Expe imen al and nume ical assessmen
o a high-pe o mance elec omagne ic
ib a ion ene gy ha es e in a
double-deck ailway unnel
Vic o O do ˜
nez1, Hassan Li a i1, Robe A cos1,2, Jo di Romeu1and Behshad Noo i3
Abs ac
This pape e alua es he pe o mance o an elec omagne ic ib a ion ene gy ha es e o powe ing wi eless senso
ne wo ks in ailway unnels. A ield es was conduc ed in a double-deck ailway unnel, measu ing ib a ions as well
as he mechanical and elec ical esponses o a p o o ype o he ha es e du ing 139 passing ains. Nume ical
simula ions ha e been ca ied ou o es ima e he ha es e ’s ou pu pe o mance om which a good ag eemen
has been eached when compa ing he expe imen al and simula ed induced ol ages. Using he alida ed model
and measu ed ib a ion da a, he ha es e ’s pe o mance adop ing a ully equency- uned esonan sys em o
di e en implemen a ion loca ions, such as he unnel wall and he ail, has been simula ed. Cumula i e elec ical
ene gy gene a ed by he ha es e o di e en loca ions is p esen ed o he o al pe iod o ailway-induced ib a ion
measu emen s. Maximum cumula i e elec ical ene gies o app oxima ely 1805 mJ, 0.52 mJ, and 7838 mJ ha e been
es ima ed o be gene a ed by he ha es e when placed on he in e io loo , he wall, and he ail, espec i ely, in abou
nine hou s o ope a ion.
Keywo ds
Elec omagne ic ib a ion ene gy ha es e , Railway-induced ib a ion, S uc u al heal h moni o ing, Vib a ion-based
gene a o , Ballas less ack
acks, specially a he ail (Zhang e al. 2024;Gao e al.
2017;Yang e al. 2021;Gao e al. 2016). None heless, he
high ampli udes o ib a ion ha a e ypically induced in
hese sys ems, pa icula ly in he ail whe e displacemen s
and accele a ions o ib a ion can each 12 mm (Sadeghi
e al. 2017;Pan e al. 2019) and 30 g (Gao e al. 2017),
espec i ely, may pu a isk he s uc u al in eg i y o
he mechanical subsys em o he ha es e o educe i s
eliabili y and li espan (Kim e al. 2017).
The p esen pape is ocused on he applica ion o VEHs
in o he subsys ems o he ailway sys em, such as slabs,
sleepe s, and he unnel s uc u e. Vib a ion le els in hese
loca ions a e usually signi ican ly lowe han hose a he ail.
Consequen ly, p oducing enough elec ical ene gy on hei
basis can esul in a challenging ask o mos ib a ion-
based gene a o s. Only a ew s udies ha e p oposed VEHs
o be ins alled on hese o he subsys ems o he ailway
sys em. Fo ins ance, Hou and his colleagues de eloped an
1Acous ical and Mechanical Enginee ing Labo a o y (LEAM), Uni e si a
Poli `
ecnica de Ca alunya (UPC), c/Colom, 11, 08222 Te assa
(Ba celona), Spain.
2Se a H´
un e Fellow, Uni e si a Poli `
ecnica de Ca alunya (UPC).
3AV Ingenie os, c/Joan XXIII, 23, 08173 S . Cuga del Vall`
es (Ba celona),
Spain.
Co esponding au ho :
Vic o O do˜
nez, Acous ical and Mechanical Enginee ing Labo a o y
(LEAM), Uni e si a Poli `
ecnica de Ca alunya (UPC), c/Colom, 11, 08222
Te assa (Ba celona), Spain.
Email: ic o .hugo[email p o ec ed]
In oduc ion
Nowadays, he e is a subs an ial and inc easing demand o
using ailway anspo a ion sys ems o mobilizing people
in hei daily ac i i ies and ans e ing goods o all ypes
o indus ial pu poses due o hei sa e y, e iciency, and
punc uali y among o he anspo a ion sys ems. Railway
sys ems a e playing, hus, a i al ole in he connec i i y
and economic de elopmen o mode n socie ies. Hence, i
is o g ea impo ance o main ain ailway ne wo k sys ems
in op imum wo king condi ions. Fo his pu pose, onboa d
and ack-side elec ical de ices such as ul a-low-powe
senso s (Pe ez e al. 2020; Wang e al. 2021; Zuo e al.
2021) o s uc u al heal h moni o ing (SHM) o ail oad
ehicles and ailway acks a e ypically employed. When
access o he elec ici y g id is complex o una ailable, hese
senso s a e no mally powe ed by ba e ies. Ba e ies p o ide
a con inuous and s able powe supply, bu , un o una ely,
hey a e no a cos -e ec i e solu ion (Lin e al. 2015) ha
also in oduces new con lic s o main enance and logis ics
pe sonnel. Since kine ic ene gy associa ed wi h ib a ions
induced by ailway a ic i s a bundan , he e i s a high
po en ial o ib a ion ene gy ha es e s (VEHs) o sca enge
ha ene gy o powe ing wi eless senso s (Zuo e al. 2023).
In he las ew yea s, se e al designs o VEHs ha e
been p oposed by di e en esea che s o onboa d ail oad
ehicle pu poses, mainly ins alled on he bogie sys em o he
ailway ehicle (Cao e al. 2023; Pe ez e al. 2020; O iz
e al. 2014; B adai e al. 2018; Pa k and Kim 2016; De
Pasquale e al. 2012), and also o be ins alled in ailway
2
and desc ibed in he nex sec ion has been expe imen ally
es ed in he men ioned ailway sys em unde i s no mal
ope a ing condi ions. Va ious nume ical simula ions ha e
also been conduc ed o alida e he simula ion me hodology
in a eal scena io and o de e mine he ou pu pe o mance
o he EMVEH model in i s ac ual condi ion as well
as o he case when i s na u al equency is uned o
op imize he elec ical powe gene a ion. Mo eo e , o en ich
his in es iga ion, a simula ion o he pe o mance o he
ab ica ed p o o ype model i ually applied o he wall
and ail o he unde g ound unnel unde e alua ion a e
also exposed, based on expe imen al ib a ions measu ed a
hese wo loca ions. Finally, he cumula i e elec ical ene gy
gene a ed by he ab ica ed p o o ype in each case s udy and
loca ion is p esen ed o he o al pe iod o ailway-induced
ib a ion measu emen s o ha e a gene al pe spec i e o i s
applicabili y o powe ing WSNs in an unde g ound ailway
en i onmen . Due o he high-pe o mance capabili ies o he
p oposed EMVEH p o ided by i s ing-shaped a chi ec u e
and Halbach con igu a ion, he esul s p esen ed in his pape
on he ha es ed ene gy om he slab and e en he unnel
wall po en ially demons a e he applicabili y o he p oposed
de ice in his con ex . The p esen a icle can also se e as a
su ey o ib a ion le els occu ing in a double-deck ailway
unnel ha could be employed, o example, o es o he
ib a ion ene gy ha es ing de ices o applica ions in his
kind o unde g ound ailway sys ems.
Me hodology
Desc ip ion o he EMVEH
The employed EMVEH (O do˜
nez e al. 2022) is mainly
consis ing o a “Magne in-line coil” elec omagne ic
ansduce mechanism based on h ee ing magne s wi h a
linea Halbach a ay con igu a ion ha concen a es hei
magne ic ield in he inne space o he mechanism whe e
a single e ically-cen e ed concen ic coil has been loca ed.
Speci ically, i consis s o one adial ing magne loca ed in
be ween wo axial ing magne s wi h epelling o ces. This
pa icula s uc u e allows o inc easing he esonan mass
wi hin ixed dimensions o he ansduce and o educe he
coil esis ance o he same numbe o u ns, enhancing he
powe gene a ion capabili y o his de ice. Mo eo e , wo
helical comp ession sp ings ha e been selec ed as he elas ic
elemen s o he oscilla ing sys em, which is also composed
o he h ee ing magne s and a magne holde .
The na u al equency o he ha es e (61.7 Hz) is
designed o be wi hin he ange o ailway-induced ib a ions
in unnels, which a e usually be ween 30 Hz and 100 Hz o
all componen s excep he ails (Balas egui e al. 2013;Gup a
e al. 2008). S ill, his does no mean ha i is expec ed o be
exac ly uned o one o he mos dominan equencies o he
sys em esponse. The o e all dimensions o he ab ica ed
p o o ype (including i s ex e nal case) a e 2.55 cm o adius
and 4.7 cm o heigh , gi ing a o al olume o 96 cm3.
The es o geome ical cha ac e is ics and p ope ies o he
employed de ice a e ho oughly p esen ed in he men ioned
p e iously published wo k o he au ho s (O do˜
nez e al.
2022).
elec omagne ic ib a ion ene gy ha es e (EMVEH) o be
applied in he slab ack o Guangzhou Me o (Hou e al.
2018). The nume ical simula ion esul s o he pe o mance
o he p oposed de ice es ima ed a peak powe densi y alue
o 176.5 µW/cm3, which is also epo ed o be much highe
han ha o mos exis ing simila de ices. La e on, he
same au ho s p oposed in Hou e al. (2021) a mul ilaye
piezoelec ic ib a ion ene gy ha es e (PVEH) mean o
be applied a he edge o he slab in he loa ing slab
ack sys em (FSTS) o he ailway b idge sys em unde
s udy. Di e en nume ical simula ions we e ca ied ou o
de e mine ha by ins alling 144 o hese de ices, a anged
on 36 uni s o he FSTS, he amoun o elec ical ene gy
p oduced in 17 hou s o ain ope a ion would each 31.4
kJ. As a esul , hey ha e a exceeded he 12.85 mJ equi ed
in he wo king cycle o each wi eless senso ne wo k (WSN)
node used in hei moni o ing sys ems. Ga i e al. (2016) also
p esen ed a nume ical in es iga ion o how much ene gy can
be ha es ed wi h a single-deg ee-o - eedom (SDOF) linea
VEH om he e ical ib a ion o a sleepe o he G ea
Wes e n Main Line in he Uni ed Kingdom as an In e ci y
125 ain passed by a a speed o 195 km/h. Resul s indica e
ha he maximum ene gy ha could be ha es ed in his
sys em is abou 0.25 J pe uni (kg) o ene gy ha es e
mass a a equency o abou 17 Hz. Cahill e al. (2014)
in es iga ed he easibili y o piezoelec ic-based ene gy
ha es ing on a single-span s eel-conc e e composi e ailway
b idge in Sweden o di e en ypes o passing ains.
Expe imen al esul s de e mined ha he p oposed VEHs can
p oduce an elec ical ou pu up o 588 µW du ing he passage
o a passenge ain.
The p e ious li e a u e e iew discussed ib a ion ene gy
ha es ing de ices ha di ec ly ans o m he kine ic ene gy
o he linea ib a ion o elec ical powe . Howe e ,
al e na i e ene gy ans o ma ion echnologies ha e been
applied o design and de elop o he ypes o ib a ion-
based gene a o s o he ailway sec o . Among hem, a
popula ca ego y comp ises de ices ha con e he linea
displacemen o he ail in o o a ional mo ion o d i e
elec ical gene a o s. Some examples o hese ypes o VEHs
can be ound in (Zhang e al. 2016; Pan e al. 2019; Gao
e al. 2020; Wang e al. 2012; Lin e al. 2018b,a). Howe e ,
i is wo h no ing ha hese VEHs end o be bulky and ha
hei applica ion is es ic ed o he ail i sel , becoming a less
sui able al e na i e o powe WSNs.
Nowadays, conc e e slabs a e common componen s
o mode n ailway sys ems. Moun ing VEHs on unnel
conc e e slabs p esen s se e al ad an ages compa ed o
o he loca ions wi hin he unnel. Essen ially, hey a e la
and ex ended su aces ha acili a e he ins alla ion, he
mechanism o ixa ion, a nd he u pscaling o he de ice
(i e e equi ed). Also, when an EMVEH is ins alled
on a conc e e slab ins ead o a ail sys em, he e is a
lack o elec omagne ic in e ac ions ha could o he wise
a ec he dynamic esponse o he de ice (Kuang e al.
2021). In his con ex , his pape a emp s o assess a
Halbach-based EMVEH o ha es ing he kine ic ene gy
o he ib a ion induced by unde g ound ailway a ic on
a conc e e slab ha pe o ms as he in e io loo o a
double-deck unnel o Me o Ba celona. Fo his pu pose,
he ab ica ed p o o ype de eloped in (O do˜nez e al. 2022)
METHODOLOGY 3
S udy o he in luence o he ib a ion ampli ude
on he pe o mance o he EMVEH p o o ype
In he e e enced s udy, he au ho s p esen an expe imen al
cha ac e iza ion o he ab ica ed EMVEH p o o ype using
sinusoidal base exci a ion applied by an elec odynamic
shake , wi h a cons an ampli ude o 0.03 g. Howe e , he
ib a ion le els induced by ain a ic can a y signi ican ly
om his alue. To cha ac e ize he p o o ype pe o mance
a di e en ampli udes, he labo a o y es s epo ed in
O do˜
nez e al. (2022) ha e been u he complemen ed
o he p esen wo k wi h esul s a wo o he exci a ion
ampli udes: 0.006 g and 0.15 g o inpu RMS accele a ion.
The co esponding esul s a e depic ed in Figs. 1and 2,
illus a ing he ansmissibili y and he induced ol age
ans e unc ion (TF) o he ansduce . These equency
esponse unc ions desc ibe he ela ionships be ween he
base accele a ion, measu ed using wo accele ome e s, and
bo h he accele a ion o ib a ion o he esonan mass and
he induced ol age o he ha es e . Resul s indica e ha
60 61 62 63 64
F equency (Hz)
101
102
103
T ansmissibili y
Inpu acc. = 0.006 g
Inpu acc. = 0.03 g
Inpu acc. = 0.15 g
Figu e 1. T ansmissibili y o he ab ica ed p o o ype
conside ing a ious alues o he inpu RMS accele a ion.
60 61 62 63 64
F equency (Hz)
101
102
103
Induced Vol age TF (V/g)
Inpu acc. = 0.006 g
Inpu acc. = 0.03 g
Inpu acc. = 0.15 g
he damping o he ab ica ed p o o ype is highly dependen
on he inpu ampli ude, wi h a signi ican educ ion in
pe o mance as he ampli ude inc eases. This can be be e
obse ed om he no malized powe densi y (NPD) ( e e
o Appendix A o he o mula ion) ob ained o he
h ee exci a ion ampli udes, 0.006 g, 0.03 g, and 0.15 g,
which a e 62.2 mW cm−3g−2, 16.1 mW cm−3g−2, and
1.2 mW cm−3g−2, espec i ely. These NPD alues a e
compu ed conside ing he echnical speci ica ion and de ails
p esen ed in O do˜
nez e al. (2022). Howe e , ib a ion le els
induced by ailway a ic in a unnel sys em, pa icula ly
hose nea he esonan equency o he ha es e , all wi hin
he lowe ange o he RMS alues conside ed in hese
labo a o y es s. The e o e, i can be concluded ha he
ab ica ed p o o ype is expec ed o achie e high pe o mance
when ha es ing ene gy in a ailway unnel en i onmen .
Expe imen al ield es
Desc ip ion o he es si e: Wi h he aim o e alua ing he
pe o mance and applicabili y o he p e iously men ioned
EMVEH on ailway unnels, wi h a special ocus on conc e e
slab componen s, an expe imen al ield es was ca ied ou
on a unnel sec ion o Me o Ba celona. Mo e speci ically,
he ield es was conduc ed in a sec ion o he double-deck
ailway unnel o lines L9 and L10 o Me o Ba celona
nea To assa s a ion, loca ed a L’Hospi ale de Llob ega
in Ba celona, Spain. The gene al dimensions o his double-
deck unnel co espond o an inne diame e o 10.9 m and
a hickness o 0.336 m, whe eas he wid h and heigh o he
in e io loo ha suppo s ain passages in he uppe deck
a e 10 m and 0.3 m, espec i ely. As indica ed in Fig. 3(a),
wo ailway acks exis on each unnel deck, all based on
UIC54 ails wi h s anda d gauge. The ab ica ed p o o ype
was ins alled on he middle poin o he in e io loo , loca ed
be ween ailway lines 1 and 2, as obse ed in Fig. 3(b).
Mo eo e , expe imen al ib a ion measu emen s on he wall
and he ail we e conduc ed in pa allel o es s on he in e io
loo loca ion. I is wo h men ioning ha subway ains
in lines L9 and L10 ypically pass h ough ailway line 2
on he uppe deck in one di ec ion and on he lowe deck
o he opposi e one, while ailway line 1 is dedica ed (in
bo h cases) o special si ua ions. Mo eo e , subway ains o
bo h lines a e scheduled o a i e a To assa s a ion a he
same ime wi h a pe iodici y o app oxima ely 480 seconds.
Howe e , since he measu emen si es we e no a he s a ion
bu deepe inside he unnel, he e is a passing di e ence
o app oxima ely 120 seconds be ween ains ha each
To assa s a ion a he same ime om opposi e di ec ions.
Consequen ly, he ailway-induced ib a ion measu emen s
coming om he ains on each deck can be easily iden i ied
in he ib a ion measu emen s a he in e io loo , wall, and
ail loca ions.
Field es se up: Fig. 4shows he expe imen al se up
adop ed o conduc he p oposed ield es . On he one hand,
he physical p o o ype o he EMVEH was wax- ixed o a
s eel pla e ha was i s glue- ixed on o he in e io loo .
Two PCB Piezo onics accele ome e s 352C65 (Acc1 &
Acc2) wi h a equency ange o 0.5 Hz o 10000 Hz and
a sensi i i y o app oxima ely 100 mV/g we e magne ically
Figu e 2. Induced ol a ge ans e unc ion (TF) o he
ab ica ed p o o ype conside ing a ious alues o he inpu
RMS accele a ion.
4
1.53 m
D E
1.53 m
1.0 m
(09(+
5DLOVOLQH
5DLOVOLQH
Figu e 3. The ield es en i onmen . (a) Schema ic o he unnel and loca ion o he EMVEH. (b) Gene al iew o he physical
p o o ype moun ed on he in e io loo o he double-deck unnel si e.
a) b)
Acc3
P o o ype
Acc1 & Acc2
LMS SCADAS
$FFHOHURPHWHURQUDLO1.5 m
$FFHOHURPHWHURQZDOOF)
Figu e 4. Expe imen al se up adop ed in he ield es . (a) Moun ing con igu a ion o he h ee accele ome e s and he p o o ype.
(b) Schema ic o he double-deck unnel and he moun ing loca ions o he accele ome e s on he wall and ail. (c) Connec ion o
he da a acquisi ion sys em and compu e .
RESULTS AND DISCUSSION 5
physical componen s o he sys em. Figs. 5and 6show
diag ams o he model implemen a ion o he open ci cui
ope a ion case (wi hou ex e nal load esis ance) and o he
closed ci cui ope a ion case (wi h ex e nal load esis ance),
espec i ely.
Mo eo e , he e a e wo main inpu s in hese nume ical
algo i hms: The i s inpu used in all simula ion cases is
he ex e nal base exci a ion, co esponding o he ailway-
induced ib a ion measu emen s a each loca ion. The
second inpu comp ises all mechanical, elec omagne ic, and
coil pa ame e s o he ab ica ed p o o ype, which ha e
been es ablished and/o expe imen ally es ima ed in he
design p ocess and expe imen al alida ion o he ab ica ed
p o o ype in O do˜
nez e al. (2022). Howe e , i is impo an
o no e ha he na u al equency o he ha es e will be
modi ied in hese simula ions ( om one case o loca ion
o ano he ) as hey a e conside ing equency-un uned and
equency- uned condi ions. I is also impo an o no e ha
he damping coe icien employed in he simula ions is based
on labo a o y es s o an inpu RMS accele a ion o 0.03
g, as his alue was ound o p o ide esul s mos closely
ma ching he expe imen al da a. This damping coe icien
was applied in all simula ions, no jus hose ela ed o
he ab ica ed p o o ype, as i is expec ed ha an imp o ed
e sion o he p oposed EMVEH design will exhibi mo e
s able damping beha iou .
Resul s and discussion
Expe imen al esul s
In e io loo loca ion: The ailway-induced ib a ion and
ha es e esponse signals measu ed in he p e iously
desc ibed expe imen al campaign allow o de e mining
he dominan equencies and accele a ion le els a he
in e io loo loca ion selec ed in his in es iga ion, as
well as analyzing he mechanical beha io and elec ical
pe o mance o he ab ica ed p o o ype. In his ega d,
Figs. 7and 8show he accele a ion spec al densi y (ASD)
and accele a ion spec um in one- hi d oc a e bands o he
ib a ion signals induced by he passage o ains on he
lowe and uppe decks, espec i ely, while Fig. 9illus a es
he accele a ion and induced ol age spec a in one- hi d
oc a e bands o he EMVEH esponse o all 139 passing
ains. The accele a ion esponses and induced ol age o
he one- hi d oc a e band esul s a e p esen ed in e ms o
dB wi h a e e ence o 10−6and 1, espec i ely. The one-
hi d oc a e bands a e no malized using he a e age ime ha
akes he i s and he las wheel o he ain o pass om
he same poin . I is ele an o men ion ha Figs. 7and 8
deno e he a e age o measu ed accele a ions in Acc1 and
Acc2, om which dominan equencies a e ound o occu
a abou 50 Hz o bo h he lowe and uppe deck passing
ains. Howe e , as expec ed and obse ed in Fig. 9(a), he
dominan equency o he mechanical subsys em is a ound
63 Hz, which is consis en wi h he na u al equency o he
ab ica ed EMVEH. Consequen ly, he maximum induced
ol age also happens a he one- hi d oc a e band o 63 Hz,
as can be obse ed in Fig. 9(b). This in o ma ion allows o
de e mining ha he ab ica ed p o o ype is no pe o ming
a i s bes since he na u al equency o he ha es e is
no ma ching he mos dominan equencies o he ib a ion
ixed o he s eel p la e o m easu e he i npu ailway-
induced ib a ion, while one PCB Piezo onics minia u e
accele ome e 352B10 (Acc3) wi h a equency ange o
2 Hz o 10000 Hz and a sensi i i y o app oxima ely 10
mV/g was wax- ixed o he esonan mass o he p o o ype
o measu e i s esponse, as obse ed in Fig. 4(a). On
he o he hand, wo accele ome e s ha e been employed
in his expe imen al se up, one ixed o he unnel wall
and he o he o he ail, o measu e hei ailway-induced
ib a ion esponse. Fig. 4(b) shows a schema ic o he
loca ion o hese wo accele ome e s wi hin he unnel. Fo
he sake o eliabili y, each accele ome e was p e iously
calib a ed wi h an IMI 699A02 handheld shake . Based on
his expe imen al es se up, he ib a ion measu ed om
hose i e accele ome e s and he elec ical esponse o he
ha es e we e acqui ed o nine consecu i e hou s using
he LMS SCADAS da a acquisi ion sys em (Fig. 4(c)),
conside ing a sampling equency o 512 Hz, om which a
o al o 139 passing ains in bo h di ec ions we e eco ded.
Mo e speci ically, his c o esponds o 7 0 a nd 6 9 passing
ains unning h ough he uppe and lowe decks o he
unnel, espec i ely.
EMVEH nume ical simula ion
Di e en nume ical simula ion cases ha e been conduc ed o
es ima e he elec ical ou pu pe o mance o he p oposed
EMVEH applied o he in e io loo o he double-deck
unnel sec ion unde s udy. Fi s , he equency-un uned
de ice, which co esponds o he ab ica ed p o o ype model,
was simula ed. This simula ion aimed o compa e he
induced ol age (unde open ci cui ope a ion condi ions)
o ha ob ained expe imen ally, assessing he accu acy o
he p oposed nume ical algo i hm o he speci ic measu ed
inpu signals. Second, he load ol age and elec ical
ou pu powe (closed ci cui ope a ion condi ion) o he
equency-un uned de ice ha e been es ima ed. Thi d, he
o e all ou pu pe o mance o he ab ica ed p o o ype model
has been simula ed o he case o a equency- uned
sys em. Fu he mo e, simula ions o he elec ical ou pu
pe o mance o a equency- uned EMVEH model applied o
he wall and he ail o he double-deck unnel sec ion unde
s udy ha e been also ca ied ou . The aim o including hese
simula ions is o demons a e he capabili ies o he p oposed
ha es e in unde g ound ailway applica ions om a global
pe spec i e.
The expe imen ally measu ed ailway-induced ib a ion
signals (a he in e io loo , w all, a nd ail) co espond
o andom ib a ions mainly gene a ed by he wheel- ail
con ac o passing ains. The e o e, he elec ical esponse
o he ha es e o hese ib a ions also co esponds o a
ansien andom induced ol age. To simula e he esponse
o he EMVEH o hese ansien andom signals, a nume ical
ime-domain algo i hm implemen ed in Simulink has been
de eloped based on he go e ning equa ions and modeling
app oach p esen ed in O do˜nez e al. (2022); O do˜nez e al.
(2021); O donez e al. (2021). A ho ough e iew o he
heo y and go e ning equa ions unde lying he employed
simula ion me hodology is p esen ed in Appendix A o
he eade ’s con enience. In his p oposed implemen a ion,
he physical modeling blocks o he Simscape ex ension o
Simulink ha e been employed o ep esen some o he ac ual
6
Figu e 5. Diag am o he nume ical algo i hm implemen ed in Simulink o compu ing he ansien induced ol age o he
ab ica ed ha es e model o an open ci cui ope a ion case and inpu andom ib a ions.
Figu e 6. Diag am o he nume ical algo i hm implemen ed in Simulink o compu ing he ansien load ol age and ou pu powe
o he ab ica ed ha es e model o a closed ci cui ope a ion case and inpu andom ib a ions.
passages numbe s 8 and 98), and he emaining one is
ela ed o a lowe deck ain passing ( ain passage 49).
The ailway-induced ib a ions and EMVEH esponses
gene a ed by he men ioned ains a e illus a ed in Figs. 10
and 11, espec i ely. The ime his o ies a e p esen ed in a
conca ena ed iew o compa ison pu poses. As app ecia ed
in Fig. 10(a), he e ical ailway-induced ib a ion can each
peak ampli udes o up o 0.7 g, while he ASD o each
o he chosen passing ains, depic ed in Fig. 10(b), allows
o de e mining ha he mos dominan equencies o he
in e io loo esponse a e 49.2 Hz, 36.9 Hz, and 54.3 Hz,
espec i ely. Besides, Fig. 11(a) shows ha esponses o he
sou ce. Ne e heless, he na u al equency o his de ice
has been designed wi hou knowing hese pa icula alues,
bu modi ying i o his o any o he applica ion (once he
dominan equencies a e iden i ied) i s a s imple ask ha
mainly in ol es edesigning he helical comp ession sp ing
pa ame e s.
E en hough a ela i ely consis en pa e n was obse ed
when analyzing he 139 ailway-induced ib a ion esponses,
he ib a ion signals induced by h ee non-consecu i e ain
passages wi h clea ly di e se ampli udes and dominan
equencies we e selec ed. Two o hese chosen e en s a e
associa ed wi h ains passing by he uppe deck ( ain
RESULTS AND DISCUSSION 7
8 10 12.5 16 20 25 31.5 40 50 63 80
F equency (Hz)
Accele a ion (dB e . 10-6 g)
0 20 40 60 80
F equency (Hz)
$6' (g/Hz)
ED
40
60
80
100
120
0
0.2
0.4
0.6
0.8
Figu e 7. Railway-induced ib a ion esponse (a e age accele a ion eco ded by Acc1 and Acc2) o he 69 passing ains on he
lowe deck in e ms o (a) accele a ion spec al densi y and (b) one- hi d oc a e bands. G ey lines ep esen he esponse o each
passing ain, while black lines co espond o hei a e age.
8 10 12.5 16 20 25 31.5 40 50 63 80
F equency (Hz)
Accele a ion (dB e . 10-6 g)
0 20 40 60 80
F equency (Hz)
$6' (g/Hz)
ED
40
60
80
100
120
0
0.2
0.4
0.6
0.8
Figu e 8. Railway-induced ib a ion esponse (a e age accele a ion eco ded by Acc1 and Acc2) o he 70 passing ains on he
uppe deck in e ms o (a) accele a ion spec al densi y and (b) one- hi d oc a e bands. G ey lines ep esen he esponse o each
passing ain, while black lines co espond o hei a e age.
8 10 12.5 16 20 25 31.5 40 50 63 80
F equency (Hz)
60
80
100
120
140
Accele a ion (dB e . 10-6 g)
8 10 12.5 16 20 25 31.5 40 50 63 80
F equency (Hz)
-100
-80
-60
-40
-20
0
20
Induced Vol age (dB e . 1 V)
DE
Figu e 9. The one- hi d oc a e band spec a o he mechanical and elec ical esponses o he EMVEH p o o ype o he 139
passing ains in e ms o (a) he accele a ion eco ded by Acc3 and (b) he induced ol age. G ey lines ep esen he esponse o
each passing ain, while black lines co espond o hei a e age.
I is in e es ing o no ice how simila he accele a ion
and induced ol age cu es o he EMVEH a e, showing
he linea i y o he ans o ma ion p ocess om kine ic
o elec ical ene gy o he p o o ype, as well as i s high
sensi i i y. Also, as obse ed in Fig. 11, he expe imen al
esul s o he mechanical and elec ical esponses o he
oscilla ing mass can each peak ampli udes o up o 5.6 g,
whe eas Fig. 11(b) illus a es he expe imen ally measu ed
induced ol age o he ab ica ed EMVEH o an open ci cui
ope a ion case, wi h a maximum peak ampli ude o almos 4
V.
8
0 20 40 60
Time (s)
-1
-0.5
0
0.5
1
Accele a ion (g)
a)
WKW ain WKW ain 9WKW ain
0 20 40 60 80
F equency (Hz)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
A6' (g/Hz)
b)
I
n
49.2 Hz
I
n
54.3 Hz
I
n
36.9 Hz
Figu e 10. Railway-induced ib a ion esponse a he EMVEH p o o ype loca ion (a e age accele a ion eco ded by Acc1 and
Acc2). (a) Time his o ies o he selec ed samples. (b) Accele a ion spec al densi y o he ib a ion induced by each passing ain
sample.
0 20 40 60
Time (s)
-6
-2
-4
0
2
4
6
Accele a ion (g)
a)
0 20 40 60
Time (s)
-5
0
5
Induced Vol age (V)
b)
Figu e 11. Time his o ies o he mechanical and elec ical esponses o he ab ica ed p o o ype o he h ee ain samples unde
s udy. (a) The expe imen ally measu ed accele a ion eco ded by Acc3. (b) The expe imen ally measu ed induced ol age.
RESULTS AND DISCUSSION 9
Simula ion and alida ion o he
equency-un uned EMVEH on he in e io loo
To alida e he p oposed simula ion models p esen ed in
he p e ious sec ion, he induced ol age esponses o he
ab ica ed p o o ype ha e been simula ed, and he esul s
ha e been compa ed wi h he expe imen al measu emen s
ca ied ou . Hence, a na u al equency o 61.7 Hz has been
employed in hese simula ions, co esponding o he exac
na u al equency o he p o o ype. The expe imen al and
simula ed induced ol age esul s o he p oposed ha es e
on he in e io loo loca ion o he h ee ain passages
selec ed a e p esen ed in Fig. 14. This igu e allows o
de e mining ha a good app oxima ion has been eached
by he simula ion in e ms o ampli ude and shape. This
can be app ecia ed in mo e de ail in he mo ing RMS
(mRMS) esul s, which a e shown o bo h simula ed and
expe imen al signals in he same igu e. The mRMS has been
calcula ed conside ing an in eg a ion ime o one second.
Also, he RMS induced ol age o each passing ain has
been compu ed and p esen ed in Table 1 o bo h he
expe imen al and simula ed esul s as a e e ence alue o
es ima e he ela i e e o o he simula ion. In his manne ,
he p oposed nume ical algo i hm, implemen ed in Simulink,
is alida ed o es ima ing he gene a ed ol age o a SDOF
EMVEH subjec ed o andom ib a ion wi h a maximum
de ia ion o abou 13.58%. I is ound ha one o he main
easons o hese disc epancies be ween he expe imen al
and simula ion esul s is he obse ed sligh changes in he
mechanical damping o he sys em each ime he ha es e
p o o ype is eassembled.
Mo eo e , Fig. 15 illus a es he esul s o he simula ion
o he load ol age and elec ical ou pu powe . The load
esis ance alue u ilized in his simula ion co esponds o
10910 Ωsince i was p e iously de e mined as he op imal
load esis ance o his de ice (O do˜
nez e al. 2022). Fo
hese pa icula samples, a maximum peak ampli ude o
app oxima ely 3.45 V and 1.10 mW a e obse ed o he load
ol age and elec ical ou pu powe , espec i ely, while he
elec ical ene gy gene a ed by he EMVEH o each sample
o passing ains numbe s 8, 49, and 98 has been es ima ed o
be 0.98 mJ, 0.34 mJ, and 0.43 mJ, espec i ely. Ne e heless,
i is ele an o emind he eade a his poin ha he
cumula i e ene gy ha es ed by he EMVEH in esponse o
he 139 passing ains o each case s udy and loca ion will
be p esen ed a he end o his sec ion.
Simula ions o he equency- uned EMVEH
In e io loo loca ion: Fo simula ions o he equency-
uned case, he na u al equency o he ab ica ed p o o ype
model is now se o 49.2 Hz o ma ch he mos dominan
equency when analyzing he a e age ASD o all 139
passing ains, which coincides wi h he mos dominan
equency o he h ee e alua ed exci a ion samples. The
esul s o hese simula ions a e depic ed in Fig. 16, om
which i can be obse ed ha he load ol age and ou pu
powe induced by he ib a ions gene a ed by he passage
o ains numbe s 8 and 98 a e d ama ically highe han
hose gene a ed by ain numbe 49. The explana ion o his
beha io educes o he dominan equencies o he ib a ion
signal o ain 49, p e iously ound o be occu ing a ound
ha es e mainly ampli y he signal co esponding o ain
numbe 8 when i s mos dominan equency (49.2 Hz) is
a he om he na u al equency o he ha es e (61.7 Hz)
han ha o ain numbe 98 (54.3 Hz). The explana ion o
his beha io is ela ed o he highe peaks o ain numbe 8
in he ange o 60 Hz o 63 Hz han hose co esponding o
ain numbe 98.
Wall loca ion: Following he same c i e ia and p ocedu e
as wi h he in e io loo loca ion, he 139 ailway-induced
ib a ion measu emen s on he wall ha e been di ided as
hey co espond o ains passing h ough he uppe and
lowe decks o he unnel. The ib a ion signals induced
by h ee non-consecu i e ain passages we e chosen o
hei pa icula s udy, and ime his o ies a e p esen ed in
a conca ena ed iew o compa ison pu poses ( he same
p ocedu e is also employed o he ail loca ion exhibi ed in
he ollowing subsec ion). Fig. 12 illus a es he expe imen al
adial ailway-induced ib a ions on he unnel wall o he
selec ed samples consis ing o he same h ee passing ains
p e iously analyzed in he case o he ha es e placed on
he in e io loo o he d ouble-deck unnel. A s obse ed
in Fig. 12(a), low ib a ion le els a e occu ing a he
unnel wall, wi h a maximum peak ampli ude o abou
0.035 g, co esponding o almos 20 imes less ampli ude in
compa ison o he maximum peak accele a ion ampli ude o
he h ee ain samples a he in e io loo . Besides, he ASD
o each passing ain sample, shown in Fig. 12(b), allows o
de e mining ha hei mos dominan equencies a e 67.7
Hz, 67.6 Hz, and 67.7 Hz, espec i ely.
Rail loca ion: The expe imen ally measu ed e ical
ailway-induced ib a ions on he ail a e depic ed in Fig.
13. In con as o he samples employed in he in e io
loo and unnel wall e alua ions ( ains numbe s 8, 49, and
98), he samples used o he ail loca ion co espond o
ains going only h ough he uppe deck, meaning ha ain
numbe 49 has been eplaced by ain numbe 50. The eason
o his decision is ha he ib a ion esponses on he uppe
deck ail due o ains passing h ough he lowe deck a e
d as ically lowe (Clo e al. 2016) compa ed o hose going
h ough he uppe deck, as one could expec , and illus a ing
hese signals in he same plo o e s no isual in o ma ion.
None heless, lowe deck ains will be conside ed in he
inal cumula i e elec ical ene gy es ima ion. As app ecia ed
in Fig. 13(a), accele a ions a he ail can each maximum
peak ampli udes o a ound 30 g, a exceeding he peak
accele a ions a he wall and in e io loo . Ye , hese e y
high ampli udes seem o be an ex ao dina y esponse
occu ing only o he ib a ion measu emen s o ain
numbe 8, which can occu due o he a iabili y in wheel
oughness, axle weigh s, and e en sligh a ia ions in he
ain speed, b aking, o accele a ion pa e ns passing h ough
he si e unde s udy. Howe e , e y high peak ampli udes
o app oxima ely 10 g a e also obse ed in esponse o he
passage o ains 50 and 98. Addi ionally, he mos dominan
equencies o he samples unde s udy a e ound o be 58.4
Hz, 58.5 Hz, and 70.8 Hz o he passing ains numbe s 8,
50, and 98, espec i ely.
16
(Sp eemann and Manoli 2012). Fig. 20 depic s he ci cui
ep esen a ion o he elec omagne ic subsys em connec ed
in se ies o a load esis ance Rl(Beeby and Kazmie ski
2011). The go e ning equa ion o his ci cui , hen, can be
exp essed as
Lc
di( )
d + (Rc+Rl)i( ) = ε( ),(3)
in which Lcis he coil induc ance, i( )is he cu en lowing
h ough he coil, and Rcis he coil esis ance. By neglec ing
he coil induc ance unde he assump ion o low equencies
o ib a ion, he cu en can be ound o be
i( ) = k ˙z( )
Rc+Rl
,(4)
which leads o ha he ol age Vlac oss he load esis ance
and he co esponding elec ical ou pu powe Pou can be
es ima ed as
Vl=Rl
Rl+Rc
k ˙z( ),(5)
and
Pou =V2
l
Rl
.(6)
Figu e 20. Ci cui diag am ep esen a ion o he
elec omagne ic subsys em o he ene gy ha es e .
Acco ding o Lenz’s law, a eedback elec omagne ic o ce
Feis gene a ed due o he cu en lowing h ough he coil,
and i can be w i en as (Williams e al. 2001)
Fe=k i( ) = k2
Rc+Rl
˙z( ).(7)
The elec omagne ic o ce can also be exp essed as a
p oduc o he elec omagne ic damping coe icien and
he ela i e eloci y o he oscila ing mass. Consequen ly,
he elec omagne ic damping coe icien induced by he
elec omagne ic subsys em o he ansduc ion mechanism
can be ound o be (Saha 2011;Thein e al. 2019)
ce=k2
Rc+Rl
.(8)
The maximum powe ans e heo em would lead one o
se Rl=Rc o ob ain maximum elec ical ou pu powe .
S ill, ha app oach does no conside he e ec o he
elec omagne ic damping on he mechanical beha io . In
u n, he op imal load esis ance ha maximizes he ou pu
powe o an EMVEH is gi en by (M¨
osch and Fische aue
2019)
Rl=Rc+k2
cm
.(9)
Ene gy ha es ing pe o mance
To quan i y he pe o mance o a VEH, Beeby e al.
(2007) ha e p oposed a o mula o NPD. I consis s o he
gene a ed elec ical ou pu powe , no malized o he squa e
o he inpu accele a ion ampli ude o ib a ion ¨
Yand he
ha es e ’s o al olume V, as
NPD =Pou
¨
Y2V.(10)
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