Predicting Rail Corrugation Based on Convolutional Neural Networks Using Vehicle’s Acceleration Measurements

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 . Re e ences 1. G assie, S. Rail co uga ion: Cha ac e is ics, causes, and ea men s. P oc. Ins . Mech. Eng. Pa F J. Rail Rapid T ansi 2009, 223, 581–596. [C ossRe ] 2. Zhao, Y.; Zhao, C.; Wang, L.; Wang, P. A ail co uga ion e alua ion me hod using ac al cha ac e iza ion based on s uc u e unc ion me hod. Wea 2022,506, 204454. [C ossRe ] 3. Liu, X.; Wang, P.; Wan, F. Fo ma ion mechanism o ail co uga ions in hea y-haul ail line. J. China Railw. Soc. 2000,22, 98. 4. Wang, Z.; Lei, Z.; Zhao, Y.; Xu, Y. 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