Ci a ion: Haghbin, M.; Chiachío, J.;
Muñoz, S.; Escalona F anco, J.L.;
Guillén, A.J.; C espo Ma quez, A.;
Can e o-Chinchilla, S. P edic ing Rail
Co uga ion Based on Con olu ional
Neu al Ne wo ks Using Vehicle’s
Accele a ion Measu emen s. Senso s
2024,24, 4627. h ps://doi.o g/
10.3390/s24144627
Recei ed: 7 May 2024
Re ised: 10 July 2024
Accep ed: 13 July 2024
Published: 17 July 2024
Copy igh : © 2024 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/).
senso s
A icle
P edic ing Rail Co uga ion Based on Con olu ional Neu al
Ne wo ks Using Vehicle’s Accele a ion Measu emen s
Masoud Haghbin 1,* , Juan Chiachío 1, Se gio Muñoz 2, Jose Luis Escalona F anco 2, An onio J. Guillén 3,
Adol o C espo Ma quez 4and Se gio Can e o-Chinchilla 5
1Depa men o S uc u al Mechanics and Hyd aulic Enginee ing, Andalusian Resea ch Ins i u e in Da a
Science and Compu a ional In elligence (DaSCI), Uni e si y o G anada (UGR), 18001 G anada, Spain;
jchiachio@ug .es
2Depa men o Ma e ials and T anspo a ion Enginee ing, Escuela Técnica Supe io de Ingenie ía,
Uni e si y o Se ille, 41092 Se ille, Spain; [email p o ec ed] (S.M.); [email p o ec ed] (J.L.E.F.)
3Depa men o Managemen , Complu ense Uni e si y o Mad id, 28040 Mad id, Spain; [email p o ec ed]
4Depa men o Indus ial Managemen , Escuela Técnica Supe io de Ingenie ía, Uni e si y o Se ille,
41092 Se ille, Spain; [email p o ec ed]
5School o Elec ical, Elec onic and Mechanical Enginee ing, Uni e si y o B is ol, B is ol BS8 1TR, UK;
se gio.can e [email p o ec ed]
*Co espondence: masoudhaghbin@co eo.ug .es
Abs ac : This pape p esen s a deep lea ning app oach o p edic ing ail co uga ion based on on-
boa d olling-s ock e ical accele a ion and o wa d eloci y measu emen s using One-Dimensional
Con olu ional Neu al Ne wo ks (CNN-1D). The model’s pe o mance is examined in a 1:10 scale
ailway sys em a wo di e en o wa d eloci ies. Du ing bo h he aining and es s ages, he
CNN-1D p oduced esul s wi h mean absolu e pe cen age e o s o less han 5% o bo h o wa d
eloci ies, con i ming i s abili y o ep oduce he co uga ion p o ile based on eal- ime accele a ion
and o wa d eloci y measu emen s. Mo eo e , by using a G adien -weigh ed Class Ac i a ion
Mapping (G ad-CAM) echnique, i is shown ha he CNN-1D can dis inguish a ious egions,
including he ansi ion om damaged o undamaged egions and one-sided o wo-sided co uga ed
egions, while p edic ing co uga ion. In summa y, he esul s o his s udy e eal he po en ial o
da a-d i en echniques such as CNN-1D in p edic ing ails’ co uga ion using online da a om he
dynamics o he olling-s ock, which can lead o mo e eliable and e icien main enance and epai
o ailways.
Keywo ds: ail co uga ion; deep lea ning; con olu ional neu al ne wo ks; G ad-CAM
1. In oduc ion
Co uga ion is a common de ec in ail con ac a eas wi h impo an implica ions
in sa e y, se iceabili y, and cos [
1
]. E en when he dep h o he wa es is ypically less
han 1 mm, ail co uga ion can se e ely impac passenge com o by causing abno mal
accele a ions and loud noises. In addi ion, i is one o he p ima y easons o damage
and wea s bo h he wheels and ails, leading o highe main enance cos s and se ice
dis up ion [
2
,
3
]. Acco ding o nume ous esea che s, he oo cause o his de ec lies in he
sel -exci ed ib a ions and esonance o he wheel– ail sys em. Howe e , his sel -exci ed
ib a ions pe spec i e is no uni e sal, and many pa ame e s such as ini ial egula i y,
bending mode, o sional ib a ion, and ma e ial mechanics ( ail elas ic modulus, ail
Poisson’s a io, s i ness o as ene s, e c.) con ibu e o co uga ion gene a ion [2,4–6].
Since 1895, many a emp s [
7
–
9
] ha e been ca ied ou on labo a o y expe imen s,
ield es s, and analy ical and nume ical models o p edic co uga ion [
5
]. Be o e 1970, he
esea ch on his opic ocused on s a is ical and expe imen al analysis as well as aspec s
ela ed o ail ma e ial p ope ies, ic ion, empe a u e a ia ions, and o he ele an
Senso s 2024,24, 4627. h ps://doi.o g/10.3390/s24144627 h ps://www.mdpi.com/jou nal/senso s
Senso s 2024,24, 4627 2 o 18
ac o s [
10
]. A e 1970, esea che s s a ed o use analy ical and nume ical models o
unde s and he impac s o esonance, plas ic de o ma ion, and esidual s ess, among o he
ac o s, on ailway co uga ion [10–12].
Fo example, Igeland and Ilias (1997) [
13
] p esen ed a non-linea model o p edic
ail co uga ion on sho -wa eleng h longi udinal i egula i ies. They applied a ious
non-linea ac o s, such as he shi o con ac poin and he dis ibu ion o wea wi hin he
con ac a ea. In 2003, Nielsen [
14
] in oduced a nume ical model o analyzing ail-head
co uga ion on s aigh ails based on dynamic ain– ack in e ac ion. He concluded ha
longi udinal slip in he wheel– ail con ac in e ace played a key ac o in causing his
damage, and his esul s showed a s ong ag eemen when compa ed o ield obse a ions.
Sun and Simpson (2008) [
15
] ca ied ou nume ical modeling and labo a o y expe imen s,
which e ealed ha a igh e cu e can cause inc eased c eepage be ween he wheel and ail,
hus causing he wheel s ick-slip p ocess, which is a signi ican ac o in he de elopmen
o co uga ion.
Va ious s udies ha e a emp ed o p edic co uga ion g ow h h ough equency
domain analysis, mainly using Fas Fou ie T ans o m (FFT) models concen a ing on
he in e ac ion be ween wheel and ail a a ious speeds [
16
–
18
]. Employing a ield
in es iga ion and Fini e Elemen (FE) s a egies, Chen e al. (2020) [
19
] de e mined he
wa eleng hs and equencies o ail co uga ions in h ee dis inc ield sys ems. Thei
indings indica e ha co uga ion is nea ly ce ain o occu in he inne ail o a igh ly
cu ed ack. Howe e , in he case o smoo h cu ed and angen ial acks, hey ound
ha ic ion-induced sel -exci ed ib a ion does no occu because he c eep o ce is no
sa u a ed. In line wi h his s udy, Wang e al. (2020) [
4
] de eloped an FE model o simula e
ail co uga ion in Cologne egg as ene sec ions in small adius cu es. The model consis s
o h ee sub-models: ehicle, ack and wheel– ail con ac models. Thei wheel– ail con ac
model comp ises he dynamic model o he wheel- ack and he non-dynamic model o
ic ion and wea o ail ma e ial. A e in eg a ing he ic ion and wea model in o he
dynamic model, i was e ealed ha side wea mainly occu s on he ou e ail. In con as ,
co uga ion ends o appea on he inne ail. Despi e he success o hese physics-based
app oaches in es ima ing co uga ion, hey a e ime-consuming, compu a ionally expensi e,
and sensi i e o simpli ying assump ions and bounda y condi ions [
20
]. I is essen ial o
in es iga e al e na i e modeling s a egies u he o add ess hese d awbacks.
Machine Lea ning (ML) models a e popula nowadays due o hei excellen capabili y
o ackle complex p oblems by e icien ly handling non-linea i ies in unce ain sys ems [
21
].
In ea ly in es iga ions, ML models, pa icula ly hose u lizing images, such as Two
Dimensional Con olu ional Neu al Ne wo ks (CNN-2D), ha e been used o iden i y
co uga ion de ec s and aul segmen a ion in ailways [
22
–
25
]. Ne e heless, he e has been
a clea need o measu e he co uga ion geome y p ope ies using abula da a ob ained
h ough o wa d eloci y and accele a ion senso s, which a e becoming inc easingly
accessible nowadays.
Despi e hei impo ance o esea ch, only a ew s udies ha e a emp ed o p edic
co uga ion geome y p ope ies such as dep h and wa eleng h using accele a ion and
senso da a. Xie e al. (2021). [
20
] success ully p edic ed co uga ion on me o lines
using a no el Deep Lea ning (DL) model ha e ec i ely in eg a ed a One-Dimensional
Con olu ional Neu al Ne wo k (CNN-1D) classi ie wi h a hyb id K iging Su oga e
Model (KSM) and Pa icle Swa m Op imiza ion (PSO) algo i hm. In he s udy, CNN-1D
was applied o de ec he ail co uga ion’s s a e and classi y i s wa eleng h, ollowed by
adop ing he KSM-PSO o es ima e i s dep h cha ac e is ics. Acco ding o hei indings,
he gene a ed esul s we e in ag eemen wi h he obse ed da a. In line wi h his s udy,
Xie e al. (2023) [
26
] de ec ed he ail co uga ion oughness quan i a i ely using a modi ied
e sion o CNN-1D named Recu en Con olu ional Ne (RCNe ). They used axle box
accele a ion signals as he inpu pa ame e s. The model was ained using ield da a and
compa ed agains o he DL echniques, such as Long-Sho Te m Memo y (LSTM) and
Senso s 2024,24, 4627 3 o 18
Recu en Neu al Ne wo ks (RNNs). Thei indings demons a ed ha RCNe was supe io
o o he models in accu a ely p edic ing co uga ion oughness.
The insigh s gained h ough ML me hods ha e p o en o be aluable in p edic ing
co uga ion on ailways. Howe e , an impo an esea ch challenge emains: p edic ing
ailway co uga ion p ope ies using kine ic da a om olling s ock collec ed du ing no mal
ailway ope a ion. In his con ex , his pape aims o add ess he ollowing objec i es:
•
de elop a deep lea ning model o accu a ely ep oduce he ail’s co uga ion p o ile
a di e en o wa d eloci ies using kine ic da a om he ehicle;
•
in es iga e he c i ical ailway egions ha a e impo an o co uga ion p edic ion
by DL models.
In pa icula , he p oposed modeling s a egy employs o wa d eloci y and accele a ion
da a in he x ( o wa d) and z ( e ical) di ec ions om he ehicle, which a e commonly
a ailable in eal ailway sys ems.
The co uga ion was p edic ed using CNN-1D, and he G adien -weigh ed Class
Ac i a ion Mapping (G ad-CAM) analysis was hen used o gain a be e unde s anding o
he model’s pe o mance. The CNN-1D model is ained using acqui ed da a abou he
ehicle’s accele a ion and eloci y collec ed a a labo a o y scale in he ailway esea ch
g oup o he Uni e si y o Se ille. The esul s ob ained con i m he sui abili y o he
p oposed da a-d i en modeling app oach in p edic ing he comple e ail’s co uga ion
p o ile using jus kine ic da a om he ehicle.
The emainde o his pape is s uc u ed as ollows. Sec ion 2p esen s he esea ch
me hodology, which includes a de ailed desc ip ion o he expe imen al se up and
p ep ocessing echniques, he DL echnique used, he design o he model a chi ec u e,
and hype -pa ame e selec ion. Sec ion 3will p esen he main indings, discuss hei
implica ions, summa ize limi a ions, and sugges u u e esea ch di ec ions. Finally,
conclusions a e p o ided in Sec ion 4. The esea ch me hodology o his s udy is illus a ed
in Figu e 1.
Design o CNN-1D
a chi ec u e &
hype -pa ame e s selec ion
Sec ions (2.3) & (2.3.1)
Sec ion (2.2)
E alua ion o CNN-1D
model’s esul s
Sec ion (3.1)
E alua ion me ics
o models’ pe o mance
Sec ion (2.3.2)
G ad-CAM analysis
Sec ion (3.2)
P e-p ocess o ga he ed
expe imen al da a
Expe imen al se up
& ga he ing da a
Sec ion (2.1)
Figu e 1. P ocess o he de eloped me hodology o he p edic ion o ailway co uga ion using
CNN-1D.
Senso s 2024,24, 4627 4 o 18
2. Ma e ial and Me hods
2.1. Desc ip ion o Expe imen al Se up
This sec ion explains he expe imen al se up used o ga he he da ase s. Conside ing
he di icul y o ca ying ou expe imen s on ac ual ail oad ehicles and acks, he ailway
esea ch g oup o he Uni e si y o Se ille buil a 1:10 scaled ack acili y, comp ising
a 90 m long scaled ack and an ins umen ed scaled ehicle [
27
]. The 1:10 scaled ack
acili y whe e he expe imen s we e conduc ed is p esen ed below. The expe imen s we e
ca ied ou on a 5-inch wide and 90 m long scaled ack buil on he oo o he School
o Enginee ing o he Uni e si y o Se ille. Figu e 2shows he plan iew o he scaled
ack: an ae ial pho og aph (Figu e 2a) and a schema ic plan iew o he ack cen e line
(Figu e 2b).
(a) Ae ial pho og aph.
Posi ion x (m)
0 10 20 30 40 50 60
Posi ion y (m)
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
Co uga ed
egion
(b) Plan scheme o he ack cen e line.
Figu e 2. Plan iew and geome y de ails o he scaled ack.
The designed ack includes s aigh egions, ansi ions, and cu es. The ed ec angle
highligh s he s aigh co uga ed egion in Figu e 2b. This egion has a leng h o
3.6 me e s (m), s a ing a a ack leng h
s
= 54.9 m and inishing a
s
= 58.5 m. Bo h ails in
his egion ha e been machined o include a ealis ic co uga ion p o ile. The co uga ed
p o ile gi en o he su ace o he ail is based on a combina ion o ou ha monic wa es o
5, 10, 20, and 30 mm wa eleng h wi h ampli udes o 30, 45, 60, and 75 mic ons, espec i ely
(see Figu e 3). As he e is no phase di e ence be ween he ou wa es combina ion, i
esul s in he 60 mm pe iodic i egula i y shown in Figu e 3. This p o ile (60 mm long) has
been epea ed consecu i ely un il eaching he o al leng h o 3.6 m.
0 10 20 30 40 50 60
s (mm)
-200
-150
-100
-50
0
50
100
150
200
Co uga ion p ofile (mm)
Wa e ype Wa eleng h Ampli ude
1 5 30
4 30 75
2 10 45
3 20 60
(mm) (mm)
Figu e 3. P o ile o he designed co uga ion.
Figu e 4a shows a de ail o he co uga ed egion machined in he scale ack. In
addi ion o co uga ion, he ack has long wa eleng h i egula i ies a ec ing ehicle
dynamics. Howe e , since his s udy aims o p edic ails’ co uga ion, he e ec s o he
long wa eleng h i egula i ies on he accele ome e signals a e sub ac ed by il e ing he
signals wi h a high pass il e .
The scaled ailway ehicle used in his wo k was designed and buil by he ailway
esea ch g oup o he Uni e si y o Se ille. As shown in Figu e 4b, he scaled ehicle is
Senso s 2024,24, 4627 5 o 18
a single bogie consis ing o wo igid wheelse s, a p ima y suspension wi h eigh helical
sp ings connec ing bo h wheelse s wi h he bogie ame. To egis e he accele a ion in
he axle box, wo uni-axial piezoelec ic accele ome e s ha e been ins alled in he le
axle box in he on wheelse o he ehicle in longi udinal (x) and e ical (z) di ec ions.
Addi ionally, one high-p ecision encode egis e s he o a ion o he wheels, om which
he dis ance a elled by he ehicle (
s
) and i s o wa d eloci y (
V
) is calcula ed. All he
expe imen al da a a e acqui ed and synch onized by a da a acquisi ion sys em moun ed
on he ehicle a an acquisi ion a e o 5000 Hz. The ollowing pa ag aphs p o ide a b ie
explana ion o he moni o ing amewo k designed o ack deg ada ion in his s udy.
(a) De ail o he co uga ed segmen .
Accele ome e s Encode
Ride di ec ion
(b) Moni o ed ehicle.
Figu e 4. Expe imen al se up de ails.
The es bench o moni o ack deg ada ion in ol es an au oma ed inspec ion ehicle
equipped wi h a ious ad anced senso s and measu emen ools. The ehicle comp ises
wo main pa s: he body and he measu ing axis, which a e connec ed by a sphe ical
join o allow o o a ion isola ion. The body has a ac ion sys em wi h igid wheels
powe ed by a b ushless elec ic mo o and di ec gea ansmission, ensu ing he axis
s ays cen e ed on he ack. The measu ing axis, he main componen o he ehicle,
includes a linea guide and wo mo ing ca iages. I is equipped wi h a p ecision encode ,
induc i e senso , Ine ial Measu emen Uni (IMU), inclinome e , and Linea Va iable
Di e en ial T ans o me (LVDT) o measu e ack gauge a ia ion accu a ely. A NImyRIO-
1900 con olle (Na ional Ins umen s, Aus in, TX, USA) and a mini-PC wi h 3G connec i i y
a e used o con ol he ehicle and acqui e senso da a. The cloud-based da a handling and
p ocessing amewo k is buil on Mic oso Azu e, ollowing he RAMI 4.0 hie a chical
model. A Le el 0, physical asse s and p ocesses a e managed by senso s and de ices
connec ed ia PLCs, Fieldbus, dis ibu ed sys ems, o se e s, wi h da a communica ed

Senso s 2024,24, 4627 6 o 18
o he cen al sys em using Azu e IoT Edge o eal- ime da a ansmission. A Le el
1, da a inges ion and p ocessing occu h ough Azu e Da a Lake S o age o long- e m
da a e en ion and Azu e Da a Explo e o sho - e m analy ics. Le els 2 and 3 in ol e
model and digi al win managemen using Azu e Machine Lea ning and Cosmos DB o
de elop p edic i e models and Digi al Twin De ini ion Language (DTDL) o de ine digi al
en i ies. Finally, Le el 4 acili a es use in e ac ion h ough Powe BI, p o iding eal- ime
decision-making suppo . Figu e 5illus a es he es bench con igu a ion used in his
s udy o moni o ack deg ada ion.
Sys em o he sys ems
(Senso s, Signal p ocesse , e c. )
Physical En i ies
(Le el 0)
Adap e s
Da a Reposi o y Me ada a Reposi o y Cloud
compu ing
Da a Inges ion &
P ocessing
(Le el 1)
Model Reposi o y Model Managemen On ologies
Model Managemen
(Le el 2)
Digi al P ocess Managemen
Digi al Se ices Managemen
Twin Managemen
(Le el 3)
Use In e ace & Con ol
Use In e ac ion
(Le el 4) Powe BI
Azu e
Machine Lea ning
Azu e
Cosmos DB
S eam
Analy ics
Azu e
Func ions
Azu e
Da a Explo e
Azu e
IoT Cen al
Azu e
Digi al Twins
Figu e 5. Flowcha o he es bench o moni o ing ack deg ada ion.
2.2. Desc ip ion and P ep ocessing o he Ga he ed Da ase s
To p edic ailway co uga ion, labo a o y expe imen s men ioned in he p e ious
sec ion measu e h ee inpu a iables: o wa d eloci y (
V
), accele a ion in he z-di ec ion
(Az), and accele a ion in he x-di ec ion (Ax) [20]. To ensu e no a iable domina es due o
i s scale,
Az
and
Ax
a e no malized by
V2
. I is hen assumed ha he co uga ion depends
on a g oup o dynamic ac o s as ollows:
Co uga ion = V,Ax
V2,Az
V2(1)
The inpu and ou pu a iables a e p ep ocessed using he mo ing Roo Mean Squa e
(RMS) o imp o e he signal quali y and mi iga e noise. U ilizing he RMS me hod o
p ep ocess he da a is use ul in eal-wo ld scena ios whe e aw signals, such as accele a ion
and eloci y da a, a e a ec ed by in e e ence om ib a ions o o he mechanical
componen s and da a sequences a e no pe ec ly aligned in ime. The RMS me hod
aids in educing noise and empo al misalignmen by a e aging he squa ed alues o he
signal o e a speci ic ime window, he eby smoo hing ou sho - e m luc ua ions and
emphasizing he unde lying end in he da a. I is ma hema ically exp essed as ollows:
xRMS[i] =
u
u
1
N
i
∑
k=i−N+1
x2[k](2)
Senso s 2024,24, 4627 7 o 18
whe e
xRMS[i]
e e s o he RMS alue a he
i
h poin ,
N
iden i ies he numbe o da a
poin s, and
x[k]
indica es he alue o he signal a he
k
h poin . These inpu a iables we e
ga he ed a
V=
0.50 m/s and
V=
1.00 m/s. Table 1shows he inpu a iable ange o
each eloci y.
Table 1. Range o inpu a iables u ilized o p edic co uga ion.
O iginal Values
V(m/s) Vmin Vmax Ax
V2min
Ax
V2max
Az
V2min
Az
V2max
0.50 0.435 0.513 −4.62 7.677 −3.7249 3.297
1.00 0.941 0.988 −3.102 3.527 −2.339 2.1908
RMS Values
V(m/s) Vmin Vmax Ax
V2min
Ax
V2max
Az
V2min
Az
V2max
0.50 0.07 0.381 0.003569 0.452 0.005149 0.146
1.00 0.168 0.787 0.00649 0.749 0.1031 0.294
Figu e 6illus a es a compa ison be ween he o iginal and he RMS o he inpu and
ou pu signals a V=1.00 m/s, which o e s a clea ision o he da a ans o ma ion.
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
0.94
0.95
0.96
0.97
0.98
V (m/s)
O iginal signal
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
0.17
0.175
0.18
0.185
0.19
RMS-V (m/s)
RMS signal
(a) Top: o iginal eloci y signal; bo om: RMS eloci y signal.
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
-4
-2
0
2
4
Ax/V2 (1/m)
O iginal signal
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
0
0.2
0.4
0.6
0.8
RMS-Ax/ V2 (1/m)
RMS signal
(b) Top: o iginal Ax
V2signal; bo om: RMS p ocessed Ax
V2signal.
Figu e 6. Con .
Senso s 2024,24, 4627 8 o 18
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
-2
-1
0
1
2
Az/V2 (1/m)
O iginal signal
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
0
0.1
0.2
0.3
RMS-Az/V2 (1/m)
RMS signal
(c) Top: o iginal Az
V2signal; bo om: RMS p ocessed Az
V2signal.
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
-2
-1
0
1
2
Co uga ion (m)
10-4 O iginal signal
55 55.5 56 56.5 57 57.5 58
Dis ance a elled (m)
7
7.5
8
8.5
9
RMS-Co uga ion (m)
10-5 RMS signal
(d) Top: o iginal co uga ion signal; bo om: RMS p ocessed co uga ion signal.
Figu e 6. Compa a i e analysis o o iginal signals and hei co esponding RMS ans o ma ion o
V=1.00 m/s.
2.3. Deep Lea ning P edic i e Models o Co uga ion P edic ion
Va ious deep lea ning a chi ec u es, such as Recu en Neu al Ne wo ks (RNNs) and
Long Sho -Te m Memo y (LSTM), we e ini ially adop ed and op imally con igu ed o
add ess he p oblem. Howe e , esul s showed poo gene aliza ion due o he complexi y
o he p oblem and due o he ac ha he pas alues o he a ge a iable (co uga ion)
canno be used as inpu he e, since eal- ime measu emen s o co uga ion a e no a ailable
in eal scena ios. This issue made i imp ac ical o use an au o eg essi e componen
app oach in ime se ies using RRNs and LSTM, which elies on pas alues o he dependen
a iable ( a ge ) as inpu . Ins ead, one-dimensional con olu ional neu al ne wo ks
(CNN-1D) showed supe io p edic i e capabili y o his p oblem and we e adop ed in
his esea ch.
Con olu ional Neu al Ne wo k 1D (CNN-1D) is a powe ul deep lea ning model
designed o deal wi h he di icul ies o ime se ies eg ession [
28
]. This capabili y is
pa icula ly impo an because ime se ies da a o en con ains complex empo al pa e ns,
noises, and ou lie s ha can challenge adi ional machine lea ning me hods o cap u e he
pa e ns accu a ely [
29
]. The CNN-1D model is a modi ied e sion o CNN-2D ha can
adjus con olu ional laye s ypically used in ideos and images o 1D sequences [
30
,
31
].
Senso s 2024,24, 4627 9 o 18
This capabili y allows he CNN model o handle empo al da a, making i a sui able choice
o p edic ing one-dimensional sequences a each ime s ep [
32
]. Fu he de ails o he
CNN-1D model can be ound in [30].
This s udy adop s he iple-laye CNN-1D a chi ec u e, which comp ises h ee
consecu i e con olu ional laye s and wo dense laye s. Each con olu ional laye has
app op ia e ke nel sizes and is equipped wi h Rec i ied Linea Uni (ReLU) ac i a ion
unc ions o enhance he lea ning p ocess. A e he con olu ional laye s, he ou pu s o
hese laye s a e la ened and hen p ocessed h ough wo ully connec ed laye s, which
use linea ac i a ion unc ions. Finally, he ou pu o he las laye is he p edic ion o
co uga ion. The a chi ec u e o he de eloped CNN-1D is illus a ed in Figu e 7.
This igu e shows he p ocess o passing inpu da a h ough mul iple con olu ional
laye s o ex ac pa e ns. The la ening laye hen con e s he ou pu om he con olu ional
laye s in o a one-dimensional ec o , p epa ing i o inpu in o he ully connec ed laye s. In
a ully connec ed laye , each neu on in one laye is connec ed o e e y neu on in he nex
laye . The numbe o neu ons o nodes in each laye is deno ed by he e m “uni ”. This is he
inal s ep in he p ocessing o gene a e he ou pu . Each laye has di e en hype -pa ame e s,
which a e explained in de ail in Sec ion 2.3.1.
Laye -1:
Ke nel Numbe =256
Ke nel Size=4
Ac i a ion=ReLU
S ides=1
Padding=Valid
Laye -2:
Ke nel Numbe =128
Ke nel Size=4
Ac i a ion=ReLU
S ides=1
Padding=Valid
Laye -3:
Ke nel Numbe =64
Ke nel Size=4
Ac i a ion=ReLU
S ides=1
Padding=Valid
Laye -4:
Numbe o Uni s=10
Ac i a ion=Linea
Laye -5:
Numbe o Uni s=1
Ac i a ion=Linea
V=0.5 m/s : 3 × 47,952
V=1.0 m/s : 3 ×22,816
Inpu laye s Con olu ional laye s Fla en laye Fully connec ed laye s Ou pu laye
Figu e 7. A chi ec u e o he p oposed CNN-1D model.
2.3.1. The T aining P ocess and Hype -Pa ame e Selec ion
This sec ion discusses he selec ion o hype -pa ame e s o cla i y how we imp o e
he model’s pe o mance and ensu e i s eliabili y. The ke nel uni is he co e o he CNN-
1D model used o ime se ies analysis; he e o e, he accu a e selec ion o he numbe
o ke nels and hei sizes plays a c ucial ole in he model’s e iciency. Cap u ing he
ea u es and pa e ns elied on he numbe o ke nels. Inc easing he numbe o ke nels
when he da a is insu icien can lead o o e i ing issues [
33
]. De e mining he op imal
numbe o ke nels is c ucial based on ask complexi y, ne wo k dep h, and compu a ional
esou ces [34].
Ke nel size e e s o he window leng h ha con ol es o e he da a. The size o
his window can be di e en o each con olu ional laye . The la ge ke nel size leads o
cap u ing he b oade pa e n, while he smalle ones a e be e o pa icula de ails [
35
].
In his s udy, a ious numbe s o ke nels and ke nel sizes we e iden i ied o he p oposed
model. The model employed 256, 128, and 64 ke nels o p edic co uga ion in h ee
consecu i e CNN laye s. The size o he ke nels was se o 4 o he model ac oss di e en
o wa d eloci ies. The size o he con olu ion ke nel is ixed a 4 o balance he ade-o
be ween cap u ing su icien ea u es and compu a ional e iciency. In p ac ical applica ions,
he choice o con olu ion ke nel size depends on he inpu da a’s speci ic cha ac e is ics
and he desi ed de ail le el. I is o en bene icial o expe imen wi h di e en ke nel sizes
and e en design con olu ional laye s wi h a ying ke nel sizes o cap u e di e se ea u es
a mul iple scales. To ackle he dynamic challenges, such as shi ing be ween obse ed and
p edic ed esul s, a ial and e o s a egy has been applied o a i e a he a o emen ioned
hype -pa ame e s. Ou ial-and-e o app oach was based on he ini ial anges o hype -
Senso s 2024,24, 4627 16 o 18
The uning o hype -pa ame e s is also a challenging s age. In his s udy, selec ing
he app op ia e ke nel size and lea ning a e p o ed c ucial in sol ing da a-shi ing
and educing gene aliza ion e o s. The ailu e o he models o cap u e he damage
pa e ns a high o wa d eloci ies due o ewe da a poin s emphasizes he need o mo e
labo a o y expe imen s.
In u u e wo ks, physics-based models and da a-d i en echniques shall be used o
enhance he accu acy and e iciency o p edic ions o bo h low and high eloci ies. This
de elopmen helps us exploi bo h app oaches’ po en ial o imp o e model p edic abili y.
Fu he mo e, he co uga ion p edic ions can be in eg a ed in o a highe -le el ailway
main enance model o analyze he impac o di e en le els o damage on he o e all
ailway ope a ion and main enance.
4. Conclusions
The modelling o ehicle- ack dynamics is s ill a undamen al challenge in he ailway
indus y. In his sense, inco po a ing he new ad ances in a i icial in elligence and da a
analysis opens a new doo ha complemen s he esul s o physics-based models and
leads o a be e unde s anding o deg ada ion p ocesses and hei causes. This wo k
demons a es how new a i icial in elligence echniques can be use ul in sol ing challenging
enginee ing p oblems, such as ailway co uga ion p edic ion, which has been pa ially
unsol ed using physics-based me hods. The p esen s udy e alua es he capabili y o CNN-
1D o ep oduce co uga ion damage in ailway sys ems based on ehicle kine ic da a
aken a wo di e en o wa d eloci ies. The s udy uses he mo ing Roo Mean Squa e o
o wa d eloci y and accele a ion in he longi udinal and e ical di ec ions, no malized by
he squa e o eloci y, as inpu a iables o p edic co uga ion. The indings e eal ha he
CNN-1D model can ep oduce he co uga ion p o iles wi h ela i ely high accu acy.
G ad-CAM analysis was also applied o de e mine egions wi h a highe impac on
p edic ed esul s. The G ad-CAM analysis e ealed CNN-1D’s capabili ies o dis inguish
be ween di e en ailway egions, such as undamaged as well as one-sided and wo-sided
damaged egions. Rega dless o in o ming he model abou a ious ansi ion egions on
he ailway, he CNN-1D model success ully de ec ed and assigned di e en ac i a ion
in ensi y alues o da a in ansi ion egions o p edic co uga ion, which shed ligh
on i s obus in e nal decision-making p ocess o map he ela ionship be ween inpu s
and ou pu s.
The esul s o his s udy con ibu e o enhancing p oac i e main enance in ailways
by accu a ely p edic ing ail co uga ion and de ec ing damage du ing no mal ailway
ope a ion. Speci ically, he p oposed p edic i e co uga ion modeling app oach enables
moni o ing o he s a e o deg ada ion o ex ensi e ailway segmen s and e en he en i e
ne wo k since i is based on kinema ic da a collec ed du ing ope a ion. This p edic i e
modeling can also be in eg a ed wi hin a whole-sys em condi ion-based main enance
modeling scheme, employing Pe i ne s o simila me hods o suppo an icipa ed and
da a-d i en main enance decision making.
Au ho Con ibu ions: M.H.: Concep ualiza ion, Me hodology, W i ing—o iginal d a , and
Visualiza ion. J.C.: Supe ision, Concep ualiza ion, Me hodology, Valida ion, and W i ing— e iew
& edi ing. S.M.: Labo a o y expe imen s, Fo mal analysis, and W i ing—o iginal d a . J.L.E.F.:
Labo a o y expe imen s, Fo mal analysis, and W i ing— e iew. A.J.G.: Fo mal analysis and
W i ing— e iew & edi ing. A.C.M.: Fo mal analysis and W i ing— e iew, S.C.-C.: Me hodology,
Valida ion, and W i ing— e iew. All au ho s ha e ead and ag eed o he published e sion o
he manusc ip .
Funding: This wo k has been de eloped wi hin he amewo k o he p ojec Geminhi (Digi al model
o In elligen Main enance based on Hyb id p ognos ics models) (G an US-1381456, ounded by
Jun a de Andalucía, Andalucía FEDER 2014–2020) and he AMADIT P ojec (PID2022-137748OB-C32),
unded by MCIN/AEI/10.13039/501100011033/FEDER, EU.
Ins i u ional Re iew Boa d S a emen : No applicable.

Senso s 2024,24, 4627 17 o 18
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : Da ase a ailable on eques om he au ho s.
Acknowledgmen s: The au ho s would like o acknowledge he aluable con ibu ion gi en by
Daniel Molina Cab e a o his commen s and use ul discussions.
Con lic s o In e es : The au ho s decla e ha hey ha e no known compe ing inancial in e es s o
pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape .
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