Abs ac — Failu e diagnos ics as a pa o condi ion
moni o ing (CM) echnique is ine i able in mode n indus ial
p ac ice. Condi ion Based Main enance (CBM) iden i ies all
p oblems ha cause u he ailu es and sugges s main enance
pe iods. Reducing main enance cos s and enhancing sys em
a ailabili y a e la gely depends on in o ma ion p o ided by
p ecise and accu a e ailu e diagnos ics. The app oach can be
used widely in he se e al ield o he indus y. Da a acquisi ion
is ela ed o measu emen hen da a p ocessing, ea u e
ex ac ion is needed, inally ailu e iden i ica ion. In his pape
Suppo Vec o Machine (SVM) is discussed how o be used
o diagnosing machines and machine elemen s. The aim o
using SVM is o diagnose he sys em a a ce ain momen o
p edic i s ac ual s a e in he u u e. SVM is p og essing
apidly se e al new ad ances a e e ealed as he pa o
machine lea ning echniques. Due o expe imen s SVM
e iciency could be app oxima ely 90% o e en highe .
Keywo ds—Bea ing es - ig, ailu e diagnos ics, machine
aul , machine lea ning, suppo ec o machine
I. INTRODUCTION
I is c i ical o main ain machine heal h and ex ending he
li e ime o i s c i ical p ocesses, minimizing eme ging
cos s du ing ope a ion. Diagnosing he impending
ailu es is one o he signi ican end, p ognosis o he
emaining use ul li e ime (RUL) o he equipmen is
ano he majo challenge in schedule main enance
ope a ions so ha maximize eliabili y. Scheduled
main enance p ac ices end o educe machine li e ime
and inc ease down- ime, esul ing in loss o p oduc i i y.
In elligen moni o ing sys em can educe main enance
cos s, a oid ca as ophic ailu es and inc ease machine
a ailabili y. To de elop an e ec i e diagnos ic and
p ognos ic sys em deep unde s anding o he bea ing
beha io is well ad ised. Condi ion based main enance
(CBM) as a leading main enance echnique in ol es
moni o ing machine condi ion and p edic ing machine
ailu e. I is c i ical as a pa o p e en i e main enance o
educe cos s and inc ease eliabili y. Condi ion
moni o ing (CM) is an e ec i e me hod o moni o ing
machine s a e pa ame e s like ib a ion, empe a u e,
wea deb is analysis and noise moni o ing.
Lo o app oaches ha e been al eady de ined in
main enance enginee ing o de e mine and moni o he
ac ual s a e o o a y machines, ecip oca ing machines,
and elec ical machines. Bea ings, gea s as basic o a y
machine y a e success ully moni o ed by ib a ion signal
analysis, cylinde p essu e signal can be moni o ed in
in e nal combus ion engines and ecip oca ing
comp esso s, measu ing o powe consump ion and hea
dis ibu ion a e ypical o moni o ing elec ical
machines. Fu he me hods include noise measu emen ,
oil wea deb is analysis, in a ed spec um analysis,
cu en analysis, powe analysis.
II. FAILURE DIAGNOSTIC
All ailu e diagnos ics consis o h ee main s eps, da a
acquisi ion and collec ion, da a p ocessing, and ailu e
pa e n ecogni ion. (Fig. 1.)
Fig. 1. Failu e diagnos ic s ages
A e he measu emen p ocess he aw signal equen ly
con ains lo o noise, i s signal- o-noise (SNR) a io is
low. In his o m i is impossible o ob ain he necessa y
in o ma ion abou he signal i s noise should be
elimina ed o educed. S a is ical based ea u es o
example ms alue, peak alue, mean alue, a iance,
ku osis, c es ac o a e ypical ea u es o be ex ac ed
om he signal. Time domain ea u es in machine aul
diagnosis is published by se e al esea che s. [8] Mos ly,
hey a e applied o in es iga ing non-pe iodic signals
and ini ial aul s o bo h bea ings and gea s. Fo
equency domain analysis Fas Fou ie T ans o m (FFT)
is commonly applied ha ex ac ea u es, used o
pe iodic signals, i can de e mine de ec s o bea ings and
gea s. The main d awback o Fas Fou ie T ans o m
(FFT) is ha i is only applicable o ans o ming a
s a iona y signal. Fo non-s a iona y signal he Sho - ime
Fou ie T ans o m [14] o he Wa ele ans o m [4] can
be applied. Fea u e ex ac ion is domain speci ic and
signal speci ic. The e a e some ways a ailable o
de e mine he c oss-co ela ion be ween ea u es,
classical s a is ics such as F- es , Chi-squa ed es , a ie y
FAILURE DIAGNOSTICS WITH SVM IN
MACHINE MAINTENANCE ENGINEERING
K isz ián DEÁK1, Im e KOCSIS2, A ila VÁMOSI3, Zol án KEVICZKI4
1deak.k isz [email protected]
2[email p o ec ed]deb.hu
3[email p o ec ed]eb.hu
4zol an.ke iczki@schae le .com
o me hods a ailable o e alua e ea u e pe o mance, a e
applied o es he pe o mance o each indi idual ea u e
[10] and he elie algo i hm is ano he classical me hod
[6]. Fea u e ex ac ion is necessa y in machine aul
diagnosis and gene al app oach is o ob ain as many
ea u es as possible because mo e ea u es gi e mo e
eliable in o ma ion. Bu lo o addi ional ea u es make
he compu a ional ime and cos mo e and he abili y o
he diagnos ics sys em o make e icien diagnosis is
dec eased, mo eo e i ele an ea u es complica e he
whole diagnos ics sys em educing i s capabili y o make
e ec i e analysis.
Fig. 2. shows he so-called peaking phenomenon [10]
inc easing he numbe o ea u es can only imp o e he
pe o mance ini ially, bu a e a c i ical numbe o
ea u es, he pe o mance dec eases. Theo e ically,
in ini e da a se s would enhance he capabili y o
diagnos ics model bu ha ing so la ge models a e nea ly
impossible in eal condi ions.
Fig. 2. Peaking phenomenon [18]
In o de o inc ease he pe o mance o he diagnos ics
model ea u e selec ion is necessa y. In his p ocess he
numbe o selec ed ea u es is dec easing o a alue ha
e en accep able o accomplish p ope u he diagnosis.
Remo ing he i ele an ea u es is one o he mos
accep ed me hod in his ield. Mainly subse ea u e
selec ion and indi idual ea u e selec ion a e used as wo
basic app oaches o ea u e selec ion. Resea che s [12]
de ined ha each ea u es should be anked on p io i y
and less impo an one o be emo ed he o he s a e
applied. SVM weigh all ea u es in he inpu space, and
hese weigh s can be e alua ed du ing he aining
p ocess [9]. Mo e impo an ea u es ge highe sco e o
weigh s, less impo an ones ge smalle alues o nea ly
ze o. SVM algo i hm was in en ed by Vladimi N.
Vapnik and so ma gin was p oposed by Co inna
Co es and Vapnik in 1993 and published 1995. SVM has
been success ully applied o a numbe o applica ions
anging om pa icle iden i ica ion, ace
iden i ica ion, and ex ca ego iza ion, o engine knock
de ec ion, bioin o ma ics, and da abase ma ke ing [2].
As o u he possible applica ions he e a e esea ches
abou op imiza ion e.g. he Op imiza ion o he Shape o
Axi-Symme ic Rubbe Bumpe s [20].
As i was men ioned ha app op ia e numbe o ea u es
is well ad ised o op imize calcula ion ime and machine
aul diagnosis sys em. Classi ie e o a e measu es;
dis ance measu es; in o ma ion measu es; dependence
measu es; and consis ency measu es [3] a e commonly
used o measu ing he pe o mance o he model,
classi ie e o a e measu es a e mos ly deba ed.
Sea ching o minimum subse o ea u es is exhaus i ely
sea ched ield. Ac ual condi ion o he machine can be
ep esen ed by he ea u es ex ac ed om he da a se s.
De e mining he p ede ined h eshold is a majo ask
ea u e’s alue abo e a p ede ined h eshold may imply a
possible ailu es, se e i y o he ailu e is indica ed by he
de ia ion om he p ede ined h eshold.
Gene ally, h eshold alue is e alua ed by
expe ience, he alue ha di e he in ac s a us o he
machine om he aul y condi ion. The Ku osis, he
ou h no malized s a is ical momen , co esponds o he
peak alue o he da a. Fo an undamaged bea ing, he
alue is equal o h ee in equencies. Ku osis alue is
mo e use ul, when i is compa ed wi h he RMS, c es
ac o , and peak alue. The C es Fac o is he a io o
he peak accele a ion o he RMS alue. C es ac o is a
good indica o o small size de ec s; al hough, when
localized damage g ows, he alue o he c es ac o
dec eases signi ican ly because o he inc easing RMS.
So, ku osis o 3 can be as h eshold o make di e ence
be ween heal h and aul y bea ings. In eal indus ial
ci cums ances he e is no enough da a o de e mine his
alue in all wo king condi ions e e ing o all machines
in di e en ope a ing en i onmen s. K-nea es neighbou
[10], Bayesian classi ie , lea ning algo i hms as classical
pa e n ecogni ion echniques a e equen ly applied o
de e mine h eshold o bounda y om a ailable da a.
Lea ning algo i hm inds he op imal decision unc ion
au oma ically om he a ailable da a and disc imina e
di e en pa e ns.
Non-Linea classi ie s such as A i icial Neu al Ne wo ks
(ANN) and SVM can be used in supe ised and
unsupe ised lea ning. Classi ying da a is a common ask
in machine lea ning. Gi en da a poin s belong o one o
wo classes, and he goal is o decide which class
a new da a poin is in. To de ine suppo ec o machines
and i s linea classi ie s, a da a poin is iewed as a p-
dimensional ec o a lis o p numbe s, and he pu pose
o decide whe he i can be sepa a ed such wi h a (p − 1)-
dimensional hype plane. This is called a linea classi ie .
Bes hype plane should be chosen ha ep esen s he
la ges sepa a ion o ma gin in o he wo d, be ween he
wo classes. In his case he dis ance om he
hype planes o he nea es da a poin on each side is
maximized. I such a hype plane exis s, i is known as
he maximum-ma gin hype plane and he linea classi ie
i de ines is known as a maximum ma gin classi ie .
Fig. 3. SVM classi ica ion p inciple [18]
Supe ised lea ning pai s he inpu and ou pu da a.
Fea u e ec o s ex ac ed om he signal can be used as
inpu da a. SVM is sensi i e o noise in he signal
especially when aw da a is used o he inpu o he SVM
sys em. The pe o mance o he ained SVM can be
e alua ed by using a se o es da a. In e nal coe icien s
a e chosen by he supe ising lea ning. Dec easing he
eal ou pu and he p edic ed ou pu is impo an o ge
he aining esul as he op imal decision.
III. ONE CLASS SUPPORT VECTOR MACHINES
Co ec main enance ac ions is only possible i
diagnos ics o he machine y is sa is y he equi emen s.
The pu pose o his ac ion is o educe main enance cos
and enhance eliabili y and sys em a ailabili y. The
Suppo Vec o Machine (SVM) me hod can be
in e p e ed as a ans o ma ion o pu he lowe
dimensional da a o a highe dimension space. Suppo
ec o machine cons uc s a hype plane o se o
hype planes in a high o in ini e-dimensional space,
which can be used o classi ica ion, eg ession. The
hype planes in he highe dimensional space a e de ined
as he se o poin s whose do p oduc wi h a ec o in
ha space is cons an . SVM ge s non sepa able pa e ns
o sepa a ed pa e ns he exis ing ailu e o incipien
ailu e is ge ing mo e iden i iable because ailu e
diagnos ics is in he highe dimensional space. The co e
me hod o SVM is o use he maximal ma gin me hod o
de ea he o e i ing p oblem ha makes he model i
special da a se s. Small sample size p oblems a e sol ed
by using he maximal ma gin app oach.
Suppo Vec o Machine (SVM) is a s a e-o - he-a
me hod, equen ly used as nonlinea classi ie o
lea ning algo i hm which is able o e alua e au oma ically
dependency be ween da a and de ined as a eg ession
p oblem. SVM es ima e he connec ion be ween
p edic i e a iables and explana o y a iables. Maximal
ma gin app oach and ke nel me hod a e combined in
SVM o make p edic ion as Fig. 4. p esen s. Suppo
Vec o Machine (SVM) is a classi ica ion and eg ession
me hod. Suppo Vec o machines uses hypo hesis space
o a linea unc ions in a high dimensional ea u e space.
SVM can be ained wi h a lea ning algo i hm om
op imiza ion heo y.
Fig. 4. SVM based diagnos ics classi ie a chi ec u e
Good sepa a ion is achie ed by he hype plane ha has
he la ges dis ance o he nea es aining da a poin o
any class, he unc ional ma gin. The SVM decision
unc ion is an applica ion o he ke nel unc ion and
Lag angian op imiza ion me hod is used o ob ain he
op imal decision unc ion om he aining da a [7].
SVM is gene ally sui able o wo-class asks.
The decision unc ion is used o p edic he ou pu o
a gi en inpu . The maximal ma gin me hod is applied o
imp o e he accu acy o he p edic ion.
Fo machine lea ning algo i hms, he ke nel ick is a
way o mapping obse a ions om a gene al se S in o
an inne p oduc space V (equipped wi h i s na u al
no m), wi hou ha ing o compu e he mapping explici ly.
I can ans o m he p oblem om a lowe dimension o a
highe dimension, while he compu a ion complexi y does
no change. T ans o ming he p oblem om a lowe o a
highe dimension makes he app oxima ion unc ion mo e
lexible wi h i s da a, educing he isk o empi ical e o .
Wi h ewe SVs (suppo ec o s, da a aking e ec )
he gene aliza ion abili y is imp o ed. Fu he mo e, as
he decision unc ion is comp ised o SVs, ha ing ewe
SVs can educe he compu a ion complexi y.
The op imal solu ion o he SVM is achie ed by he
use o a quad a ic op imiza ion p oblem. The con ex
p ope y o he o mula ion makes he solu ion unique.
The SVM u ilizes he Lag angian op imiza ion me hod o
sol e his p oblem.
The o iginal op imal hype plane algo i hm p oposed
by Vapnik in 1963 was a linea classi ie . The o iginal
p oblem is de ined in ini e dimensional space.
Some imes he se s o disc imina e a e no linea ly
sepa able in ha space. Howe e , in 1992, Be nha d E.
Bose , Guyon and Vapnik sugges ed a way o c ea e
nonlinea classi ie s by applying he ke nel ick o
maximum-ma gin hype planes. The esul ing algo i hm is
o mally simila , excep ha e e y do p oduc is eplaced
by a nonlinea ke nel unc ion. Polynomal ke nels,
Gaussian adial basis unc ion a e used equen ly.
In s a is ical lea ning heo y he p oblem o supe ised
lea ning is o mula ed as ollows. Taking a se o aining
da a {(xi, yi)} in Rn  R sampled acco ding o unknown
p obabili y dis ibu ion P(x, y), and a loss unc ion V(y,
(x)) ha measu es he e o , o a gi en x, (x) is
p edic ed ins ead o he ac ual alue y. The p oblem
consis s in inding a unc ion ha minimizes he
expec a ion o he e o on new da a ha is, inding a
unc ion ha minimizes he expec ed e o [16]:
dxdy)y,x(P))x( .y(V
Maximum ma gin is gi en as [15]-[17]:



 d
1i
2
i
w
bwx
mina g)x(dmina gina gm
Fo calcula ing he SVM we see ha he goal is o
co ec ly classi y all he da a. Fo ma hema ical
calcula ions we ha e,
I yi= +1;
I yi= -1; wxi + b ≤ 1
Fo all i; yi (wi + b) ≥ 1
In his we p esen he QP o mula ion o SVM
classi ica ion [15]-[17]-[18]-[19]. This is a simple
ep esen a ion only.
SV classi ica ion:



l
1i
i
2
K
, C min
i
y i (xi)  1 - i, o all i i  0
SVM classi ica ion, Dual o mula ion:
  

l
1i
l
1j
jijiji
l
1i
i
α)x,xK(yyαα
2
1
α min
i
0  i  C, o all i;
0y
l
1i
ii 


Va iable i is called slack a iable and i measu es he
e o made a poin (xi, yi). T aining SVM becomes
qui e challenging when he numbe o aining poin s is
la ge. A numbe o me hods o as SVM aining ha e
been p oposed [15]-[17]-[19].
IV. EXPERIMENTAL STUDY
In gene al, SVM applica ions can be classi ied in o
wo ca ego ies: ailu e diagnos ics such as no el y
de ec ion and mul i- ailu e disc imina ion; and secondly
eliabili y da a analysis, such as eliabili y p edic ion and
sys em eliabili y assessmen . The e a e some examples
whe e SVM can be used in main enance enginee ing.
Plane a y gea boxes a e widely used in machine
indus y and o he hea y-du y indus y such as
helicop e s, hea y-du y ucks, and o he la ge-scale
machine y. Plane a y gea boxes a e able o unde ake
hea y-du y asks wi h high o que need.
The e a e wo app oach o in es iga ing machine
elemen , bea ings o gea ailu es, li e- es s and sho -
e m es s by c ea ing a i icial aul s on he bea ing
elemen s. Manual pi ing damage expe imen s we e
designed and implemen ed o p o ide ib a ion da a
co esponding o di e en le els o gea pi ing damage.
In ou esea ches, spa k e osion was c ea ed wi h EDM
o lase machine. To alida e he uzzy app oach es - ig
had been buil which has 5 indi idual olle bea ings.
One o hem was moni o ed by measu ing ib a ion
accele a ion le el. The lis o measu ing ins umen s ha
a e used in he measu emen :
- PCB 603C01 accele ome e
- Bea ing es - ig (Fig. 5.)
- NI 9234 DAQ
- NI Lab iew Sound and Vib a ion Measu emen
- TESTO 476 s oboscope
- Soundbook measu emen sys em
Fig. 5. Bea ing es ig o alida ion
Fo he measu emen w i en in his pape , PCB603C01
accele a ion senso was used. I was a ached s ongly on
he op o he bea ing house wi h magne p o iding
enough o ce o keep he senso and p oduce ideal
ci cums ances o u he ope a ions. Bo h Soundbook
ib a ion measu emen sys em, Samu ai So wa e, and
Na ional Ins umen (NI) de ices we e used o he
measu emen , namely NI DAQ 9234. NI DAQ 9234 has
a 4-Channel, ±5 V, 51.2 kS/s pe Channel, 24-Bi IEPE
de ice wi h 51.2 kS/s pe -channel maximum sampling
a e; ±5 V inpu , 24-bi esolu ion; 102 dB dynamic
ange; an ialiasing il e s. So wa e-selec able AC/DC
coupling; AC-coupled (0.5 Hz), so wa e-selec able IEPE
signal condi ioning (0 o 2 mA), sma TEDS senso
compa ibili y, NIST- aceable calib a ion a e he ypical
ea u es o his de ice used in he bea ing ib a ion
measu emen s. Di e en i ual ins umen s we e buil in
Lab iew so wa e o make ib a ion and spec um
measu emen . The simples applied is showed in Fig. 6.
1bwxi
Fig. 6. Vi ual Ins umen (VI) o ib a ion measu emen
In his esea ch, spa k e osion was c ea ed wi h lase
machine (Fig. 7.) hen geome ical measu ed unde
Olympus BX61 op ical mic oscope. A i icial spall was
658 um in diame e and 257 um deep on he inne ing o
he 6206 ype bea ing. Being a plas ic cage bea ing balls
could be emo ed easily be o e c ea ing he aul . BPFI
was calcula ed, basically by 2880 1/ min engine speed,
exac o a ion speed was measu ed and BPFIs we e
ecalcula ed.
Fig. 7. A i icial bea ing aul on he inne ace
BPFO (ball passing equency ou e ace), BPFI (ball
passing equency inne ace), FTF ( undamen al ain
equency), BSF (ball spin equency) can be calcula ed
in Hz wi h he ollowing o mulas by knowing he con ac
angle (), o a ion speed ( ), numbe o olle s, ou e ing
diame e (D), and inne ing diame e (d) o he bea ing.
Acco ding o calcula ions engine speed is 48 Hz, BPFO
171,84 Hz, BPFI 260,16 Hz, FTF 19,2 Hz, BSF 112,32
Hz by using he ball bea ing in he alida ion es . Fig. 8.
indica es he ime domain spec um o he bea ing,
ib a ion alue is no mal.
Fig. 8. Time domain spec um o he measu ed bea ing
F equency-domain (FFT) analysis o he ib a ion signal
is he mos widely used app oach o de ec ing olle -
bea ing de ec s. The in e ac ion o de ec s in olling
elemen bea ings p oduces impulses. Impulses gene a e
he na u al equencies o bea ing elemen s and housing
s uc u es, ha causes peaks in he ib a ion ene gy
spec um. Compa ing he calcula ed aul equencies
wi h he measu ed alues he exac aul s can be e ealed.
Fig. 9. p esen s he ib a ion spec um o he bea ing.
Fig. 9. F equency domain spec um o he measu ed bea ing
The gene al algo i hm o SVM based diagnosis can be
seen on Fig. 10. Tes and aining da a ed he sys em and
make pe o mance e alua ion by using ea u es.
Fig. 10. Algo i hm o bea ing aul de ec ion wi h SVM [21]

Diagnosis a e app oxima ely 90% was eached in he
expe imen s hus SVM me hod could be applied
e icien ly in machine aul diagnos ics. Se e al
measu emen s we e pe o med by applying bea ings wi h
di e en aul s. SVM diagnos ics sys em is able o
dis inguish heal hy and aul y bea ings. Fu he
expe imen s a e planned o in es iga e ou e ace aul s,
cage aul s and ball aul s. Mo o Cu en Signa u e
Analysis, MCSA es s a e planned as well, a me hod o
moni o ing machine y in he indus y by means o i s
elec ical cu en s. Mo o cu en signa u e analysis
(MCSA) has p o en o be a highly aluable p edic i e
main enance ool.
V. CONCLUSION
Condi ion Moni o ing (CM) is i al pa in main enance
enginee ing. P ope main enance can educe cos and
imp o e eliabili y. Lo o me hods a e used o diagnose
he machines o hei componen s such as o a y
machine ies e.g. bea ings, gea s. These machine elemen s
end o su e se ious damages ha a e measu ed by
mos ly ib a ion measu emen echniques because o i s
simplici y. Addi ional measu emen s can be used such as
empe a u e measu emen , wea deb is analysis, oil
analysis o c ea e a complex diagnos ics condi ion
moni o ing sys em. SVM has been success ully applied
o a numbe o applica ions in indus y. Classi ying
da a is a common ask in machine lea ning, linea and
non-linea classi ica ion is applied used hype plane o
sepa a e poin s belongs o wo classes. Ke nel ick is a
way o mapping obse a ions om a gene al se S in o
an inne p oduc space V. I can ans o m he p oblem
om a lowe dimension o a highe dimension. SVM has
lo o applica ion in main enance enginee ing. The SVM
has been used o diagnose ailu e in olling elemen
bea ings, induc ion mo o s, machine ools, pumps,
comp esso s, al es, u bines, and a ious o he
machines. Enginee ing expe imen s show he easibili y
and e ec i eness o his me hod, he diagnosis a e
nea ly 90% o e en mo e so SVM me hod can be applied
e icien ly in many in es iga ions. Tes igs
measu emen s a e p o ed he e iciency o SVM ools in
machine aul diagnosis. La e as pa o u he
expe imen s bea ing wi h ou e ace aul s, cage aul s,
ball aul s will be examined. Mo eo e , Mo o cu en
signa u e analysis (MCSA) could be applied as a mode n
ool o machine diagnos ics. Mul iplied measu emen s
using bo h ib a ion and mo o cu en signa u e analysis
is possible o enhance he e iciency o he sys em, e en
empe a u e measu emen could be used o make mo e
accu a e measu emen s.
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