Extrapolation of weight from smart scale data

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 [1] Kang, JS. & Chung, K. & Hong, E.J. 2021 Mul imedia knowledgebased b idge heal h moni o ing using digi al win. DOI: h ps://doi. o g/10.1007/s11042-021-10649-x [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 Managemen . IEEE Access. PP. 1-1. 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