machines
A icle
Vib odiagnos ics Faul s Classi ica ion o he Sa e y
Enhancemen o Indus ial Machine y
Daniel Zu h 1,* , Pe Blecha 1, Tomas Ma ada 1, Ros isla Huzlik 1, Ji i Tuma 1, Ka la Ma ado a 1
and Voj ech F kal 2


Ci a ion: Zu h, D.; Blecha, P.;
Ma ada, T.; Tuma, J.; Huzlik, R.;
Ma ado a, K.; F kal, V.
Vib odiagnos ics Faul s Classi ica ion
o he Sa e y Enhancemen o
Indus ial Machine y. Machines 2021,
9, 222. h ps://doi.o g/10.3390/
machines9100222
Academic Edi o : An onio J. Ma ques
Ca doso
Recei ed: 3 Sep embe 2021
Accep ed: 23 Sep embe 2021
Published: 30 Sep embe 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, 616 69 B no, Czech Republic;
[email p o ec ed].cz (P.B.); [email p o ec ed].cz (T.M.); huzlik@ u b .cz (R.H.); [email p o ec ed].cz (J.T.);
[email p o ec ed].cz (K.M.)
2TOSHULIN, a.s., Wolke o a 845, 768 24 Hulin, Czech Republic; [email p o ec ed]
*Co espondence: [email p o ec ed].cz
Abs ac :
The cu en digi iza ion o indus ial p ocesses is leading o he de elopmen o sma
machines and sma applica ions in he ield o enginee ing echnologies. The basis is an ad anced
senso sys em ha moni o s selec ed cha ac e is ic alues o he machine. The ob ained da a need o
be u he analysed, co ec ly in e p e ed, and isualized by he machine ope a o . Thus he machine
ope a o can gain a six h sense o keeping he machine and he p oduc ion p ocess in a sui able
condi ion. This has a posi i e e ec on educing he s ess load on he ope a o in he p oduc ion o
expensi e componen s and in moni o ing he sa e condi ion o he machine. The key elemen he e is
he use o a sui able classi ica ion model o da a e alua ion o he moni o ed machine pa ame e s.
The a icle deals wi h he compa ison o he success a e o classi ica ion models om he MATLAB
Classi ica ion Lea ne App. Classi ica ion models will compa e da a om he equency and ime
domain, he da a sou ce is he same. Bo h da a samples a e om eal measu emen s on he CNC
e ical machining cen e (CNC-Compu e Nume ical Con ol). Th ee basic s a es ep esen ing
machine ool damage a e ecognized. The da a a e hen p ocessed and educed o he use o he
MATLAB Classi ica ion Lea ne app, which c ea es a model o ecognizing aul s. The a icle aims
o compa e he success a e o classi ica ion models when he da a sou ce is a da ase in ime o
equency domain and combina ion.
Keywo ds:
ib odiagnos ics; classi ica ion lea ne app; machine lea ning; MATLAB; Py hon; classi i-
ca ion model; unbalance
1. In oduc ion
The cu en de elopmen o Indus y 4.0 b ings, in addi ion o he digi iza ion o
p oduc ion, he collec ion o la ge amoun s o da a, which a e sui able o he use o a -
i icial in elligence me hods. Pa icula ly in he ield o echnical diagnos ics, his opens
possibili ies o he ea ly de ec ion s a e o an objec (machine) based on he measu ed da a,
which a e ob ained om di e en s anda d diagnos ic me hods (e.g., ib odiagnos ics,
he modiagnos ics o elec odiagnos ics) and i is possible o use special me hods o ech-
nical diagnos ics such as measu ing he magne ic ield o he machine [
1
]. I is he e o e
a mul i-pa ame e diagnos ic ha can mo e accu a ely de ec , iden i y, and localize he
eme ging aul , hanks o a combina ion o inpu da a om di e en a eas o diagnos ics.
Vib a ions a e an impo an ca ie o in o ma ion abou he condi ion o o a ing
equipmen and his ac is commonly used in he ield o ib odiagnos ics. This a icle
ocuses on he machining cen e and he e i is possible o use he ib odiagnos ic sys em
o de ec o he in o ma ion such as machining quali y o ool damage. Thus, unexpec ed
s a es can be de ec ed by a ib odiagnos ic signal, which may indica e a aul o a sa e y
isk. Howe e , hese signals a e unexpec ed and a simple e alua ion mechanism canno
be designed, o example, wi h he de ec ion o equen ailu es o o a y machines such
Machines 2021,9, 222. h ps://doi.o g/10.3390/machines9100222 h ps://www.mdpi.com/jou nal/machines
Machines 2021,9, 222 2 o 19
as misalignmen , unbalance, o bea ing damage. In hese cases, i is app op ia e o use
sel -lea ning a i icial in elligence me hods, i.e., hey can lea n o ecognize a aul condi ion
om his o ical da a o a speci ic machine o speci ic machining ope a ions.
In he de elopmen p ocess o sma machine ools capable o ope a ing wi hin he
amewo k o indus y 4.0, i is necessa y o implemen isk analysis al eady du ing
he machine design s age no only in e ms o po en ial damage o he heal h o he
machine ope a o (acco ding o ISO 12100 [
2
]), bu also in e ms o quali y managemen and
moni o ing o he capabili y o he manu ac u ing p ocess on he machine ool (acco ding
o ISO 9001 [
3
]). We can apply he good echnical p ac ice as desc ibed in IEC 31010 [
4
]
and hen implemen he necessa y diagnos ic ools in o he machine design o modi y his
machine design so ha he measu emen unce ain y o he senso sys em (acco ding o
ISO 3534-1 [
5
]) would no a ec he in e p e a ion o he measu ed da a and he subsequen
decision-making p ocesses in a nega i e way. A ypical example could be ea ly de ec ion
o ool damage and subsequen b inging he machine o a sa e s a e. B eaking and ejec ing
he ca bide inse om a ool holde can cause damage o he anspa en gua d o he
machine’s wo king a ea, and hus lead o a subsequen loss o i s sa e y unc ion, o i
may cause i e e sible damage o he machined su ace. The e o e, by ea ly de ec ion o
a machine aul , we can p o ec he heal h o he ope a o as well as educe he inancial
losses caused by poo p oduc ion o inc eased wea o he sma machine’s spindle.
This a icle will, he e o e, compa e classi ica ion me hods ha can de ec a speci ic
aul om eal da a, namely a missing inse on a machining ool, he absence o which
could ha e occu ed due o ool damage. A me hod will be used whe e p edic o s o
machine lea ning will be e alua ed in ad ance and hei choice is he e o e up o he expe .
The co ec choice o p edic o s has a majo impac on he classi ica ion success a e. The
au ho s o he wo k ha e al eady deal wi h he issue o e alua ing ib odiagnos ic signals
in [
6
–
8
]. The idea o using a i icial in elligence me hods in diagnos ics is desc ibed in
o he publica ions such as in [
9
–
12
] , whe e a i icial in elligence me hods a e used o he
ecogni ion o gea box aul s. Also, in he pape [
13
] au ho s ocus on he classi ica ion
using neu al ne wo ks in he plane a y gea . The a icle [
14
] uses a i icial in elligence
me hods o ecognize he shape o a o a y machine sha ’s o bi ; i is a pic u e classi ica ion
acco ding o he shape o sha o bi . The aim o his esea ch is o de e mine a as me hod
( eal- ime e alua ion) o he imely e alua ion o a ailu e ha would educe he sa e y o
he machine. Thus, he p ima y goal is no o diagnose he condi ion o he machine, such
as a bea ing o gea box ailu e, and o p edic esidual li e, bu o de ec ailu es ela ed o
machine sa e y and o wa n he ope a o immedia ely.
This a icle has se e al goals and hey a e:
•
Ve i y ha he missing inse on he ool is de ec able on he ib odiagnos ic signal
measu ed on he machine spindle.
• Selec and compa e p edic o s om ime and equency domains.
• E ec spindle speeds on he classi ica ion success a e.
• Selec and compa e he mos success ul classi ica ion me hods
• E alua e de ec ion success a e o aul - ee s a e
I is assumed ha he p ocess o da a collec ion and e alua ion akes place on an IPC
(Indus ial PC) compu e nea he machine ( o example IPC SIMATIC PC-based, whe e
one IPC will be p epa ed o each CNC machine), and he lea ning and model gene a ed
p ocess will ake place on a se e con aining comme cial so wa e such as MATLAB
(se e will be used o many CNC machines). Lea ning and expo ing he model is an
impo an ope a ion and will ake place unde s ic supe ision. The c ea ed MATLAB
model will be expo ed o he use o indi idual IPCs wi hou MATLAB.
The Py hon en i onmen also includes Machine Lea ning ools such as sciki [
15
] o
A ap used in [
16
], howe e in his case he ambi ions a e o be used in a sa e y en i onmen
and he au ho s he e ely on he p o essional Ma lab en i onmen . In he u u e, he abo e-
men ioned oolboxes will be used and es ed o e alua e he condi ion o he machine.
Machines 2021,9, 222 3 o 19
Py hon en i onmen is used o signal p ocessing, he MATLAB and Classi ica ion
Lea ne App [17] a e used o da a classi ica ion.
2. Expe imen al P ocedu e
The da a we e ob ained om he machine MCV 754 QUICK (Figu e 1), i is a h ee-axis
CNC (Compu e Nume ical Con ol) machining cen e, mo e in o ma ion can be ob ained
on he manu ac u e ’s websi e [
18
]. The ob ained da a a e om he measu ing ins umen
Mic olog CMXA48 and he measu emen pa ame e s a e in he Table 1.
Table 1. Measu emen pa ame e s o Mic olog CMXA48.
Measu emen Pa ame e s:
Analysis ype: Accele a ion ime domain
Uni s: g
F equency ange: 1000 Hz
Y-Axis uni s: g
WAV (Wa e o m Audio File Fo ma ) File Pa ame e s:
Bi s pe sample: 16
Samples pe second: 2560
A e age by es pe second: 10,240
Fo ma : PCM (Pulse Code Modula ion)
Figu e 1. CNC e ical machining cen e MCV 754.
The ins umen Mic olog uses a CMSS 2111 accele ome e senso ha has been a -
ached o he spindle wi h a magne . The posi ion o he senso on he machine is shown
in Figu e 2. Used ool H490 F90AX D040-4-16-12 has he possibili y o changing he ee h
(inse s), which a e ixed wi h a sc ew, as shown in Figu e 3. Th ee s a es/classes we e
chosen o he expe imen , namely:
•Class 0—Tool in he aul - ee s a e (Figu e 3-le )
•Class 1
—Tool wi hou inse (ca bide inse ), bu wi h sc ew-simula ion o damage
and b eakage o an inse (Figu e 3-middle)
•Class 2 —Tool wi hou inse and sc ew (Figu e 3- igh )
Machines 2021,9, 222 4 o 19
CMSS 2111 accele ome e
Figu e 2. Placemen o he CMSS 2111 accele ome e o he machine MCV 754.
Expec ed measu able changes a e caused by he unbalance o he ool when his
ib a ion is ansmi ed o he spindle. The ailu e o unbalance is cha ac e ized by an
inc ease in ib a ions in he egion o he i s ha monic equency. The unbalance is
desc ibed in he [19–21] and is di ided in o a s a ic unbalance and a dynamic unbalance.
The i s expe imen e i ied ha he missing inse was e lec ed in spindle ib a ions
a 700, 1050, and 1400 RPM. The esul s a e shown in Figu e 4, which shows he a ea a ound
he i s ha monic equency. The aim o his expe imen was o de e mine a which spindle
speeds he mani es a ions a e isible in he equency spec um and which speeds a e
sui able o da a collec ion in a machine lea ning da ase . F om he esul , i is e iden ha
a he speed 700 RPM he e ec o he unbalances in he equency domain is insigni ican ,
and he e o e unde ec able. Fo his eason, speeds we e selec ed o ob ain a da ase om
1000 o 1500 RPM.
Figu e 3.
The ool H490 F90AX D040-4-16-12 in aul - ee s a e-
Class 0
(
le
), wi hou he inse
Class 1 (middle) and wi hou he inse and wi hou he sc ew Class 2 ( igh ).
2.1. Da ase Ob ain
Fo each s a e/class, a se ies o da a was measu ed o di e en ope a ing speeds ha
a e wi hin he ecommended speed ange o he ool. Speci ically, he speed was om
1000 RPM o 1500 RPM a e he s ep o 50 RPM in wo epe i ions and 20 s is main ained a
each speed le el. The o al ime is he e o e 20
×
11
×
2 = app ox. 440 s o one s a e (class).
The speed se ing was p og ammed and s a ed o each s a e in he same way, Figu e 5
shows he ime eco d o he speed change o e ime. The aim is o ob ain da a a a wide
ange o ope a ing speeds. The da a we e cap u ed in a eco de mode, i.e., one long ime
eco d was ob ained, which was la e p ocessed in o indi idual samples, which o med a
da ase o machine lea ning.
Machines 2021,9, 222 5 o 19
10 15 20
0
2
4
Accele a ion (g)
10-4 C0 700RPM
FFT
1H
max(1H)
10 15 20
0
2
4
Accele a ion (g)
10-4 C1 700RPM
FFT
1H
max(1H)
10 15 20
F equency Hz
0
2
4
Accele a ion (g)
10-4 C2 700RPM
FFT
1H
max(1H)
15 20 25 30
0
2
4
10-4 C0 1050RPM
FFT
1H
max(1H)
15 20 25 30
0
2
4
10-4 C1 1050RPM
FFT
1H
max(1H)
15 20 25 30
F equency Hz
0
2
4
10-4 C2 1050RPM
FFT
1H
max(1H)
20 25 30 35 40
0
2
4
10-4 C0 1400RPM
FFT
1H
max(1H)
20 25 30 35 40
0
2
4
10-4 C1 1400RPM
FFT
1H
max(1H)
20 25 30 35 40
F equency Hz
0
2
4
10-4 C2 1400RPM
FFT
1H
max(1H)
Figu e 4.
The i s es o he e ec o he aul in equency domain (C0
−
C2 a e Class 0
−
Class 2,
1H— i s ha monic equency, max(1H)—maximum o he i s ha monic equency).
0 50 100 150 200 250 300 350 400
Time (s)
900
1000
1100
1200
1300
1400
1500
1600
Re olu ion pe Minu e (RPM)
RPM Measu emen o Da aSe
Figu e 5. The a ia ion o he spindle speed o e ime du ing he da ase ob ain.
2.2. P edic o s
P edic o s a e a bi a y pa ame e s, and hei alues (o combina ions he eo ) de e -
mine he p ope ies o he class being sea ched. I hese pa ame e s did no adequa ely
e lec he p ope ies o he class, he da a classi ica ion would no be success ul. An ex-
ample o he use o a p edic o is he known a ea o image da a p ocessing. The inpu is
in o ma ion abou indi idual pixels and a ull HD esolu ion (1920
×
1080) i is mo e han
2
×
10
6
pixels and each pixel con ains in o ma ion abou h ee colou s (RGB). This amoun
o da a is disp opo iona ely la ge and con ains a lo o useless in o ma ion, so he e is a
need o educe da a such as educing he numbe o colou s, edge de ec ion, and mo e. The
ou pu s o his educ ion a e p edic o s, which a e he inpu o a i icial in elligence, and
based on hei alues (and hei combina ions) i is possible o classi y indi idual classes.
The p ope ies o p edic o s should be:
• Clea ly desc ibe he class p ope ies (s a e)-imp o ed achie emen classi ica ion

Machines 2021,9, 222 6 o 19
• Low compu a ional complexi y-speeds up he p edic o calcula ion
• Low numbe o p edic o s-speeds up he lea ning and e alua ion p ocess
The inpu da a in ib odiagnos ics a e ime domain signals. In his pa icula case, he
sampling equency is 2560 Hz (sampling pe iod is app oxima ely 0.4 ms), which means
2560 alues e e y second o eco ding o one axis. I is, he e o e, necessa y o educe
his da a low and e alua e sui able p edic o s om i , which will be he inpu o a i icial
in elligence. The aim is o selec app op ia e p edic o s and compa e hei impac on he
success o da a classi ica ion.
2.3. Da a P ocessing and Selec ion o P edic o s
In his a icle, a me hod is chosen ha classi ies da a in o indi idual classes based on
p edic o s. The selec ion and calcula ion o p edic o s a e pe o med be o e he classi i-
ca ion o da a and he co ec choice o hese p edic o s has a signi ican impac on he
esul s o he classi ica ion and i is necessa y o know he issue and ha e expe ience wi h
simila expe imen s. The au ho o he a icle has al eady deal wi h his issue in [
7
,
8
] and
e i ied which p edic o s a e applicable o a simila ype o p oblem. This a icle will
compa e he classi ica ion successes o ime and equency domain p edic o s and hei
combina ions. I was also necessa y o choose he leng h o he ime signal and di ide he
esul ing samples. The imes o 0.25 s and 0.5 s we e chosen and again he ad an ages and
disad an ages o hese leng hs we e compa ed. The ollowing p edic o s we e used.
P edic o s om he ime domain:
•Speed-Cu en RPM du ing one sample
•RMS-Roo Mean Squa e o accele a ion ampli udes om one sample
•STD-The s anda d de ia ion o he accele a ion ampli udes om a single sample
•PCA
-P incipal Componen Analysis ealized wi h sciki lea n lib a y R2 (wi h pa am-
e e s n_componen s = 1 and explained_ a iance_ = 0) [22]
The esul is a ec o ha con ains 4 p edic o s o each sample (RPM, RMS, STD and
PCA); he alues in his ec o a e u he labelled as “T p edic o s”.
F equency domain p edic o s a e based on FFT (Fas Fou ie T ans o m) equency
analysis pe o med using he NumPy lib a y “S anda d FFTs” [
23
] and a ange o 4 o
100 Hz is used. The minimum alue o 4 Hz is de e mined by he minimum measu ing
ange o he senso used. The maximum alue o 100 Hz is he maximum alue o he
occu ence o he i s ha monic in all ope a ing speeds o he ool and any oo h equency.
The maximum ope a ing speed is 1432 RPM, he maximum oo h equency is he e o e
(1432 ×4)/60 = 95.47 Hz, he e o e he maximum equency o 100 Hz was chosen.
•Speed-Cu en RPM du ing one sample
•Spec um ene gy (eF)
-calcula ed as
∑A (i)2
o he 4–100 Hz ange, whe e
A (i)
a e ampli udes o spec al lines.
•A (i)
- he sequence o ampli udes o indi idual spec al lines o equencies 4–100 Hz
The esul is a ec o whose size a ies acco ding o he leng h o he signals used,
i.e., di ision in o indi idual samples. Fo example, i he signal is 0.25 s long and has a
sampling equency o 2560 Hz, he si ua ion is as ollows:
N= s· =2560 ·0.25 =640
Bin(∆ ) = s
N=2560
640 =4
Fo ange 4–100 Hz:
NBin = max − min
Bin =100 −4
4=24
Machines 2021,9, 222 7 o 19
Fo a 0.25 s signal ( 1), he ou pu will be a ec o con aining 26 (24 + 1 + 1) p edic o s
o each da a sample. The disad an age o such a sho signal is he equency esolu ion
(
Bin
) o 4 Hz, whe e his alue may be insu icien . Fu he mo e, signals wi h a leng h o
0.5 s will be compa ed. The e is he ollowing si ua ion
N= s· =2560 ·0.5 =1280
Bin(∆ ) = s
N=2560
1280 =2
Fo ange 4–100 Hz:
NBin = max − min
Bin =100 −4
2=48
Fo a 0.5 s signal ( 2), he ou pu will be a ec o con aining 50 (48 + 1 + 1) p edic o s
o each da a sample. Wi h his signal dis ibu ion, we ge a equency esolu ion
∆
(
Bin
)
o 2 Hz, which is mo e sui able han he p e ious case, bu we ge only hal o he samples
o machine lea ning om he limi ed eco ding.
The esul ing ec o o equency domain p edic o s con ains he measu ed RPM
alue, he calcula ed Spec um ene gy alue (labeled as eF) and he sequence o ampli udes
o indi idual spec al lines (A 1 o A 24 o 1 and A 1 o A 48 o 2), calcula ed using he
FFT unc ion, see Figu e 6. The alues in his ec o a e u he labelled as “F p edic o s”.
Bo h a ian s will be compa ed wi h each o he .
The de ailed da a p ocessing p ocedu e is as ollows:
Da a p ocessing (ou side MATLAB)
• Combina ion o ib a ion channel and acho channel da a
• Spli ing he signal acco ding o he selec ed ime ( 1 = 0.25 s o 2 = 0.5 s)
•
Checking whe he he change is no g ea e han 10 RPM du ing he du a ion ( 1 o
2) (elimina ion o ansien s)
• So ing he signal in o indi idual classes
•
P edic o calcula ion, o each sample (T- ime domain, F-F equency domain o FT-all
p edic o s)
•
Sa ing p edic o s o a ile acco ding o indi idual classes (p epa a ion o MATLAB)
P ocessed in MATLAB:
• Random mixing and me ging o da a o indi idual classes in o one da ase
• E alua ing in he en i onmen “Classi ica ion lea ne app”
• Gene a ing and sa ing he mos success ul model
Ve i ica ion o he gene a ed model:
• Randomly selec ed n samples om each class (selec ed n = 100 pe class)
• Accu acy and TPR (T ue posi i e a e) and FNR (False nega i e a e) e alua ed
• Resul s displayed and sa ed as he Con usion ma ix
Figu e 6.
Scheme o p edic o s calcula ion using IPC (“eF”—Spec um ene gy, “A 1” o “A n”— he
sequence o ampli udes o indi idual spec al lines).
Machines 2021,9, 222 8 o 19
3. Classi ica ion Me hods
Classi ica ion Lea ne App (CL) compa ed di e en classi ica ion me hods o de e -
mine which me hods a e app op ia e o he p oblem. This applica ion allows you o
compa e di e en me hods and hen selec and c ea e a model con aining he selec ed
me hod (chosen we e he mos success ul). The indi idual me hods a e desc ibed in mo e
de ail in [
24
]. Da ase s we e es ed on all me hods ha CL allows and hei success is in a
Tables 2–4. The numbe o epe i ions o he lea ning p ocess was 10 o each model, and he
in e al es ima e was calcula ed using “The Con idence in e al” [
25
] wi h
alpha = 0.05
.
Fu he mo e, he hype pa ame ic op imiza ion p o ided by Ma lab was e i ied. Each
winning model was subjec ed o hype pa ame ic op imiza ion wi h he same da ase , and
hese esul s a e shown in Table 5. Due o he ime consuming, only one epe i ion was
pe o med, he a e age imp o emen o he p edic ion accu acy wi h hype pa ame ic
op imiza ion is only 0.55%. Models wi hou hype pa ame ic op imiza ion we e used o
u he alida ion.
B ie ly, hese a e he ollowing classi ica ion me hods:
Table 2.
Resul ing success a e o classi ica ion o indi idual me hods o expe imen s wi h sample ime 1 (0.25 s). The bes
esul s a e ma ked in bold.
1R1T 1R1F 1R2T 1R2F 1R3T 1R3F 1R4T 1R4F
Fine ee 79.9 ± 0.55 69.9 ± 1.66 67.9 ± 1.14 80.1 ± 1.23 63.9 ± 0.95 94.1 ± 0.32 59.4 ± 0.60 73.2 ± 0.37
Medium ee 77.2 ± 0.89 59.4 ± 1.29 62.3 ± 0.89 79.2 ± 1.29 55.6 ± 1.15 94.1 ± 0.32 54.9 ± 0.40 67.1 ± 0.24
Coa se ee 76.8 ± 0.54 47.2 ± 1.08 57.6 ± 0.89 72.4 ± 0.97 51.6 ± 0.98 94.5 ± 0.46 52.9 ± 0.29 58.1 ± 0.42
Linea disc iminan 74.1 ± 0.30 60.1 ± 0.95 56.8 ± 0.30 74.1 ± 0.80 51.8 ± 0.62 95.0 ± 0.30 51.3 ± 0.18 64.3 ± 0.19
Quad a ic disc iminan 74.2 ± 0.52 69.1 ± 1.41 59.9 ± 0.20 81.4 ± 0.86 44.7 ± 0.93 95.6 ± 0.58 52.3 ± 0.07 69.5 ± 0.18
Gaussian Nai e Bayes 69.6 ± 0.68 57.5 ± 1.13 56.7 ± 0.38 73.7 ± 0.61 42.0 ± 0.65 91.1 ± 0.61 48.8 ± 0.12 59.2 ± 0.37
Ke nel Nai e Bayes 68.1 ± 0.51 60.3 ± 0.88 60.8 ± 0.61 77.0 ± 0.82 48.1 ± 0.82 94.0 ± 0.31 53.6 ± 0.16 64.1 ± 0.19
Linea SVM 73.0 ± 0.50 60.3 ± 0.80 57.1 ± 0.56 75.4 ± 0.93 51.9 ± 0.62 94.9 ± 0.51 52.1 ± 0.13 65.1 ± 0.23
Quad a ic SVM 73.5 ± 0.31 73.8 ± 1.06 59.9 ± 0.49 83.5 ± 0.50 48.9 ± 0.69 96.9 ± 0.28 51.2 ± 0.80 74.6 ± 0.26
Cubic SVM 73.0 ± 0.73 78.6 ± 1.11 60.2 ± 1.08 85.2 ± 0.59 34.9 ± 1.15 96.6 ± 0.31 35.5 ± 0.80 83.4 ± 0.35
Fine Gaussian SVM 73.8 ± 0.93 71.0 ± 1.20 65.3 ± 1.13 67.4 ± 1.07 55.9 ± 0.87 70.2 ± 1.80 61.7 ± 0.19 79.0 ± 0.65
Medium Gaussian SVM 71.7 ± 0.45 73.9 ± 0.64 60.5 ± 0.60 83.1 ± 0.71 50.7 ± 0.97 96.7 ± 0.48 57.6 ± 0.24 75.6 ± 0.27
Coa se Gaussian SVM 73.0 ± 0.44 57.2 ± 0.84 57.2 ± 0.54 71.4 ± 0.96 49.8 ± 0.87 93.5 ± 0.23 52.8 ± 0.13 65.4 ± 0.17
Fine KNN 82.2 ± 0.63 75.0 ± 1.24 78.7 ± 1.12 80.2 ± 0.94 74.5 ± 0.66 89.6 ± 0.59 77.5 ± 0.21 81.7 ± 0.29
Medium KNN 72.1 ± 0.72 53.5 ± 0.69 59.7 ± 0.78 64.8 ± 0.79 51.6 ± 0.86 81.4 ± 0.74 60.9 ± 0.32 67.7 ± 0.37
Coa se KNN 68.4 ± 0.30 44.9 ± 1.00 56.2 ± 0.59 65.5 ± 0.92 47.8 ± 0.83 75.2 ± 1.11 59.3 ± 0.18 64.5 ± 0.11
Cosine KNN 68.2 ± 0.98 55.7 ± 0.94 57.4 ± 1.06 63.0 ± 0.61 51.4 ± 1.57 81.2 ± 1.13 59.4 ± 0.30 66.6 ± 0.17
Cubic KNN 72.1 ± 0.73 55.4 ± 1.26 59.2 ± 0.94 64.0 ± 1.07 51.3 ± 1.10 78.1 ± 2.12 60.9 ± 0.23 66.8 ± 0.27
Weigh ed KNN 82.8 ± 0.40 76.1 ± 1.01 80.6 ± 1.24 81.8 ± 0.70 75.3 ± 0.84 89.4 ± 0.77 78.5 ± 0.31 82.6 ± 0.34
Boos ed T ees 79.0 ± 0.95 72.9 ± 1.12 65.2 ± 1.05 84.3 ± 0.90 61.5 ± 1.04 35.4 ± 0.00 57.0 ± 0.39 71.5 ± 0.31
Bagged T ees 84.1 ± 0.58 76.9 ± 1.13 78.8 ± 1.19 77.0 ± 1.00 75.7 ± 0.94 96.1 ± 0.39 78.4 ± 0.27 84.4 ± 0.33
Subspace Disc iminan 73.4 ± 0.42 59.6 ± 0.83 55.6 ± 0.61 73.0 ± 0.64 52.3 ± 0.44 95.3 ± 0.32 51.1 ± 0.11 63.2 ± 0.29
Subspace KNN 82.1 ± 0.67 72.6 ± 1.18 76.3 ± 1.16 74.8 ± 0.71 74.7 ± 0.98 84.3 ± 1.64 75.5 ± 0.25 77.4 ± 0.51
RUSBoos ed T ees 76.9 ± 0.58 64.1 ± 1.34 63.4 ± 0.97 82.4 ± 1.03 61.5 ± 1.57 66.6 ± 9.85 55.8 ± 0.41 68.4 ± 0.28
Machines 2021,9, 222 9 o 19
Table 3.
Resul ing success a e o classi ica ion o indi idual me hods o expe imen s wi h sample ime 2 (0.5 s). The bes
esul s a e ma ked in bold. No e: F-model ailed (one o mo e o he classes ha e singula co a iance ma ices).
2R1T 2R1F 2R2T 2R2F 2R3T 2R3F 2R4T 2R4F
Fine ee 81.8 ± 1.70 72.9 ± 1.79 65.5 ± 1.58 85.1 ± 1.39 63.3 ± 2.23 94.2 ± 0.60 62.6 ± 0.48 82.9 ± 0.81
Medium ee 81.6 ± 1.61 72.8 ± 1.67 62.4 ± 1.86 85.1 ± 1.39 60.3 ± 2.21 94.2 ± 0.60 58.1 ± 0.52 73.9 ± 0.74
Coa se ee 75.7 ± 0.78 55.2 ± 1.02 58.0 ± 1.12 79.4 ± 1.60 59.5 ± 1.69 94.1 ± 0.95 53.9 ± 2.25 60.9 ± 0.39
Linea disc iminan 76.9 ± 0.90 70.6 ± 2.28 55.1 ± 0.83 84.4 ± 1.46 59.0 ± 0.86 97.7 ± 0.31 54.5 ± 0.24 72.0 ± 0.17
Quad a ic disc iminan 72.3 ± 0.86 F 53.3 ± 0.75 F 50.5 ± 1.05 F 54.3 ± 0.31 83.2 ± 0.28
Gaussian Nai e Bayes 68.2 ± 0.67 67.2 ± 1.68 52.6 ± 1.17 74.2 ± 1.60 41.0 ± 0.59 85.4 ± 0.50 51.8 ± 0.31 64.5 ± 0.51
Ke nel Nai e Bayes 69.3 ± 0.99 77.8 ± 1.46 50.7 ± 0.77 84.6 ± 1.92 48.0 ± 1.22 98.4 ± 0.72 55.0 ± 0.27 74.4 ± 0.27
Linea SVM 74.2 ± 0.76 71.7 ± 0.78 55.7 ± 1.30 83.1 ± 1.35 59.9 ± 0.78 95.7 ± 0.43 55.7 ± 0.27 72.7 ± 0.28
Quad a ic SVM 77.4 ± 0.72 84.0 ± 1.87 55.4 ± 1.40 89.5 ± 0.84 61.6 ± 0.99 98.0 ± 0.50 56.6 ± 0.31 87.4 ± 0.33
Cubic SVM 76.8 ± 1.25 84.9 ± 1.76 54.0 ± 1.54 88.2 ± 0.83 54.8 ± 1.85 97.9 ± 0.67 39.3 ± 1.35 89.6 ± 0.31
Fine Gaussian SVM 78.6 ± 1.38 73.9 ± 1.65 64.9 ± 1.81 75.4 ± 2.42 64.0 ± 1.07 72.9 ± 1.47 63.9 ± 0.34 71.7 ± 0.34
Medium Gaussian SVM 76.7 ± 1.85 84.9 ± 1.95 56.2 ± 1.17 87.8 ± 1.30 62.1 ± 1.07 97.9 ± 0.49 60.9 ± 0.30 84.7 ± 0.30
Coa se Gaussian SVM 71.8 ± 1.07 58.1 ± 0.64 54.3 ± 0.91 72.0 ± 1.29 50.8 ± 1.18 81.7 ± 0.59 55.4 ± 0.21 70.0 ± 0.22
Fine KNN 86.2 ± 1.61 82.0 ± 2.13 78.4 ± 1.44 83.2 ± 1.52 74.7 ± 1.77 91.7 ± 1.19 78.3 ± 0.46 85.1 ± 0.40
Medium KNN 69.9 ± 1.28 59.3 ± 1.82 54.5 ± 1.62 70.8 ± 1.39 59.5 ± 2.03 85.1 ± 1.19 64.2 ± 0.21 73.6 ± 0.45
Coa se KNN 49.9 ± 1.05 53.9 ± 1.09 52.0 ± 1.21 54.9 ± 1.37 58.5 ± 0.95 72.0 ± 0.68 61.8 ± 0.24 68.3 ± 0.20
Cosine KNN 64.0 ± 0.91 62.5 ± 1.53 57.9 ± 1.09 67.6 ± 1.26 57.7 ± 1.73 84.2 ± 1.12 61.7 ± 0.33 73.5 ± 0.61
Cubic KNN 71.5 ± 1.23 59.1 ± 1.32 55.7 ± 1.14 69.4 ± 1.36 60.8 ± 1.43 79.9 ± 0.75 64.0 ± 0.39 72.5 ± 0.32
Weigh ed KNN 87.6 ± 1.61 81.7 ± 1.69 78.7 ± 1.41 84.3 ± 0.87 77.7 ± 1.68 91.5 ± 1.46 79.6 ± 0.40 86.2 ± 0.43
Boos ed T ees 87.1 ± 1.19 79.6 ± 1.29 70.6 ± 1.80 37.3 ± 0.00 70.3 ± 2.40 36.7 ± 0.00 60.3 ± 0.37 81.3 ± 0.38
Bagged T ees 88.4 ± 1.18 79.9 ± 1.18 77.2 ± 1.38 87.8 ± 1.22 77.4 ± 1.30 94.3 ± 1.21 79.8 ± 0.39 86.0 ± 0.41
Subspace Disc iminan 75.5 ± 0.86 71.6 ± 1.59 51.7 ± 0.80 84.1 ± 1.34 58.6 ± 1.13 96.9 ± 0.41 53.7 ± 0.20 71.1 ± 0.12
Subspace KNN 85.0 ± 1.59 73.4 ± 1.41 72.5 ± 2.22 78.3 ± 2.00 73.7 ± 1.97 85.5 ± 1.93 76.7 ± 0.36 79.7 ± 0.49
RUSBoos ed T ees 86.2 ± 1.44 77.7 ± 1.53 67.1 ± 1.56 47.9 ± 3.86 62.6 ± 2.08 76.0 ± 9.04 59.4 ± 0.34 77.6 ± 0.46
3.1. Classi ica ion T ees
Bina y decision ees o mul iclass lea ning [
26
]. This me hod is easy o in e p e
and as o da a p edic ion, has low memo y equi emen s, bu may no achie e su icien
p edic ion accu acy. Decision making akes place h ough a ee s uc u e om he begin-
ning ( oo ) o he inal class (lea es). The me hod was p obably i s published by J. Ross
Quinlan in 1975. The es ed a ian s a e:
• Fine ee
• Medium ee
• Coa se ee
3.2. Disc iminan Analysis
Regula ized linea and quad a ic disc iminan analysis [
27
]. This me hod is easy o
in e p e and as o da a p edic ion o la ge da ase s. Using “Quad a ic Disc iminan ”
inc eases memo y equi emen s. I is one o he me hods o N-dimensional s a is ical
analysis (mul i a ia e s a is ical analysis), whe e, based on he decision ule, objec s a e
di ided in o g oups acco ding o p obabili y densi ies. The me hod was p obably i s
published by Ronald Fishe in 1936. The es ed a ian s a e:
• Linea disc iminan
• Quad a ic disc iminan
Machines 2021,9, 222 16 o 19
Time Consump ion o P edic ion
The ime consump ion o he p edic ion is highly dependen on he pe o mance o he
compu ing uni ha will pe o m he p edic ion. In gene al, he ime-consuming p ocess is
he lea ning o he model, bu his ope a ion is only pe o med once when he sys ems a e
deployed o when a new da ase is a ailable o lea ning. Thus, he lea ning p ocess can
be e icien ly scheduled and is no c i ical o he unning o he sys em.
Mo e impo an is he p edic ion ime and he possible eac ion o he sys em o a
possible p oblem. The p edic ion ime consis s o wo s eps, namely da a p ep ocessing,
i.e., ex ac ion o p edic o s, and hen he p edic ion i sel . These imes we e es ed on a
pe sonal compu e wi h In el(R) Co e(TM) i7-2600 CPU @ 3.40 GHz, 16 GB RAM and a
simila con igu a ion is possible o he cu en IPC. Time was measu ed o 100 epe i ions
each ime o elimina e andom a ia ions in pe o mance. Measu ed ime includes only
compu a ion ime wi hou loading o sa ing da a om eco ding media. Winning models
o he mos challenging a ian s con aining all p edic o s ( ime and equency domain)
we e used. Fo expe imen T1R4, he winning model was “Bagged T ees” and he esul s
a e as ollows. The da a p ocessing ime o 100 epe i ions is 1.13 s and he p edic ion ime
o 100 epe i ions is 5.12 s, ha is, he a e age o al ime is (1.13 + 5.12)/100 = 0.0625 s i.e.,
62.5 ms. Fo T2R4 expe imen , he winning model was “Cubic SVM” and he esul s a e
as ollows. The da a p ocessing ime o 100 epe i ions is 2.04 s and he p edic ion ime
o 100 epe i ions is 1.43 s, ha is, he a e age o al ime is (2.04 + 1.43)/100 = 0.0347 s i.e.,
34.7 ms. The measu ed imes a e only app oxima e and depend on many ci cums ances,
also he e is a possibili y o op imizing he classi ie selec ion acco ding o i s p edic ion
ime. Fo ou pu poses, he achie ed imes a e su icien .
6. Implemen a ion o he T ained Model
The p ocedu e o implemen ing a ained model is as ollows. The model can be
gene a ed as a unc ion o MATLAB, o as sou ce code in C language, hen i is easy o
compile i o any pla o m. I s unc ion (abili y o classi y) does no change o e ime
because he e is no lea ning p ocess. Howe e , p o ided he condi ions ha e changed o
a new da ase is a ailable, i is possible o s a he lea ning p ocess again and ain he
model o he new da a.
Figu e 12 schema ically shows he possible connec ion o he se e wi h indi idual
clien s. Each IPC pe o ms da a collec ion and especially imely e alua ion based on a
ained model ha was lea ned in he MATLAB en i onmen on he se e and hen
expo ed. The p ocess is as ollows:
(a) Da a acquisi ion and lea ning p ocess
•
The se e eques s da a om indi idual IPCs and c ea es a da ase o c ea ing a clas-
si ica ion model (Da a is p edic o s-i e alua es IPCs, only p edic o s a e ansmi ed).
•
I he e is a su icien amoun o da a (o condi ions ha e changed, e c.), hen MATLAB
pe o ms lea ning and c ea es a ained classi ica ion model o a speci ic IPC and
expo s i o he C language ( his MATLAB allows).
• The ained model is sen o a speci ic IPC.
Indi idual machines and hei IPCs can be dis ibu ed anywhe e in di e en places
and he e will be only one se e wi h MATLAB, which will gene a e a model o a speci ic
machine and send i o a speci ic IPC. I necessa y, he MATLAB SW can be eplaced by
ano he sys em, howe e , he unc ionali y will be main ained and he change will be made
on only one se e .
(b) E alua ion p ocess
•
IPC pe o ms da a collec ion and p edic o calcula ion- his is a simple ope a ion
and can be pe o med in any p og amming language, o simplici y and a ailabili y
Py hon was chosen, which pe o ms s a is ical ope a ions and equency analysis.
•
Pe o ms classi ica ion using MATLAB c ea ed and ained model, which was ex-
po ed o C language (Py hon allows o un code in C language).

Machines 2021,9, 222 17 o 19
Such a opology and pa i ioning allows o easy changes on bo h he IPC and se e -
side, including changing he p og amming en i onmen .
As o he speci ic deploymen o moni o ing he machine, i is impo an o no e
ha nowadays i is no easy o implemen elemen s o a i icial in elligence in he sa e y
segmen , whe e i is necessa y o ce i y he so wa e and e i y i s unc ions. Howe e ,
i is possible o deploy a simila sys em only as an in o ma i e elemen ha would ale
he ope a o , bu no in e e e wi h he ope a ion o he machine. The use o a i icial
in elligence me hods is pa icula ly ad an ageous in he ield o echnical diagnos ics o
he e alua ion o mul iple c i e ia and ope a o ale s.
Figu e 12. IPC and se e loca ion opology.
7. Resul s and Discussions
Figu e 9summa izes he esul s in g aphical o m and exp esses he dependence o
he p edic o s on he spindle speed. Fo p edic o s om he equency domain, an inc ease
in success wi h inc easing speed is e iden due o a mo e p onounced mani es a ion o an
unbalance aul in he equency spec um (inc easing he i s ha monic). In con as , ime
domain p edic o s achie e a highe success a e a lowe speeds han equency domain
p edic o s. Thus, using all p edic o s ( ime and equency) inc eases he success a e a
lowe speeds and does no dec ease a highe speeds. The igu e also ocuses on he
de ec ion o a aul - ee s a e, i.e., assuming ha we modi y he classes only o he aul - ee
s a e (class0) and any aul s a e (class 1 o 2), hen i is ob ious ha he success o aul - ee
de ec ion will inc ease because we do no include misclassi ica ion be ween class 1 and
class 2, which a e simila . This is impo an i we only wan o de ec a aul - ee condi ion
and in any o he case, an ope a o wa ning is issued.
Impo an esul s a e shown in he Tables 2–4, which compa e he successes o indi-
idual classi ica ion me hods. Fu he mo e, Figu es 10 and 11 compa e he successes o he
classi ica ion o indi idual classes and he mos impo an is he compa ison in Figu e 9,
which shows he success o he classi ica ion and he success o aul - ee s a e de ec ion,
whe ewi h a ian R4 (TF mix- he combina ion o all speeds), 97% o 1 and 98% o 2
success a e is achie ed.
Machines 2021,9, 222 18 o 19
8. Conclusions
The a icle aimed o e i y he possibili ies o a i icial in elligence o he classi ica ion
o machine ool ailu e based on an expe imen om a eal machine. Ea ly de ec ion o
he diso de is an impo an ac o in p o ec ing he heal h and elimina ing damage. The
use o a i icial in elligence me hods b ings he possibili y o c ea ing uni e sal algo i hms,
which, hanks o he abili y o lea n, adap o a speci ic machine, and a speci ic phase
o machining.
The desc ibed me hod app oaches he possibili y o using a i icial in elligence o
da a classi ica ion, in his case o he classi ica ion o a ious machine s a es. A simila
me hod can be used o classi y any classes, whe e only a change o p edic o s ha desc ibe
he p oblem sough is needed.
The choice o p edic o s used is an impo an ac o which, oge he wi h he ope a ing
condi ions, in luences he success o he classi ica ion. Fu u e expe imen s will ocus on
he possibili y o de ec ing a aul condi ion o a ool du ing machining and will ocus on
ob aining a la ge da ase wi h di e en machining condi ions.
Au ho Con ibu ions:
Resou ces, So wa e, W i ing—o iginal d a , D.Z.; W i ing—o iginal d a ,
P.B.; Valida ion, Visualiza ion, T.M.; Resou ces, J.T.; W i ing— e iew and edi ing, R.H.; Valida ion,
K.M.; Resou ces, V.F. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This esea ch was suppo ed by he Minis y o Educa ion, You h and Spo s o he Czech
Republic and The Eu opean Union-Eu opean S uc u al and In es men s Funds in he ame o
Ope a ional P og amme Resea ch De elopmen and Educa ion-P ojec : Machine Tools and P ecision
Enginee ing (P ojec No. CZ.02.1.01/0.0/0.0/16_026/0008404).
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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