1
Vol.:(0123456789)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s
Assessmen o pa emen de lec ion
unde ehicle loads using a 3D‑DIC
sys em in he ield
Ca los Núñez‑Temes1, Guille mo Bas os1*, Ma cos A za‑Ga cía1, Albe e Cas o1,
Jose An onio Lo enzana Fe nández2, Juan O iz‑Sanz1, Ma ía Po ela2,
Ma iluz Gil‑Docampo & F ancisco Ja ie P ego3
This s udy aims o in oduce he use o 3D‑digi al image co ela ion (DIC) o he in si u es ing o
pa emen s and o suppo he de elopmen o echniques o a apid e alua ion o he conse a ion
s a us o exis ing oads. Li le esea ch was ound on his opic. The passage o a ca wheel on an
asphal pa emen was adop ed as a case s udy. The DIC measu emen s we e compa ed o hose
ga he ed by con ac senso s. F om a quali a i e poin o iew, he DIC measu emen s cap u ed he
ealis ic shape o a de lec ion basin. F om a quan i a i e poin o iew, he de lec ion alues p o ided
by he DIC sys em had a mean e o o 0.015 mm and a s anda d de ia ion o 0.011 mm. A he
momen o highes load, hese e o s had a mean alue and s anda d de ia ion o − 0.016 mm and
0.021 mm, espec i ely. Thus, o imp o e he accu acy o he sys em, we p opose modi ying he
came a suppo , speckle pa e n, and con ol o na u al ligh .
Roads a e key public in as uc u e since hey cons i u e a basic equi emen o he social and economic de elop-
men o any coun y1. Roads equi e p ese a ion, main enance, epai and ehabili a ion2,3. To plan and pe o m
hese ac ions, eliable in o ma ion is needed abou he s a us o p ese a ion o oads.
The challenging aspec o oad assessmen lies in i s s uc u al s a e. The adi ional echniques o s udy-
ing he mechanical p ope ies o bi uminous pa emen s and conc e e consis o labo a o y es ing o samples
by using ex ensome e s, s ain gauges, and linea - a iable di e en ial ans o me senso s o measu e sample
de o ma ion4–7.
The insi u modulus and c i ical s esses and s ains o pa emen s ha e been de e mined by measu ing he
e ical de lec ion o pa emen wi h alling weigh de lec ome e s since he 1970s8 and as alling weigh de lec-
ome e s since 20159. The p esen pape desc ibes de lec ion measu emen s o asphal pa emen using he digi al
image co ela ion (DIC) echnique o explo e he easibili y o pe o ming es s in he ield wi h he accu acy o
labo a o y echniques. Ou objec i es we e o explo e he in oduc ion o DIC echnology o es ing pa emen
in he ield and, in pa icula , o accu a ely measu e he de o ma ion o asphal pa emen h ough 3D-DIC (also
known as s e eo-DIC).
Backg ound on es ing pa emen in he ield. Se e al insi u nondes uc i e es ing p ocedu es o
pa emen a e a ailable. The main p inciple consis s o applying a load o known alue o he pa emen and
analyzing he di ec ion and size o he induced de o ma ion10. The mos common de o ma ion is in he e ical
di ec ion11–13.
In ield es s, he e a e h ee ypical me hods o de lec ion measu emen : s a ic load-based de lec ome e ,
which p o ides he maximum de lec ion unde a s a ic load14; s a iona y dynamic impac de lec ion measu e-
men , as he alling weigh de lec ome e (FWD)15; and mo ing dynamic de lec ion measu emen , e.g. he lase
dynamic de lec ome e (LDD), which cap u es he de lec ion along a line on he pa emen as he ehicule
mo es16,17. Though he s a ic load-based Benkelman beam has been used ex ensi ely in India and se e al o he
coun ies o s uc u al e alua ion o in-se ice pa emen s, he FWD is conside ed o be he mos app op ia e
equipmen 14,18.
OPEN
1CIGEO – Ci il and Geoma ics Resea ch G oup, Ag o o es y Enginee ing Depa men , Uni e si y o San iago de
Compos ela, Highe Poly echnic School (Lugo), 27002 Lugo, Spain. 2PEMADE – Resea ch Pla o m on S uc u al
Wood Enginee ing, Ag o o es y Enginee ing Depa men , Uni e si y o San iago de Compos ela, Highe
Poly echnic School (Lugo), 27002 Lugo, Spain. 3Depa men o R+D+I o Mis u as, S.A., O ense, Spain. *email:
[email p o ec ed]
2
Vol:.(1234567890)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
Me hods applying s a iona y dynamic loading allow he measu emen o he de lec ion basin unde s eady-
s a e loads o impac s. This ype o equipmen consis s o an oscilla ing o ce gene a o , a calib a ion uni and
se e al de lec ion-measu ing de ices ( ansduce s, accele ome e s, seismome e s, e c.)19,20. The FWD is he
accep ed wo ldwide s anda d15,21. I is moun ed in a ehicle ha mus be s a iona y o pe o m a es a he desi ed
loca ion20. The FWD impa s a dynamic load o a pa emen s uc u e; he dynamic load is simila in magni ude
and du a ion o ha o a mo ing wheel load, ypically 50 kN22,23, and anging om 7 o 150 kN o he s anda d
FWD24. A ligh e sion (LWD) applies 1–15 kN and a ious hea y e sions (HWD) apply up o 250 kN25. The
peak de lec ions a each es loca ion a e measu ed in mic ome e s. Fi s in oduced in Eu ope, FWD has been in
use in he Uni ed S a es since he 1980s21. The U.S. Fede al Highway Adminis a ion websi e p o ides in o ma-
ion abou he mos commonly used s eady-s a e de ices and FWDs19. FWDs use a ealis ic simula ion o ac ual
wheel loading and ha e he abili y o measu e load ans e ac oss join s and c acks26.
Howe e , FWDs also ha e d awbacks; hei s a iona y ope a ing mode limi s he co e age o a es si e in a
gi en ime, and in e up ions due o s op-and-go ope a ions can dis u b a ic and cause haza dous condi ions.
To con inuously measu e pa emen de lec ions a highe speeds, ex ensi e e o s ha e been ca ied ou o e
he pas decades o de elop me hods using mo ing ehicula loads and con inuous p o iling de ices15. Some
o bo h s a iona y dynamic loading27 and mo ing dynamic loading de ices15 adop ed he es p inciple o he
Benkelman beam es . Some examples a e he a ic speed de lec ome e (TSD)28,29, olling weigh de lec ome e
(RWD)30,31, olling dynamic de lec ome e (RDD)32,33, and oad de lec ome e (RDT)34. Elsei i e al.35 compa ed
hese de ices and ound ha he RDT and he RWD can acqui e da a while mo ing a 96.6km/h wi h de lec ion
accu acies o 0.25mm and 0.064mm, espec i ely.
Cu en ly, new measu emen echniques a e gaining momen um o cha ac e izing he e ogeneous ma e ials36.
In pa icula , DIC sys ems a e inc easingly used in es ing in ci il enginee ing labo a o ies37 and o de e mining
asphal mic os uc u e38,39, s udying c ack ini ia ion and damage dis ibu ion40,41, and alida ing models42,43.
In oduc ion o DIC. As he equi emen s o in o ma ion abou a specimen inc ease, he la ge-scale
deploymen o wi ed s ain gauges becomes mo e labo ious and expensi e. In addi ion, s ain gauges a e suscep-
ible o d i and damage44. To add ess hese limi a ions, DIC was in oduced in he 1980s as a con ac less sens-
ing me hod ha eco ds g ayscale digi al images du ing he loading o a specimen and applies image p ocessing
echniques o es ima e he ull- ield de o ma ion o he specimen45.
The basic ope a ion in DIC in ol es acking poin s (o pixels) in consecu i e pho os. He e ogeneous ma e i-
als can ha e su ace ea u es ha su ice as a na u al pa e n ha acili a es his acking. Howe e , an a i icial
pa e n, called a speckle pa e n, is usually applied o he su ace o acili a e image co ela ion. Fo each pai o
images, ma ching is pe o med be ween subse s o he speckle pa e n. The subse s a e usually squa e bu can also
be con o mal, in o de ha geome ies cap u e he ou line o a pa icula pa o egion46. Two key pa ame e s
in a DIC calcula ion a e he subse size and s ep size47. The subse size is c i ical o he accu acy o he compu ed
displacemen s48. A e he ull- ield displacemen s a e e alua ed, spa ial s ains a e gene ally compu ed om he
displacemen s wi h a spa ial de i a i e49,50.
Since he in oduc ion o he i s DIC echnology, he quali y o he digi al images and p ocessing algo i hms
ha e imp o ed eno mously. Due o i s lexibili y and a e y simple measu emen se up ( wo synch onized cam-
e as and ligh ing), DIC echniques a e applied widely, no only in he ield o enginee ing bu also in medicine,
mul imedia, conse a ion o cul u al he i age, e c.51. Cu en ly, DIC me hods wi h high sensi i i y and accu acy
a e u ilized o es ing specimens and, mos ecen ly, o es ing whole s uc u es. I is possible o ob ain sub-pixel
accu acy o DIC measu emen s by means o in e pola ion o image in ensi y be ween pixels. Mos comme cial
DIC packages in eg a e op imized in e polan s, allowing o de ec image a ia ions up o 0.02 pixel. Depending
on he scene con igu a ion, his esolu ion le el could e en each sub-mic on accu acies52.
Resea che s ha e p o ed he u ili y o DIC o measu ing de o ma ions in labo a o y es ing o wood53,
conc e e54, mason y55, glass panels o cu ain walls56, and composi es57, e c. Measu emen s using DIC in he ield
a e becoming mo e widesp ead, including applica ions in me al addi i e manu ac u ing58,59, welding-induced
de o ma ions60, ees61,62, he mal ba ie coa ings63, and ai c a c ashes64, om he mic o- o he s uc u al
scale65. Se e al insi u expe imen s we e ca ied ou also in ci il enginee ing on conc e e b idges66; o he la ge
s uc u es67; diaph agm walls, which a e used as a suppo o deep exca a ions68; and displacemen s and s ains
o pipelines due o empe a u e a ia ions o he luid68.
Se e al au ho s ha e discussed he a ac i eness o DIC o es ing pa emen s. In ac , his echnique has
been applied success ully in he labo a o y in comp ession es s69,70, a igue es s71, shea es s72 and indi ec
ensile es s73,74. Howe e , ew s udies ha e been pe o med in he ield37. DIC has al eady been es ed on mo -
ing ehicles by Shoop e al.75 and in s uc u al moni o ing. These au ho s used DIC o cap u e he oughness o
e ain a he millime e scale, as hei objec i e was o imp o e he maneu e abili y o ehicles by moni o ing
he oad o e ain su ace be o e and a e a i e passes o e i . The high spa ial esolu ion achie able wi h DIC,
could allow o measu e he pa emen de lec ion induced by con en ional ehicle loads. This would ep esen a
key ad an age o DIC o e o he majo pa emen assessmen echniques men ioned abo e, and would make i
possible o dispense wi h he use o hea y owed equipmen . Ne e heless, his echnology is no ye being used
o i s highes po en ial as a eliable and lexible me hod o measu ing displacemen s and s ains a high spa ial
esolu ion in he ield76.
3
Vol.:(0123456789)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
Ma e ials and me hods
This s udy examined a pa emen buil nea he asphal plan owned by he pa ing company Ex aco S.A. in no h-
wes Spain (42.204193° la i ude and − 7.791827° longi ude), in a conso ium o h ee mo e p i a e o ganiza ions
and wo uni e si y esea ch g oups. The pa emen was buil as an expe imen al s e ch o 25m long and 3.5m
wide, wi h he geome y o a con en ional oad lane.
The pa emen sec ion adop ed (Fig.1a) consis s o a 5cm wea ing cou se o ho bi uminous mix AC 16 su
50/70 D (acco ding o he Spanish s anda d UNE-EN 13108-1:2019) wi h a bi umen con en o 5.0% and wi h
0.5% o he addi i e ich in lignin, a 5cm in e media e laye wi h a ho bi uminous mix AC 22 su 50/70 D
wi h a bi umen con en o 5.0% and wi hou addi i es, and a 16cm base laye based on a i icial g a el ZA 0/32.
The sub-base was made up o a 20cm laye o soil s abilized insi u wi h also 2% o he lignin- ich addi i e. A
geo ex ile sepa a es he buil laye s om he na u al g ound. The co-p oduc ich in lignin om he eucalyp us
wood panel indus y77 was added in he ho bi uminous mix, aiming o educe he p opo ion o binde . The
objec o s udy o ha p ojec was o know how his addi i e a ec s he wo kabili y o he mix, he cons uc ion
o he pa emen and i s long- e m beha io .
A speckle pa e n was sp ayed on he moni o ed egion o in e es o he pa emen , using a ine ae osol
whi e coa ing ollowed by a spo dis ibu ion o black pain (25–40% o co e age). The DIC equipmen was he
comme cial A amis 3D sys em by GOM GmbH (B aunschweig, Ge many), wi h dual 12M e 03 came as and
Ti ana B 24-mm lenses. As shown in Fig.1b, he DIC came as we e moun ed on ipods. The came as ha e
12-megapixel esolu ion and a maximum image cap u ing a e o 25 ps a maximum esolu ion78, and he angle
be ween hei op ical axes was 25.2°.
The i s s age in he gene al wo k low o s e eo-DIC (Fig.2) is he sys em calib a ion ( equi ed o s e eo
iangula ion). Fo each came a o a ypical s e eo-pai , calib a ion aims o ind he in insic pa ame e s (de ining
he geome ic and op ical cha ac e is ics o he came a) and he ex insic pa ame e s (de ining he posi ion and
he o ien a ion o he came a wi h espec o a e e ence coo dina e sys em). These pa ame e s can be calcula ed
h ough he compa ison o op ically measu ed de o ma ions and heo e ical p edic ions, o which images o
a calib a ion pla e wi h known dimensions a e no mally used. In pa icula , A amis 3D uses i s own in-house
calib a ion pla e wi h a egula g id o do s and au o-de ec able coded a ge s and a speci ic calib a ion ou ine
based on he Bundle Adjus men (BA) me hod. The use is equi ed o ake a se ies o s e eo pai s o images by
a ying he posi ion o he pla e ( o a ions and ansla ions). BA allows o he es ima ion o bo h he in insic
and ex insic came a pa ame e s by using hese epe i i e obse a ions o spa se scene poin s in hose di e en
iewing di ec ions79,80. Toge he , he in insic and ex insic pa ame e s se e o desc ibe he ans o ma ion ha
maps each 3D ma e ial poin P in he global coo dina e sys em in o i s image poin on he came a senso 81. As
hese pa ame e s (came a poses) de ine o hemsel es he ela ionships be ween he image space and he 3D
space, he e is some lexibili y wi h ega ds o calib a ing he came as ou side o he ac ual expe imen al se up.
Fo his eason, he came as can i s be calib a ed in a ho izon al posi ion (Fig.2a) and o ien ed owa ds he
pa emen a e comple ing he p ocedu e.
The second s age o DIC p ocessing consis s in acking he speckled pa e n in he sequence o s e eo-images
o he su ace du ing he es . This p ocess in ol es mul iple 2D-DIC co ela ion uns, including c oss-pai and
Figu e1. Expe imen al se up: (a) diag am o pa emen s uc u e and da a acquisi ion sys ems, and (b) o e all
se up o he equipmen used o moni o he wheel load.
4
Vol:.(1234567890)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
c oss-came a subse ma ching, whe e he image om one came a is he e e ence image and he image om
he o he came a is he de o med image. Du ing his p ocess, he so wa e co ela es homologous poin s along
he whole da ase , iden i ying hei coo dina es in each o he images. Then, he calib a ion pa ame e s om
s age 1 a e used o pe o m a s e eo- iangula ion which ans o ms he 2D poin s ma ched in s age 2 o each
s e eo-pai in o poin clouds. In o de o ob ain a mo e e icien 3D da a analysis, poin clouds a e con e ed o
iangula meshes. The su ace displacemen s along he es can inally be ob ained by using 3D su ace com-
pa ison algo i hms.
Da a was acqui ed on a sunny and windless day, wi h empe a u es anging om 17.1 o 23.6°C, alling
wi hin he ecommended ange o DIC ope a ion83. The majo p oblems wi h he empe a u e in indoo DIC
expe imen s usually occu because almos all came as and ligh s become ho e han oom empe a u e when
un con inuously. Ou doo s, his p oblem should be in pa minimized, bu ins ead, o he ele an issues ha
could in oduce e o s in DIC esul s may a ise. Some o hese po en ial issues a e he he mal expansion o he
componen s o he came as, he lenses, o he moun ing s uc u es and he induced con ec i e ai cu en s. In
ha sense, se e al p ecau ions ha e been aken o p e en possible e o s. The came as and o he equipmen we e
no calib a ed o used o ake measu emen s un il hey ha e eached a s able ope a ing empe a u e in he ield
(a leas 15min). On he o he hand, he ligh ing equi ed o DIC may in oduce hea wa es ha could e ac
ligh be ween he es su ace and he imaging sys em. A special “cool” (blue) LED sou ce wi h an in eg a ed an
was used (Fig.1b) o minimize his e ec .
We also eco ded he de lec ion alues h ough ou 1-µm-p ecision ex ensome e s, which we adop ed as
he e e ence. In addi ion, ou e e ence poin ma ke s ( ie poin s) we e a ached o hese senso s o ead hei
displacemen acco ding o he DIC de ice, as p esen ed in Fig.3. Ex ensome e 1 was closes o he loaded a ea.
The compa ison o he DIC eadings a hese poin s wi h he eadings p o ided by he ex ensome e s allowed a
di ec assessmen o he ag eemen be ween he DIC de ice and he con ac senso s.
The minimum dis ance be ween he middle poin be ween he came a lenses and he loaded g ound was
380mm. The measu ed a ea had a wid h o 195mm and a maximum leng h o 205mm app oxima ely, which
dec eased du ing he es o he minimum leng h o 145mm, because he wheel pa ially obs uc s he iew o
Figu e2. Wo k low wi h he co e s eps in s e eo-DIC p ocessing: (a) S e eo calib a ion p ocedu e o ind
in insic and ex insic pa ame e s o he op ical sys em; (b) c oss-co ela ed 2D-DIC and (c) 3D-DIC pos -
p ocessing o calcula e 3D coo dina es o he iangula mesh’s e ices and o de i e he ull- ield displacemen s.
Adap ed om A za e al.82.
5
Vol.:(0123456789)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
he came as. The ex ensome e s we e a ached o a squa e aluminum beam, and hey we e lowe ed un il hey
made con ac wi h he asphal pa emen .
The loading wheel was ini ially placed 2280mm om he DIC-moni o ed a ea. The pa emen was loaded by
a pass o a mo ing ca , mo e speci ically h ough one o i s wheels, wi h a load o app oxima ely 3.8 kN. The i e
co e ed an app oxima ely ec angula a ea o 135mm in he di ec ion o mo ion and 190mm in he o hogonal
di ec ion. The pass o he wheel s a ed a e he con ac senso s s abilized.
Resul s and discussion
A e he sensing equipmen was u ned on and he ex ensome e s s abilized, he ehicle mo ed a app oxima ely
78mm/s. The DIC sys em acqui ed he images wi h a shu e speed o 1/500s and a a equency o 0.5 images
pe second, esul ing in a o al o 21 images. The e o e, in e ms o DIC p ocessing, we conside 20 ime “s eps”,
as he so wa e ma ches he pa e n be ween he e e ence image ( i s ) and he o he ones, compu ing he dis-
placemen s o he pa e n in each one o hese momen s.
The noise- loo was measu ed ac oss he e ical de o ma ion along a line pa allel o he wheel mo ion (see
Fig.4). This noise is a mul iple o he spa ial s anda d de ia ion o he quan i ies-o -in e es (QOI) compu ed
unde condi ions in which he QOI should be ze o. I does no e lec any sys ema ic bias e o s ha may be
Figu e3. GOM’s au o-de ec able a ge s ( ie poin s) a ached o he ex ensome e s.
Figu e4. The line ac oss which he noise- loo was e alua ed.
6
Vol:.(1234567890)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
p esen in he QOI, bu only he andom a iance e o o he QOI83. In his case, he QOI is he de lec ion. We
ob ained he noise- loo by aking he i s 9 s eps. They a e conside ed quasi-s a iona y, wha is co obo a ed no
only by he DIC images, bu also by he eadings o he ex ensome e s. These eadings indica e ha signi ican
de lec ion (> 0.01mm) a e only de ec able om s ep 12 onwa ds. A ep esen a i e sample o he noise- loo is
p esen ed o h ee s eps in Fig.5a–c. In s ep 6 (Fig.5c), he wheel axle was a 1728mm on he X axis. In hese
g aphs, he de o ma ion eached a posi i e peak o 0.29mm and a nega i e peak o − 0.09mm. The Q-Q plo
(Fig.5d) o hese da a e eals ha hey i a no mal dis ibu ion. The z-sco e o hese ex eme alues anged
Figu e5. Noise baseline compu ed om DIC p ocessing. Sample o ini ial s eps no a ec ed by he wheel load:
(a) S ep 2; (b) S ep 4; (c) S ep 6; (d) he Q-Q plo o s ep 2.
7
Vol.:(0123456789)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
om 2.4 o 8.4. We hypo hesize ha his was he esul o ame misma ching due o he po en ial poo quali y
o he speckle pa e n in some speci ic a eas. In ac , du ing he unloaded s eps, he de lec ion in some o hese
a eas al e na ed be ween posi i e and nega i e alues, as shown in Fig.5. These anomalous da a we e a oided by
applying in he DIC so wa e a median il e o h ee poin s o he alues o displacemen . In hese ini ial s eps,
he de ec ed de lec ions a e no ela ed o he pa emen load.
Wi h ega d o he noise in he de ec ion o he ie poin s (au o-de ec able a ge s), in he ou i s S eps, when
he ca wheel eached a dis ance o he senso s o 1.85m, he epo ed alues had a mean o absolu e alues o
1.2µm and a s anda d de ia ion o 1.1µm. The maximum absolu e alue was 3.3µm, which is he 4.3% o he
maximum alue epo ed.
An adequa e balance be ween exposu e ime and he mo ing eloci y is essen ial o limi mo ion blu in DIC.
The noise- loo can be conside ed he mos conse a i e es ima e o he maximum allowable objec mo ion
o e he cou se o he exposu e ime83. In his case, he es ima ed displacemen pe exposu e is almos negligible
(~ 0.4µm) and much lowe , in any case, han he noise- loo (conside ing a e y conse a i e es ima e o he
displacemen eloci y o he poin s on speckled pa e n (~ 0.2mm/s) and he exposu e ime employed (1/500s)).
A sample o ep esen a i e load condi ions is p esen ed in Fig.6a–i. The cap u ed de o ma ion becomes mo e
e iden in s ep 11, as i can be seen in Fig.6c. In iew o he images o s ep 13 and s ep 16, he came as cap u ed
no only he pa emen nex o he i e bu also pa o he a ea behind and on o he i e, espec i ely.
The a ia ion wi h ime o he poin P (in oduced in Fig.6) is shown in Fig.7. This igu e also con ains he
posi ion o he wheel o e he es , h ough i s X coo dina e.
The de lec ion in he e ical di ec ion is displayed in Fig.8 along se en cu es spaced 30mm apa .
These cu es a e he in e sec ion be ween he pa emen su ace and e ical planes ha a e pa allel o he
ex ensome e s.
The e ical displacemen along he se en cu es is shown in Fig.9 o s ep 16, which cap u ed he deepes
basin. The de lec ion o he pa emen unde he senso s was calcula ed by in e pola ing he DIC-based cu es.
Figu e6. Rep esen a i e de lec ion condi ions cap u ed by he DIC sys em. The di ec ion o wheel mo ion is
he X-axis and he bo de o he pa emen con ac a ea coincides app oxima ely wi h Y = 160mm. The poin P is
he closes poin in which measu es we e eco ded in all s eps.
8
Vol:.(1234567890)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
Time
s ep
ime
(s)
X coo dina e
(mm)
12 -2040
24 -1884
36 -1728
48 -1572
510-1416
612-1260
714-1104
816-948
918-792
10 20 -636
11 22 -480
12 24 -324
13 26 -168
14 28 -12
15 30 144
16 32 300
17 34 456
18 36 612
19 38 768
20 40 924
Figu e7. Va ia ion wi h ime o : (le ) he de lec ion a poin P; ( igh ) he cen e poin o he loaded a ea. The
X axis is ep esen ed in Fig.4.
Figu e8. Colo map o he de lec ion basin and se en measu ing lines a s ep 16. Gene a ed wi h GOM Inspec
P o (A amis 3D 2019, GOM GmbH, B aunschweig, Ge many).
9
Vol.:(0123456789)
Scien i ic Repo s | (2022) 12:9491 | h ps://doi.o g/10.1038/s41598-022-13176-3
www.na u e.com/scien i ic epo s/
A ai ly uni o m de o ma ion was measu ed in he ields o iew o all he came as along 180mm in he wheel
mo ion di ec ion and in he o hogonal di ec ion. Those de lec ion cu es we e in e pola ed o build a 3D su -
ace, which is shown in Fig.10. F om a quali a i e poin o iew, he DIC sys em pe o med a ealis ic cap u e
o he de o ma ion on he pa emen .
The assessmen o he DIC was pe o med om he de o ma ion de ec ed by DIC on wo se s o elemen s. The
i s se o elemen s is he ie poin s (see Fig.3). In pa icula , he di e ence was calcula ed be ween he mobile
poin s and he ixed poin s o he senso s (ΔZ DIC). The second se o elemen s is he poin s o he pa emen
ha we e in con ac wi h he senso s. Only he wo senso s closes o he wheel pass a ea (Ex . 1 and Ex . 2)
we e used in he analysis, as he mo e dis an ones did no egis e signi ican a ia ions abo e hei noise- loo
du ing he es . Since he senso s hemsel es block he isibili y o he poin s o con ac om he iew o he
Figu e9. Ve ical displacemen o he pa emen along he sampled lines a s ep 16.
Figu e10. De o med su ace a s ep 16.
