POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
Assessmen o Pa ially Conduc i e C acks om
Eddy Cu en Non-Des uc i e Tes ing Signals
using Suppo Vec o Machine
Ladisla JANOUSEK1, Ma ina RADILOVA2, Mihai REBICAN3, Milan SMETANA1
1Depa men o Elec omagne ic and Biomedical Enginee ing, Facul y o Elec ical Enginee ing,
Uni e si y o Zilina, Uni e zi na 1, 010 26 Zilina, Slo ak Republic
2Depa men o Telecommunica ions, Facul y o Elec ical Enginee ing, Uni e si y o Zilina, Uni e zi na 1,
010 26 Zilina, Slo ak Republic,
3Depa men o Elec ical Enginee ing, Facul y o Elec ical Enginee ing, Uni e si y Poli ehnica o Bucha es ,
Splaiul Independen ei 313, 060 042 Bucha es , Romania
ladisla[email p o ec ed], ma ina.zacha iaso [email p o ec ed], [email p o ec ed],
[email p o ec ed]
DOI: 10.15598/aeee. 13i3.1393
Abs ac . This pape deals wi h a h ee-dimensional
non-des uc i e e alua ion o pa ially conduc i e
c acks om eddy cu en es ing signals. An SUS316L
pla e specimen con aining a c ack is non-des uc i ely
inspec ed by he eddy cu en me hod using nume ical
simula ions. An ex ensi e da abase o eddy cu en e-
sponse signals is p epa ed while dimensional pa ame-
e s o a c ack oge he wi h i s pa ial conduc i i y
a e a ied in wide anges. A Suppo Vec o Machine
classi ica ion algo i hm is employed o sol e he elec-
omagne ic in e se p oblem. The acqui ed signals a e
employed o aining he algo i hm and o es ing i s
pe o mance. I is demons a ed ha he Suppo Vec-
o Machine algo i hm is able o p ope ly classi y de-
ec ed de ec s in o p ope classes wi h e y high p oba-
bili y e en he pa ial conduc i i y o a de ec ed c ack
oge he wi h i s wid h a e unknown.
Keywo ds
Eddy cu en s, non-des uc i e e alua ion, pa -
ially conduc i e c acks, suppo ec o ma-
chine.
1. In oduc ion
New app oaches such as Sys em Heal h Moni o ing
and Condi ion Based Main enance a e nowadays em-
ployed o assessmen o s uc u al in eg i y o a i-
ous componen s and s uc u es. The mode n me h-
ods ollow h ee consecu i e phases - de ec ion o non-
homogenei ies, hei diagnosis and inally p ognosis o
hei u he de elopmen . The i s wo phases a e
inhe en ly associa ed wi h Non-Des uc i e E alua ion
(NDE) o ma e ials. Enhancing NDE me hods is he e-
o e e y impo an o eliable assessmen o s uc-
u es.
NDE echniques a e based on nume ous physical
p inciples and phenomena. Eddy cu en es ing
(ECT) is one o he widely u ilized elec omagne ic
NDE me hods. ECT wo ks on he basis o an in e ac-
ion o ime- a ying elec omagne ic ield wi h a con-
duc i e body acco ding o he Fa aday’s elec omag-
ne ic induc ion law. The e a e many ad an ages such
as high sensi i i y o su ace b eaking de ec s, high in-
spec ion speed, con ac -less inspec ion, e sa ili y, and
ma u i y o nume ical means ha accoun o con in-
uously enla ging applica ion a ea o he ECT, mainly
in nuclea , pe ochemical and a ia ion indus ies [1].
On he o he hand, ECT is a ela i e me hod and he
in e se p oblem is ill-posed [2]. The e o e, e alua ing
dimensions o a de ec ed de ec om ECT esponse sig-
nals can be qui e di icul [3]. ECT ins umen s p o ide
aw da a wi h limi ed o absen capabili y o in e p e -
ing quan i a i ely he da a [4]. Typically, e alua ion
elies on calib a ed cu es measu ed on p e- ab ica ed
e alons and on he skills o an ope a o . Recen ly, he
p og ess in powe ul compu e s has allowed de elop-
ing o au oma ed p ocedu es o make decisions. Qui e
sa is ac o y esul s a e epo ed by se e al g oups o
au oma ed e alua ion o a i icial sli s [3] and e en o
se e al pa allel no ches [5]. Howe e , e alua ion o eal
c
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c acks, especially s ess co osion c acking (SCC), om
ECT esponse signals emains s ill e y di icul .
SCCs a e qui e di e en in compa ison wi h a i icial
sli s o e en o o he ypes o eal de ec s. C oss sec-
ions o SCC equen ly show b anched s uc u e and
a g oup o c acks usually occu s in wha is known as a
colony. The local opening o SCC is usually e y small,
e.g. ens o mic ome e s; howe e , a damaged egion
i sel is much b oade . SCC con ains many unb oken
ligamen s bo h in dep h and opening di ec ions, which
makes SCC pa ially conduc i e [6]. In he case o
a i icial EDM no ches he wid h is usually conside ed
ixed in he in e sion p ocess o ECT signals. Howe e ,
o c acks wi h non-ze o conduc i i y he wid h a ec s
he signal and i has o be conside ed unknown du ing
econs uc ion [7]. I means ha he addi ional a i-
ables should be aken in o accoun o e alua ion o a
de ec ed SCC ha conside ably inc eases ill-posedness
o he in e se p oblem [2]. Thus, many unsa is ac o y
esul s a e epo ed when he au oma ed p ocedu es
o iginally de eloped o non-conduc i e c acks a e em-
ployed in he e alua ion o SCCs. I is s a ed ha one
o he possible easons is lack o su icien in o ma ion
[3].
S anda d ECT inspec ion is pe o med in such a way
ha an ECT esponse signal is acqui ed du ing a wo
dimensional scanning o an ECT p obe o e a su ace o
he es ed ma e ial. Howe e , only a one-dimensional
signal is hen employed o he e alua ion; a esponse
signal along a de ec ed c ack leng h is ex ac ed om
he whole da a se . Only h ee pa ame e s a e es i-
ma ed / he c ack su ace leng h, posi ion o i s cen e
and a maximum dep h. The c ack wid h and i s con-
duc i i y a e se be o e he in e sion wi hou knowl-
edge o hei ac ual alues.
The au ho s al eady p oposed new app oach o he
h ee-dimensional econs uc ion o pa ially conduc-
i e c acks such as o example SCCs [8]. The unique-
ness o he p oposal lays in he u iliza ion o wo-
dimensional ECT esponse signals while he es ima-
ion o he h ee-dimensional c ack p o ile is pe o med.
The pa ial conduc i i y o a c ack and i s wid h as
well a e conside ed unknown du ing he econs uc ion.
The abu sea ch s ochas ic me hod was used o sol e
he in e se p oblem.
Suppo Vec o Machine (SVM) classi ica ion algo-
i hm is newly employed o ackle assessmen o pa -
ially conduc i e c acks in his pape .
2. Nume ical Model
A pla e specimen ha ing he elec omagne ic pa am-
e e s o a s ainless s eel SUS316L is inspec ed in his
s udy. The specimen has a hickness o = 10 mm, a
conduc i i y o σ= 1.35 MS·m−1and a ela i e pe -
meabili y o µ = 1. A single su ace b eaking c ack
appea s in he pla e. I is modelled as a cuboid ha ing
di e en elec omagne ic p ope ies om he base ma-
e ial. Con igu a ion o he pla e ( egion Ω0) wi h he
c ack ( egion Ω1is shown in Fig. 1. The c ack egion
Ω1(22 ×2×10 mm3) shown in de ails in Fig. 2 is uni-
o mly di ided in o a g id composed o nx×ny×nz
(11×5×10) cells in leng h, wid h and dep h di ec ions,
espec i ely, de ining a possible c ack geome y. The
dimensions o each cell a e 2.0×0.4×1.0mm3.
A new eddy-cu en p obe p oposed by he au ho s
is employed o he nea -side inspec ion o he pla e
[8]. I consis s o wo ci cula exci ing coils posi ioned
apa om each o he and o ien ed no mally ega ding
he pla e su ace. The ci cula coils a e connec ed in
se ies bu magne ically opposi e o induce uni o mly
dis ibu ed eddy cu en s in he pla e. The exci ing
coils a e supplied om a ha monic sou ce wi h a e-
quency o 5 kHz and he cu en densi y 1 A·mm−2.
ECT esponse signal is de ec ed by a small ci cula coil
loca ed in he cen e be ween he exci ing coils o gain
high sensi i i y as he di ec coupling be ween he ex-
ci ing coils and he de ec o is minimal a his posi ion.
The con igu a ion o he new p obe is shown in Fig. 3.
Dimensions o he de ec ing coil a e as ollows: an in-
ne diame e o 1.2 mm, an ou e diame e o 3.2 mm
and a winding heigh o 0.8 mm. The de ec ing coil is
o ien ed along he z-axis acco ding o he coo dina e
sys em shown in Fig. 3.
Ω0
x
Ω1
1
2
C ack
ny
1 2 x
1
z
n
P obe
n
y
Scanning
Fig. 1: Con igu a ion o pla e specimen wi h c ack egion.
Two-dimensional scanning, he so called C-scan, is
pe o med o e he c acked su ace wi h a li -o o
1 mm. The eal and imagina y pa s o he induced
ol age in he de ec ing coil a e sensed and eco ded
du ing he inspec ion.
The as - o wa d FEM-BEM analysis sol e using
da abase [9] is adop ed he e o he ECT esponse sig-
nals simula ion. Ac ually, a e sion o he da abase al-
go i hm upg aded by he au ho s in p e ious wo ks [5]
o he compu a ion o he ECT signals due o mul iple
c acks is used in his pape . The da abase is designed
o a h ee-dimensional de ec egion and no as usu-
ally o a wo-dimensional one whe e a c ack wid h is
c
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1 2 nx
nn
n
1
2
z
1
2
y
n
Fig. 2: C ack model.
x
z
pla e
23
14
35
10
exci ing
coils
de ec o s
Fig. 3: ECT p obe con igu a ion.
conside ed ixed. Thus, he ECT esponse signals can
be simula ed also o pa ially conduc i e c acks wi h
a iable wid h using he same da abase gene a ed in
ad ance. The a ea o he simula ed wo-dimensional
ECT signals has su ace dimensions o 100 ×28 mm2.
The numbe o scanning poin s in he wo di ec ions is
50 and 70, espec i ely.
In o al, 6050 scena ios a e simula ed, while he
c ack pa ame e s a e changed as ollows:
•leng h: om 2 o 22 mm wi h a s ep o 2 mm,
•wid h: om 0.4 o 2.0 mm wi h a s ep o 0.4 mm,
•dep h: om 0 o 10 mm wi h a s ep o 1 mm,
•pa ial conduc i i y: om 0 o 10 % o he base
ma e ial conduc i i y.
3. Suppo Vec o Machine
Suppo Vec o Machine (SVM) is ela ed o he supe -
ised lea ning me hods ha analyse da a and ecognize
pa e ns. I is a non-p obabilis ic bina y linea model
based classi ie . The aining algo i hm cons uc s a
model ha ep esen s pa e ns as poin s in he ec o
space. Such mapped pa e ns o he sepa a e classes
a e di ided by a gap ha is as wide as possible [10].
De elopmen o he classi ica ion sys em includes da a
sepa a ion in o aining and es ing se s. Each ins ance
in he aining se con ains ea u es o he obse ed
da a and he class labels. The aining se consis s o
he ins ance - label pai s (xi, yi),i= 1,2, ..., l, whe e
xi∈Rnand y={1,−1}l. The SVM equi es solu ion
o he op imiza ion p oblem [11]:
minw,b,ξ (1
2wTw+c
l
X
i=1 )ξi,(1)
wi h subjec o:
yiwTφ(xi) + b≥1−ξi, ξi≥0,(2)
whe e φ(xi)maps xiin o a highe dimensional space
and C > 0is he egula iza ion pa ame e . Due o pos-
sibly high dimensionali y o he ec o a iable ωone
usually sol e he ollowing dual p oblem de ined as:
minα1
2αTQα −eTα,(3)
subjec o:
yTα= 0,0≤αi≤C, (4)
whe e i= 1,2, ..., l and e= [1,1, ..., 1]Tis he ec-
o o all ones o he leng h l, Q is an lby lpos-
i i e semide ini e ma ix, Qij ≡yiyjK(xi, yj)and
K(xi, xj)≡φ(xi)Tφ(xj)a e he ke nel unc ions [10],
[11].
As soon as he p oblem Eq. (1) is sol ed, he op imal
w sa is ies he e m Eq. (3) and he decision unc ion
is as ollows:
sgn wTφ(x+b)= sgn l
X
i=1
yiαiK(xi, x) + b!,(5)
a e his s ep, yiαi∀i, b label names suppo ec o s
and o he in o ma ion such as ke nel pa ame e s a e
s o ed in he model [11].
The e a e ou basic ke nel unc ions: linea , polyno-
mial, adial basic unc ion (RBF) and sigmoidal unc-
ion. Each o he ke nels has one o mo e pa ame e s
o be se depending on he pa icula ype. The mos
equen ly used ke nel unc ion - RBF is de ined as [11]:
K(xi, yj) = exp −γkxi−yjk2, γ > 0.(6)
The quali y o SVM models depends on he p ope
se ing ( uning) o SVM hype -pa ame e s p ocess
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called SVM model selec ion. This is a challenging p ob-
lem due o he inclusion o ke nels in he SVM. On he
one hand, SVMs can implemen a a ie y o ep esen-
a ions ia he choice o he ke nel. On he o he hand,
ke nel speci ica ion de ines a simila i y me ic (da a en-
coding) in he inpu space, which complica es model
selec ion [12].
Fig. 4: G id sea ch algo i hm.
Acco ding o [12], SVM model selec ion depends in
gene al on wo pa ame e s:
•pa ame e s con olling he "ma gin" size,
•model pa ame e iza ion, which is he choice o ke -
nel ype and i s complexi y pa ame e s.
Success ul uning o SVM pa ame e s equi es a con-
cep ual unde s anding o hei ole and hei e ec on
he gene aliza ion abili y. I is impo an o make a
dis inc ion be ween SVM pa ame e s con olling he
ma gin size and hose con olling he model lexibili y.
Fo example, he ma gin size is con olled by pa am-
e e Cand he model lexibili y is con olled by he
ke nel pa ame e s desc ibed abo e. As o eg ession
p oblems, he wid h o he insensi i e zone (in e sely
ela ed o ma gin size) is con olled by he alue o
, and he model lexibili y can be con olled by he
ke nel complexi y pa ame e and/o he egula iza ion
pa ame e C.
Figu e 4 shows a G id Sea ch app oach belonging
o he exhaus i e app oach o model selec ion, and
also op imized pa ame e uning using an e olu iona y
algo i hm. The g id sea ch is one o he widely used
app oaches o model pa ame e selec ion.
4. Recons uc ion o Pa ially
Conduc i e C acks
A design o econs uc ion scheme and pa icula e-
sul s o he au oma ic econs uc ion o a de ec ed de-
ec a e p esen ed in his sec ion. The p ocess o de-
eloping he econs uc ion algo i hm can be summa-
ized as ollows. The la ge da abase o he eddy cu -
en esponse signals is buil a i s acco ding o he
explana ion p o ided in sec ion 2. The calcula ed e-
sponse signals a e hen di ided in o he aining and
he es ing se s. The signals om he aining se s a e
ead by he algo i hm o ain he classi ie . A e he
SVM is ained, he signals om he es se s a e used
o alida ion. The la e signals a e classi ied in o de-
ined classes acco ding o he c ack?s dimensions and
i s pa ial conduc i i y o p o ide esul s o he h ee-
dimensional c ack econs uc ion.
The o he possibili y on he con a y o he de e -
minis ic me hod o he SVM pa ame e s se ing is o
exploi an e olu ion op imiza ion echniques usually
based on s ochas ic p ocesses. These me hods a e able
o ind solu ions ha can be e y close o he op imal
ones e en on he mul imodal unc ion wi h many local
ex emes [10]. In he expe imen , C-SVM o mula ion
wi h RBF ke nel unc ion is used. This o mula ion o
SVM equi es se ing o wo cos pa ame e s:
•pa ame e Cwhich has he alue be ween 2−5and
220,
•pa ame e γwhich is be ween 2−20 and 25.
The sea ch me hod o selec ing nea - op imal pa-
ame e s is called he g id sea ch. This me hod ex-
haus i ely calcula es K- old C oss-Valida ion (CV) ac-
cu acy o e e y combina ion om he de ined egion
o pa ame e s Cand γ. Fo ins ance, i pe o ming
a coa se sea ch o egion be ween 2−5and 220 o he
pa ame e C, one could choose o y e e y cos pa-
ame e 2m o m=−5,−4, ..., 0, ..., 19,20. Fo each o
hese Cpa ame e s, one y e e y γa he alue 2m o
m=−20,−19, ..., 0, ..., 4,5. This sea ch equi es un-
ning SVM aining o 676 di e en pa ame e s com-
bina ions. This echnique is e y ime consuming e en
o sea ching o wo model pa ame e s [10].
Table 1 p o ides he dis ibu ion o a numbe o sig-
nals o he aining and he es ing se s o SVM models
including pa ame e s ob ained using g id sea ch algo-
i hms, which a e used o ain he SVM models. Fi-
nally, he accu acy o aining SVM models and es ing
signals a e shown in Tab. 1, oo. The bes esul s a e
ecei ed o SVM model 98.0727 %. Only wo om he
550 es signals a e no co ec ly classi ied in o p ope
classes. The signal o a c ack wi h ollowing pa am-
e e s: leng h 20 mm, wid h 2 mm, dep h 9 mm and
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Tab. 1: Resul s o SVM.
T aining Tes ing CγT aining Tes ing
signals signals accu acy[%] accu acy[%]
6050 550 19.7 5.0 98.3140 87.4545
6050 550 19.9 4.3 98.1818 87.4545
5500 550 19.7 5.0 98.0727 99.6364
5500 550 19.9 4.3 98.0 99.6364
pa ial conduc i i y 6 % o he base ma e ial conduc-
i i y is classi ied as a c ack wi h pa ame e s: leng h
20 mm, wid h 2 mm, dep h 10 mm and pa ial conduc-
i i y 6 % o he base ma e ial conduc i i y. I means
ha he e is a di e ence o c ack dep h iden i ica ion
o 1 mm (10 %). The same misclassi ica ion appea ed
o he c ack wi h he same dimensional pa ame e s
and pa ial conduc i i y o 5 % o he base ma e ial
conduc i i y. I can be s a ed ha he SVM algo i hm
classi ied he es ing signals in o p ope classes wi h
e y high accu acy.
5. Conclusion
The pape deal wi h a h ee-dimensional econs uc-
ion o pa ially conduc i e c acks om eddy cu en
non-des uc i e es ing signals. A la ge da abase o
he eddy cu en esponse signals was de eloped us-
ing nume ical simula ions. The esponse signals we e
calcula ed o a wide a ie y o c ack dimensional pa-
ame e s and i s pa ial conduc i i y. A pa o he
calcula ed signals was used o ain Suppo Vec o
Machine algo i hm employed o au oma ic assessmen
o a de ec ed c ack. The c ack wid h and i s pa ial
conduc i i y we e aken as addi ional a iables in he
in e sion p ocess. The algo i hm was es ed on he
o he pa o signals. I was e ealed ha he Suppo
Vec o Machine classi ica ion algo i hm can classi y he
signals in o p ope classes wi h e y high p eciseness.
This me hod has a e y high and s ill unlocked po en-
ial in he ield o non-des uc i e e alua ion.
Acknowledgmen
This wo k was suppo ed by he Slo ak Resea ch and
De elopmen Agency unde he con ac s No. APVV-
0349-10 and APVV-0194-07. This wo k was co- unded
by a Slo akia-Romania join g an by he Slo ak Re-
sea ch and De elopmen Agency unde he con ac
No. SK-RO-0011-12 and he ANCS unde he G an
No. 654/2013.
Re e ences
[1] JANOUSEK, L., T. MAREK and D. GOM-
BARSKA. Eddy cu en non-des uc i e e alu-
a ion o conduc i e ma e ials. Communica ions.
2006, ol. 7, no. 1, pp. 29–33. ISSN 1335-4205.
[2] YUSA, N., H. HUANG and K. MIYA.
Nume ical e alua ion o he ill-posedness
o eddy cu en p oblems o size eal
c acks. NDT and E In e na ional. 2007,
ol. 40, iss. 3, pp. 185–191. ISSN 0963-8695.
DOI: 10.1016/j.nd ein .2006.10.012.
[3] JANOUSEK, L. and M. SMETANA. Unce ain y
in dep h e alua ion o pa ially conduc i e c acks
om eddy cu en es ing signals. Communica-
ions. 2011, ol. 13, no. 2, pp. 55–60. ISSN 1335-
4205.
[4] RUBINACCI, G., A. TAMBURRINO and
S. VENTRE. Fas nume ical echniques o
elec omagne ic nondes uc i e e alua ion.
Nondes uc i e Tes ing and E alua ion. 2009,
ol. 24, iss. 1-2, pp. 165–194. ISSN 1058-9759.
DOI: 10.1080/10589750802195568.
[5] REBICAN, M., Z. CHEN, N. YUSA, L.
JANOUSEK and K. MIYA. Shape econ-
s uc ion o mul iple c acks om ECT sig-
nals by means o a s ochas ic me hod. IEEE
T ansac ions on Magne ics. 2006, ol. 42,
iss. 4, pp. 1079–1082. ISSN 0018-9464.
DOI: 10.1109/TMAG.2006.870967.
[6] YUSA, N. and K. MIYA. Discussion on
he equi alen conduc i i y and esis ance o
s ess co osion c acks in eddy cu en sim-
ula ions. NDT and E In e na ional. 2009,
ol. 42, iss. 1, pp. 9–15. ISSN 0963-8695.
DOI: 10.1016/j.nd ein .2008.09.007.
[7] CHEN, Z., M. REBICAN, N. YUSA and K.
MIYA. Fas simula ion o ECT signal due
o a conduc i e c ack o a bi a y wid h.
IEEE T ansac ions on Magne ics. 2006,
ol. 42, iss. 4, pp. 683–686. ISSN 0018-9464.
DOI: 10.1109/TMAG.2006.870973.
[8] JANOUSEK, L., M. REBICAN, M. SMETANA,
T. STRAPACOVA and A. DUCA. Th ee-
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 240

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
dimensional econs uc ion o pa ially conduc-
i e c acks om ECT esponse signals. S udies
in Applied Elec omagne ics and Mechanics. 2014,
ol. 39, iss. 1, pp. 331–338. ISSN 1383-7281.
DOI: 10.3233/978-1-61499-407-7-331.
[9] CHEN, Z., K. MIYA and M. KUROKAWA. Rapid
p edic ion o eddy cu en es ing signals using A
-φme hod and da abase. NDT and E In e na-
ional. 1999, ol. 32, iss. 1, pp. 29–36. ISSN 0963-
8695. DOI: 10.1016/S0963-8695(98)00025-5.
[10] HRIC, M., M. CHMULIK and R. JARINA. Model
pa ame e s selec ion o SVM classi ica ion using
Pa icle Swa m Op imiza ion. In: 21s In e na-
ional Con e ence Radioelek onika. B no: IEEE,
2011, pp. 387–390. ISBN 978-1-61284-322-3.
[11] CHANG, C.-C. and C.-J. LIN. LIBSVM: A Li-
b a y o Suppo Vec o Machines. [online]. A ail-
able a : h p://www.csie.n u.edu. w/~cjlin/
pape s/libs m.pd .
[12] CHERKASSKY, V. S. and F. MULIER. Lea ning
om da a: concep s, heo y, and me hods. 2nd ed.
Hoboken: Wiley-In e science, 2007. ISBN 04-716-
8182-2.
Abou Au ho s
Ladisla JANOUSEK was bo n in Michalo e. He
g adua ed mas e s udy a he Depa men o Powe
Elec ical Sys ems, Facul y o Elec ical Enginee ing,
Uni e si y o Zilina in 1997. He con inued wi h Ph.D.
s udy a he same depa men in he ield o elec ic
machines and g adua ed in 2002. He became an
associa e p o esso in he ield Theo y o Elec ical
Enginee ing in 2007. Cu en ly he wo ks a he
Depa men o Elec omagne ic and Biomedical En-
ginee ing, Facul y o Elec ical Enginee ing, Uni e si y
o Zilina. His esea ch ac i i ies a e ocused on elec o-
magne ic me hods o non-des uc i e e alua ion and
in luence o elec omagne ic ield on li ing o ganisms.
Ma ina RADILOVA was bo n in Zeliezo ce
in 1985, Slo akia. She ecei ed he Ph.D. deg ee in
2013 a he Depa men o Telecommunica ionsand
Mul imedia, Uni e si y o Zilina. Since Sep em-
be 2013 she is a esea che a he Depa men
o Telecommunica ions, Uni e si y o Zilina. He
esea ch in e es includes digi al image p ocessing,
seman ic analysis o mul imedia con en , image and
ideo classi ica ion and e ie al o MPEG-7 s anda d.
Mihai REBICAN was bo n in Bucha es , Ro-
mania. He ecei ed he B.Sc. deg ee in Elec ical
Enginee ing and he M.Sc. deg ee in Elec ical En-
ginee ing om he Facul y o Elec ical Enginee ing,
Uni e si y Poli ehnica o Bucha es , Romania, in
1996 and 1997, espec i ely. His Ph.D. disse a ion,
de ended in 2007, a he same uni e si y, deal wi h
elec omagne ic ield analysis in eddy cu en non-
des uc i e es ing. He is now Associa e P o esso
a he Depa men o Elec ical Enginee ing, Facul y
o Elec ical Enginee ing, Uni e si y Poli ehnica o
Bucha es . His esea ch ocuses on nume ical analysis
o elec omagne ic ield, non-des uc i e e alua ion by
eddy cu en es ing, op imiza ion s ochas ic me hods.
Milan SMETANA was bo n in Pop ad. He
g adua ed mas e s udy a he Depa men o Elec-
omagne ic and Biomedical Enginee ing, Uni e si y
o Zilina in 2006. He con inued wi h Ph.D. S udy a
he same depa men in he ield o elec omagne ic
enginee ing and g adua ed in 2009. He became an
associa e p o esso in 2013. Cu en ly he wo ks a
he same depa men . His esea ch ac i i ies a e
ocused on elec omagne ic me hods o nondes uc i e
e alua ion.
c
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