer and accumulation of information, and evaluation of the raw sigrals and
images cormnon to nondestructive testing methods. Commonly used methods include
ultrasonic, magietic ﬂux leakage, radiogaphic, penetrant and eddy current techniques. A

brief introduction to some of these methods follows.

1.2.1 Ultrasonic NDT

Based on the principle that solid materials are good conductors of sound waves
and that waves are reﬂected by interfaces or internal material dislocations, beams of high-
frequency sound waves are introduced into the test object for detection of subsurface
ﬂaws in the material. The transducer used in ultrasonic NDE is usually a piezoelectric
element excited by an extremely short electrical discharge, to generate an ultrasonic
pulse. Conversely, an electrical sigral is generated when it receives an ultrasonic sigial.
In general, the probe is coupled to the test material via air, gel or water to minimize
sigral attenuation and back scattering at the probe-material interface. As sound energy
propagates through the material, a ﬁaction of the energy is reﬂected back when

discontinuities are encountered in the wave path. These reﬂected waves due to

 

discontinuities in the object are used for detection of the ﬂaw. The reﬂected beam is

subsequently analyzed to deﬁne the presence and location of ﬂaws or discontinuities.

The most commonly used ultrasonic testing technique is in the pulse-echo mode,
wherein sound is introduced into a test object and reﬂections (echoes) are returned to a

receiver from internal imperfections or from the part’s geometrical surfaces.

The merits of ultrasonic inspection include sensitivity to both surface and
subsurface discontinuities, superior depth of penetration when compared to other
methods, higher accuracy in determining the position, size, and shape of defect and
minimal test object preparation. However, ultrasonic inspection also has its drawbacks.
Defects oriented parallel to the sound beam may be undetected. Accessibility of the
surface for inspection is also an issue. Finally, the skills and training required for
ultrasonic inspection is more extensive compared to other methods. Applications include
inspections for voids, cracks, and laminations, inspections of welds and thickness

measurements [3].

1.2.2 Radiographic NDE

This technique involves the use of penetrating gamma or X-radiation to examine
parts and products for imperfections. An X-ray machine or radioactive isotope is used as
a source of radiation. Energy from the source propagates through a test specimen and the
radiation is directed through a part and onto ﬁlm in order to project an image on the

receiver (X-ray ﬁlm) or recording plane on the opposite side. Signiﬁcant differences in

the received sigral intensity can be interpreted in terms of defects and anomalies in the
test object. Any imperfection in the test object is indicated as density changes in the ﬁlm
in the same manner as how medical X-ray shows fractured bones [3]. All abnormalities in
the test object are viewed on the recording plane as light or dark spots compared to the

rest of the material depending on the properties of the material and anomaly.

Radiogaphic applications fall into two distinct categories, namely, evaluation of
material properties and evaluation of manufacturing and assembly properties. Material
property evaluation includes the determination of composition, density, uniformity, and
cell or particle size. Manufacturing and assembly property evaluation is normally
concerned with dimensions, ﬂaws (voids, inclusions, and cracks), bond integity (welds,

brazes, etc.), and veriﬁcation of proper assembly of component pieces.

1.2.3 Electromagnetic NDT

In electromagretic NDT methods, the energy source is electric and magretic
ﬁelds. Some of the popular electromagnetic methods are potential drop, magreto-static
leakage ﬁeld, and eddy current methods. The magnetic leakage ﬁeld technique uses direct
current as the excitation source, while the eddy current method uses an alternating
current. In this thesis work, the particular area of interest in electromagnetic NDT
techniques is the eddy current testing method. The eddy current induced in the test
specimen are affected by the variation of one or more properties such as magietic

permeability, electric permittivity or electric conductivity of the test specimen.

Consequently the measured signal carries information about the shape, size and location
of defects in conducting materials.
1.3 Eddy Current Inspections of Heat Exchange Tubes in Nuclear Power Plants
Eddy current testing methods are widely used for inspecting heat — exchange
tubes in steam generators in nuclear power plants. Figure 1.1 shows the typical layout of
the heat transfer system in nuclear power plants. Nuclear ﬁssion in the reactor generates
heat energy which is conveyed via the primary coolant circulating within the nuclear
vessel. The primary coolant dissipates the heat energy into a water-steam mixture as it is
circulated through a set of tubes in the steam generator. The hi gh-pressure vapor is forced
through the secondary loop and is used to drive the steam turbines. While in primary
loop, the coolant is radioactive, the coolant in the secondary loop is not radioactive. It is
critical to keep the radioactive coolant from contaminating the non-radioactive coolant
water [5]. Frequent inspection of the steam generator tubes is therefore mandatory in

order to keep the whole system free from radioactive leakage.

Secondary Loop

 
 
 
  

Pressurizer

n- ”www.-

I': Circulating
- Pump

 

Primary Loop

Figure 1.2 Heat transfer system in nuclear power plants [5]

During the tube inspection, an eddy current probe is inserted at one end of the heat
exchange tube after which it translates at constant velocity towards the other tube end. As
the eddy current probe describes a raster scan within the tube, its impedance is measured
as a function of time (or location in the tube). The data obtained in the inspection process
must be calibrated and compensated for the variation in probe characteristics and
instrument conﬁguration settings. The sigral is then analyzed and interpreted in terms of
location, shape and size of defect in tube wall. This thesis describes the development and

evaluation of procedures for proﬁling defects in the steam generator tube wall.

1.2 Scope of Thesis

This thesis addresses the problem of defect characterization using neural network
interpolation techniques. The radial basis function neural network is the ﬁamework in
which features ﬁ'om eddy current data are analyzed for defect characterization purposes.
A radial basis function (RBF) is a real-valued function whose value depends only on the
distance from its center, referred to as the basis center. These functions are used in
function approximation, time series prediction, and control. A weighted combination of
radial basis ﬁrnctions can be used to interpolate any continuous function with arbitrary
accuracy on a compact interval. In this thesis they are used for approximating the depth
proﬁle of a defect.

This thesis is organized as follows:

0 Chapter 2 introduces the principles of eddy current testing techniques and gives a

brief description of the theory of the eddy current method. This chapter also

includes the description of the measurement system used to inspect the steam

generator tubes in nuclear power plants. In addition, a description of data analysis
system including data preprocessing and sigral enhancement is included.

Chapter 3 gives an overview of conventional defect proﬁling methods. The merits
and demerits of these techniques are discussed in this chapter. The radial basis
function theory is described alongside the implementation of the concept for the
purpose of defect proﬁling.

Chapter 4 describes the neural network and the radial basis function neural
network in particular. The method of implementation of the radial basis function
neural network for steam generator tube depth proﬁling is explained.

Chapter 5 ﬁrst provides a description, comparison and conclusion of the
experimental results obtained using conventional defect proﬁling methods and the
radial basis function interpolation approach. The effect of noise and eddy current

data ﬁltering on the defect proﬁling method is also demonstrated.

CHAPTER 2

2.1 Principles of Eddy Current Testing and Its Application in Steam Generator
Tube Inspection [14]

The basic principle underlying eddy current inspection methods can be illustrated
with a simple arrangement shown in Figure 2.1. When a coil carrying an alternating
current is brought in close proximity to an electrically conducting, non-ferromagnetic test
specimen, an alternating magnetic ﬁeld is established. This ﬁeld causes currents to be
induced in the conducting test specimen in accordance with Faraday’s law of
electromagretic induction. The induced currents are called eddy currents since they
follow closed circulatory patterns that are similar to eddies found in water bodies. The
alternating eddy current, in turn, establishes a ﬁeld whose direction is opposite to that of
the original or primary ﬁeld. Consequently, the net ﬂux linkages associated with the coil
decreases. Since the inductance of a coil is deﬁned as the number of ﬂux linkages per
ampere, the effective inductance of the coil decreases relative to its value if it were to be
suspended in air. The presence of eddy currents in the test specimen also results in a
resistive power loss. The effect of this power loss manifests itself as a small increase in
the effective resistance of the coil. An exaggerated view of the changes in the terminal
characteristics of the coil is shown in Figure 2.2 where the variation in resistance and
inductance is plotted in the impedance plane. When a ﬂaw whose conductivity differs
from that of the host specimen is present, the current distribution is altered.
Consequently, the impedance of the coil changes relative to its value obtained with an

unﬂawed specimen, as shown in Figure 2.2. Systems that are capable of monitoring the

changes in impedance can, therefore, be used to detect ﬂaws in a specimen that is

scanned by a coil.

     
     

Conducting
Material

Figure 2.1 Principles of Eddy Current Testing [3]

X A. Coil in the air.
B. Coil over a nonferromagietic specimen
A with a ﬂaw or defect.
C. Coil over a nonferromagretic specimen
without a ﬂaw or defect.

 

 

= R

Figure 2.2 Impedance plane trajectory of a coil over a non-ferromagretic specimen [3]

2.2 Eddy Current Transducers

Eddy current transducers may be categorized according to coil conﬁguration into
absolute and differential eddy current transducers [5]. Absolute eddy current transducers,
usually consisting of a single coil, directly measures the absolute coil impedance rather
than its differential value and can detect both gadual and sharp changes. However a
disadvantage in using absolute transducers is that small changes of the impedance due to
a ﬂaw are often superimposed on the large value [5]. The obvious limitation of this form
of inspection is that no difference in cross-section occurs if a defect is continuous for the
whole length of the material [7].

Furthermore, lift — off and probe wobble can mask the small changes of coil
impedance due to defects thereby making sigral analysis difﬁcult.
In contrast, differential eddy current transducers consist of a pair of coils with a
conﬁguration such that the net value of the impedance is the vector difference of the
individual coil irnpedances. Undesirable effects due to lift — off and probe wobble is
eliminated because they generally have the same impact on both coils [5]. In general,
differential eddy current transducers more sensitive to impedance change than absolute

eddy current transducers.

11

 

 

 

 

 

 

 

)-=o
Differential output
J L_

Absolute output

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.3 Differential and absolute outputs [7]

2.3 Multi-frequency Eddy Current Signals
2.3.1 Skin Effect

The skin effect is the tendency of an alternating electric current (AC) to distribute
itself within a conductor so that the current density near the surface of the conductor is
greater than that at its core. That is, the electric current tends to ﬂow at the "skin" of the
conductor. The skin effect causes the effective resistance of the conductor to increase
with the frequency of the current [14].

Mathematically, the current density J in an inﬁnitely thick plane conductor

decreases exponentially with depth 6 from the surface, as follows:

J = J "5“
Se ................ (2)

where d is a constant called the skin depth. This is deﬁned as the depth below the surface

of the conductor at which the current density decays to l/e (about 0.37) of the current

density at the surface (J5). It can be calculated as follows:

12

................... (3)

where

p = resistivity of conductor

co = angular frequency of current = 2n X ﬁ'equency

u = absolute magretic permeability of conductor and is equivalent to the product
of 110 and [1,, where no is the permeability of ﬁee space and u, is the relative
permeabilty of the conductor.

Due to skin effect in test specimen, single frequency eddy current testing does not
provide an exhaustive evaluation of steam generator tubes at all tube depths. However,
multi-frequency eddy current testing circumvents this limitation by providing extra
characteristic information at various portions of the tube depth. This is because lower
ﬁequencies have larger skin depths and hence detect strong indications of support
structures that are located outside of the tube such as support plates. On the other hand,
higher ﬁequencies have shallower skin depths and detect strong indications of ﬂaws
located closer to the surface. Multi-frequency eddy current testing involves measuring
coil impedance simultaneously using several excitation frequencies in one probe pull [6].
The availability of multi-frequency data also allows for the suppression of undesired

discontinuities and enhances ﬂaw classiﬁcation and characterization results.

2.3.2 Eddy Current Testing Probes
Three types of multi-frequency probes are used in practice namely the bobbin coil

probe, rotating probe coil and array probe. The bobbin coil probe consists of two

13

nominally identical coils connected in a differential mode and excited at multiple
frequencies. Due to the relatively low resolution in raster scan, the bobbin coil probe is
mainly used for the initial detection of possible degradation to quickly determine those
areas of the tube requiring additional inspection with other types of probe that have

improved ability to size and characterize degadation, such as rotating probes [6].

The array probe is a relatively newer probe type and is desigred to provide higher
resolution coverage of the tube with inspection speeds approaching that of bobbin coil
inspection. However, the resolution of the probe, especially along the circumferential

direction, is poor [6].

From a resolution measurement perspective, the rotating probe coil (RPC) is the
most superior eddy current probe. The eddy current data used for the implementation of
the depth proﬁling methods described in subsequent chapters were obtained using the
rotating probe coil. This is large due to the relatively high resolution offered by the
system. Figure 2.5 shows a probe consisting of a low frequency pancake coil, plus-point
coil and high-frequency pancake coil rotating and translating inside a tube. Typical
sigrals generated by a multi-frequency-rotating probe testing system are shown in Figure
2.6 where the trigger sigral marks the probe circumferential position and is used to
transform the one-dirnensional sigral to form a two—dimensional image. The low
frequency channel is usually desigred to locate external structures such as tube support

plates (TSP) and tube sheets (TS).

l4

Axial

direction

 

Eddycuuenteoils

Figure 2.4 Tube inspection using the rotating probe coil

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pancake _ h “A
400 kHz -
Circ 300 kHz
Tri er Channel . ‘ ‘ ‘ I I
gg .lJ H H ll ll ll ll ll ll ll l H llld
Low frequency . ' I I I | '
Sigral (20 kHz) -

Figure 2.5 Typical trigger channel sigral alongside signals from pancake and plus point
coils. [6]

The next chapter introduces the eddy current sigral pre-preprocessing stage and the

sequence of step taken to identify regions of interest. Conventional depth proﬁling

methods is also explained.

CHAPTER 3 Eddy Current Probe Data Analysis

3.1 Introduction

Several issues in the eddy current inspection system pose difﬁculty in the
characterization of ﬂaws. These include poor resolution of the probe raster scan relative
to the physical dimensions of the ﬂaw, the variation of probe axial velocity about the
nominal value and the quantization errors introduced when the analog eddy current sigral
is sampled and digitized. Furthermore, additive noise generated due to corrosion deposits,
shot and thermal noise introduce errors in sigral measurement. These factors act in

combination to make ﬂaw characterization a challenging task for the sigral analyst.

In order to extract meaningful information ﬁom the raw eddy current data, various
techniques and data manipulating operations are employed which include - in sequential
order - sigral preprocessing, ﬂaw sigral detection, classiﬁcation and characterization.
Figure 3.1 shows a schematic of the approach for eddy current data analysis for steam

generator tube evaluation

. 3.1. 1 Signal Preprocessing

This stage of the data analysis includes sigral processing algorithms that perform sigral
synchronization and calibration. The rotating probe coil system comprises three different
probe types, namely pancake, axial and circumferential plus point coil probes. Sigrals
from each of these coils can be resolved into a vertical and horizontal channel. The axial

and circumferential plus point coils are sensitive to axial and circumferential ﬂaws,

16

respectively, whereas pancake coils are sensitive to both types of ﬂaws. Each of these
coils is excited at multiple frequencies (typically 300 kHz, 200 kHz and 100 kHz) giving
rise to about 28 - 32 channels altogether in the rotating probe coil system although some
channels are redundant during the data acquisition process. The responses due to changes

in coil impedance are sampled and saved in digital format for subsequent analysis.

An alternative conﬁguration for the rotating probe uses two pancake and one plus-
point coil probes. The plus point coil consists of two coils that are oriented orthogonal to
each other [6]. The probe conﬁgurations, along with the excitation frequencies, are given
in Table 3.1. Type A and B also possess axial encoder and trigger channels. Since each
frequency component can be resolved into horizontal and vertical channels, there are 10 x
2 = 20 channels and 9 x 2 = 18 channels for type A and B respectively. In addition, two
axial encoder channels and two trigger channels bring the effective number of active

channels for type A and B to 24 and 22 channels respectively.

Table 3.1 Rotating probe conﬁgurations and inspection frequencies [6]

 

Probe Axial Circumferential Pancake HF Pancake(0.080” Plus
types (kHz) (0. l 15” diameter) diameter) Point

 

TypeA Excitation 400,300,200 400,300,200 400,300,200,
20

 

 

 

 

 

 

 

 

 

 

Frequencies
Type B (kHz) 300, 200, 100, 600, 300 300,
10 200,
100
** Type A and B possess trigger and axial encoder channels which are not included in
table.

 

 

 

 

RPC RAW DATA

 

 

 

 

 

/ SYnChronizaﬁon
- .
Signal Preprocessmg

Landmark

\L \ Detection
\

Flaw Signal Detection

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sigral
Classiﬁcation

 

 

 

 

 

Signal

Characterization

 

 

 

Figure 3.1 Schematic of Eddy Current Data Analysis

3.1.1.1 Synchronization

During tube inspection, the angular velocity of the RPC deviates minimally from
its nominal value which, in turn, varies the number of samples per pitch as the probe
translates along the length of the tube along a spiral path. In order to provide accurate
synchronization points for each probe rotation, a trigger sigral is generated
simultaneously during probe operation. The trigger sigral consists of four local
synchronization pulses generated at 72°, 144°, 216° and 288° and a main synchronization
pulse which occurs at 360° as shown in Figure 3.2. Figure 3.3 shows the wrapping of a

one-dimensional eddy current sigral into a two-dimensional representation.

18

\main sync

’OM
M ‘/ local sync

Figure 3.2 Coil conﬁgurations for trigger sigral acquisition [6]

Axial
Direction

 

nan-Olumnmu

 

 

 

   

In in er in mi rm m1 at
Amplitude

Circumferential direction

Figure 3.3 (Leﬁ) One-dimensional eddy current signal. (Right) Eddy current data
representation in two-dimension after synchronization [6]

19

3.1.1.2 Calibration

For proper sigral classiﬁcation, it is imperative to determine properties such as
voltage or phase of the test specimen sigral, by measurement or comparison with sigrals
ﬁ'om standard or reference specimen for which such sigral properties are known. The
reference specimen must possess similar metallurgical properties and physical
dimensions as the material being inspected. Notches of known depths are introduced into
the reference specimen in order to set a standard voltage and phase (by sealing and
rotation respectively) for the reference notch sigral, and in turn, the test specimen signal.
This is essential in order that actual defects may be properly classiﬁed relative to the

reference defects.

Proper classiﬁcation and characterization of tube degradations is signiﬁcantly dependent,
among others, on sigral phase. Phase lag of EC sigrals provides a reasonable estimate of
the ﬂaw depth and by setting a suitable phase interval in which the phase lag of
characteristic ﬂaw sigrals are contained, noise-discrirrrination algorithms may be used to
reduce or eliminate false calls from pseudo-ﬂaw sources such as support-plates and

corrosive deposits.

20

 

Figure 3.4 Impedance plane representation showing phase characteristics of 100% TW
and 80% TW notch depth [6]

Figure 3.4 shows the impedance plane representation of a signal from a tube
support plate, a 100% through wall (TW) ﬂaw and an 80% inner diameter ﬂaw [6]. The
three sigrals have distinctive phase characteristics and this discriminating property can be
used to determine the sigral class and estimate depth of a ﬂaw. In order to correct for
possible phase offset due to differing probe responses and instrumentation setup, a phase
calibration process is applied in industrial practice. As standard practice in industry, the
phase corresponding to the 100% TW notch sigral from the calibrating tube is rotated by
a calibration phase factor P so that the resultant phase is 35° measured anti-clockwise
from the negative x-axis. All test data from this calibration group undergoes the same
extent of phase rotation given by P. This process is done independently for each

frequency channel and coil type data.

21

In voltage scaling, the magritude of the sigral corresponding to a through-wall
hole is ﬁrst scaled to a ﬁxed value giving a magritude calibration factor M. The
magritude calibration factors, one for each frequency, are obtained by normalizing the
maximum magritude of the data ﬁ'om a 100% through-wall defect to a ﬁxed value
(usually 20 volts). The raw test data is then sealed by this same factor M, channel-by-
channel. These magritude scaling factors are computed for each coil at its primary
frequency, typically the highest frequency (300 kHz) of coil excitation — and applied to
the corresponding data in each channel [6]. In other words, the magritude scaling factor
obtained by calibrating the 300 kHz channel data (axial, circumferential and pancake) is

applied to the 200 kHz and 100 kHz ﬁ'equency channels.

3.1.1.3 Tube Support Segmentation

Since ﬂaws are more likely to develop in the vicinity of support plates and other
support structures, a low ﬁequency measurement is ﬁrst used to identify the location of
such regions. Figure 3.5 shows a typical image obtained after segmentation. In practical
eddy current testing, low frequency sigrals (usually at 10 kHz or 20 kHz) are used to
locate external support structures such as tube support plates (TSP) or top of tube sheet
sigrals (TTS). The data from the tube is then segnented into smaller regions around each
support structure, which are analyzed separately with defect positions reported relative to

these support structures.

As shown in Figure 3.5, an edge enhancement operation using a Sobel edge detector is

employed to identify the edges of the TSP. The source image is represented by f (x, y)

where (x, y) denote the pixel locations of the image. The Sobel edge magritude image

22

|Vf (x, y] is given by

 

lVf(x.y)| = «91;;le +[ 1851)]2

=Jvoe+e®r a,

where s is the vertical edge detection ﬁlter, and t is a horizontal edge detection ﬁlter

 

given below:

 

 

 

 

S :: -2 (Jay) 2 t= (Icy)

 

 

 

 

 

 

 

 

 

 

 

 

(3-2)
The magritude of Vf (x, y) is then compared with a threshold T to determine

candidate boundary points. Assuming x = l,..., M and y = 1, ..., N; where M and N
represent the number of columns and rows respectively in the two dimensional

representation of the eddy current signal, then the threshold T is set at [23]

 

T=rfﬂlﬂz+azl (3-3)

where ,B is a constant, p is the mean, and 0‘ is the variance of the image deﬁned by

1 M N M N 2
PEN-22m»,ﬁﬁ/zgwsw) (34)

x=1 y=1 x=1 1

 

23

Axial direction (pixels)

Axial direction (pixels)
AXIal direction (pixels)

..5

800

900

     

1000

20 40 so so ' 20 40 so so 20 40 so so
Circumferential direction (pixels) Circumferential direction (pixels) Circumferential direction (piXBIS)
(a) (b) (C)

Figure 3.5 TSP Segmentation: (a) Low Frequency Signal, (b) Binary Image after Sobel
edge detection, (c) Segmented Signal

The location ofthe TSP is then marked as the segment start point. Since the width ofthe
TSP is ﬁxed, it is also used as an axial scale standard to convert distance measures in

image pixels to true distance (inches or millimeters).

3.1.1.4 Tube Support Suppression

Once support regions have been identified, sigrals from these structures need to
be suppressed to enhance ﬂaw signals (see ﬁgure 3.6). This suppression consists of two
steps. The ﬁrst step removes signals from structural discontinuities, such as tube support
plates or tube sheets, by removing the median value in each circumferential revolution.
Here, the median value is treated as the defect-free reference sigral. The second step is to

remove low frequency noise. The median value along the axial direction is subtracted to

24

accomplish this objective. Let 5,. be the signal from the ith element along the column
(circumference) or row (axial) directions and let N represent the total number of columns

and rows in the image. If m, is the median of the sigral from the 1"“ column or row, then

the suppressed signal is expressed as

s.=s.—m., i=1,2,~--,N. (3-5)

I I I

u—ami—n.x>
h—l”u.x>

Doﬂ-"OoH—uc
no-~oo-—U

 

Circumferential direction
(a) (b)
Figure 3.6 TSP Suppression: (a) vertical component of raw eddy current data at 300 kHz
(b) data after TSP suppression
3.2 Band-Pass Filtering, Adaptive Thresholding and ROI Detection
Band-pass ﬁltering is used to remove undesired artifacts and noise signal
indications in the eddy current data. First, consider a low-pass ﬁlter that attenuates high

frequency components of the signal that exists beyond a speciﬁed frequency denoted by

25

distance Do from the origin of the centered transform. This two-dimensional ideal low—

pass ﬁlter has the transfer function

S( )_ l D(u,v)SDo (36)
u,v — 0 D(u,v)>Do .......... .

\
__-_,
I

«1"

’’’’’

0.8

0.6

ma:--—-u3>

  
   

0
Frequency

(u axis) -1 Frequency

(v axis)

Figure 3.7a Ideal Band Pass Filter

where D0 is a speciﬁed non-negative quantity and D(u,v) is the distance from point (u,v)
to the origin in the frequency domain . Assuming the synchronized two-dimensional eddy
current data is of size M x N, then the centered transform which is also of the same
dimension has its origin at (u,v) = (M/2,N/2). As a result, the distance from any point

(u,v) to the center (origin) of the Fourier transform is deﬁned as [31]
D(u,v)=[(u—M/2)2 +(v‘—N/2)2]“2 ....... (3.7a)

A band-pass ﬁlter removes or attenuates a band of frequencies about the origin of the

Fourier transform. An ideal band-pass ﬁlter is given by the expression

26

0, D(u,v) < (Do ~ %)
S(u,v) = 1, (Do —-P::) S D(u,v) S (Do + g)

0, D(u,v) > (D0 + g)

..................... (3.7b)

where W is the width of the pass-band and D0 is its radial center [31]. Figure 3.7a shows
a surface plot of an ideal band pass ﬁlter and ﬁgure 3.7b shows the performance of band

pass ﬁltering on the raw data.

   

A A
x
x .
. i
1
a a
l l
Flaw
Signal D
D . . .
i Indication r
r
r
e
e
c . c
t t
i Undesired Artifact i
' o
0 ~
n
n .
Circumferential Direction (pixels) Circumferential Direction (pixels)

(3) (b)

Figure 3.7b Band pass ﬁltering in the two-dimensional frequency domain. (a) vertical
component of raw eddy current data at 300 kHz (b) data after band-pass ﬁltering

27

Following ﬁltering, a region detection algorithm is used to identify potential
locations of ﬂaw signal indications, called the Regions of Interest (ROI). The R01 is
obtained using adaptive thresholding. Eddy current data collected from different locations
in the tube possess different signal characteristics and hence thresholding schemes have
to be adaptive based on the quality of data at hand. One method involves setting an
absolute threshold for magritude and an interval threshold for phase values. In magnitude
thresholding procedure, signals whose magnitude is less than the threshold level are
treated as noise and set to zero. In phase thresholding or phase gating, signals with phase
angles outside a speciﬁed interval (ﬂaw plane) are eliminated. In an alternate ROI
detection procedure an adaptive thresholding scheme is used to optimally vary the
threshold value for different regions in the tube. This scheme computes the histogarn of

voltage values in a local segnent of image. The threshold is then computed as:
t = ,u + K [max(VL ) — min(VL )] (3.8)
where, p. = Median of the voltage values in a local (segnented) region of the image

V1, = Set of voltage values that lie in three bins around the median value in the

voltage histogram of the local (segnented) region of the image

K = Constant, chosen based on the magritude of the 20% axial ID defect in the

corresponding calibration ﬁle

t = Threshold chosen for the local region

A single threshold computed using mean u and standard deviation 0 of the data

collected from more than one tube region often yields sub-optimal performance during

28

ﬂaw detection. The variant of the adaptive thresholding scheme computes individual
thresholds for data from different tube sections based on their local statistics. The ROI

detection scheme can be represented mathematically as follows:

r

= ﬂaw, ixii2r.

noise, Ix; |< 2', (39)

where Tr = 77 percentile (X r) is threshold for sample xk in rth tube region
and n is a scalar ranging from 0 to 100. The binary images obtained by thresholding the
ﬁltered data is fused by performing a logical intersection of the binary images across
frequencies channels. Such data fusion results in high detection rates along with low false
call rates. Figure 3.8 and 3.9 shows the performance of band pass ﬁltering on sample

data, and ROI detection using adaptive thresholding.

.--'.'

    

. _ Axial 1!
direction a E Circumferential direction direction 0 Circumferential direction
Figure 3.8 TTS suppression using band pass filtering for a tube containing a
circumferential defect along the edge of the TTS (a) Original +Pt Circumferential 300
kHz (b) Filtered +Pt Circumferential300 kHz

29

—-m—..x>

=o—l.ﬂOo—1_-U

U
1500

 

Axial 500 20
direction 0 0 Circumferential direction

. Figure 3.9 Thresholding algorithm performance for the tube shown in +Pt
Circumferential 300 kHz

Flaw Signal Indication
. 21])
, B
Drilled (B)
100
- Threshold
0

 

888
f >

  
 

:o—-.-.o¢-g-1_..U

Flaw Signal Indication

11]] .
Free Span (C)
50 C
Circumferential Direction
Circumferential Direction ThICShOId

D0 005 0.1 0.15 0.2
Figure 3.10a ROI detection using region based adaptive thresholding algorithm.

 

 

30

3.3 Classification

After the regions of interest (ROIs) are identiﬁed, a classiﬁcation algorithm is
applied to classify each ROI into one of several classes. Figure 3.103 shows the image of
vertical component of the thresholded eddy current RPC data with potential defect
indications identiﬁed after ﬁltering. Each of these indications is processed individually by

the classiﬁcation routines.

The classiﬁcation module consists of two steps, namely, feature extraction and
classiﬁcation. A feature extraction algorithm is used to extract features ﬁ'om the
preprocessed data in the ROI. Features such as maximum magritude in the ROI and its
corresponding phase value are samples of features. The extracted features are subjected
to a classiﬁcation algorithm or rules for discriminating between actual defects and noise.
The rule base contains a set of heuristically obtained rules that are that are formed by
using predicate logic [6], and are applied sequentially to eliminate false calls, and retain
true ﬂaw indications. For example, let the maximum magritude (vertical 300 kHz axial
channel) in a region of interest be denoted as M. Furthermore, let the corresponding
phase values across 300 kHz, 200 kHz and 100 kHz axial channel be denoted as P3, P2

and P1 respectively. Then the following rules apply for calibrated ﬂaw data:

1. Outer diameter (OD) axial ﬂaw:
0 P3 235, P2 235, P1 235 (deﬁnes ﬂaw plane for OD defects)
0 P35 180, P2 5 180, P; S 180 (deﬁnes ﬂaw plane for OD defects)

0 P3 2 P2 2 P1 (deﬁnes order in ﬂaw plane)

31

2. Inner diameter (ID) axial ﬂaw:

0 P320, P; 20, P120 (deﬁnes ﬂaw plane for ID defects)

0 P3 < 35, P; < 35, P. < 35 (deﬁnes ﬂaw plane for ID defects)

0 P3 2 P2 2 P. (deﬁnes order in ﬂaw plane)
3. Maximum magnitude in ROI, m 2 M

Figure 3.1% shows an illustration of ROI classiﬁcation using the rule bases. M is

typically obtained by identifying a conservative lower bound above which the
magnitudes of ﬂaw sigral indications in the training data are greater.

Calbrated Data Binary Image alter thresholding Classiﬁed ROI’s

    

200

Noise

lUED .
Axtal ﬂaw
1200 indications
1800

20 40 60 80 an in an m 20 40 60 80

400
500
800

1000

1200 1200

1400 1400

1600 lBC[

 

18C[

   

Figure 3.10b ROI classiﬁcation for axial ﬂaw indications and noise using rule—bases.
The magenta and black rectangles in (c) correspond to classiﬁed axial ﬂaws and noise
respectively
3.4 Defect Characterization
Defect characterization is the estimation of the depth proﬁle of the detected defect
ROIs. Several factors contribute to distortion of the measured eddy current sigral. One
example is the limitation of the resolution of inspection system relative to the ﬂaw length.

In other words, the resolution of the horizontal eddy current scans in a two-dimensional

32

ROI must be sigriﬁcantly larger than the length of the crack in order to obtain a depth
proﬁle at each horizontal slice. Another factor is that the probe speed changes during the
inspection process which introduces errors in the collected data. Additive noise generated
during the scan due to the presence of contaminants and surface roughness can also
introduce noise. Furthermore, when an analog signal is sampled to generate a digital
signal, quantization errors are introduced. This can lead to additional distortion of the
signal. All these issues make defect characterization in steam generator tubes a very
challenging task. The different contemporary characterization algorithms implemented

for defect proﬁling are explained in this section [24].

3.4.1 Calibration Curve

In current industry practice, simple characterization schemes are used to estimate
the ﬂaw length and depth proﬁle for each flaw indication in the processed sigral. One of
the most widely used approaches for sizing defects is the calibration method. In this
procedure, a calibration curve relating ﬂaw depth to corresponding signal phase (or
magnitude) is obtained from the calibration specimen of similar metallographic properties
and physical dimension as the test specimen. For a given defect sigral, its equivalent
depth is predicted using simple interpolation methods. For example, we assume that the
calibration curve f is piece-wise linear between each of the known mapping points. The
phase and magritude computed from ﬂaws in the calibration standard tube are used to
construct the function f. Figure 3.11 and 3.12 shows typical phase and magritude

calibration curves respectively.

33

During inspection, for a given defect sigral, the relationship used to predict the defect

depth when the signal phase is b is given by [3.10]:

 

 

 

 

 

 

 

 

b—
f(b)= f(a)+ c—: [f(c)-f(a)] ................... (3.10)
100
P 300kHzOD
e 90 — 200kHzOD
, 100kHzOD
so ..
c
e 70 ~
n
t so L
a
g 50 '
e
40 _
D 30 ' q
C
P 20 ’
t
h 10 l’
0 4'0 S0 80 100 120 I40 160

Phase (degrees)

Figure 3.11(a) Phase calibration curves

34

é

 

8 8

8

ooemﬁttoorrmv-u
8 5‘

 

 

 

 

 

 

 

D 30 — 300 kHz ‘
e + 200 kHz
p 20 —i— 100 kHz ‘
I 10
h i
U l l l I I
o 5 10 15 20 25 so
Magnitude (volts)

Figure 3.12 (b) Magnitude calibration curves

The defects impressed on the calibrating specimen are man-made and have
dimension that are untypical of cracks due to corrosion or inter granular attack that occur
naturally in the tube during the normal operation of the steam generator. Artiﬁcial ﬂaws
created for the purpose of calibration usually give a higher signal response as compared
to naturally occurring cracks having the same maximum depth. This is because naturally
occurring cracks are thinner and ﬁner in width than calibrating notches. As a result, the
thinner a 100% TW crack as compared to the 100% TW calibration notch, the more it
falls short of the 20V magritude and 35° phase standards after calibration. It is therefore
common to see 100% TW cracks with a phase between 50° - 66° and magnitudes of
about 4V. For this reason, the calibration method is inherently ﬂawed and cannot

accurately characterize ﬂaws.

35

3.4.2 Enhanced Calibration Curve

An alternative approach which may yield better characterization results is to ﬁt a
curve to the data of magnitude and corresponding maximum depth values obtained from
training ﬂaws. The magnitude and maximum depth coordinates are plotted and the curve
is ﬁtted in a least square sense to the scatter plot. This curve can be represented by the

general expression:
10g.(ﬂaw.....) = a0 + a1 log.(ﬂaw,.....-....) ................ (3.11)
The coefficients a0 and al are empirically determined from the available data set. Figure

3.13 shows a magritude calibration curve constructed using the logarithmic mapping.

The resultant curve again serves as the calibration curve.

 

Lh

  
 

 

 

 

 

 

 

 

P
e
I' 4.5 —i
c
e
n 4 - r
t
a
3.5

8 ——.——— 300 kHz on
e 200 kHz OD

3 _ .......... 100 kHz 01)
D
e
p 2.5 ’ -
t
h

.4 -3 -2 -i n l 7 3 4

Log of Magnitude

Fig 3.13 Magritude calibration curve using equation (5)

36

3.4.3 Model Based Proﬁling

Another approach for defect proﬁling is the use of numerical models [33] in an
iterative framework. An application of this method lies in the use of a computational
model, such as the ﬁnite element model [34]. The underlying idea of this approach is
illustrated in the schematic diagram shown in ﬁgure 3.14. It starts with an initial estimate
of the defect proﬁle parameters and solves the corresponding forward problem to
determine the corresponding signal. The error between the estimated and measured
sigrals, F, is minimized by updating the defect proﬁle iteratively. However, this method

tends to be computationally expensive as it requires execution of a 3D FE model in each

 

 

 

 

 

 

 

 

 

 

 

iteration to achieve the desired proﬁle. Experimental

Input Setup

Initial Defect
Proﬁle g Forward Model .
I Yes
Forward Model
No
Update Defect Desired Defect
T Proﬁle Proﬁle

 

 

 

 

 

 

 

 

 

Figure 3.14 Iterative inversion method for solving inverse problems

This thesis aims to investigate a more sophisticated approach for ﬂaw
characterization which employs the use of a trained radial basis function for mapping
magritude and phase values utilizing data at all available frequency obtained from the
plus-point coil onto an estimated depth value. Mathematically, this approach provides a
nonlinear mapping from an input vector (signal feature) space on to an output vector

(defect depth proﬁle) space. The next chapter introduces the underlying concepts of the

37

radial basis function neural network (RBFNN). A proposed ﬂaw length estimation

technique is also explained.

CHAPTER 4 Artiﬁcial Neural Networks

4.1 A Little Biology

The human brain consists of a specialized network of billions of highly
interconnected cells called neurons (see ﬁgure 4.1). Each cell receives electrical signals
from as many as 10,000 other cells and transmits or inhibits an output signal based upon
the input signal pattern [10]. Although modern science may not have an exhaustive
knowledge about the mechanism and functionality of the human brain, it is possible to

mimic some of its abilities such as learning, pattern recogrition and generalization.

The biological neuron consists of four main parts: the body, the incoming channels,
the outgoing channel(s), and the connection points between neurons, which are called
synapses. In other words, the synapses are the gateway for neuron-to-neuron sigral
transmission. A neuron receives many sigrals from other neurons at the synapses in
which some processing occurs before the sigrals are sent down the incoming channel to
the neuron body. This sigral processing is basically achieved by weighing each incoming
signal with the result that each of these sigrals has a different excitation effect on the
neuron. As such, the synapse is traditionally an ampliﬁer or attenuator of input sigrals,
which in turn have a stronger or weaker effect on the receiving neuron. A highly excited

neuron sends out an output sigral while an inhibited one does not (see ﬁgure 4.2).

38

dendrites

     
 

myelin
sheath

 

Figure 4.2 Synaptic connections with a neuron [17]

The primary fimction of the neuron body is to combine all the incoming signals and
determine if the total is enough to send out a signal. In other words, a comparison with an
activation threshold is the decisive criterion for transmitting or inhibiting an output
sigral. Learning occurs in the brain in the form of changes to the synaptic weights [10].
There are a few theories which have been developed to explain how the learning process

works. The general opinion is that synapses change over time as sigrals are received, and

39

this constitutes learning. Knowledge is captured in bits and pieces by the weights
synapses attach to the incoming sigrals. As a result, knowledge is spread out across many

neural connections.

4.2 Artiﬁcial Neural Network

An artiﬁcial neural network (ANN) is a densely interconnected group of
computational nodes or neurons that uses a mathematical model for processing
information. ANN is a massively parallel, distributed processor with the capability to
store and retrieve experiential knowledge [8]. The characteristics of the network are
determined by the nature of the processing elements, and strengths of the
interconnections, known as synaptic weights, which are used to store the knowledge. The
network acquires knowledge by a learning process, which modiﬁes the synaptic weights
in an orderly fashion to achieve a desired objective. The basic neuron model is the single
layer perceptron which accepts an n-dimensional vector and performs a weighted sum,
adds a bias and passes the result through a nonlinear function to yield an output. The
primary use of a perceptron is in pattern classiﬁcation. Patterns are distinct features that
are derived from sigrals of different classes. The single layer perceptron can discriminate
between two classes by separating them with a linear decision boundary in the feature
space. The perceptron model cannot generate nonlinear decision boundaries and as a
result cannot be used in most real world pattern recogrition problems, wherein classes are
not linearly separable [8]. A multilayer perceptron network overcomes this limitation

and can generate highly nonlinear decision boundaries for classiﬁcation problems.

40

4.3 Neurons

Biological and artiﬁcial neural networks alike contain neurons which are
interconnected in order to transfer information from a source to a destination. The
knowledge of a network does not reside solely in a speciﬁc part of the network but is
distributed across the interconnections between the neurons. Every neuron computes its
own output by ﬁnding a weighted combination of the input signals, generating an
activation level and transmitting that to an output or a transfer function. The collection of

weights arranged in rows and columns is called the weight matrix.

 

Figure 4.3 A simple neural network showing connected nodes [18]
4.4 Layers
A neural network consists of neurons connected to each other in layers. The
conﬁguration of the layer structure plays an important role when building a neural
network to achieve a desired goal. Some of these neurons are in direct contact with the
outside world and are usually responsible for directly receiving external stimuli from a
source or delivering directly to a ﬁnal destination point. However, some neurons

communicate with other neurons are called the hidden neurons.

41

The architectural layout of the basic neural network, as shown in ﬁgure 4.3, contains
the input layer, the hidden layer and the output layer. External stimuli from the outside
world, such as a continuous or digital electrical sigral, temperature, pressure or light
energy, are fed into the network by the input layers. The received information is sent to
the hidden layer neurons which lie between the input and output layers. The hidden layer
forms a complex network of neural components that project the neural network’s solution
to the problem. The output neurons further process information obtained from the hidden
neurons. The output information at this point is the neural network’s response to the input
information [10]. A variety of neural network architectures and learning algorithms have
been developed to address a variety of applications, which mainly differ from each other

in the network architecture and deﬁnition of the function computed at each node.

4.5 Radial Basis Functions
Radial basis functions are radially symmetric functions for which the response
decreases monotonically with distance ﬁom a central reference point. A special class of

radial functions is the Gaussian which is deﬁned mathematically by

h(:c) = exp (— (M " CM)

r2

 

................... (4. 1 )
where x is the input vector, c is the position vector of the basis centre in the multi-

dimensional space and r is its standard deviation (see ﬁgure 4.4).

42

 

 

 

 

CI

‘4' r ‘- c.-
4 O 2

Figure 4.4 Gaussian with c = 0 and r = 1

4.6 Radial Basis Function Neural Networks

A radial basis function (RBF) is a powerful tool for interpolation in multi-
dimensional space. The architecture of RBF networks, in its most basic form, involves
three layers as shown in Figure 4.3: an input layer of source nodes, 3 single hidden layer
which operates as a kernel node, and an output layer. The nodes in the hidden layer are
characterized by a set of basis functions, typically a Gaussian basis function. The centers
of the basis functions are determined from a scatter plot of variables by using a clustering
algorithm. The spread (standard deviation) of the basis functions are proportional to the
cluster size. The objective of the network is to determine an input-output mapping
function using the training data. The mapping function determined by the output
interconnection weights is determined by a matrix inversion step (assuming matrix is
invertible). The mapping estimated provides the best ﬁt to the data in a statistical sense.
The mapping is accomplished in two stages. First, a nonlinear transformation connecting
the input layer to the hidden layer is deﬁned by a set of radial basis functions. A linear
transformation is then performed between the hidden layer and output layer.
Subsequently, an interpolation is performed during a generalization process with

unknown data [20]. In contrast to statistical analysis where approximations are performed

43

on complete data sets, RBF’s use a subset of data with the aim of estimating the

characteristics of data outside the subset by interpolation techniques.

Suppose we want to approximate a real valued function f(x) by s(x) given the set of
values f = (fl, ..... , ﬂ.) corresponding to the real-valued input points x = {x}, ...... , xn},
then an expression for s(x) using RBF’s is given in equation (4.2) where p(x) is a

polynomial,

s(x) = p(x) + 24.430 x — xi I) ............... (4.2)

.1,- is a real-valued weight, I * | represents the Euclidean norm, 4) is the basis function and
Ix — xil is a measure of the distance between x and the basis center xi. Proper training of
the network requires optimization of the weight parameters which is critical to reducing
the error between f(x) and s(x). A simple training algorithm to achieve this stems from

the gradient descent approach. Gradient descent is based on the observation that if the

real-valued objective function H(w) is deﬁned and differentiable in a neighborhood of a
point a, then H(w) decreases fastest if one goes from a in the direction of the negative

gradient of H(w) at a (i.e. along -AH(W)) [19]. It follows that, if

b = a — 7 [-AH (w)] ................ (4.3)

44

for y > 0 a small enough number, then H(a) Z H(b). With this observation in mind, one
starts with a guess W0 for a local minimum of H(w), and considers the sequence Wo ,

WI, W2 ...such that

WU + 1) = WU) " J’i—AH(W)] ..................... (4.4)

We then have H(Wo) Z H(Wl) _>_ H(Wz) . . .. and the sequence Wt converges to the

desired local minimum. In particular, gradient descent training requires that the weights
be adjusted at each time step by moving them in a direction opposite from the gradient of

the objective function [19].

4.7 Depth Proﬁling Using RBFNN

In the proposed depth proﬁling algorithm using RBFNN, there are two major steps. The
ﬁrst step is to estimate the length of the defect and the second step is depth proﬁle along
the length of the defect. Length is typically deﬁned along the axial direction for axial

cracks and along the circumferential direction for circumferential cracks.

4.7.1 Length Estimation

The ROI selected by an analyst typically contains a region around the defect.
Due to the presence of additive white and colored noise in the eddy current data, it is
essential to accurately discriminate between noise and true defect indications in the
measured signal for the purpose of depth proﬁling. Setting a magritude threshold and/ or

a phase interval are two possible strategies towards this goal. However, the efﬁcacy of

45

this approach is compromised when eddy current data of low sigral to noise ratio is
analyzed. From empirical studies, the magritude thresholding and phase windowing
method produces satisfactory ﬂaw length estimates when the signal to noise ratio is high
and defect depth value is over 30% TW. Flaw length estimation techniques employed in
this research relies on an adaptive threshold scheme based on the statistical properties of
the synchronized calibrated two-dimensional eddy current signal in the region on interest

(ROI).

Peak Voltage

   

Baseline Voltage . '°

Figure 4.5 Calibrated ﬂaw magritude distribution (in volts) showing base-line and peak
voltage inside region of interest
In order to deﬁne the parameters required for the proposed ﬂaw length estimation
technique, consider the surface plot of the ROI in ﬁgure 4.5. The ratio, 7, of the
maximum sigral magritude and the base-line magnitude inside the ROI (see ﬁgure 4.5)

follows an empirical relationship with the optimum magritude (11) threshold given by

46

77 =aexp{—/l[y—yo]}% ................... (4.5)

where the constants 0., A. and yo are determined empirically from the available proﬁling
data such as shown in ﬁgure 4.6. The curve in ﬁgure 4.6 was obtained by ﬁnding the
coefﬁcients of a piece-wise polynomial that ﬁts the scatter plot in a least-squares sense as

given in equation (4.6). From the piece-wise curve ﬁt, a, A. and 70 can be determined.

10*exp [-0.0151*(7- 1)], “y S 152

Threshold = {
1.0, otherwise

 

 

 

 

 

 

(4.6)

12 F f T

‘* ¢ 1"
«p-
‘O' * *-
*+ ‘i *i‘ * ‘i *
-2 1

U 50 100 150 2(1) 250 3(1)

Ratio of maximum magnitude in R01 to baseline

Figure 4.6 Empirical relationships between optimum thresholds and ratio of peak to base
line voltages in ROI

The ﬂaw length is estimated by multiplying the number of horizontal slices that contain
magritudes greater than the threshold with the axial scale (length units per horizontal

slice) to yield the ﬂaw length in inches. A sample ﬂaw length estimation process is

47

shown in ﬁgure 4.7. The number of horizontal slices having magnitudes greater than the

computed threshold is averaged across frequency channels.

 

A A
X X 5
i i 10
a a 15
l l
20
d d 75
i . i Circumferential direction
1' r Circufnfefentihldiiec'tibn'ﬁiiiie'ls)
e C
c c
t t
i i
O O
n n

  

     

Circumferential direction Circumferential direction

w

LU W w
. . . . . z
Circumferential direction (pixels) Circumferential direction (pixels)

Figure 4.7 Length estimation scheme. Left: vertical component of raw eddy current data
at 300 kHz with R01 indicated. Top right: Magnitude distribution in ROI with 29
horizontal slices. Bottom right: Binary image of thresholded ROI. Axial s an of the
effective ROI (corresponding to white pixels) ranges from the 8m to the 22n horizontal
slice making a total of 15 slices. Estimated length of defect equals 15 multiplied by the
axial scale (length units per horizontal line scan)

Current thresholding schemes employ statistical variance of data within the region
of interest for threshold computation. Typical threshold levels are set at 2 or 3 times the
standard deviation. However, this scheme becomes ﬂawed if the dimension of region of
interest is not ﬁxed. In the event that the ROI is selected manually in a semi-automated
length estimation scheme, the standard deviation of the signal magritude within the ROI
becomes dependent on the selected ROI size and, in turn, affects the ﬂaw length estimate.

This process poses a poor repeatability strategy. On the other hand, the proposed method

48

offers better repeatability as the maximum magnitude in the R01 is a constant. The base-
line voltage, however, can be made independent of ROI size by applying a two
dimensional median ﬁltering operation in the signal pre-processing stage. Therefore, the
computation for y in equation 4.5 is a constant irrespective of the ROI size and, in turn,
yields a constant threshold. Figure 4.8 and 4.9 shows the effect of varying the size of the
ROI engulﬁng a defect signal indication using the conventional and proposed methods
respectively. In the proposed length estimation procedure, the number of horizontal slices
having magnitudes greater than the computed threshold is 13 in all four ROI’s selected.
In contrast, the lengths estimated by choosing the magnitude threshold to be twice the
standard deviation in the different ROIs are 11, 12, 12 and 13 in the order of increasing

ROI size.

 

510152025 10 2D 30

4.8 Effect of varying ROI size on length estimation using twice the standard
deviation in ROI as threshold

 

10 20 30 1o 20 an
4.9 Effect of varying ROI size on length estimation using proposed length
estimation scheme

4.7.2 Depth Profiling

The second step in defect characterization is depth proﬁling. After length estimation
process is completed, eddy current signals lying within the defect are used for defect
depth proﬁling. Each horizontal slice of the eddy current data in the 2D R01 is mapped to

a single depth value using a trained RBF neural network.

4.8 Training the Network

In order to optimize network performance, the network is trained using eddy current
data from laboratory-simulated ﬂaws with the corresponding metallographic depth
proﬁles (MET). The training data provides consistent and accurate correspondence
between the measured magnitude or phase values and the depth values obtained from
metallographic examination. The regions of interests in the synchronized and calibrated

eddy current data are broken down into horizontal slices as shown in ﬁgure 4.8.

50

Xi: [M300 M200 M100 P303 P200 P100]

    

2‘:
. iii

Figure 4.10 ROI showing arbitrary feature vector structure

From each horizontal slice, the maximum absolute magnitude and its corresponding
phase value is computed across all available frequencies in the Plus-Point axial channel.
This feature vector arrangement is depicted in ﬁgure 4.8 where feature vector at slice i

Xi = [M300 M200 M100 P300 P200 P100] (4-7)

where M300, M200 and M100 represent the maximum magnitude per horizontal slice across
300 kHz, 200 kHz and 100 kHz respectively; P300, P200 and P100 represent the
corresponding phase value across 300 kHz, 200 kHz and 100 kHz respectively. The
phase in this context refers to the difference between 180° and the arctangent of the ratio
of the vertical amplitude to the horizontal amplitude both corresponding to the location of
the maximum magnitude in the horizontal slice in question. In other words, if a pair of
corresponding horizontal slices — N elements in length — in the vertical and horizontal

channels are denoted V and H, then the magnitude vector, M, is computed as

M =JV2 +17!2 .......... (4.8)

51

Assuming the maximum absolute value in M, denoted as m, corresponds to the xth

element in the slice, then the phase, P, is computed as

P =180° - arctan(—;[[—:]]) ........... (4.9)

In this research work three magnitude and three phase values obtained at 300 kHz, 200

kHz and 100 kHz make up the feature vector for training.

The corresponding MET result for each region of interest is sampled or interpolated so as
to make the number of sample points consistent with the number of horizontal slices in

the region of interest in question. Figure 4.9 shows a sample MET result and the resized

 

 

 

 

 

 

 

 

Original MET result Resized MET Result
en . . . . . $ 1' . . . -

P

C 70 . .1 73 .

r

C so . 50 .

e

n 50 4 50 .

t

a 5.0 - 4 4D -

g

e I] ' 3n .

D 20 - m-

e

p 10 10 -

t

c J l l l l l J l 3 l I I 1 l J I
h 0 2 4 8 8 10 12 14 16 1a 20 0 2 4 5 a 1D 12 14 18
Length units in axial direction Length units in axial direction

Figure 4.11 Original and modiﬁed MET result
version to be used for training the network. This resizing procedure can be deﬁned
mathematically by the following procedure
0 Let the number of sample points in the original MET be X and let the number of

horizontal slices for ﬂaw length estimation (obtain by thresholding the ROI) be Y.

52

Then the length units for the modiﬁed MET will be sample points with ascending
values 0, (Y/X), 2 x (Y/X), 3 x (Y/X)... Y.

0 Assuming ND, 0D, NL and UL are the modiﬁed depth vector, original depth
vector, modiﬁed length vector and old length vector respectively The

corresponding depth values for the modiﬁed MET result is given by

[(0D(round(£)*(i+1))—0D(round(£)*i)*(NL(i)-0L(round(£)*i)]
ND(i) = Y Y Y

 

X X — 0D(round(£) * i)
0L(round(-;,—)*(i+1))-0L(round(—Y-)“i) Y

(4.10)
i= 1, 2 ....Y-l;

where “round (3;) ” rounds the ratio of X to Y to the nearest integer. Furthermore, if the

number of horizontal slices available for training is M, then the input feature matrix is an

M x 6 matrix that is mapped onto a l x M MET result array.

4.9 Training Parameters of RBFNN

The RBF neural network can be deﬁned mathematically as [22]

i=P
y = sz‘fql x_ ti ”’07) + W0 ....... (4.9a)
i=1

where x is the input vector in R” and y is the output vector in R”. The hidden layer of

RBFNN consists of P centers of radial basis functions denoted as t,- , i = 1, P. f is a

53

scalar valued radial basis function and the scalar quantity 0 is the spread or radius of the

ith center, t,-. w,- is the weight vector corresponding to the ith center.

The training of the RBFNN involves estimating the parameters wi, ti and oi (collectively

denoted as 9) from the available training data. 6) is deﬁned as
G) = {(wiatiaai) I i =1,...,n} ...4.9b
The mapping of RBFNN can be compactly represented using the notation,

5" = f(x.-, 6).The objective of training is to minimize the squared error between the

predicted values and true values of y.-'s and can be denoted as [22],
. - 2
9 -m1n {H y.- - f(x; , 9) || } (4.10)
A

The minimization problem is typically highly ill conditioned and the solution is
regularized for each parameter separately using suitable constraints. Following sections

review training algorithms for estimating each parameter.

4.9.1 Selection of Centers of Basis Functions (ti) [22]

This involves the optimal computation of centers in training data clusters. Since the class
information is unknown prior to training the RBFNN, unsupervised clustering approaches
are used. The unsupervised clustering can be performed using number of approaches but
the K-means clustering approach is deployed in this research. K—means clustering is
extremely intuitive and simple algorithm and produces near optimal results in most cases.
However, it is sensitive to the starting point of the operation and incorrect selection of

starting point may result into bad clustering performance [22]. An Iterative Self-

54

Organizing Data Analysis Techniques (ISODATA) clustering process as described in

[22] is an enhanced version of K-means clustering.

4.9.2 Selection of Spreads or Radii of the Centers (03-) [22]

The determination of spread of each center can be done using the Iterative Self-
Organizing Data Analysis Techniques (ISODATA) algorithm described in [22]. This
algorithm computes the two critical properties that are useful in determining the spread,
which are: (1) Inter-cluster distances (yi's) and (2) Intra-cluster distances (si's).

The yi's and si's are deﬁned as [22],

7,. = min{|| t, —tj ||,j =1,...,P;j at i},i =1,...,P
.......... (4.12)

s, = max{|| x, —t,. 1|, j = i,...,P},z’ =1,...,P
yi's give information about the distance of the nearest neighboring cluster. When the
spread of a center is based on this parameter, the basis function covers the entire space
between all the neighboring clusters thereby providing a complete mapping of the input

space covered by the training data.

4.9.3 Computation of Weights (wi) [22]

In order to estimate the weights, the input feature matrix and the output MET results must
be known. Let the number of training samples be M. The input training data can be
represented in the form of a matrix X of dimensions M x 6 and output data can be
represented by a matrix Y of dimensions M x I. As described in [22], using the input
data, a radial power basis function, centers and their spreads the matrix of basis function

can be computed as,

55

1

17031) = (II x, ‘1; H2 +1) 0’ ,l' = 19°": 11;} =1,---, P (4.13)

F has dimensions 6 x P. The RBFNN equation in matrix form can then be written as,
FW = Y (4.14)

The weight matrix W of dimensions P x M can be computed using the pseudo inverse of
matrix F and output matrix Y. However, direct use of pseudo inverse in an ill conditioned
problem results in an impractical solution. Hence there is need for using a regularization
procedure. The solution of equation 4.14 can be regularized using Landweber-Fridman
[27] type iterative algorithm. The details of this regularization scheme can be found in
[22]. This method is computationally quite efﬁcient and also provides good
regularization performance. This scheme is used throughout this thesis. The next chapter
describes the experimental analysis and results for depth proﬁling using the calibration

curves and the RBF neural network.

56

CHAPTER 5 Experimental Analysis and Results

5.1 Introduction

In this chapter, two variants of depth proﬁling schemes using the RBF neural
network are described. The ﬁrst, referred to a RBFl, is implemented by mapping a six-
dimensional feature vector comprising three magnitude and three phase values (as
described in chapter 4) onto its corresponding a scalar depth value determined ﬁom
metallographic analysis. The second variant of the RBF approach, referred to RBF2,
maps the six dimensional feature vector onto a three dimensional output vector consisting
of a consecutive sequence of 3 depth values obtained ﬁom metallographic results. The
rationale for RBF2 is that knowledge of the depth information in the neighborhood of an
arbitrary horizontal slice may contribute to improve the depth estimation corresponding
to the same arbitrary slice. The performance of both methods is compared alongside the
results obtained from calibration curves. Figure 5 .1 shows a schematic of the overall

implementation of the depth proﬁling procedure using the RBFNN.

Calibrated ROI (training data) and
associated MET

 

Flaw Length Estimation

L

Feature Matrix Computation

l

Test Data —-} “3“? Length Neural Network
Estimation l

Predicted Depth Proﬁle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.1 Schematic of the overall approach using RBFNN

57

5.2 Experimental Methodology

Using the length estimation procedure described in Chapter 4, a subset of the total
number of horizontal slices in the R01 is ﬁrst obtained. This subset corresponds to the
horizontal slices vectors for which the maximum magnitude along its individual length
are equal or above the predetermined voltage threshold given by equation (4.5). By
multiplying the number of horizontal slices in this subset with the axial scale — given in

length units per slice — length of the ﬂaw in inches is determined.

The peak magnitude and phase at multiple frequencies for each horizontal slice is
computed and entered in a feature matrix for training the network alongside the
corresponding MET depths values. A general mathematical representation for the RBFl
framework is given as

0(1) = R131"”1[X(j)] (5-1)
for X= [M300 M200 M100 P300 P200 P100] as deﬁned in section 4.8, j is the current
observation; F and D denotes the feature vector and corresponding depth estimate
respectively; M100, M200, and M300 are the magnitude values computed at 100 kHz, 200
kHz and 300 kHz respectively; P100 P200 P300 are the phase values computed at 100 kHz,
200 kHz and 300 kHz respectively. For the RBF2 network, the general representation

using similar notation is given as

13(1) = RBFZIFU - 1), 17(1), F(J' +1)] (52)

58

Figures 5.2 — 5.7 show the scatter plot of features magnitude and phase values obtained
from the training data at 300 kHz, 200 kHz and 100 kHz against the corresponding depth
from metallographic result. From inspection of Figs. 5.2, 5.4 and 5.6 it is apparent that
there exist some correlation between magnitude values and ﬂaw depth. Similarly, by
inspection of Figs. 5.3, 5.5 and 5.7 it is evident that there exists some correlation between
phase values approximately ranging between 35 and 180 degrees and ﬂaw depth at all
frequencies. This relationship is expected as the ﬂaws analyzed in this research work are

outer diameter axial ﬂaws.

 

 

 

 

100 r {2”,} e : gt: .1 4.:
+ + it *
90 +* * 4 «1r ~
411-
411-
A 80" H “
a! “if *4} **
s ... r ,
§ 60_:'.*. +1. ** .4
a-
E ﬁn, 4:
0 1t
t 5%: * ‘
IL 1*
F“ 4031+ 11+ ‘
3 +
.:
g 304-} ‘
5 20+ _
1:: A
0w 0.5 1 1.5 2 2.5
Magnitudew)

Figure 5.2 Scatter plot of magnitude vs. depth for training sample at 300 kHz

59

 

 

 

 

1w I I T I I I T
90~ a; .
4-
s °°‘ 44?. ‘
5 70- ﬂ —
r *1?
4
a 60» a? _
w 4
E ““4 4 *
g 50L. _*_ _.
E 40 4&4} :
g 4 4 1*
.C
E 30f 44 * —
20~ 4 _
4
#4 -
10» 4 i ii 4 4
O:A&*#ﬁl .r.*l t .4. “L* 4L * 1.1. .r..l.r.
0"" 50 ‘ 100 1§o " 360 250 360 330 400
Phase(deg)

Figure 5.3 Scatter plot of phase vs. depth for training sample at 300 kHz

 

 

 

 

100 I “BET 4. 4 4 44 4. 4 4
4 41!- + it
90» if * 4 4 -
4
4
§ 80 444* 1* 4
z 4 *4 t 1*
*-' 70* 444* 4* 4 ~
g by “t 4 4 4
*t 4 4
4
§, 60_*:. *4" *1. _.
E 134,, 4
9 50" 4 it “
a 44
ﬁ 4054 4 ‘
3 4
.c .J
3’ 30’
E
I- 20-4- .1
-Il-
1:; A
o" 0.5 1 1.5 2 2.5 3

Magnitude (V)

Figure 5.4 Scatter plot of magnitude vs. depth for training sample at 200 kHz

60

 

 

400

 

 

_ _ _ q a _ _ a
.. *xrw
“m3
w
0
.. *1%
.i.
4 4w
4 ....2
m.
N
- -3
H" W
..T
.=.
44 4
- .m
4.4 4 4 44 1
$4
ﬁg 4. $.ﬁ1ﬁﬂriﬁH .__.. 4. ....
4. 4.
a 4 44 4 4 Hm
.14
L i— f p _ 4 _ 4 L*..:.O
m m w m w w .o. ...... m m 0

at 580 $2528 :85 599,:

Figure 5.5 Scatter plot of phase vs. depth for training sample at 200 kHz

 

 

 

 

a — J u d _ u _ lﬁ 2
..r
.ﬁ .8.
1
.... i.
44.4 16.
km. 1
....
e4 .4.
1
4. ...4 4
. 12.
.... )
4 1W
e
. -1.m
i... am
m.
..8M
...4 0.
4.
ﬂ 4.
-4 ... -e.
4 ... 4... 4.4 o
4
.4
FM” 4
- 4. r.
4 4 +4“. 0
4. *4.
4.
4. 4. 2
r #4 $4.4. + 4. ”...0.
.....4 .. .444
L . .+p . b p O
m m m m m w w w m ..

g 580 32:88.". :55 632.:

Figure 5.6 Scatter plot of magnitude vs. depth for training sample at 100 kHz

61

Through Wall Percentage Depth (%)

Figure 5.7 Scatter plot of phase vs. depth for training sample at 100 kHz

fP (H x _ ti “)30.) = (H x _ti ”2 +1)ai (5.3)

The overall training data is randomly divided into training set and test set. Roughly 70%

100

70-

‘75

20~

10~

 

 

44

$44444

*4
4*
at

W
*4

4*

+4

1

 

1:1

200
Phase (deg)

62

250

300

layer nodes. The power function is deﬁned in equation (5.3)

ul-
‘I’

'1!-

it

After defect length estimation, horizontal slices that contain magnitudes greater than
the threshold are used to compute the feature matrix and applied to train the RBFNN as
described in previous section [22]. The centers of the basis function are computed using
the Iterative Self-Organizing Data Analysis Techniques (ISODATA) algorithm, the radii
are computed using intra-cluster distance and the weights are computed using the method

of regularization described in Chapter 4. A power basis function is used in the hidden

—1

of the data is used for training and the remaining 30% is used for testing. Figure 5.8(a)-

 

(c) shows the proﬁling results obtained for three flaws — whose depth proﬁles have been
predetermined using metallographic techniques — using the classical magnitude
calibration curve approach (CC), log magnitude curve and the two RBF neural networks,
RBFl (one feature vector per depth) and RBF2 (three feature vector per depth). These
ﬂaws were randomly selected from a database of similar ﬂaws whose depth proﬁles have
been experimentally determined by metallographic analysis. This database is generally

referred to as the Examination Technique Speciﬁcation Sheet (ETSS).

on
vv

 

 

( I l
q + tog Mag QMH-b

 

 

 

IM‘ —u— Mag 300kHz
70 i \i ----------- RBF2 .4
, \ --°-- RBF1
5. ............... } ......... ' . » —MET

 

Percentage Depth
b
o
I

 

 

 

 

63

 

 

    
     
      

 

 

 

 

   

 

 

 

 

 

 

 
 

 

 

 

 

Percentage Depth

 

 

 

 

(C)

i:
20 e =: _
l:
“a
‘5 ‘ + log Mag 300kHz _ ‘
—0— Meg 300kHz g
10 _ .............. RBF2 é ..
--o-- RBF1 g
MET
5 E -
I
!
l l J l l l I;
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Lengh (inches)
(b)
50 , , . . . —"'— log Mag 300kHz
-0— Mag 300kHz
-------------- RBF2
--o-- RBF1
50 MET
4o
30 -
20 -
1 _
l L v v - l
"6 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Length (Inches)

 

I
+ log Mag 300kHz
—~— Mag 300kHz

 

RBF2
--o-- RBF1

—MET

 

  

 

 

    

 

0.8
Lengh (Inches)

0.6

4

 

 

—0— Meg 300kHz

RBF2
--o-- RBF1

...-mum.

 

 

 

‘ + log Mag 300kHz

 

on
UV

 

70-

.........

......

 

_
o

60*—

 

      

.............
.........
.

p
o

0"

5 4 3
Egon 09:5an

0.8

0.5

0.4
Length (inches)

0.3

0.2

 

 

   

(e)
65

 

 

 

 

 

+ log Mag 300kHz
—0— Mag 300kHz

45 — RBF2

R --0-- RBF1

' —
40 — ." “t 1‘ MET

to ‘. 9
I E

35 ~ ,’ I f -

Percentage Depth
ﬂ 8
l I
‘~
N
.....-—-0""-”

8
I
-.. ~n-u-—.o-

 

 

0.--.--.....--—
I

 

(0
Figure 5.8(a - 1) Comparison of metallographic ﬂaw proﬁles with proﬁles
generated by different algorithms.

The RBF] and EBF2 networks are seen to consistently outperform the traditional
approaches. In order to compare the effective lengths and depths of defect proﬁles
generated using various techniques alongside the metallographic depth proﬁle, the

Electric Power Research Institute has developed two standard indices namely

Burst Effective Length which provides an estimate of the effective length of a

defect.

Burst Effective Depth which refers to the effective defect depth.
Figures 5.9-5.11 shows the comparison of the burst effective depth and length for sample

proﬁles obtained using the RBF neural network and the corresponding metallographic
proﬁles.

66

 

    

 

 

 

US 07 08

length

 

 

 

3" __Estimated Proﬁle
7,, _MET

%0
0

D

C 0

P 0

t

h 0
ﬂ
9“ ° Axial distance " M M
depth

EH 0

- length

 

 

 

Figure 5.9 Top Leﬁ: two-dimensional representation of calibrated eddy current data
signal with arrow pointing to sample training ﬂaw indication. Top Right: Metallographic
(MET) results plotted against neural network estimated depth proﬁle. Bottom Left:
Structural Proﬁler showing Burst Effective Length and Depth of MET (in red). Bottom
Right: Structural Proﬁler showing Burst Effective Length and Depth of Estimated proﬁle

(in red)

67

_Estimated Proﬁle
__ MET

   

%so»

 

./l‘

 

Axial distance

 

 

 

 

 

 

Figure 5.10 Top Left: two-dimensional representation of calibrated eddy current data
signal with arrow pointing to sample training ﬂaw indication. Top Right: Metallographic
(MET) results plotted against neural network estimated depth proﬁle. Bottom Left:
Structural Proﬁler showing Burst Effective Length and Depth of MET (in red). Bottom
Right: Structural Proﬁler showing Burst Effective Length and Depth of Estimated proﬁle
(in red)

68

 

        

 

 

 

 

 

 

 

 

m.
% ”’
71).
D 00'
e so-
P an)
t 30.
h 29L __Estimated Proﬁle
MET
If!L _
Axial distance
de th (1 th
3., P / ep
au
60 U sol
40 40
20 at
|ill-0 01 02 nr 0‘ 35 36 07 JG [)1 0.3 ”i "l 05 06
length length

 

Figure 5.11 Top Left: two-dimensional representation of calibrated eddy current data
signal with arrow pointing to sample training flaw indication. Top Right: Metallographic
(MET) results plotted against neural network estimated depth proﬁle. Bottom Left:
Structural Proﬁler showing Burst Effective Length and Depth of MET (in red). Bottom
Right: Structural Proﬁler showing Burst Effective Length and Depth of Estimated proﬁle
(in red)

69

Linear Regression Straight Line Fit
Slope=0.809, intercept = 16.886

 

 

 

 

 

 

 

 

 

 

 

100
so
. K e
00
70 y. /
WT . /.
Burst 60
Effective - .
(%) 40 /
30 /’
2° f
10
0

 

 

 

 

 

 

 

0 20 40 so 80 100
Esimated Burst Effective Depth (%)

Figure 5.12(a) MET- Estimated Burst Effective Depth Correlation Statistics

Linear Regression Straight Line Fit
Slope=0.888, intercept = 3.837

100

 

,0 .
,0 /
m /

... /

MET Burst 10
Effective 0
Length '

(inxlOz) o-——— '

 

 

 

 

\t

 

 

 

 

0

.. A"
f

 

 

V

 

 

 

 

 

 

0

 

0 2O 40 60 00 100

Esimated Burst Effective (in x 102)
Figure 5.12(b) MET- Estimated Burst Effective Length Correlation Statistics

70

From ﬁgures 5.12(a) and 5.12(b), the slope of the linear ﬁt between the pool of
metallographic and estimated burst effective lengths and depths are approximately 0.93
and 0.94 respectively. This is an indication of a sufﬁciently trained neural network and an
efﬁcient length estimation procedure. The result in ﬁgures 5.13(a) and 5.13(b)
respectively show the burst effective depth and length statistics for depth proﬁle of test
ﬂaws generated using the radial basis function neural network (RBFl) and the enhanced

magnitude calibration curve method.

 

MET
BED,

  

 

 

 

y=0.8321x+l7.057
R2 = 0.8632
y=0.568x+0.1515
R2 = 0.5808
cm 2000 0.1!) sum 80m 101.01 .
NDE BED, %TW NDE BEL,in

 

 

Figure 5.13(a) Performance statistics of RBF results on test data

y=0.4884x+0.166
R2 = 0.5317

y=0.7827x+20.776
R2 = 0.7914

   

 

 

 

 

 

0111 21m 401:0 III] 0101 101.10 .
NDE BED, %TW NDE BEL”
Figure 5.13(b) Performance statistics of enhanced magnitude calibration
curve results on test data

71

The neural network outperforms the magnitude proﬁling procedure as the correlation
of the burst effective length and depth between MET and estimated neural network depth

proﬁle are closer to unity as compared to magnitude generated results.

5.3 Uncorrelated Noise Removal in Eddy Current Data

The signal to noise ratio in eddy current data is a major factor that determines the
accuracy of a predicted ﬂaw depth proﬁle. As it would be expected, accurate depth
measurements are obtained when the signal to noise ratio of the test data is comparable to
the training data. This prompted a study of the relationship between estimated depth
measurements obtained from denoised eddy current data and estimates from
metallographic techniques. In this approach, the eigenvalues corresponding to the
covariance matrix of the R01 are determined and only signiﬁcant eigenvalues are used to
reconstruct a relatively noise free data set. Using the Karhunen-Loeve transformation, the
eigenvectors corresponding to the two most signiﬁcant eigenvalues of the ROI
covariance matrix was used to reconstruct a cleaner version of the noisy eddy current
data. Figures 5.14(a)-(d) and 5.14(e)-(f) show the surface plot of the absolute voltage
values for two samples of eddy current data collected using the plus point coil probe at
300 kHz and 200 kHz and the corresponding ﬁltered version.

From experimental analysis, selecting the eigenvectors belonging to the two most

signiﬁcant eigenvalues eliminates most of the uncorrelated signal within the R01.

72

Flltered 300 kHz channel

   
 

__l__J.....L.__/

 

60
o 0
Figure 5.14(a) Magnitude values for noisy ROI in 300 kHz channel. (b) Filtered version.
Noisy 200 kHz channel

     

’1
I
J ‘1 0.x
0.04 I : ‘I
' N 0.04 I
. l 1
0.02 ' .
ﬁ' 0.02 I
I ~1
I I
I

  

- ‘ Filtered 300 kHz clannel

 

Figure 5.14(e) Magnitude values for noisy ROI in 300 kHz channel. (f) Filtered version

73

Noisy 200 kHz channel

Filtered 200 kHz channel

 

Figure 5.14 (g) Magnitude values for noisy ROI in 200 kHz channel. (h) Filtered version

Although, the ﬁltered eddy current data may appear better suited to do depth
proﬁling analysis, this is not necessarily the case. This is because the minimum and
maximum magnitude values (and therefore the corresponding phase) per line scan is
sometimes signiﬁcantly altered in the denoising process and information about true depth
is lost as a result. The depth proﬁles generated by the trained RBF neural network for
both noisy and relatively noiseless data (which was obtained using the proposed

algorithm) for those shown above are shown in ﬁgures 5.15(a) and 5.15(b).

74

300 kHz 200 kHz .
_Est1mated Proﬁle

_ MET

    

 

 

 

 

H
D
e l
P
a t I
. h
I n ‘
=I I! I I ll IE I 12 1 I
200 kHz Axral distance (In)
I H 7 - -7 _7 7 —
_Estimated Proﬁle
' ' _ MET
% l
I
D a
e
u: p 3
t
h a
U
.u

 

 

 

   

i Axial distance (in)

Figure 5.15(a) Top Leﬁ: Noisy ROI, Top Right: Corresponding depth proﬁle vs. MET
Bottom Leﬂ: Filtered ROI, Bottom Right: Estimated depth proﬁle versus MET.

75

300 kHz 200 kHz

 

_Estimated Proﬁle
_ MET

    

8

8

Percenm Mir (‘3)
8

3

 

 

 

 

 

Axial distance (in)

 

 

300 kHz 200 kHz ....
7° _Estimated Proﬁle
.. 00- _MET
an A50.
g...

nun E39

nul 20

III 10
re a - .. - ... z: a a n 0.1 0' Axial distance (in) a M '

   

Figure 5.150)) Top Leﬁ: Noisy ROI, Top Right: Corresponding depth proﬁle vs. MET
Bottom Leﬁ: Filtered ROI, Bottom Right: Estimated depth proﬁle versus MET.

In order to further investigate the impact of noise on feature computation, a
simulation of typical eddy current data was generated by injecting zero mean
uncorrelated noise into a sample with high signal to noise ratio. Features (magnitude and
phase) for each line scan in the 300 kHz channel was computed (see ﬁgures 5.17 and
5.18) and ﬁgure 5.16 shows a simulated magnitude distribution for different noise

variances.

76

      
    
 

2 4 6 8 1O 12 14
STD= 0.2098

2 4 6 8 101214
STD=0.3194

 

2468101214 ' 2468101214

Figure 5.16 shows calibrated magnitude distribution in ROI’s corrupted
with zero mean noise having different levels of standard deviations (STD).

Max Volts measured in Axial Direction versus Noise SD

1.4 l I I ﬂ l r I I

 

0.6 r

 

Magnitude (Volts)

 

0,4 _ ‘ ' r —-— SD = 0.1

----- SD = 0.1562
-----+- SD = 0.2098
0.2 ~ .. + SD = 0.2638
.9— SD = 0.3194

 

 

 

 

 

n l l l l l

l 1 l
0 2 4 6 8 1O 12 14 16 18
Line Scan Index (Axial Direction)

Figure 5.17 Plot of magnitude values for each circumferential line
scan in ROI for various noise standard deviations.

77

Corresponding Phase measured in Axial Direction versus Noise SD
180 I I l I I I l l

 

160 —

120—

 

Phase (Deg)
a

 

 

 

 

 

 

 

80 —
60 _
40 —'k— so = 0.2098
---o--- so = 0.2638
--e—- so = 0.3194
20 — _
0 l l l l l l l l
0 2 4 6 8 10 12 14 16 18

Line Scan Index (Axial Direction)

Figure 5.18 Plot of phase values for each circumferential line
scan in ROI for various noise standard deviations.

The efﬁciency of the proposed noise elimination method was investigated on the
test specimen. By introducing random uncorrelated noise with zero mean and different
variance levels into the ROI and the performing the denoising operation, the depth proﬁle
for each of the resulting ROI was generated and compared with the MET proﬁle. The
depth proﬁles for the uncorrupted ROI and the ROI’s in which random noise of lmown
variance is introduced are plotted in ﬁgure 5.19 alongside the MET ground truth data. By
inspection, it is observed that ﬁltering the noisy ROI does not improve depth proﬁling

results using the RBF neural network.

78

Percentage depth Percentage depth

Percentage depth

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SD =0 —0— Estimated (noisy)
4m
‘W +Estimated (ﬁltered) I:
+MEI E.
3
G)
50' i”
I:
3
i
” "0‘.'1' 0.2 0.3 0.4 0.5 013' 0.7
axial distance
so = [11552 —'— Estimated (noisy)
1m . . . +Estimated (ﬁltered)
—+-MET 5
8
Z
w- r
C
i
if
” "0,1 0.2 0.3 0.4 0.5 05' 07
axial distance
411') SD=025$ *Estimated (noisy)
'W ' ' +Estimated (ﬁltered) I:
+MET g
3
50- S’
A _ .. E
'1" i W" E
if
” ' 0.1' 0.2 0.3 0.4 0.5 08' 0.7
axial distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

so = 0.1 —— Estimated (noisy)
1m . 4 +Estimated (ﬁltered)
—¢—MET
50
” ' '0‘.'1' 0.2 0.3 0.4 0.5 0.0' 0.7
axial distance
.m SD=0.2[m V *Estimated (noisy)
'W 1 ' ' +Estimated (ﬁltered)
—1i—MET
50
0.1 112 0.3 0.4 0.5 115' 117
axial distance
SD = 0.3194 —— Estimated (noisy)
1m . - +Estimated(ﬁllered)
—o—MET
50» P/\ .
” ' 0.1' 0.2 0.3 0.1 0.5 06' 0.7
axial distance

Figure 5.19 Depth proﬁles of MET against estimated proﬁle generated after introducing
noise of known variance and after ﬁltering

79

 

CHAPTER 6 Conclusions and Summary

The objective of this thesis is to develop a novel steam generator tube defect
characterization scheme by multi-dimensional interpolation of features from eddy current
data. The vehicle deployed in the interpolation process is a radial basis function neural
network which is trained by mapping signal magnitude and phase at different frequencies
and contiguous slices in a two-dimensional ROI onto a predetermined metallographic
depth proﬁle (MET). Automation of depth proﬁling algorithms precipitated the
requirement for an accurate ﬂaw length estimation procedure which has also been

developed in this project.

The performance of the defect depth proﬁle and length estimation using the
enhanced magnitude calibration curve and the radial basis function neural network was
evaluated on 36 blind test data for which metallographic ground truth were available.
From a linear regression perspective, the burst effective depth (BED) and length (BEL)
obtained using the RBF network was more accurately correlated with the BED and BEL
of the MET — having a Pearson's co-efﬁcient of regression of 0.8632 and 0.5808
respectively. On the other hand, the Pearson's co-efﬁcient of regression for BED and
BEL using the enhanced magnitude calibration curve was 0.7914 and 0.5317
respectively. This demonstrates that the defect depth estimation procedure using neural
networks in conjunction with the length estimation scheme offer a more accurate

evaluation technique.

80

The corruption of eddy current data by noise, however, degrades the performance
of the RBF network. This is largely due to the fact that the signal magnitude and phase
computed as input features to the network are signiﬁcantly deviant from those computed
in training the network. Furthermore, the features values become more deviant from the
training pattern as the signal to noise ratio increases. Filtering noisy signals is not an
effective method for signal restoration since the feature information may be lost in the
process. However, at low noise levels fairly consistent defect depth proﬁles and lengths
are obtained when the novel defect characterization procedure is used. RBF] generally
performed better than RBF2 due to the signiﬁcantly lower error achieved when
minimizing the squared error between the predicted depth values and true depth values
during the training stage (as described in equation 4.10) of RBFl as compared to RBF2.
This is expected when training with ﬂaw signal indications with low signal to noise ratio
as is typical for ﬂaw signal indications whose corresponding maximum depth is below
40% TW. Generally, the lower the signal to noise ratio, the lesser is the absolute
correlation between the signal vector and the corresponding depth value. Furthermore, it
is a possibility that the contribution of depth information from neighboring horizontal
slices in the ROI becomes less reliable as the signal to noise ratio decreases. This would,

in turn, yield more training error in RBF2 as compared to RBF].

Possible future work in this direction may include increasing the dimensionality
of the input feature vector space for depth prediction by using ﬂaw signal indication with
signiﬁcantly high signal to noise ratio and mapping four or more contiguous horizontal

slices in the R01 to a depth value. In addition, training the RBF] and RBF2 neural

81

network with a larger database of ﬂaw signal indications may yield more accurate depth
proﬁle estimates for a wider range of degradation types. Another potential application of
the RBF neural network in depth proﬁle estimation is to assist in the examination of
cracks in other components of the steam generator such as the reactor vessels and their
internal core shrouds as there have been several instances of cracking in these
components [32]. Furthermore, training the RBF neural network for estimating depth
proﬁles for other ﬂaw types and degradations such as pitting, inter-granular attack and

dents are directions worth exploring.

82

10.

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86

 

 

 

 

 

 

 

 

 

 

 

 

 

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