Depósi o de In es igación de la Uni e sidad de Se illa
h ps://idus.us.es/
This is an Accep ed Manusc ip o an a icle published by Else ie in
Measu emen , Vol. 183, on Oc obe 2021,
a ailable a : h ps://doi.o g/10.1016/j.measu emen .2021.109765
Copy igh 2021 Else ie . En idUS Licencia C ea i e Commons CC BY-NC-ND
Measu emen o ail oad ack i egula i ies using an au oma ed
eco ding ehicle
Ped o U daa,∗
, Ja ie F. Acei unob, Se gio Mu˜nozc, Jos´e L. Escalonaa
aDepa men o Mechanical and Manu ac u ing Enginee ing, Uni e si y o Se ille, Spain
bDepa men o Mechanical and Mining Enginee ing, Uni e si y o Ja´en, Spain
cDepa men o Ma e ials and T anspo a ion Enginee ing, Uni e si y o Se ille, Spain
Abs ac
This pape p esen s he design, cons uc ion and expe imen al alida ion o a scaled ailway ehicle o
he au oma ed and quick su ey o he geome y o an expe imen al scaled ack. The me hod, ha can
be ex ended o ull scale acks, alida es he measu emen s o he au oma ed eco ding ehicle (ARV)
by compa ison wi h espec o a p ecise bu slow manual measu ing me hod (MMM). The wo-axle
ehicle, which is powe ed by a b ushless DC mo o , has i s leading axle ins umen ed wi h a LVDT, an
inclinome e , a e lec o and a p ecision encode . These senso s, oge he wi h he help o a o al s a ion,
allow he measu emen o he scaled ack geome y and i s i egula i ies ollowing an op imiza ion
p ocedu e ha i s de e mines he ideal ack cen eline. The ARV has been es ed on a scaled ack
and i s measu emen s a e alida ed wi h he MMM esul s showing a good ag eemen be ween bo h
app oaches.
Keywo ds: T ack su eying, ins umen ed ailway ehicle, scaled ack, ack i egula i ies,
expe imen al alida ion, au oma ed eco ding ehicle.
1. In oduc ion1
An accu a e knowledge o he ack geome y is essen ial o gua an ee he sa e y o he olling s ock.2
This is because he dynamic esponse o a ailway ehicle [1] is highly in luenced by ack i egula i ies3
[2, 3]. Thus, ope a o companies a e con inuously in es ing human and ma e ial esou ces on he su ey4
and main enance o hei ailway in as uc u es. La ge ack i egula i ies esul on la ge wheel- ail5
con ac o ces, ha end up comp omising he in eg i y o he ack and, he mos impo an , he sa e y6
o he passenge s. These i egula i ies can also p oduce dis u bing sounds o he nea by owns o he7
ack [4] and educe he com o o he ehicle [5, 6].8
Rail i egula i ies can be unde s ood as geome ical de ia ions o he ail c oss-sec ions om an ideal9
ack geome y. They can be di ided in o wo gene al g oups: (1) dis ibu ed ack i egula i ies and (2)10
isola ed ack de ec s. The i s g oup appea s as egula pa e ns along he ack wi h mul iple wa e-11
leng hs ha depend on he damage mechanism, i.e. ail wea [7] o olling con ac a igue (RCF). This12
g oup o i egula i ies is usually quan i ied by he ou well-known a iables used in he indus y: ack13
gauge, c oss le el, e ical p o ile, and alignmen . The isola ed ack de ec s, which a e he esponsible14
o many o he unsa e ehicle esponses, appea mo e a ely bu may also ha e egula pa e ns. They15
∗Co esponding au ho : [email p o ec ed]
P ep in submi ed o Measu emen Ap il 18, 2021
accoun o changes in he ail c oss sec ion a speci ic loca ions, such as in poo d ain a eas, b idges, o 16
u nou s [8].17
Enginee s ha e been wo king o decades on he de elopmen o new me hodologies and measu ing18
appa a us o he p ecise measu emen o ack i egula i ies and simula ion models and p ocedu es ha 19
help o de e mine and imp o e he com o o he ide [9, 10, 11]. This is e idenced by he nume ous20
pa en ed ideas and scien i ic s udies ound in he li e a u e. Some o he oldes in en ions a e based on21
simple mechanical measu ing me hods [12] o ins umen ed wheelse s [13] and o he s mo e ecen use22
senso ized ailed ehicles [14] o compu e ision echniques [15]. Nowadays, he e a e also labo a o y23
ehicles such as he Taiwanese EM-50 o he inspec ion o high-speed lines, he Bulga ian EM-120 o 24
he inspec ion o he ca ena ies [16] o he Spanish Seneca ack and ca ena y inspec ion ehicle. These25
a e jus a small sample o he nume ous measu ing sys ems ha ha e been and a e cu en ly being used26
in he ailway indus y o su eying he ack.27
In gene al, ack measu ing me hods can be classi ied in o manual su eys and au oma ed o dynamic28
su eys. On one hand, manual me hods a e no mally based on he use o an ins umen ed olley ha 29
is manually pushed by a human ope a o along he ack unde analysis. On he o he hand, au oma ed30
me hods a e based on he use o a labo a o y ehicle. This one can be ins umen ed wi h ine ial and31
na iga ional senso s o a measu emen o he ack based on he dynamic esponse o he ehicle o 32
dis ance measu ing de ices. The la e a e used in he so-called cho d me hods which a e applied in33
he ho izon al and e ical e sine measu emen o ails [17]. An ex ended su ey o ack i egula i y34
measu ing me hods can be ound in [18]. The Eu opean s anda d EN-13848-3:2009 [19] egula es he35
measu ing ea u es and equi emen s o ack measu ing sys ems.36
Fo hei simplici y, p ecision and obus ness, manual olleys a e he mos widely-used appa a us37
o he inspec ion o he ack in he ailway indus y. Thei use can be conside ed o p o ide a di ec 38
measu emen since he olley is equipped wi h senso s such as a dis ance ansduce and an inclinome-39
e o he measu emen o ack gauge and c oss-le el, espec i ely, bo h also known as ela i e ack40
i egula i ies. I also includes a o al s a ion and/o a GPS ecei e o he measu emen o he absolu e41
posi ion o he ack cen eline. An example o one o he comme cial ack measu ing olleys ha can42
be ound in he ma ke is he Ambe Su ey GRP 1000 by Ambe g Technologies [20]. The e a e also43
o he e sions o manual olleys ocus on he measu emen o ail co uga ion. The la e a e based on44
he use o se e al high-p ecision lase senso s o he su ey o he ail heads [21]. I can be also ound in45
he li e a u e some p o o ype olleys ha , on he basis o he con ec ional models, y o o e come hei 46
slow pe o mance. An example is he wo k p esen ed by Chen e al. in [22, 23]. The au ho s p opose47
a senso s usion algo i hm be ween he GPS and an Ine ial Measu ing Uni (IMU) ha allows a as e 48
su ey o he ack using his olley wi hou lea ing behind he accu acy equi emen s o a high speed49
line. A simila expe imen al olley called REGEOS is p esen ed in he wo k o Akpina e al. [24, 25]. In50
his case, a Kalman il e algo i hm is p oposed o de e mine ack cen e line geome y, ack gauge and51
supe -ele a ion, ha shows an excellen pe o mance acco ding o he In e na ional Union o Railway52
(UIC) s anda ds. Jiang e al. p esen in [26] an algo i hm ha ies o o e come he low acquisi ion53
equency o a o al s a ion combining i s measu emen wi h a high p ecision ine ial senso ins alled on54
2
he olley and he measu emen o some known landma ks along he ack unde analysis. Despi e o 55
hei p ecision and good pe o mance, he use o hese de ices ha e he handicap o being e y slow when56
measu ing he ack, ha used o be a ound one kilome e pe hou . They a e a alid solu ion o he57
inspec ion o sho ack segmen s o occasional measu emen bu no o a ull ack measu emen o 58
con inuous ack moni o ing.59
As an al e na i e o he manual su ey o a ack, au oma ed o dynamic me hods a e p esen ed. In60
his case, he ack i egula i ies a e ob ained in an indi ec manne using he measu emen o se e al61
senso s o di e en ypes ha a e ins alled on a labo a o y ehicle. The key o hese me hods lies in62
a compu a ional model o he ehicle and he ack [27] ha uses as inpu s he measu emen o he63
ins alled senso s and i is able o de e mine he ack i egula i ies based on he dynamic esponse o he64
ehicle. Ce ainly, he sophis ica ion o he model a ec s he inal esul s o he es ima ion model. In he65
wo k o Sagadeghi e al. [28] he au ho s demons a e ha in a slab ack a 3D model o he wheel- ail66
in e ac ion is equi ed o a co ec es ima ion o he con ac o ces. An example o an au oma ed me hod67
is he wo k o Tsunashima e al. [29] whe e he e ical i egula i y o he ack is es ima ed om he68
ca -body ib a ion using a Kalman il e and a simpli ied model o he ehicle. Wes eon e al. in [30]69
p esen an al e na i e way o measu e he e ical ack i egula i y using he pi ch angle measu ed by70
a gy o senso and accele ome e s ins alled on he bea ing boxes om an in-se ice ailway ehicle. The71
es ima ion o ack i egula i ies om he dynamic esponse o a ehicle is no an easy ask as shown in72
he wo k o Ka is e al. [31]. In his wo k, he au ho s y o ind a co ela ion be ween he dynamic73
esponse o he ehicle and he exci a ion gene a ed by he ack i egula i ies using a simple model o 74
he ehicle. They conclude ha hey do no always coincide in absolu e alues and s anda d de ia ions.75
The wo k o A. De Rosa e al. [32] is ocused on he indi ec measu emen o la e al ack i egula i ies.76
In his wo k he au ho s use a mode n machine lea ning algo i hm o iden i y he la e al de ec s o he77
ack. Ano he in e es ing wo k is he one p esen ed by Wei e al. [33] whe e he alignmen o he78
ack is de e mined h ough a double in eg a ion o he accele a ion measu ed by se e al accele ome e s79
placed on he ehicle. In oducing he measu emen o he senso s in a compu a ional simula ion model80
o he ehicle hey a e able o de e mine di e en anges o alignmen on he measu ed ack. In he81
wo k o Escalona e al. [34], a ack measu emen sys em ha can be ins alled on in-se ice ehicles82
and combines a kinema ic model, a compu a ional ision sys em and ine ial measu emen is p esen ed.83
The men ioned sys em show a s ong po en ial o he au oma ed inspecion o acks. In conclusion,84
dynamic me hods ha e he clea ad an age o being much as e compa ed wi h he manual olleys85
due o he ac ha hey a e based on he use o in-se ice ehicles. Howe e , he ack measu emen 86
ob ained om an in-se ice ehicle is no as accu a e as using a manual olley since he dynamics o 87
he ehicle is included in he measu emen . This is explained in [35], whe e a e y in e es ing analysis88
o he measu ing p ecisions ob ained wi h manual olleys and labo a o y ehicles is p esen ed. As a89
summa y, i can be said ha he ailway indus y is ending owa d au oma ed ack su ey sys ems90
ins alled on in-se ice ehicles combining con en ional senso iza ion (ine ial o dis ance senso s) wi h91
mode n compu a ional ision echniques [36] and a i icial in elligence algo i hms [37]. This could allow92
a daily moni o ing o he ack esul ing on a educ ion o he main enance cos o he in as uc u e93
3
hanks o an an icipa ed in e en ion. The e a e also in e media e solu ions ha a e nei he a manual94
me hod no an au oma ed one. An example is he ack inspec ion wagon p esen ed by Chang e al. in95
[38]. An inno a i e sel -p opelled measu ing olley ins umen ed wi h a wide a ie y o senso s such as96
accele ome e s and compu a ional ision came as, ha allows a as and accu a e measu emen o he97
ack. The men ioned ehicle is es ed on a labo a o y ack in which i egula i ies ha e been a i icially98
in oduced. Finally i should be no ed ha compu a ional ision echniques a e gaining g ound on he99
ack su eying business. An example is he ballas ack inspec ion sys em p esen ed by Sadegui e al.100
in [39]. This sys em p o ides an index ha is a unc ion o de ici s and excess o ballas in he ack.101
As a esponse o he needs posed by he ailways indus y in e ms o ack measu emen based on he102
dynamic esponse o he ehicle, he Mechanical Enginee ing esea ch g oup o he Uni e si y o Se ille103
ha e been wo king o o e wo decades on he de elopmen o new compu a ional mul ibody model104
o mula ions [40, 41] o he s a e obse a ion om in-se ice ailway ehicles. To gua an ee he accu acy105
and good pe o mance o any compu a ional model, he scien i ic me hod equi es o be expe imen ally106
alida ed. Howe e , ge ing he access o a eal ailway ehicle and ack is no always inexpensi e107
nei he possible. As an al e na i e, his esea ch g oup has been ecen ly using scaled ehicles and acks108
o i s in es iga ions on ailway dynamics [42, 43]. Al hough he dynamic esponse o an scaled ehicle109
canno be di ec ly ex ended o ull-scaled ehicles, he u ilisa ion o scaled sys ems ep esen an easy110
and ela i ely inexpensi e way o expe imen ally alida e new compu a ional mul ibody models and new111
heo e ical app oaches wi hou comp omising he sa e y o he passenge s o he in eg i y o he ack.112
In his sense, he p oposed me hod applied o a scaled ehicle and ack, is no a ec ed by he ehicle113
dynamics, and can se e as a design s a egy o he applica ion o he measu emen o ack i egula i ies114
a eal acks. In hese acks, geome y is con inuously changing due o empe a u e e ec s, mo emen s115
o he ounda ion and he mos impo an , due o he e ec o he wheel- ail con ac o ces exe ed by he116
ehicles. Conside ing he ac ha he ehicle dynamics is highly in luenced by he ack i egula i ies,117
i is undamen al o know he geome y o he ack unde analysis wi h he g ea es possible accu acy,118
educing his way unce ain ies du ing he alida ion p ocess o new compu a ional models o a unning119
ehicle sa e y analysis. Indeed, in an ideal scena io, he ack should be measu ed jus immedia ely be o e120
an expe imen and in ha case a as an eliable measu ing me hod is equi ed. In he wo k o Acei uno121
e al. [44] a possible measu ing me hod is p esen ed bu despi e i s p ecision, i s slowness does no make122
i e y ope a ional. Tha is eason why he goal o his manusc ip is o p esen a no el scaled ailway123
ehicle o he au oma ed ack su ey and calcula ion o ack i egula i ies. The ehicle is no based on124
he adi ional ”cho d-me hod”, ha would equi es a la ge sys em o accoun o high wa eleng hs. The125
ehicle is powe ed by a DC mo o and equipped wi h a LVDT, an inclinome e , a p ecision encode and a126
e lec o ( a ge p ism o he o al s a ion). Using he ehicle wi h he suppo o he o al s a ion, he127
scaled ack geome y can be easily ob ained wi hin minu es. The ack measu emen and i egula i ies128
ob ained wi h he p oposed au oma ed inspec ion me hod a e compa ed wi h a e y accu a e bu slow129
manual measu ing me hod, esul ing on an g ea ag eemen be ween bo h app oaches.130
The pape is o ganised as ollows: Sec ion 2 is de o ed o he design and ins umen a ion o he131
ARV and he measu ing p ocedu e. In Sec ion 3 he MMM is explained in de ail. Sec ion 4 deals wi h132
4

he ack cen e line op imiza ion p ocess and he calcula ion o ack i egula i ies. The expe imen al133
alida ion o he ARV and he esul s compa ison wi h he MMM a e desc ibed in Sec ion 5. Summa y134
and conclusions a e p esen ed in Sec ion 6.135
2. Au oma ed eco ding ehicle (ARV) and measu ing p ocedu e136
T ack i egula i ies ha e a g ea impo ance o ailway ope a ion. Depending on hei magni ude,137
hey migh be only a ma e o ide com o o e en comp omise he ide sa e y leading o a de ailmen 138
scena io. Thus, a co ec iden i ica ion and cha ac e iza ion o ack i egula i ies esul s undamen al in139
ailway simula ion. In he ailways indus y, ack i egula i ies a e di ided in wo g oups, ela i e and140
absolu e ack i egula i ies. Rela i e i egula i ies a e he gauge a ia ion and he c oss-le el. While141
absolu e ack i egula i ies a e he alignmen and he e ical p o ile. An ex ended desc ip ion o ack142
i egula i ies can be ound in [45].143
The o iginal idea o his wo k was he de elopmen o a scaled Au oma ed Reco ding Vehicle (ARV)144
such ha , in a sho ime pe iod, he ack geome y could be measu ed and la e on, ack i egula i ies145
calcula ed. In he case o he scaled ack subjec o s udy in his esea ch, ha ing a as p ocedu e146
o measu ing he ack is e en mo e impo an since he geome y can be manually modi ied i needed.147
Figu e 1 (a) shows he mechanisms ha a e used as he sleepe s o he scaled ack. Each o hem allows148
he a ia ion o ack gauge, can angle and he ela i e heigh be ween bo h ails. The ull ack includes149
900 mechanism dis ibu ed along i s 90 me e s o leng h (see Fig. 1 (b)). Wi h he au oma ed eco ding150
ehicle p esen ed in his pape , he scaled ack can be easily measu ed be o e any expe imen al campaign151
wi h a scaled ailway ehicle [46, 43], minimizing ha way possible unce ain ies in he compu a ional152
simula ion due o e o s in he de ini ion o ack i egula i ies.153
(a) (b)
Magne ic
beacon
Figu e 1: (a) T ack sleepe s. (b) T ack o e all iew
2.1. Mechanical design o he ARV154
The au oma ed eco ding ehicle CAD design is illus a ed in Fig. 2 (a). I has wo di e en pa s:155
he d i e sys em, consis ing on he ehicle’s body and ac ion wheels, and he measu ing axle (see Fig.156
5
2 (b)). Bo h pa s a e connec ed h ough a sphe ical join as ske ched in he igu e. This mechanical157
join isola es he o a ions o he ehicle’s body and he measu ing axle.158
(a) (b)
Sphe ical
join Sphe ical
join
Guide
ail
T ac ion
wheel
Le
ca iage
Righ
ca iage Guide
wheels
Vehicle’s
body
T ac ion
sp ing
Figu e 2: (a) Au oma ed eco ding ehicle CAD. (b) Isola ed measu ing axis CAD
The undamen al elemen o he inspec ion ehicle is i s measu ing axle ep esen ed on Fig. 2 (b). I 159
includes wo ca iages ha slide along a guide ail. Two pai s o guide wheels keep he ca iages a ached160
o he ails, which ensu es ha e ical wheels lie in he same ela i e loca ion wi h espec o he ail161
c oss-sec ion hus a oiding la e al wheel- ail displacemen ha may occu in o he measu ing ehicles. A162
ac ion sp ing gua an ees he con ac be ween he la e al guide wheels and he ou e side o bo h ails.163
The s i ness o he ac ion sp ing has been calcula ed acco ding wi h he maximum ehicle’s eloci y164
in o de o gua an ee a pe manen con ac be ween bo h la e al wheels and he ails. A hi d e ical165
wheel ins alled on he le ca iage (see Fig. 3 (b)) a oids he measu ing axis o pi ch-o e when mo ing166
o wa d. This mechanical assembly allows he measu ing axis o ollow he ack geome y pe ec ly while167
i is pushed by he ehicle’s d i e sys em.168
The d i e sys em is shown wi h u he de ails on Fig. 3. As i can be obse ed, he bel d i e is169
ac ua ed by a b ushless DC mo o . The ou pu sha is connec ed o a di e en ial ha d i es he ac ion170
wheels, which a e cylind ical, no conical, o minimize he in luence ha he oll o he ac ion axle may171
ha e in he measu ing axle. In addi ion, because he guidance o he ehicle is achie ed due o he la e al172
wheels and ac ion sp ing o he measu ing axle, he ac ion wheels a e wide enough o nego ia e he173
cu es p ope ly. The di e en ial gua an ees he co ec pe o mance o he ehicle while i nego ia es he174
cu e sec ions o he ack.175
6
(a) (b)
T ac ion
wheel
B ushless
DC mo o
Gea box
Bel
d i e
Diffe en ial Ve ical wheel
430 mm
245 mm
102 mm
Figu e 3: (a) Side iew o he eco ding ehicle. (b) Bo om iew o he eco ding ehicle
The ehicle has been manu ac u ed in aluminium and 3D p in ed PolyLac ic Acid (PLA). I is 430176
mm long and 245 mm wide wi h a o al mass o 6.5 kg. The measu able ack gauge ange is 107 mm o177
157 mm and he maximum yaw o a ion o he measu ing axis is ±35◦. The ehicle is powe ed wi h an178
indus ial quali y b ushless elec ic mo o Maxon-ECi30-GP32C-ENC16EASY-MK2. The d i e wheels179
can each a maximum angula eloci y o 20π ad/s ha co esponds o a o wa d eloci y o 5 m/s. I 180
should be no ed ha , such eloci y does no co espond wi h he maximum eloci y ecommended o 181
he measu emen o he ack as i will be explained la e in his manusc ip .182
2.2. Ins umen a ion o he ARV and da a acquisi ion sys em183
Figu es 4 and 5 show he inal assembly o he au oma ed eco ding ehicle. I is ins umen ed wi h184
an LVDT, an inclinome e , a p ecision encode and a e lec o . These senso s allow he measu emen o 185
ack geome y and i egula i ies. As explained be o e in his sec ion, ela i e ack i egula i ies a e he186
gauge a ia ion and c oss-le el. They a e he easies o de e mine since hey a e di ec ly ob ained om187
he measu emen o he LVDT and he inclinome e . In his case, he ehicle uses a 5mm- ange high188
p ecision LVDT SCHREIBER SM347.10.1.S wi h a maximum accu acy o ±12.5 mic ons. The senso 189
body is a ached o he igh ca iage while he od is in pe manen con ac wi h he le ca iage hanks190
o an in e nal sp ing. The inclinome e has a ange o ±10◦and i is ins alled on he le ca iage.191
The ac ion sp ing, which is expanded when he ehicle is on he ack, ends bo h ca iages owa ds192
a minimum sepa a ion be ween bo h guide wheels, being in ha way he measu ing axle pe pendicula 193
o bo h ails. Thus, i can be assumed ha he measu ing axle ollows he ack i egula i y. While194
measu ing, he mo emen o he le ca iage is locked o he guide ail and i is he igh ca iage he195
one ha slides along he guide ail (see Fig. 5 (a)).196
7
(a) (b)
D i e
wheels
Powe
sou ce
DAQ
compu e
Encode
Inclinome e
Righ
ca iage
Reflec o
Guide
wheels
LVDT
Le
ca iage
Figu e 4: (a) F on iew o he eco ding ehicle. (b) La e al iew o he eco ding ehicle
(a) (b)
Induc i e
senso
Locking
sc ew
F on
wheels
Encode
Inclinome e
Guide
ail
Figu e 5: (a) F on iew o he ins umen ed axle. (b) Top iew o ins umen ed axle
Fo he measu emen o absolu e ack i egula i ies (alignmen and e ical p o ile), he senso s197
ins alled on he ehicle a e complemen ed wi h he measu emen o a obo ic high p ecision o al s a ion198
(see Fig. 6) ha ollows he ajec o y o a e lec o igidly ins alled on he ehicle’s measu ing axis (see199
Fig. 4 (a)). This me hod allows o cap u e he ajec o y o a ixed poin on he measu ing axis ha 200
will be used o de e mine he absolu e ack i egula i ies, as will be shown in he nex sec ion. The201
ope a ion speed o he ehicle depends on he o al s a ion capabili ies and equi ed equency con en 202
o he measu ed i egula i ies. In his con ex , acco ding o he limi s o ack i egula i ies in ull-scale203
acks gi en by EN-13848 [47], he smalles wa eleng h a D1 band (3 m) esul s in 0.3 m in he scaled204
ack. No e ha he scaled ack is en imes smalle han a ull-scale one. This minimum wa eleng h205
combined wi h he capabili ies o he o al s a ion esul s in a maximum ARV ope a ion speed o 0.9 m/s206
which gua an ees he desi ed equency con en o he measu ed i egula i ies. The p ocess o calcula e207
he absolu e ack i egula i ies is explained la e in his manusc ip . Finally, he ehicle includes a208
p ecision encode ha measu es he dis ance a elled by he ins umen ed axis. The encode is igidly209
a ached o he o a ion axis o one o he wheels o he measu ing axle. In o de o a oid possible e o s210
in he measu emen o he dis ance a elled by he ehicle, due o e en ual slides o he measu ing wheel,211
8
Table 3: Ho izon al p ojec ion o he ideal ack geome y, op imized
Sec ion Type Leng h (m)
A Tangen 21.235
B T ansi ion 1.358
C Cons an adius (24m) 25.139
D T ansi ion 7.258
E Tangen 4.483
F T ansi ion 2.766
G Cons an adius (6m) 10.989
H T ansi ion 2.169
I Tangen 12.603
Table 4: Ve ical p ojec ion o he ideal ack geome y, op imized
Sec ion Type Leng h (m)
A Tangen 20.9
B Cons an slope (+0.035%) 15.2
C Tangen 40.9
D Cons an slope (+3.2%) 4.7
E Tangen 2
F Cons an slope (-4.7%) 3.2
G Tangen 0.6
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
Measu ed
Designed
Op imized
Dis ance s (m)
0 10 20 30 40 50 60 70 80 90
Heigh z (m)
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Measu ed
Designed
Op imized
(a) (b)
Figu e 13: (a) Ho izon al p ojec ion, measu ed s designed geome y s op imized. (b) Ve ical p ojec ion, measu ed s
designed geome y s op imized
4.2. Calcula ion o he i egula i y325
Once he ideal ack geome y is op imized, ack i egula i ies can be calcula ed as he di e ence326
be ween he ideal posi ion o he ails wi h espec o hei ac ual posi ions. Figu e 14 ske ches he327
ack i egula i y de ini ion. In he igu e, ail sec ions colou ed in pale blue ep esen he ideal posi ions328
while he da k g een ones a e he measu ed posi ions o he ails. I egula i y ec o s a e de ined as329
~ li =h0yli zli iT
and ~ i =h0y i z i iT
espec i ely. These ec o s a e exp essed in a ame330
15

called ack ame (TF), ha is a ached o he ack cen e line being i s X axis angen o i , and he331
Y axis con ained in he line ha joins he le and igh ailheads, as shown in Fig. 14. The alignmen 332
ξa, gauge ξg, c oss-le el ξcand e ical p o ile ξ a e de ined as a unc ion o he componen s o he333
i egula i y ec o s using he ollowing exp essions:334
ξa= (yli +y i )/2
ξg= (yli −y i )
ξc= (zli −z i )
ξ = (zli −z i )/2
(2)
li
2L
β
δ
Y
Z
β
i
z p
y p
yl p
zl p
P
u p
Q
ul p
Figu e 14: De ini ion o he ack i egula i ies
Expe imen ally, gauge and c oss-le el a e ob ained di ec ly om he measu emen o he LVDT and335
he inclinome e . The gauge i egula i y is de ined as he di e ence be ween he measu ed gauge and he336
nominal alue o he ack. The c oss-le el is he di e ence o heigh be ween bo h ails and i can be337
easily ob ained as:338
ξc=sin(αinc)·dLV DT (3)
whe e αinc is he angle measu ed by he inclinome e and dLVDT is he ack gauge measu ed by he339
LVDT.340
Alignmen and e ical p o ile canno be ob ained in such a di ec way. I is i s equi ed o ob ain341
he dis ance be ween he op imized ack cen e line poin s and he measu ed ones. To do ha , a sys em342
o non-linea algeb aic equa ions should be sol ed, which calcula es he dis ance be ween e e y single343
measu ed poin and he closes poin a he op imised ack cen e line. Poin Piin Fig. 15 ep esen s a344
measu ed poin on he ack while poin Qiis an a bi a y poin a he op imized ack cen e line. The345
dis ance be ween bo h poin s is he no m o ec o ~
di ha can be calcula ed using he exp ession:346
~
di=~
RQi−~
RPi(4)
whe e ~
RQiis he absolu e posi ion o one poin o he op imized ack cen e line and ~
RPiis he absolu e347
posi ion o he measu ed poin .348
16
In Fig. 15, ~
Qideno es he angen ec o o he scaled ack ideal cen e line a poin Qi. Vec o ~
di
349
has o be pe pendicula o ~
Qi. Thus, he ollowing equa ion has o be ul illed:350
~
di·~
Qi= 0 (5)
The p ocess concludes a e p ojec ing ec o ~
dion he ack e e ence ame acco ding o he nex 351
exp ession:352
¯ i = (A )Tdi(6)
being A he ans o ma ion ma ix o he T ack F ame (TF) o he Global F ame (GF). As usual in353
ailways kinema ics, he GF is a ixed e e ence ame, while he TF ollows he ehicle on i s mo emen 354
along he ack. In his esea ch, he GF is assumed o be loca ed in he i s loca ion whe e he355
o al s a ion was ins alled. Due o he o ien a ion o he TF wi h espec o he ack cen e line, he356
longi udinal coo dina e X is equal o ze o. Thus, second and hi d componen s o ec o ~ i a e he357
i egula i ies o alignmen and e ical p o ile, espec i ely. Once he alignmen , c oss-le el, gauge and358
e ical p o ile a e de e mined, sys em o equa ions (2) can now be sol ed o ob ain he i egula i y ec o 359
componen s yli ,zli ,y i and z i .360
P(x ,y,z)
iPi Pi Pi
RPi
RQi
d
Q (x ,y,z)
iQi Qi Qi
Qi
s
YX
Z
Re e ence
geome y
Real
geome y
X
Z
Y
Figu e 15: Alignmen and e ical p o ile calcula ion p ocedu e
4.3. De e mina ion o he ails posi ions using he ARV361
Fo a co ec pe o mance and accu a e measu emen o he o al s a ion, he e lec o is loca ed on362
he ARV in a posi ion such ha , i is always isible o he o al s a ion du ing he measu emen o he363
ack. This equi es he e lec o o be ins alled on he op o he ARV as shown in Fig. 5 (b). Tha 364
means, he o al s a ion is no di ec ly measu ing he ack cen e line, bu a line pa allel and close o365
he la e . Conside ing ha , he le ca iage (whe e he senso s a e ins alled) is locked o he guide ail366
and he ela i e posi ion o he e lec o wi h espec o he le ail is known. As i is explained nex ,367
using he posi ion o he e lec o measu ed by he o al s a ion, he measu emen o he inclinome e , he368
17
LVDT, he encode and he inal help o he ack p e-p ocesso , he absolu e coo dina es o he ac ual369
ack cen e line can be de e mined.370
Le ail
axis
Righ ail
axis
T ack cen e
line
Reflec o
P ism
u
u
l
z
l
y
Gauge
inc
φ
Figu e 16: Kinema ics o he e lec o and he ails
Figu e 16 shows a kinema ics ske ch o he ails and he e lec o , in wi ch he la e is assumed o371
be igidly a ached o a e e ence ame yl , zl  ha mo es oge he wi h he le - on wheel ha lies372
o e he le ail. Le de ine Al as he semi-expe imen al o a ion ma ix ha ans o ms a ec o om373
he le ail e e ence ame o he global ame,374
Al =





cos(ψ)−sin(ψ)ϕincsin(ψ) + θinccos(ψ)
sin(ψ)cos(ψ)−ϕinccos(ψ) + θincsin(ψ)
−θinc ϕinc 1





(7)
whe e ϕinc and θinc a e he angles expe imen ally measu ed by he dual-axis inclinome e and ψis he375
yaw angle p o ided by he ack p e-p ocesso . Ma ix Al is linea ised assuming ha he angles o he376
inclinome e a e small alues. Taking in o accoun ha he local posi ion o he e lec o wi h espec 377
o he le ail e e ence ame ¯uP ism is known om he mechanical design o he ehicle, he ollowing378
exp ession can be es ablished:379
Rl =RP ism −Al ¯uP ism (8)
whe e Rl deno es he posi ion o he le ail axis in he global e e ence ame and RP ism is he absolu e380
posi ion o he e lec o measu ed by he o al s a ion, also exp essed in he global e e ence ame. Then,381
he absolu e posi ion o he igh ail R and he ack cen e line RT CL can be easily ob ained using382
he ollowing exp essions:383
R =Rl +Al ¯u (9)
RT CL =Rl +Al ¯uT CL (10)
being ¯u =h0−gauge 0iT
and ¯uT CL =h0−gauge/2 0iT
, espec i ely. No e ha , he gauge is384
ob ained h oughou he measu emen o he LVDT.385
18
5. Expe imen al alida ion and compa ison o esul s386
In o de o alida e he pe o mance and accu acy on he measu emen using he au oma ed eco ding387
ehicle, his sec ion p esen s an expe imen al compa ison be ween he ack i egula i ies ob ained wi h388
he ehicle and he i egula i ies d awn om he manual measu emen o he ack. The manual mea-389
su emen is conside ed as he e e ence since i has been accomplished in o ally con olled condi ions.390
Howe e , he measu emen s o he ehicle, aking in o accoun ha hey a e ob ained while he ehicle391
mo es a a ce ain speed along he ack, migh be a ec ed by he ehicle- ack dynamics.392
Figu es 17, 18 and 19 show he compa ison be ween he ela i e ack i egula i ies ob ained using393
he au oma ed eco ding ehicle and he manual me hod. In his expe imen he ehicle mo es a a394
cons an eloci y o 0.5 m/s along he ack. I can be obse ed in Fig. 17 how he gauge a ia ion d awn395
om he measu emen o he LVDT almos coincides in bo h expe imen s. These esul s ha e been396
ob ained conside ing a nominal ack gauge o 127.8 mm. In iew o he esul s, i can be said ha he397
measu emen o he LVDT is no a ec ed by he dynamics o he ehicle a he speed o 0.5 m/s. In Fig.398
19 i is obse ed ha he inclinome e ins alled in he ARV ollows he end o he manual measu emen 399
bu expe iencing la ge oscilla ions. This is some hing expec ed due o he ac ha , he c oss-le el is400
ob ained using he combined measu emen o he LVDT and he inclinome e , and he la e is a ype401
o senso ha no mally p esen s a bad dynamic pe o mance. Howe e , he obse ed di e ences a he402
speed o 0.5 m/s can be assumed o be su icien ly accu a e because he end o he manual measu emen 403
is well iden i ied. A possible al e na i e o he u ilisa ion o an inclinome e o measu e he can angle o 404
he ack is he use o an Ine ial Measu emen Uni (IMU) and a senso usion algo i hm. Two examples405
a e he algo i hms p oposed by Madwick e al. in [51] o Saba ini in [52, 53]. These algo i hms a e a406
p io i sui able o dynamic measu emen s. They combine he measu emen o he accele a ion and he407
angula eloci ies o he IMU o es ima e he absolu e o ien a ion o he senso .408
0 10 20 30 40 50 60 70 80
s (m)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Gauge Va ia ion (mm)
Manual
Vehicle
Figu e 17: Gauge a ia ion me hods compa ison
19
31 32 33 34 35 36 37 38
s(m)
-1
-0.5
0
0.5
1
Gauge Va ia ion(mm)
Manual
Vehicle
Figu e 18: Magni ica ion o gauge a ia ion me hods compa ison
0 10 20 30 40 50 60 70 80
s (m)
-6
-5
-4
-3
-2
-1
0
1
2
3
C oss Le el (mm)
Manual
Vehicle
Figu e 19: C oss-le el me hods compa ison
The epea abili y o he senso s measu emen when he ehicles mo es a di e en o wa d eloci ies409
is also analysed. Figu e 20 shows he measu emen o he ack gauge ob ained wi h he LVDT in h ee410
di e en expe imen s accomplished a 0.5, 0.7 and 0.9 m/s. I is clea ly obse ed how he measu emen 411
o he LVDT emains s able in he h ee scena ios. Howe e , he inclinome e measu emen shown in Fig.412
21 a ies signi ican ly a di e en eloci ies. This is obse ed when he ehicle nego ia es he second cu e413
o he scaled ack loca ed be ween s= 60 m and s= 75 m, app oxima ely. In his case, he cen i ugal414
o ce expe ienced by he senso ins alled in he ehicle s ongly a ec s i s measu emen when i mo es415
as e han 0.5 m/s. This can be explained gi en he ac ha he inclinome e bases i s measu emen 416
on he capaci i e mic o pendulum p inciple and he Ea h g a i y p inciple ske ches in Fig. 22. Since417
he inclinome e is an ine ial senso , he angle α ep esen ed in he igu e is highly a ec ed by he418
ehicle’s dynamics. In iew o hese esul s, i is concluded ha he measu emen o he ack using he419
ehicle mus be done a a maximum speed o 0.5 m/s (which is in ange o admissible ope a ional speeds420
desc ibed in Sec ion 2) in o de o gua an ee he co ec pe o mance o he il senso .421
20

0 10 20 30 40 50 60 70 80
Dis ance s(m)
126
126.5
127
127.5
128
128.5
129
129.5
130
T ack Gauge (mm)
VhA 0.5m/s
VhA 0.7m/s
VhA 0.9m/s
Figu e 20: Repea abili y o LVDT measu emen
0 10 20 30 40 50 60 70 80
Dis ance s(m)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Can angle (deg)
VhA 0.5m/s
VhA 0.7m/s
VhA 0.9m/s
Figu e 21: Repea abili y o inclinome e measu emen
-
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
α
α
g
Figu e 22: Func ioning p inciple o he inclinome e senso
Mo eo e , he absolu e ack i egula i ies ha e been calcula ed acco ding he p ocedu e explained in422
he p e ious sec ion. Figu es 23 and 24 show he ob ained alignmen and e ical p o ile o he scaled ack423
using he measu emen o he ARV and he MMM. The signals a e il e ed acco ding o he Eu opean424
s anda d [47] using a band-pass il e applied in he leng h domain wi h a cu -o equencies be ween 1/7425
m-1 and 1/0.3 m-1, which co espond wi h 1/70 m-1 and 1/3 m-1 in a ull-scale ack. These equencies426
a e de e mined aking in o accoun he scale educ ion o 1:10, and hey co espond wi h he D1 o D2427
ange gi en in he Eu opean s anda d. In wha ollows, all igu es conce ning measu emen s bo h wi h428
he manual and ehicle me hods, a e il e ed equally. In he Fig. 23 i is obse ed a good ag eemen in429
21
he magni ude o he alignmen be ween bo h signals. The esul an Roo Mean Squa ed (RMS) le el o 430
he di e ence be ween bo h signals is summa ized in Table 5. In his analysis he ack has been di ided431
in h ee sec ions which co espond wi h he angen sec ion loca ed a he beginning o he ack, he432
la ge adius cu ed sec ion (R = 24 m) and he sha p adius cu ed sec ion (R = 6 m).433
Table 5: RMS analysis in di e en ack sec ions
I egula i y Tangen (s=0-21m) Cu e (s=21-47m) Cu e (s=60-73m)
Gauge 2.02 ·10−4m 1.26 ·10−4m 1.24 ·10−4m
C oss-le el 1.79 ·10−4m 2.08 ·10−4m 4.71 ·10−4m
Alignmen 4.21 ·10−4m 4.99 ·10−4m 6.31 ·10−4m
Ve ical p o ile 4.58 ·10−4m 4.29 ·10−4m 4.31 ·10−4m
0 10 20 30 40 50 60 70 80
s (m)
-8
-6
-4
-2
0
2
4
6
8
Aligmen (mm)
Manual
Vehicle
Figu e 23: Alignmen o he scaled ack
0 10 20 30 40 50 60 70 80
s (m)
-5
0
5
Ve ical P ofile (mm)
Manual
Vehicle
Figu e 24: Ve ical p o ile o he scaled ack
Finally once he ou i egula i ies o ack gauge, c oss-le el, alignmen and e ical p o ile a e calcu-434
la ed, he eal posi ion o he ail’s head (see Fig. 9) gi en by yli ,y i ,zli and z i can be de e mined435
using Eq. 2. Figu e 25 shows he ob ained esul s. Looking a he Figs. 25 (c) and 25 (d) i can be436
obse ed he di e ence o heigh be ween bo h ails in he cu ed sec ions loca ed a s = [21 - 47] m and s437
22
= [60 - 73] m. This di e ence o heigh co esponds wi h he can angle manually in oduced in he scaled438
ack. In iew o hese esul s i can be concluded ha he ARV demons a es a qui e good pe o mance439
when measu ing he scaled ack geome y, being he ob ained i egula i y esul s analogous o he ones440
d awn om he MMM. In addi ion, he use o he ARV educes he measu emen ime wen y imes441
compa ed wi h he MMM. The ARV allows a as and accu a e measu emen o he ack jus be o e an442
expe imen al campaign wi h a scaled ehicle.443
23
0 10 20 30 40 50 60 70 80
s (m)
-8
-6
-4
-2
0
2
4
6
8
yL (mm)
Manual
Vehicle
0 10 20 30 40 50 60 70 80
s (m)
-8
-6
-4
-2
0
2
4
6
8
yR (mm)
Manual
Vehicle
0 10 20 30 40 50 60 70 80
s (m)
-6
-4
-2
0
2
4
6
zL (mm)
Manual
Vehicle
0 10 20 30 40 50 60 70 80
s (m)
-6
-4
-2
0
2
4
6
zR (mm)
Manual
Vehicle
(a)
(b)
( c )
(d)
Figu e 25: (a) yL, (b) yR, (c) zL, (d) zR displacemen s
24