ScienceDi ec
A ailable online a www.sciencedi ec .com
P ocedia Compu e Science 192 (2021) 2761–2768
1877-0509 © 2021 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY-NC-ND license (h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0)
Pee - e iew unde esponsibili y o he scien i ic commi ee o KES In e na ional.
10.1016/j.p ocs.2021.09.046
10.1016/j.p ocs.2021.09.046 1877-0509
© 2021 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY-NC-ND license (h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0)
Pee - e iew unde esponsibili y o he scien i ic commi ee o KES In e na ional.
A ailable online a www.sciencedi ec .com
P ocedia Compu e Science 00 (2021) 000–000
www.else ie .com/loca e/p ocedia
25 h In e na ional Con e ence on Knowledge-Based and In elligen In o ma ion & Enginee ing
Sys ems
Ex apola ion o weigh om sma scale da a
Pablo Caballe oa,*, Juan A. O egaa, Luis Gonzlez-Ab ilb
aUni e sidad de Se illa, ETS Ingenie a In o m ica, A da. Reina Me cedes s/n, E-41012 Se illa, Spain
bUni e sidad de Se illa, Facul ad de Ciencias Econmicas, A da. Ramn y Cajal, 1, E-41018 Se illa, Spain
Abs ac
In he a ea o human digi al wins, he designed model should be as close as possible o he eali y. The weigh a iable is one o
he in e es ed pa ame e s o hese ma hema ical models, as well as i s in e ac ion wi h o he i al signals. The aim o his pape is
including he in o ma ion ga he ed om weigh senso s o a pe son in i s digi al win. To do his i is desc ibed an algo i hm ha
il e s and o ecas s he human weigh o use i in indexes such as BMI. I has been applied o a eal sample and he esul s ob ained
a e good.
c
2021 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
Pee - e iew unde esponsibili y o he scien i ic commi ee o he KES In e na ional.
Keywo ds: WEIGHT; EXTRAPOLATION; ALGORITHM; DIGITAL-TWIN; SIGNAL PROCESSING
1. In oduc ion
The c ea ion o a human digi al win equi es di e en i al signals, calcula ed indexes and some me ics. Fo
complex models like hese i is necessa y o di ide in simple models which in u n can be ela ed each o he .
The moni o iza ion [1] o he humans and he ea ly disease p e en ion is he inal aim o he human digi al wins,
ying o align he a ge o s a e machine o he model wi h he pa e ns o he human-machine [2]. The la es In e ne
o Things (IoT) de elopmen s [3] ocused on he i ness p o ides o he ma ke a so o comme cial ubiqui ous de ices
[7], in pa icula sma bands and sma wa ches. Some examples such as he eal ime hea a e, he walking o es ing
hea a e, and he sleeping hou s a e s o ed in he sma wa ches like Apple Heal hKi and cloud da abases. This aw
in o ma ion can be que ied by mobile applica ions as well as complex backend sys ems.
On he o he hand, he inc emen o o e weigh and obesi y [4, 5] has also opened he ma ke o new sma de ices,
o ins ance sma scales. The weigh o he body a can be measu ed and eco ded whene e he use s wan .
∗Co esponding au ho . Tel.: +34-605-458-552
E-mail add ess: [email p o ec ed]
1877-0509 c
2021 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
Pee - e iew unde esponsibili y o he scien i ic commi ee o he KES In e na ional.
A ailable online a www.sciencedi ec .com
P ocedia Compu e Science 00 (2021) 000–000
www.else ie .com/loca e/p ocedia
25 h In e na ional Con e ence on Knowledge-Based and In elligen In o ma ion & Enginee ing
Sys ems
Ex apola ion o weigh om sma scale da a
Pablo Caballe oa,*, Juan A. O egaa, Luis Gonzlez-Ab ilb
aUni e sidad de Se illa, ETS Ingenie a In o m ica, A da. Reina Me cedes s/n, E-41012 Se illa, Spain
bUni e sidad de Se illa, Facul ad de Ciencias Econmicas, A da. Ramn y Cajal, 1, E-41018 Se illa, Spain
Abs ac
In he a ea o human digi al wins, he designed model should be as close as possible o he eali y. The weigh a iable is one o
he in e es ed pa ame e s o hese ma hema ical models, as well as i s in e ac ion wi h o he i al signals. The aim o his pape is
including he in o ma ion ga he ed om weigh senso s o a pe son in i s digi al win. To do his i is desc ibed an algo i hm ha
il e s and o ecas s he human weigh o use i in indexes such as BMI. I has been applied o a eal sample and he esul s ob ained
a e good.
c
2021 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
Pee - e iew unde esponsibili y o he scien i ic commi ee o he KES In e na ional.
Keywo ds: WEIGHT; EXTRAPOLATION; ALGORITHM; DIGITAL-TWIN; SIGNAL PROCESSING
1. In oduc ion
The c ea ion o a human digi al win equi es di e en i al signals, calcula ed indexes and some me ics. Fo
complex models like hese i is necessa y o di ide in simple models which in u n can be ela ed each o he .
The moni o iza ion [1] o he humans and he ea ly disease p e en ion is he inal aim o he human digi al wins,
ying o align he a ge o s a e machine o he model wi h he pa e ns o he human-machine [2]. The la es In e ne
o Things (IoT) de elopmen s [3] ocused on he i ness p o ides o he ma ke a so o comme cial ubiqui ous de ices
[7], in pa icula sma bands and sma wa ches. Some examples such as he eal ime hea a e, he walking o es ing
hea a e, and he sleeping hou s a e s o ed in he sma wa ches like Apple Heal hKi and cloud da abases. This aw
in o ma ion can be que ied by mobile applica ions as well as complex backend sys ems.
On he o he hand, he inc emen o o e weigh and obesi y [4, 5] has also opened he ma ke o new sma de ices,
o ins ance sma scales. The weigh o he body a can be measu ed and eco ded whene e he use s wan .
∗Co esponding au ho . Tel.: +34-605-458-552
E-mail add ess: [email p o ec ed]
1877-0509 c
2021 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
Pee - e iew unde esponsibili y o he scien i ic commi ee o he KES In e na ional.
2762 Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768
In a model, he body mass index [6] is widely used o measu e he s a us in i ness models. Some ac ions can be
sugges ed when he use is unde weigh , o e weigh o mo e.
Due o he in o ma ion is ga he ed om se e al de ices and e e y de ice can ha e one o mo e senso s; he e o e,
he collec ion o samples ha e di e en ime equencies. To ela e he signals and he e o e he collec ions o samples
need o exis in a speci ic momen , so he model is spli in s eps.
The body mass [13] o commonly called weigh has a iny ecu ency compa ed o hea a e so i is needed a
o ecas mechanism o ma ch he alues in one ime s ep. This pape will be ocused on he ex apola ion o he
weigh ecei ed om a sma scale. A e his s anda diza ion p ocess he esul ed samples can be used as da ase o
machine lea ning models o cloud compu ing calcula ions.
The pape is o ganized as ollows. Sec ion 2 exposes he p ope ies o he weigh o ge a pic u e o he p oblem.
Secondly, in Sec ion 3 he ime in e als is de ined. Then, in Sec ion 4 he ex apola ion algo i hm is desc ibed. The
acknowledgemen s a e in Sec ion 6. Finally he conclusions and u he wo ks a e de ailed in Sec ion 5.
2. P ope ies o weigh
Based on he anonymous su ey “habi s o weigh you sel ” made o his pape on in e ne o e 58 people on
Ma ch 4, 2021; he ollowing p ope ies can be in e ed om i s esul s and hey jus i y disc e izing he signal o he
weigh and aking he alues based on he close samples.
2.1. Recu ence
The high a iabili y o he hou o weigh you sel shown in Figu e 1 does no allow o p edic he momen when
he sample o he weigh is ga he ed.
Table 1. Common weigh you sel hou .
Hou Coun Pe cen age
None 8 13.8%
758.6%
8 19 32.8%
9 9 15.5%
10 2 3.4%
11 4 6.9%
12 1 1.7%
19 2 3.4%
20 5 8.6%
21 3 5.5%
None
13.8%
7
8.6%
8
32.8%
9
15.5%
10
3.4%
11
6.9%
12
1.7%
19
3.4%
20
8.6% 21
5.5%
Fig. 1. Common weigh you sel hou om Table 1.
The ecu ency pe week is also highly a iable, shown in Figu e 2. Consequen ly, i is no possible o p edic how
o en he samples a e ga he ed.
Table 2. Numbe o weighing you sel pe week.
F equency Coun Pe cen age
(Weekly) 1 14 17.7%
267.6%
3 12 15.2%
445.1%
5 15 19.0%
(Daily) 7 28 35.4%
Weekly
17.7%
2
7.6%
3
15.2%
4
5.1%
5
19%
Daily
35.4%
Fig. 2. Numbe o weighing you sel pe week om Table 2.
Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768 2763
2.2. Va iabili y
The a iabili y h oughou a day he weigh could inc ease o dec ease signi ican ly based on he quan i y o liquid
o ood, basal me abolic a e [8], ac i i y [9], ho mone le els [10], he equency o bowel mo emen [11]... So, i is
no possible o ecas ing mo e accu a e o an speci ic day.
In he opposi e case, i migh be possible measu e o he weigh ew imes in a sho pe iod o ime and i should
ep esen he same momen . In some cases, mobile applica ions [16] linked o he sma scale ask o a con i ma ion
when he di e ence is oo big. Fo he cu en p oposal, he alue o he weigh in a s ep will be he a e age o he
alues inside he same ime s ep.
3. Time in e al
As i was exposed be o e, du ing he c ea ion o a model he samples o he i al signals a e in di e en equencies,
so i is necessa y o s anda dize in ime in e als. The complex s uc u e [14] has o be con e ed in o a ime in e al
de ined by [s a ,end].
The pa ame e s epSize is he numbe o minu es o one s ep. Fo his algo i hm will be 1 min. So a ime in e al
can be de ined as he pe iod o ime [ i, i+1] whe e iis he beginning o he s ep and i+1.
i+1= i+s epS ize (1)
In he o ecas ing algo i hm some ime in e al me hods will be used, hey a e in e sec and expandMinu es.
3.1. Me hod in e sec
An in e al xin e sec s wi h an in e al ywhen hey sha e pa o hei ime. I is shown in Figu e 3.
in e sec (x,y)=y.end ≥x.s a ∧y.s a ≤x.end (2)
---------------->
x -----S-----E-----
y1 ---------s---e--- y1 in e sec s wi h he igh bounda y o x
y2 --s-----e-------- y2 in e sec s wi h he le bounda y o x
y3 -------s-e------- x con ains y3
y4 --s----------e--- y4 con ains x
Fig. 3. Possible cases o in e sec is ue.
3.2. Me hod expandMinu es
Da e ypes a e speci ic o he p og amming languages, so i is ecommended he usage o a common ep esen a ion.
Hence o h he da es will be ep esen ed in icks1[15] o ma . Due o some sys ems like Apple de ices include he
second p ecision and i is no needed, he smalles p ecision is minu e and he seconds componen can be uled ou .
The cons an icksPe Minu e is he numbe o icks in one minu e, ha is 600 000 000, and i is necessa y o
con e ime di e ence in minu es.
An in e al iis expanded in mminu es when he ield s a in mo ed mminu es be o e i and he ield end is mo ed
mminu es a e i . This me hod is used when he e a e no any samples o a ime in e al and i is need o expand he
sea ch adius.
expand(in e al,m)=[i.s a −( icksPe Minu e ×m),i.end +( icksPe Minu e ×m)] (3)
1One ick is 100 ns (nanoseconds) and da e is he numbe o icks since 12:00, Janua y 1, yea 1 in G ego ian calenda .
2764 Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768
4. P ocedu e
Below, he in ol ed me hods and he esampling p ocess a e desc ibed. The ex apola ion i sel is pa o he
me hod sea chSamples(samples, in e al) and he gene al me hod o s anda dize all he samples is he me hod
ge AllS anda dSamples(samples1,samples2, ... samplesn).
4.1. Fil e ing o bounding alues
When in o ma ion is ex ac ed om a sma de ice, a po en ial p oblem could happen, use s can add manually
alues and consequen ly ha ac ion could be a sou ce o possible e o s.
Based on a da ase [12] o 40 400 samples o heigh o 18 yea s old people, he bounding alues depending on he
gende ha e been ob ained using BMI he o mula can ollow:
bmi =weigh [kg] ÷heigh [m]2(4)
weigh i=bmi ×heigh 2
i(5)
weigh =a e age(weigh i) (6)
Table 3. Ex eme alues o weigh s depending on he gende .
Gende Th eshold
Weigh (kg)
Ex eme
Unde weigh
BMI 16
Weigh (kg)
Mode a e
Unde weigh
BMI 16
Weigh (kg)
Obesi y III
BMI 40
Weigh (kg)
Obesi y IV
BMI 50
Female Minimum 39.50 41.97 - -
Female Maximum - - 98.74 123.43
Male Minimum 45.38 48.22 - -
Male Maximum - - 113.46 141.83
The BMI alues o ex eme unde weigh and obesi y IV ha e been aken as limi s maximum and minimum e-
spec i ely due o he e a e no mo e ex eme ca ego ies. The ca ego ies mode a e unde weigh and obesi y III could be
aken in a mo e es ic i e model because mo e alues a e ou o ange. All he samples whose weigh is ou o ange
should be disca ded. This il e can be applied in ea ly s eps in ou p ocess, so i is no needed o spend space and
p ocessing ime.
4.2. Iden i y ime o ecas bounda ies
All he samples ex ac ed om he de ices usually a e wi hin a ime in e al, so hey ha e a leas a uple o h ee
alues: s a da e (samplei.s a ), end da e (samplei.end) and he signal alue (samplei. alue).
In addi ion o he samples o weigh he e a e also o he samples like hea a e o heigh , and ha bounda ies
belong o he model i sel , so he en i e se o samples is needed. One modi ica ion could be including he cu en ime
in his limi calcula ion so i will y o ex apola e un il hen.
The bounda ies will be a uple o he minimum da e o all he samples o all he signals o he cu en model and
he maximum da e o all he samples.
ge Fo ecas Bounda ies(samples1, ..., samplesn)=[min(x.s a |x∈samplesi),max(x.end|x∈samplesi)] (7)
Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768 2765
4.3. De ini ion o all in e als
I is needed o c ea e a collec ion o ime in e als, one pe s ep. The me hod ge AllIn e alsPe S ep is de ined
in Algo i hm 1.
The esul is a collec ion o s eps. E e y s ep is ollowed by he immedia e nex s ep, and all he s eps ha e he
same size.
Algo i hm 1: ge AllIn e alsPe S ep(samples1, samples2, ... samplesn)
samplesi:Inpu . Se o samples.
Resul : The se o all in e als.
1(globalS a ,globalEnd)←
ge Fo ecas Bounda ies({x.s a |x∈samples1},{x.s a |x∈samples2}, ..., {x.s a |x∈samplesn})
2in e al.s a ←globalS a
3in e al.end ←globalS a +( icksPe Minu e ×s epS ize)
4in e als ←∅
5while in e al.end <globalEnd do
6in e als ←in e als ∪{in e al}
7in e al.s a ←in e al.end
8in e al.end ←in e al.end +( icksPe Minu e ×s epS ize)
9end
10 e u n in e als
4.4. Look o a possible alue
Once he aw alues a e il e ed, Algo i hm 2 desc ibes he p ocess whe e he weigh is assigned o e e y in e al
as well as he es o he se s o samples.
I is possible o ind mo e han one samples, howe e hose alues should be close o each o he so he a e age
me hod is used.
Algo i hm 2: ge AllS anda dSamples(samples1, samples2, ... samplesn)
samples: Inpu . Se o samples. E e y sample has a s a ime, an end ime and a weigh alue.
Resul : The se o all weigh samples.
1in e als ←ge AllIn e alsPe S ep(samples)
2 esul ←∅
3 o each in e al in in e als do
4samplesInIn e al ←sea chSamples(samples,in e al)
5i |samplesInIn e al|>0 hen
6cu en S ample.s a ←in e al.s a
7cu en S ample.end ←in e al.end
8cu en S ample. alue ←a e age(x. alue|x∈samplesInIn e al)
9 esul ← esul ∪{cu en S ample}
10 end
11 end
12 e u n esul
Below in Algo i hm 3 he me hod sea chSamples is de ined. The esul is a se o samples ha a e close o ha
in e al.
The i s pa o he algo i hm co e s he co ne cases o ha ing a educed numbe o samples. This case could
happen when i is he i s ime ha he s anda diza ion p ocess is execu ed.
The second pa ies o il e all he alues ha in e sec wi h he cu en in e al, so we could say ha hey belong
o his in e al.

2766 Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768
In he hi d pa i ies o inc ease he window ime o ca ch a alue. The inc emen is de ined by he pa ame e
sea chS ep, i is he numbe o minu es o be inc emen ed (by de aul is 60). The limi o he sea ch is de ined by
he pa ame e sea chRa e cons an (by de aul i s alue is 4, so he maximum sea ch will be a qua e o he o al
ime). These pa ame e a e isually explained in Figu e 4.
Fig. 4. Visual explana ion o he pa ame e s.
A d awback o s opping he sea ch using maxSea chS ep (Algo i hm 3, line 20) is when he e a e a small se o
samples close in ime hen he di e ence be ween las Ins ance and i s Ins ance is iny, and i is also educed
by sea chRa e so he window ime maybe is no enough. A possible solu ion less es ic i e could be se a minimum
o maxSea chS ep o he leas es ic i e solu ion is emo ing ha condi ion so i always will ind a leas one sample.
Algo i hm 3: sea chSamples(samples, in e al)
samples: Inpu . Se o samples. E e y sample has a s a ime, an end ime and a weigh alue.
in e al: Inpu . Cu en in e al o e alua e.
Resul : The se o samples o a gi en in e al.
1i |samples|=0 hen
2 e u n ∅
3else i |samples|≤1 hen
4 e u n samples
5end
6
7samplesInCu en WindowTime ←{x|x∈samples ∧in e sec (in e al, x)}
8i |samplesInCu en WindowTime|>0 hen
9 e u n samplesInCu en WindowT ime
10 end
11
12 i s Ins ance ←min({x.s a |x∈samples})
13 las Ins ance ←max({x.end|x∈samples})
14 maxS ea chS ep ←((las Ins ance − i s Ins ance)÷ icksPe Minu e)÷sea chRa e
15 in e alS ize ←s epS ize
16 do
17 in e alS ize ←in e alS ize +(2 ×sea chS ep)
18 expandedIn e al ←expandMinu es(expandedIn e al, sea chS ep)
19 samplesInExpandedIn e al ←{x|x∈
samples ∧in e sec (expandedIn e al, cas SampleToIn e al(x))}
20 while samplesInExpandedIn e al =∅∧in e alS ize ≤maxS ea chS ep
21
22 e u n samplesInExpandedIn e al
Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768 2767
4.5. Algo i hm example
An example o his algo i hm is in Figu e 5. The ini ial da a is 5 in e als, om I0 o I4de ined in Table 4. The
algo i hm pa ame e s a e s epSize as 15 (min), sea chRa e as 4 and sea chS ep as 60 (min).
Table 4. Ex apola ion example da a.
In e al S a S a (Da e) End End (Da e) Weigh (kg)
I06 374 678 400 10801/21/2021 00:00 6 374 678 406 10801/21/2021 00:01 99.0
I16 374 687 040 10801/22/2021 00:00 6 374 687 046 10801/22/2021 00:01 98.0
I26 374 695 680 10801/23/2021 00:00 6 374 695 686 10801/23/2021 00:01 98.0
I36 374 704 320 10801/24/2021 00:00 6 374 704 326 10801/24/2021 00:01 99.0
I46 374 712 960 10801/25/2021 00:00 6 374 712 966 10801/25/2021 00:01 96.0
A e unning he s anda diza ion code i will gene a e 384 in e als o 15 minu es pe in e al.
In 0, 1, 2and 3 he alues a e o iginal alues. Be ween 0and 1 he e a e 2 in e als whose alues a e 98.5 kg,
his si ua ion happens due o sea ching a alue, he window ime in e sec s wi h I0and I1. Be ween 2and 3 he same
hing happens as well.
ime
weigh (kg)
I0(99.0)
I1(98.0) I2(98.0)
I3(96.0) I4(96.0)
0 1 2 3 4
Fig. 5. Ex apola ion example.
5. Conclusion and u he wo k
The di icul y o o ecas he weigh inside a day due o i s ecu ency and a iabili y has been exposed.
Some h eshold alues we e p oposed depending on he gende o il e possible w ong alues. Cases o ex eme
unde weigh o ex eme obesi y would be non-allowed alues.
The p oposed algo i hm is eady o be used and i ex apola es he weigh alue o momen s close o he o iginal
ins an . E e y s ep will ha e a disc e e alue o he weigh so i can be used o c ea e a digi al win model in conjunc ion
wi h o he signals. I he alue is ou he sea ch ange hen ha ime in e al could be disca ded i he weigh is needed.
In a gene al pe spec i e he o ecas ed alues a e alid, ne e heless o an speci ic momen he alue will depend
o how a in ime is om a eal alue.
A u u e modi ica ion could be a second pass day by day and con e ing he disc e e alues in a cu e. In e e y
day, he a ia ions a lunch o dinne could be also conside ed ne e heless a esea ch on nu i ional habi s would be
necessa y.
2768 Pablo Caballe o e al. / P ocedia Compu e Science 192 (2021) 2761–2768
6. Acknowledgemen s
This esea ch has been pa ially suppo ed by he E ol ing owa ds Digi al Twins in Heal hca e (EDITH) Resea ch
P ojec (PGC2018-102145-B-C21, C22 (AEI/FEDER, UE)), unded by he Spanish Minis y o Science, Inno a ion
and Uni e si ies.
Re e ences
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[2] Ha ez, Wael. 2020. Human Digi al Twin: Enabling Human-Mul i Sma Machines Collabo a ion. DOI: h p://dx.doi.o g/10.1007/
978-3-030-29513-4_72
[3] Ba icelli, Ba ba a & Casi aghi, Elena & Gliozzo, Jessica & Pe ini, Alessand o & Val olina, S e ano. 2020. Human Digi al Twin o Fi ness
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