1. PULSED EDDY CURRENT
DETECTION OF LOOSE
PARTS IN CANDU®
NUCLEAR REACTOR
STEAM GENERATORS
Dylan Johnston - 10063536
D.johnston@queensu.ca
Co-Supervisors:Prof. Morelli & Prof. Krause
Physics 590 Honours Research Thesis
Final Report
Submitted: September 4th, 2015

2. 1
Pulsed Eddy Current Detection of Loose Parts in CANDU® Nuclear
Reactor Steam Generators
Abstract – Degradation of support structures and other components in nuclear steam generators (SGs) can
leadto the accumulationof debrisonthe SG tube sheet.Flowinducedvibrationof loose parts can resultin SG
tube damage and eventual lossofSG efficiency.Regularinspectionofsupportstructurescan extend SG life by
detecting and monitoring flaws and cracks in SG tubes as well as identifying accumulation of loose parts.
Currently,conventional eddycurrenttechnologiesare usedtocharacterize andassessthe conditionofsupport
structures. However, these technologies do not perform well in the presence of magnetite fouling or when
loose parts are resting directly on the SG tube sheet. Pulsed eddy current (PEC) combined with a modified
principal components analysis (MPCA) was investigated as a method of detecting a variety of loose part
materials in close proximity to 16 mm outer diameter Alloy-800 SG tubes and the surrounding support
structures. Loose parts were found to be detectable for varying axial positions along the SG tube, including
when in contact with the tube sheet. When offset radially from the SG tube, 1.6 mm diameter carbon steel
parts could be detectedupto 3.2 mm away, while stainlesssteel partsofthe same size couldonly be detected
up to 1.5 mm away. Signal variation in the presence of loose parts was attributed to differences in the
amplitude ofthe transientresponsesand in relaxationtimesfordiffusionof transientmagneticfieldsthrough
the variousmaterials. The abilityto accurately detectand identifyloose partslocated in close proximityto SG
tubes establishes PEC combined with MPCA as a potential candidate for SG inspection.
I. INTRODUCTION
Steam generators (SGs), which are a standard
component in many types of thermal power
generators including nuclear reactors, are used to
convert thermal energy into electrical energy via
steam powered rotary motion of turbine
generators. Steam generators undergo regular
inspectionsinordertoextendthe lifetimeof nuclear
reactors, while providing evidence of their
continued safe operation [1]. Therefore, it is
desirable todevelopinspectionstrategiescapableof
identifying flaws and other forms of degradation
efficiently, while reducing reactor down time. Eddy
current testing (ET) and ultrasonic testing (UT) are
two such methods that are used for a wide variety
of non-destructive testing procedures, including
flaw detection, condition assessment, and flaw
growth prediction within a SG [2].
A variety of degradation modes can be present
withinthe SGsof CANDUnuclearreactors,including
stresscorrosioncracking andfrettingwearontheSG
tubing, support structure degradation and
corrosion, and the accumulation of magnetite
sludge on the SG support structures. Magnetite
sludge isa corrosionproductcomposedprimarilyof
iron oxides,howevercopperand copperoxides can
alsobe present,dependingonthe materialsusedto
construct the SG [3]. Additionally, soluble species
such as sulphates and silicates can become
concentrated in magnetite sludge, and eventually
precipitate within the porous structure of the
deposits [3].
Small metallicparts that are not attached to the
supportstructures within a SG can compromise the
integrityof aSG.Loose partsmayappearinSGsafter
maintenance is performed or can detach from
support structures due to corrosion. Accumulation
occurs primarily on top of the tube sheet of the SG
[4],eitherdirectlyonthe tube sheetitself,orresting
on top of magnetite sludge, that has already
accumulated onthe tube sheet. Loose parts thatare
in physical contact withSG tubes,whenexposedto
flow induced vibration, can cause fretting wear,
produce more metallic debris and, eventually,
compromise the integrity of SG tube structures, if
not removed [2].
Detection of these loose parts is imperative to
maintaining plant efficiency, since SG tubes are
‘plugged’ once 40% through-wall fretsare detected
[5]. Currently, ET is the primary non-destructive
testing method used to detect loose parts that lie
within 3 millimetres of SG tubes [2] and not in
contact with the tube sheet. However, the
inspection performance of ET is reduced in the
presence of the magnetite fouling [2]. Additionally,

3. 2
ET encountersdifficultiesindetectingloose partsin
the presence of ferromagnetic materials, such as a
tube sheetor othersupportstructureswithinanSG
[2].
PulsedEddyCurrenttesting(PEC) isanemerging
non-destructive testing technique that has been
developed for the inspection of nuclear and
aerospace structures [6] [7]. Instead of the
continuous sinusoidal signal utilized by ET, PEC
employsasquare wave voltagepulse toinduce eddy
currentsin conductive media. The transientvoltage
responsesinducedinthe pick-upcoilsbythese eddy
currents can be consideredas consisting of a series
of discrete frequencies [8].Thus,PEChasaspectrum
of frequencies available for interaction with the
inspected component, as opposed to the discrete
frequenciesthat are generatedby the ETdrivesignal
[9]. In addition, the approach to direct current (DC)
excitation in the pulse provides magnetization of
ferromagnetic materials, which enhances the pick-
upcoil response asopposedtohinderingit, asisthe
case in conventional ET [2]. PEC pick-up coil
responses maybe analyzedusingmodifiedPrincipal
Components Analysis (MPCA) [10] [11], which
reconstructs the signal using orthogonal basis
vectors and associated scores, reducing the
dimensionality of the data. MPCA differs from PCA
in that the data mean is not subtracted from the
original data [11].
When combined with PCA, PEC has been found
to be a robust analysistechnique [12].Inaerospace
NDT, PEC was able to detect stress-corrosion
cracking defects, which were undetectable using
conventional eddy current due to large lift-off
distance [6]. In nuclear reactor non-destructive
testing, PEC has been shown to characterize wall
loss, tube fretting wear, and corrosion of support
structuresmore successfullythanET [12],whichhas
limited performance when multiple modes of
degradation or magnetite fouling are present [2].
This report examines seven types of loose parts
made out of different metals placed in two basic
orientations. Modified PCA and the theory of
magnetic field diffusion are described in Section II,
followed by the experimental setup and a
description of the measurement technique usedin
Section III. Section IV discusses the results of using
MPCA to analyze PEC signals for detecting loose
parts, while Section V provides a conclusion and
summary of this report, as well as outlining the
future research suggested for PEC.
II. THEORY
A. Electromagnetic Diffusion
The square wave voltage pulse employed in PEC
inducestransienteddycurrentsinconductivemedia
that lie in close proximity to the drive coil. These
eddy currents are induced in a target material via
Faraday’s law of electromagnetic induction [13].
Changes in the eddy currents and associated
magnetic field can in turn be sensed using pick-up
coils. The approach to DC excitation in the pulse
provides a secondary magnetization effect in the
presence of ferromagnetic materials. The diffusion
of eddy currents is described by the diffusion
equation (7) below. We can derive this equation
beginningwithone of Maxwell’sequations, namely
Ampère’s circuital law [13](1):
𝛁⃗⃗ × 𝑩⃗⃗ = 𝜇0(𝑱+ 𝜀0
𝜕𝑬⃗⃗
𝜕𝑡
) (1)
The diffusionequationisobtainedbytakingthe curl
of both sides of the equation:
−𝛁⃗⃗ 2 𝑩⃗⃗ + 𝛁⃗⃗ (𝛁⃗⃗ ∙ 𝑩⃗⃗ ) = 𝜇0( 𝛁⃗⃗ × 𝑱) + 𝜇0 𝜀0(𝛁⃗⃗ ×
𝜕𝑬⃗⃗
𝜕𝑡
) (2)
By substituting in Ohm’s law (3), Faraday’s law of
electromagnetic induction (4) and Gauss’s law of
magnetism (5):
𝑱 = 𝜎𝑬⃗⃗ (3)
𝛁⃗⃗ × 𝑬⃗⃗ = −
𝜕𝑩⃗⃗
𝜕𝑡
(4)
𝛁⃗⃗ ∙ 𝑩⃗⃗ = 0 (5)
and using a vector identity,the diffusionequation
can be written in terms of just the magnetic field:
𝛁⃗⃗ 2 𝑩⃗⃗ = 𝜇0 𝜎
𝜕𝑩⃗⃗
𝜕𝑡
+ 𝜇0 𝜀0
𝜕2 𝑩⃗⃗
𝜕𝑡2
(6)
A goodconductorwill have alarge 𝜎 value.Thus,we
can approximate the second order term as
negligible, and the diffusion of magnetic flux, 𝐵⃗ ,at
low frequencies (<108 𝐻𝑧) can be written as [14]:
𝛁2 𝑩⃗⃗ = 𝜇𝜎
𝜕𝑩⃗⃗
𝜕𝑡
(7)

4. 3
For conductive media, the general solution to the
diffusion equation of magnetic fields (7) has the
form [14]:
𝑩⃗⃗ = 𝑓(𝑒
−
𝑡
𝜏 𝐷) (8)
Solutions of this form can oftenbe expressedas
a series of relaxation times that are dependent on
the conductivity, 𝜎, and permeability, 𝜇, of a given
material,aswellassome characteristiclengthof the
system, ℓ. The characteristic diffusion time of the
material, 𝜏 𝐷,can be estimated as [15] [14]:
𝜏 𝐷~ 𝜇𝜎ℓ2 (9)
With longer times providing increased depth of
penetration by the induced eddy currents. To
understand the complete transient response of the
system,a seriesof relaxationtimes,asdescribedby
(9), is sufficient. The eddy current diffusion time is
dominated primarily by the 𝜇𝜎 product; the
characteristiclength, ℓ,dependsonseveralphysical
parameters of the situation including the size,
proximity and orientation of the loose part.
The difference in relaxation times between
different materials and different physical situations
(eg.size,orientation,distance) isexpectedtocause
variation in the transient signal response exhibited
by the probe’s pick-up coil array. Several other
variables affect the response of the pick-up coils,
including the magnetization of the ferromagnetic
conductive materials, the temperature of the
system, the resistance of the pick-up coils, and the
back EMF induced onthe drivingpulse.However,as
these factors are not drastically different between
non-ferromagnetic materials throughout the
investigation, the variation in pick-up coil response
is expected to be dominated by the 𝜏 𝐷 term. In the
case of ferromagnetic materials,the magnetization
component is expected to dominate [16].
The measured conductivityvaluesforthe various
loose part materials are given in Table 1.
B. Modified PCA
Principal Components Analysis (PCA) is an
analysis technique used to reduce the
dimensionality of data by separating large, highly
correlated data sets into a combination of linearly
uncorrelated principal components and associated
scores [10].
The principal component of adatasetisfoundby
creatingthe covariance matrix for an n-dimensional
data set that has had the mean subtracted from
everypoint. The eigenvectors,or‘components’,and
eigenvalues of this (𝑛 × 𝑛)-matrix are then
determined. ModifiedPCA differs in that the mean
is not subtracted from the data points before the
covariance matrix iscalculated [11].Byretainingthe
data mean in this analysis, results become less
prone tosystematicoffsetscausedbya differencein
the average signals.
Due to the nature of eigenvectors, these
componentswill be orthogonal toone another.The
principal components must also be of unit length,
and therefore must be normalized [10]. The
eigenvector with the largest eigenvalue is the
principal component, and represents the greatest
variation within the data set. The second largest
component describes the next largest variation
within the data set, and so on. By ordering the
eigenvectorsintermsof theireigenvalue,highestto
lowest,arankedlistof the componentsisobtained.
The components are ranked from most significant,
to least significant, in terms of the relationships
between dimensionsof the dataset [10].Discarding
components with small eigenvalues reduces the
dimensionality of the data at the cost of removing
information from the reconstructed signal.
Generally, discarding all but the first 3-5 principal
components allows for 99% signal reproduction [6]
[7] [12].
Reconstruction of the signalisquitesimpleatthis
point:the eigenvectorsthatwere keptare organized
as the rows of a matrix, with the most significant
eigenvector at the top. Multiplying this matrix on
the leftof the transposedoriginal dataset (i.e each
row contains a separate dimension) yields the
original data solely in terms of the retained
components. The original signal, 𝒀, minus the
information discarded in higher order components,
can be represented by a sum of the retained
components, 𝑽 𝒊, multiplied by their associated
scores, 𝑠𝑖 [10].
𝒀 = ∑𝑠𝑖 𝑽𝒊 (10)
This is similar to recreating a function using a
Fourier series of harmonic basis functions and
associated Fourier coefficients, however, fewer

5. 4
terms are generally required compared to Fourier
analysis.
Using MPCA, the dimensionality of the data is
effectively reduced to the number of principal
components used to reconstruct the signal, while
signal reconstruction is accomplished through the
determination of several scores 𝑠𝑖. This method of
analysis represents a minimization of the sum
square residualsinterpretationof the result,instead
of a variance minimum interpretation, which is
obtainedinconventionalPCA [6].The programused
to perform the modified principal components
analysis was developed at RMC [11].
III. EXPERIMENTAL SETUP
A. Apparatus
Six Alloy-800 tubes, 45.7 cm in length, and one
Alloy-800 tube, 30.5 cm in length, were used to
recreate the SGtube structure forthisinvestigation.
Each tube had a wall thickness of 1.2 mm and an
outer diameter of 15.9 mm. A tube sheet support
plate of thickness 25 mm and a broach support
structure of thickness 26 mm were usedtoholdthe
Alloy-800 tubes in place (Figure 1). The 305 mm
Alloy-800tube was installed asmanufactured,while
the othersix tubes all possessedvarious degreesof
frettingwear.The unfrettedtube was usedfordata
acquisition asit representsnominal tube condition,
andwill be the SGtube referredtohereafter.The SG
tube wasmarkedwithmaskingtape forthe purpose
of offsetting the loose parts away from the tube
sheet, defined asthe axial direction (see Figure 1).
B. Loose Parts
The loose parts used in this investigation are
listedin Table1alongwiththeirrelevantdimensions
and measured conductivities. These values were
obtained using a 4-point measurement, and, aside
from lead, aluminum and tin, agree with literature
values within their uncertainty.
The brass, carbon steel and stainless steel
samples were loaned by the Canadian Nuclear
Laboratories(CNL) and are shownin Figure 2 (Top).
The tin, copper, aluminum and lead samples were
acquired and machined at Queens University and
are shown in Figure 2 (Bottom).
Material Label Diameter
(mm)
Length
(mm)
Conductivity (𝝁𝐒/𝒎)
(T=𝟐𝟐℃± 𝟐℃)
Carbon
Steel
1/16” 1.6 27.0 4 ± 0.5
1/8” 3.2 25.0
1/4” 6.3 25.9
1/2” 12.7 25.4
1” 25.4 25.6
Brass 1/8” 3.2 25.9 15 ± 3.7
1/4” 6.3 26.7
1/2” 12.7 25.9
1” 25.4 24.0
Stainless
Steel
(300
Series)
1/16” 1.6 26.2 1 ± 0.2
1/8” 3.2 25.3
1/4” 6.3 26.1
1/2” 12.7 25.7
1” 25.4 25.9
Copper 1/8” 3.2 26.3 55 ± 9.3
Aluminum 1/8” 3.2 25.7 28 ± 3.8
Tin 1/8” 3.3 29.3 8 ± 1.3
Lead 1/6” - 41.8 4 ± 0.2
Table 1 – Loose parts included in investigation (Lead part was a
rectangular prism approximately 4 mm in height and width)
Four 3.2 mm thick plastic offsetting shims,
loaned by CNL, were used to offset the loose parts
away from the SG tube wall, defined as the radial
Figure 2 - (Top) Brass, carbon steel and stainless steel 1” long
loose parts ranging from 1.6 mm to 25.4 mm in diameter.
(Bottom) 1” long copper, aluminum and tin loose parts with3.2
mm diameter, lead loose part.
Figure 1 - Steam generator tube structure withloose part in
parallel orientation; broach support not shown in figure.
Radial Offset
Axial Offset

6. 5
direction (see Figure 1). Two magnetite collars, of
thickness 2.5 mm and 3.2 mm, were used to
simulate magnetitesludgesurroundingthe SGtube.
Both collarshad a relative magneticpermeabilityof
1.9 [17]. Materialsusedtooffsetthe loose parts are
shown in Figure 3.
C. Probe
The probe used in this investigation was
developed by RMC and manufactured by CNL. The
probe head, as described elsewhere [18], consisted
of a drive coil and 8 pick-up coils: 4 located above
(front array) and 4 located below (back array) the
drive coil,spacedazimuthally at90 degree intervals,
as shown in Figure 4. Pick-up coils that were 180°
apart were paired for analysis. These pairs were
matched as closely as possible in terms of signal
response inanattemptto increase the sensitivityof
the probe to induced eddy currents.
The probe body itself has a length of 77.6 mm
andan outerdiameterof 13.5mm.The lengthof the
probe body was encased in heat shrink material,
then labeled in 2 mm increments originating at the
drive coil.The drivecoil waswoundcoaxiallyaround
the probe 127 times using 36 AWG copper wire.
Each of the eight pick-up coils was wound with 360
turns using 42 AWG copper wire. The axis of each
pick-upcoil wasorientedperpendicularlytothe axis
of the drive coil, with shielded twisted pair wire
carrying the signals from the pick-up coils to a
purpose-built amplification circuit that was
developed at RMC.
The signals from each pick-up coil were
individually amplified with a gain of 100 before
being digitized at 1MHz using a 16-bit resolution
NI6356 USB DAQ. The DAQ was connected to a
laptopcomputerthatwasusedtosave the data and
perform MPCA on the acquired data. The NI6356
USB DAQ was also used to generate the excitation
pulse, which was carried to the drive coil using a
coaxial cable.The pulse, generatedbythe USB DAQ
at 1000 Hz and 50% duty cycle, hadan amplitudeof
1.5 V. A block diagram of the equipment used for
data acquisition is shown in Figure 5.
D. Method
The probe was initially insertedintothe SG tube
a distance of 90 mm, so that the drive coil was 10
mm from the edge of the tube sheet, before
measurementsbegan.Measurementsweretakenat
2 mm intervals within the Alloy-800 SG tube as the
probe was axially translated a distance of 130 mm
through the SG tube, for a total of 65 data points.
The loose partswereaffixedtotheSGtube suchthat
they were aligned with the probe, in order to
maximize the pick-up coil response. Temperature
was recorded for each data acquisition. A timed
LabVIEW program was used to generate excitation
pulses and to collect voltage responses from the
pick-up coil array. Many data sets, spanning a wide
variety of possible loose part sizes, compositions,
andboth axial andradial offset positions,wereused
in the construction of the principal components.
3.2 mm
thick plastic
shims
2.5 mm thick
magnetite collar
3.2 mm thick
magnetite collar
1.5 mm thick
plastic shim
0.5 mm thick
plastic shim
collar
Figure 3 - Materials used to offset loose parts radially from the
SG tube.
Figure 4 – PEC Probe Schematic
Figure 5 – Block diagram of experimental setup used
for investigation.

7. 6
This ensuredthatthe sensitivity of the components
was notrestrictedtoa specificsituationof interest.
IV. RESULTS & DISCUSSION
A. Probe Response
The transient response of the probe in the
presence of just the SG tube (null trial), a 3.2 mm
diametercarbonsteel part, and a 3.2 mm diameter
copperpart, is showninFigure 6. The response was
found to exhibit a unique variation in the presence
of carbon steel, compared to the variations
observedforthe othermaterialssampled.Thiswas
attributed to carbon steel being the most
ferromagnetic material included in the
investigation.Stainlesssteel was found to have the
weakest transient response, and could not be
detected without more advanced analysis. Figure 6
clearly shows the variation in transient response
associated with differences in characteristic
diffusion times in the presence of different
materials, as discussed in Sec. II. A.
B. MPCA
The modified PCA described in Sec. II. B. was
performed ona collectionof datasets that covered
a wide range of part sizes andcompositions, inboth
radial and axial offset positions. One data set from
each situation of interest was used to generate the
principal components, as it was found that the
transient response of the probe was highly
reproducible. Additionally, the average mean
square error associated with signal reproduction
was found to be negligibly different when multiple
trials of each situation of interest were used to
generate the principal components (see Table 2 of
the Appendix).
The first four principal components were used
for signal reproduction, resulting in a reproduced
signal with an average mean square error of 1.04%
from the as-measuredsignal.Higherorderprincipal
componentswere foundto containnoise,andwere
discarded. The normalizedeigenvectorscanbe seen
in Figure 7.
The first principal component (𝑉1) accounts for
the average response of the data, and thus,
unsurprisingly, resembles the raw transient signal
shown in Figure 6. The scores associated with the
first principal component were foundto be at least
an orderof magnitude largerthanothercomponent
scores.The secondprincipal component(𝑉2) canbe
seen peaking earlier than the first principal
component, and possesses a second peak of
opposite sign. The third principal component (𝑉3)
shares a similar shape as compared with the first
principal component(𝑉1),resemblingthe rawsignal,
but peakslater in time;thissuggestsan association
with materials further from the probe, as observed
by J.Buck [12]. The final principal component(𝑉4) is
noisierthanthe previousthree,andpossessesthree
peaks.
C. Score Comparison
The most direct method of determining the
effectthe presenceof variousloosepartshadonthe
principal components scores was to compare the
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150 200
Eigenvectors[V]
Time [𝜇s]
V1 V2
V3 V4
Figure 7 - Eigenvectors constructed by performing MPCA on a
global data set
-0.5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
0.025 0.075 0.125 0.175 0.225
Voltage(V)
Time (ms)
Null Trial Transient Response
Carbon Steel Transient Response
Copper Transient Response
4.5
5
5.5
6
6.5
0.055 0.06 0.065 0.07 0.075
Voltage(V)
Time (ms)
Figure 6 - Transient voltage response of a pick-up coil in the
presence of an Alloy-800 tube, an Alloy-800 tube and a 3.2 mm
diameter carbon steel part, and an Alloy-800 tube and a 3.2 mm
copper part. Neither part possessed a radial offset.

8. 7
scores of a trial containing a loose part with the
scores of a null trial as a function of axial
displacement. It was expected that, in the absence
of a loose part, scores should be approximately
equal between data sets. Therefore, if a score
variation was observed for a collection of data
points, it could be inferred that a loose part was
present at that axial position on the SG tube.
It wasobservedthatavertical offsetwaspresent
betweenindividual datapointseveninthe absence
of loose parts.Thismade the detectionof significant
score variationdifficultaseverydata pointin a trial
showedvariationfromthe correspondingdatapoint
in the null trial. This effect was determined to be a
resultof the temperature at whichthe data set was
taken, which was found to vary by as much as 4
degrees Celsius (see Appendix Figure 1). A
‘normalizing function’ was implemented, which
aligned data points corresponding to Alloy-800
tubing,allowingthevariationdue tothe presence of
a loose part to be more readily identified.
This method of loose part identification proved
to be useful for the majority of data sets that
involved aloose partin physical contactwiththe SG
tube. Typically, data sets possessedseveral distinct
traits:A large score deflectioninthe presenceof the
tube sheet, followed by a smaller magnitude
variationfromthe null setinthe presence of aloose
part, and, finally, little to no variation from the null
set for the remainder of the data set. Figure 8
demonstrates this type of comparison for two
different principal component scores.
D. Cluster Analysis
For loose partssmallerthan6.4 mm indiameter,
as well as for parts which contained a radial offset
from the SG tube, the score comparison method of
identification could not consistently be used to
determine the presence of loose parts in individual
principal componentscores.Instead,scores of both
a null trial, and a trial of interest, were plotted in
three dimensional PCA space, in order to identify
variations as linear combinations of individual
principal component scores. Figure 9 demonstrates
that, with proper viewing angle, variations in PCA
space are more readilydetectable thaninindividual
principal componentscores,especiallywithsmaller
parts and parts with higher resistivity values.
The second, third, and fourth principal
componentscoreswere mostcommonly plottedfor
this type of analysis, since the more difficult to
detectparts demonstratedthe leastvariationinthe
firstprincipal componentscore.Thisclusteranalysis
improved the recognition of loose parts that were
already detectable using score comparison, and
allowed for smaller loose parts, with larger radial
offsets, to be detected more easily.
Cluster analysis was only applied to parts with
diameterof 3.2 mmor less,asparts largerthan this
were foundto be quite readilydetectable. Itshould
be notedthatthe temperature normalizingfunction
described in Sec. IV. C. was also implemented for
cluster analysis.
-2.30
-1.30
-0.30
0.70
1.70
2.70
3.70
-43.00
-42.00
-41.00
-40.00
-39.00
-38.00
-37.00
6.8 9.8 12.8 15.8 18.8
V2Score
V1Score
Distance(cm)
Null V1
Brass V1
Null V2
Brass V2
Figure 8 - 3.2 mm diameter brass loose part oriented parallel to
the SG tube with no axial or radial offset. Variation of both 𝑉1
and 𝑉2 from the null set at approximately 128 mm indicates the
presence of the loose part.
-0.15
-0.1
-0.05
0
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0
0.05
0.1
0.15
V3 ScoreV2 Score
V4Score
Stainless Steel (D = 1.6mm)
Null Trial
Figure 9 - 1.6 mm stainless steel loose part oriented parallel to
the SG tube with no axial or radial offset. Clustering of data
points indicates presence of loose part; score variations using
the method described in Sec. IV. C only occurred for a 25.4 mm
diameter stainless steel part in the same orientation.

9. 8
With the exception of carbon steel, Copper was
the most detectable material. Parts with higher
conductivity values were found to be more easily
detectable (Figure 10). This is attributed to the
dependence of transient response variation on
differences in characteristic diffusion times, as
discussed in Sec. II. A. The most difficult to detect
material, stainless steel, not only possessed the
largest resistivity of the materials tested, but had
the most similar resistivity value compared to the
Alloy-800 tubing used in this investigation.
As expected from Eqn. 9, loose parts that were
largerinsize were easiertodetectforboththistype
of analysis (Figure 11), as well as for the score
comparison analysis mentioned in Sec. IV. C.
Detectability was also found to decrease rapidly
whenpartswere offsetradiallyfromthe SGtube, as
seen in Figure 12. Both Figure 11 and Figure 12
demonstrate score variations attributed to
differences in the characteristic length of the
system, as described by Eqn. 9.
Score variations were found to be more distinct
when a loose part was offset radially using a
magnetite collar, as compared to a part offset
radiallybythe same amountusinganon-conducting
plastic shim, as shown in Figure 13. This result can
be attributed to the increase in flux caused by the
magnetization of the ferromagnetic magnetite
collar.
The magnitude of the score variation when the
loose part was placed in the perpendicular
orientation was smaller than when it was placed in
the parallel orientation.Furthermore,loose partsin
the perpendicularorientationwere more difficultto
detect due to the score variation from the null set
Figure 11 – Brass loose parts ranging from 3.2 mm in diameter
to 25.4 mm in diameter with no radial or axial offset. Clearly,
larger loose parts result in more pronounced score variations
-0.5
0
0.5
-1.2-1-0.8-0.6-0.4-0.20
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
V3 Score
V2 Score
V4Score
Brass (D = 25.4mm)
Brass (D = 12.7mm)
Brass (D = 6.4mm)
Brass (D = 3.2mm)
Null Trial
Figure 12 – 3.2 mm diameter carbon steel loose part in contact
with the tube sheet at various (non-magnetite) radial offsets.
Score variation magnitude drops off quickly with radial offset.
-0.4
-0.2
0
0.2
0.4
0.6
-2-1.5-1-0.50
0
0.1
0.2
V2 Score
V3 Score
V4Score
Carbon Steel (OS = 0 mm)
Carbon Steel (OS = 3.2 mm)
Carbon Steel (OS = 6.4 mm)
Carbon Steel (OS = 9.6 mm)
Null Trial
Figure 13 – 3.2 mm diameter brass loose part in contact with
tube sheet offset 3.2 mm radially by plastic shim and by 3.2 mm
thick magnetite collar (P = 1.9). Clustering in PCA space is more
obvious when offset is due to magnetite.
0.1
0.2
0.3
0.4
0.5
-0.1
0
0.1
-0.1
-0.05
0
0.05
0.1
0.15
V2 Score
V3 Score
V4Score
Brass (OS = 3.2 mm Magnetite Collar)
Brass (OS = 3.2 mm)
Null Trial (3.2 mm Magnetite Collar
Null Trial
0.1
0.2
0.3
0.4
0.5
-0.0500.050.10.150.20.25
0
0.1
0.2
0.3
0.4
V2 Score
V3 Score
V4Score
Copper (D = 3.2 mm)
Aluminum (D = 3.2 mm)
Brass (D = 3.2 mm)
Stainless Steel (D = 3.2 mm)
Null Trial
Figure 10 –3.2 mmdiameter loose parts ofvarying compositionwith no
radial or axialoffset. Materials with higher conductivities possess larger
PCA space variation. Stainless steel is slightly ferromagnetic, and thus
shows variation in the opposite direction.

10. 9
occurringfora fewernumberof datapoints,asseen
in Figure 14, due to a shorter length of interaction
with the probe
The score variation observed from a loose part
that was offset axially from the tube sheet was
found to be of the same, or of slightly lower
magnitude compared to that of a loose part in
contact with the tube sheet (Appendix Figure 2).
This effect is likely caused by the voltage
amplification due to the production of a secondary
magnetic field in the ferromagnetic tube sheet.
A summaryof the limitationsondetectabilityfor
a variety of loose parts can be found in Table 2.
E. Investigationof Multinomial Logistic
Regression (MLR)
Before PEC becomes a practical method for
identifying loose parts, a more efficient means of
detecting loose parts, and identifying the
characteristics it possesses, is required. A
multinomial logistic regression (MLR) function that
is included in MatLab was investigated for this
purpose.
MLR is a method used to generalize logistic
regression problems with more than two discrete
outcomes [19].Givenasetof independentvariables,
the model is used to classify groups of data by
calculating the probabilities of the various possible
outcomes of a categorically distributed dependent
variable [19].Inessence,datapointsare sortedinto
binsbasedontheirsimilaritytodatapointsonwhich
the model was trained on, in a logistic regression
sense.
Loose Part
(diameter)
Non-magnetite
radial offset
detectable
Magnetite radial
offset detectable
Carbon Steel
(3.2 mm)
9.6 mm 3.2 mm
Carbon Steel
(1.6 mm)
3.2 mm 3.2 mm
Brass (3.2 mm)
3.2 mm 3.2 mm
Stainless Steel
(3.2 mm)
3.2 mm -
Stainless Steel
(1.6 mm)
1.5 mm -
Aluminum
(3.2 mm)
0.5 mm 2.5 mm
Copper
(3.2 mm)
3.2 mm 2.5 mm
Tin (3.2 mm)
1.5 mm 2.5 mm
Lead
0.5 mm -
Table 2 - Magnetite and non-magnetite radial offset limitations
on detectability for loose parts in contact with the tube sheet. ‘-
‘ indicates a part could not be detected for the smallest offset
available.
The model was initiallytrainedusing entire data
setscontaining3.2 mm diameterloose parts,which
had been offset axially from the tube sheet by 30
mm. These data sets were used due to the spatial
separation between the tube sheet and the loose
part; data points could be easily categorized as
either loose part material, Alloy-800 Tube, or tube
sheet.
While the MLR model was successful at
identifying when an axially offset part was present,
it was found to have difficulties discriminating
between materialswith similar conductivity values.
Specifically, composition probabilities were split
betweencopperandaluminum, andbetweenbrass
and tin for a number of validation sets (Figure 15),
suggestingthatthe response of the pick-upcoil toa
loose part isstronglydependenton conductivity,as
expected from Eqn. 9.
The model also encountered difficulties in the
presence of anomalousdatapointswithinvalidation
sets;small score variationsinthe absence of aloose
part were identifiedaseithertin,aluminumorbrass
loose partswith greaterthan80% confidence.While
these results could be readily discounted in the
context of this investigation, in reactor this might
not be the case. Loose parts used in this
0 10 20 30 40 50 60 70
-0.5
0
0.5
1
1.5
2
Data Point
V3score
Null Trial
Carbon Steel Parallel
Carbon Steel Perpendicular
Figure 14 – 3.2 mm diameter carbon steel loose part placed in
the perpendicular and parallel orientation. The loose part has a
smaller variation when in the perpendicular orientation.
Tube Sheet

11. 10
investigationhadaknownlength. Thus, ifthe model
detected a part for less data points than the length
of a loose part, it could be discounted. However, in
reactor,debrisare of unknownsize,andthus cannot
be counted as false positives.
The model was found to perform poorly when
the validation set contained a loose part size or
radial offset that had not been included in the
training sets. In situations such as these, the
confidence of the model either decreased by as
much as 60%, or yielded several additional false
positives, depending on the material used. This
resultisnotideal,asitimpliesthatonlyorientations
and sample sizes used to train the model can be
detectedconfidently,andincludingall possibleparts
and configurations commonly found in situ in the
training set would not be a feasible task.
V. CONCLUSION & FUTURE WORK
This report investigated the use of pulsed eddy
current and principal components analysis as a
method for detecting loose parts in close proximity
to the tube sheetsof CANDU nuclearreactor steam
generators. Several materialsspanningawide range
of conductivitieswereincludedinthe investigation.
In the presence of magnetite fouling, the
identification of data point clustering in PCA space
was found to improve for several materials,
includingbrass,aluminumandtin.Incloseproximity
to ferromagneticstructures,suchasthe tube sheet,
PEC could detect a variety of loose part
compositions as small as 3.2 mm in diameter at
varying radial offsets.
PCA isa robustanalysistechniquethatiscapable
of identifyingvariationsin PECpick-upcoil response
due to the presence of conductive materials. This
result is attributed to a difference in
electromagnetic field diffusion times when
conductive materials are presentin close proximity
to the SG tube.
PEC combinedwithPCA has beendemonstrated
as being a viable analysis technique for the
detection of loose part accumulation in close
proximity to the tube sheet of SGs.
A multinomial logistic regression model was
used to calculate the probability that a loose part
was present.The model was foundto be successful
at detecting the presence of loose parts, but could
only categorize scored data that it had been
specifically trained on. Additionally, the model had
difficulty differentiating between non-
ferromagnetic materials with similar conductivity
values due to a similarity in characteristic diffusion
times.
Further investigation in the study of loose parts
detection would include identifying the effects of
azimuthal offset from a pick-up coil (by as much as
45°). The capabilities of PEC when operating at
temperatures more closely resembling those found
in-situ must also be considered. Additionally, a
model capable of more accurately identifying loose
part properties should be investigated. Artificial
neural networks may be another avenue of
investigation to achieve this goal [20].
Figure 15 – Probability that a loose part is present, that the tube
sheet is present, and the probabilities that the part is composed
of tin or brass, as determined by the MLR model.

12. 11
Appendix
Numberof RepeatedTrials Used Average Mean Square Error (V) MaximumMean Square Error (V)
1 𝟑. 𝟗𝟒 × 𝟏𝟎−𝟓
𝟏. 𝟑𝟒 × 𝟏𝟎−𝟑
2 𝟑. 𝟗𝟏 × 𝟏𝟎−𝟓
𝟏. 𝟐𝟕 × 𝟏𝟎−𝟑
5 𝟑. 𝟗𝟏 × 𝟏𝟎−𝟓
𝟏. 𝟐𝟒 × 𝟏𝟎−𝟑
10 𝟒. 𝟎𝟗 × 𝟏𝟎−𝟓
𝟏. 𝟑𝟏 × 𝟏𝟎−𝟑
Table 1 – Average and maximum mean square error associated with signal reproduction when 1, 2, 5 and 10 trials of the situations of
interest are used to generate the eigenvectors
Figure 1 – Effect of temperature on principal component scores;data points which should have the same score are offset for different
data sets, relationship between offset and temperature is linear.
-37.4
-37.3
-37.2
-37.1
-37
-36.9
-36.8
21.2 21.7 22.2 22.7 23.2 23.7 24.2 24.7 25.2
V1Score(ArbitraryUnits)
Temperature (°C)
V1 ScoreVersus Temperature
5th V1 Score Value
60th V1 Score Value
Figure 2 – 3.2 mm diameter copper loose part, parallel to and in contact with the SG tube for varying axial offsets.
Score variation magnitude is found to remain fairly constant for different axial offsets.
20 25 30 35 40 45 50
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Data Point
V2score
Offset Plotting
Null Trial
OS=0mm, H=0mm
OS=0mm, H=10mm
OS=0mm, H=20mm
OS=0mm, H=30mm

13. 12
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