IEEE INTERNET OF THINGS JOURNAL, VOL. 10, NO. 21, 1 NOVEMBER 2023 18909
Fuzzy Con olled Wa ele -Based Edge Compu ing
Me hod o Ene gy-Ha es ing IoT Senso s
Ja omi Konecny , Membe , IEEE, Michal P auzek ,Senio Membe , IEEE, and Monika Bo o a
Abs ac —The s udy p esen s a no el edge compu ing (EC)
me hod based on a disc e e wa ele ans o m (DWT) and uzzy
logic con olle sui able o applica ion wi h ene gy ha es ing
In e ne o Things (IoT) senso s. The au ho s p opose a new
solu ion o add ess in o ma ion la ency in an IoT de ice when
comp essed da a wi h high-in o ma ion densi y a e ansmi ed
o he cloud wi h high p io i y o de ailed in o ma ion is added o
he cloud when he ene gy s a e in he IoT de ice is su icien . The
solu ion po en ially deli e s a comple ely lossless scena io o low-
powe senso s, a signi ican bene i ha s a e-o - he-a me hods
do no p o ide. This a icle desc ibes he ha dwa e model o an
IoT de ice, inpu and p edic ed ene gy da a, and a me hodology
o designing he pa ame e s o DWT and uzzy logic con olle s.
The esul s o he s udy indica e ha he p oposed EC me hod
achie ed ull da a ansmission in con as o he e e ence solu-
ion which had he wo s case pa ame e s o maximum ou age
and penal ies caused by delayed da a. The a e age delay in
uploading app oxima e da a was 0.51 days wi h he p oposed
uzzy con olle EC me hod compa ed o e e ence me hods,
which ha e an a e age delay o a leas 0.91 days. The esul s also
highligh ed he impo ance o he adeo be ween in o ma ion
la ency and eliable unc ionali y. The esul s a e discussed in
e ms o an inno a i e app oach which ea u es an IoT senso
ha maximizes i s own ene gy consump ion acco ding o he da a
measu ed om speci ic pa ame e s.
Index Te ms—Da a comp ession, edge compu ing (EC), ene gy
ha es ing, in o ma ion la ency, In e ne o Things (IoT), wa ele
ans o m.
I. INTRODUCTION
THE SIGNIFICANCE o edge compu ing (EC) me hods
in he In e ne o Things (IoT) is g owing, especially in
ela ion o ansmission capaci y limi a ions in low-powe wide
a ea ne wo k (LPWAN) echnology. Mode n IoT de ices ha
ha es ene gy can be imp o ed by adap ing da a ansmis-
sion acco ding o he impo ance o he da a and he ene gy
a ailable in he ansmi ing de ice. The s udy ex ends an
Manusc ip ecei ed 27 Oc obe 2022; e ised 7 June 2023; accep ed
3 July 2023. Da e o publica ion 6 July 2023; da e o cu en e sion
24 Oc obe 2023. This wo k was suppo ed in pa by he “De elopmen o
Algo i hms and Sys ems o Con ol, Measu emen and Sa e y Applica ions
IX” o he S uden G an Sys em, VSB-TU Os a a unde P ojec SP2023/009;
in pa by he “De elopmen o a Sys em o Moni o ing and E alua ion o
Selec ed Risk Fac o s o Physical Wo kload in he Con ex o Indus y 4.0” o
he Technology Agency o he Czech Republic unde P ojec FW03010194;
and in pa by he Eu opean Union’s Ho izon 2020 Resea ch and Inno a ion
P og amme unde G an 856670. (Co esponding au ho : Michal P auzek.)
The au ho s a e wi h he Depa men o Cybe ne ics and Biomedical
Enginee ing, VSB–Technical Uni e si y o Os a a, 70800 Os a a,
Czech Republic (e-mail: monika.bo o a@ sb.cz; ja omi .konecny@ sb.cz;
michal.p auzek@ sb.cz).
Digi al Objec Iden i ie 10.1109/JIOT.2023.3292915
expe imen which compa ed neu al ne wo ks and wa ele -
based EC me hods p esen ed a he 2022 IEEE Symposium
Se ies on Compu a ional In elligence and desc ibes he appli-
ca ion o wa ele comp ession me hods de eloped o an
ene gy ha es ing de ice d i en by a uzzy logic con olle [1].
This a icle discusses he achie ed da a accu acy and sui abil-
i y o wa ele -based EC o adap i e ope a ion in a model
which uses ou yea s o his o ical da a.
The mo i a ion o he s udy is de eloping an EC me hod
which is e ec i e in managing he low capaci y o a ansmis-
sion channel, limi ed compu a ional esou ces in IoT senso s,
and a iabili y o incoming ha es ed ene gy. The s udy
p esen s a design o a compu a ionally ligh weigh solu ion
which add esses hese ene gy cons ain s and ansmission
channel limi a ions. This no el solu ion ensu es maximum da a
a ailabili y in he cloud wi h accep able da a loss and is capa-
ble o e ining cloud da a a e an accep able delay. The IoT
senso is also capable o p io i izing he ansmission o nonde-
ailed da a and subsequen ly enhancing hese da a wi h de ails
acco ding o impo ance and he quan i y o a ailable ene gy.
The main objec i es o he s udy include iden i ying he
unc ional pa ame e s, o example ene gy consump ion and
pe o mance, in an IoT senso which is powe ed by a he mo-
elec ic gene a o (TEG) ene gy ha es ing de ice and desc ib-
ing and measu ing he ansmission channel capaci y and
powe consump ion o model he senso ’s da a ansmission
equi emen s. The objec i es u he in ol e selec ing a sui -
able comp ession me hod wi h he abili y o a y comp ession
le el and designing a con ol algo i hm ha enables adjus men
o he comp ession le el wi h minimal in o ma ion loss while
ensu ing ea ly ansmission o app oxima ed da a. Finally, he
s udy e alua es he p oposed solu ion using an en i onmen al
da a se and discusses i s ea u es and deploymen possibili ies.
The p inciple o he wa ele -based EC me hod is illus a ed
in Fig. 1. An IoT de ice uses senso s o measu e pa ame-
e s in i s en i onmen and applies wa ele comp ession o
decompose he da a ob ained. Da a decomposed in o bo h
app oxima e and de ailed coe icien s a e s o ed in memo y
alongside comp ession quali y in o ma ion measu ed acco d-
ing o Goodness-o -Fi (GoF). A uzzy con olle selec s he
da a o ansmission o he cloud. The uzzy con olle inpu s
a e based on node ene gy s a e, p edic ed ene gy da a o u u e
ene gy ha es ing, and da a olume s o ed a e comp ession
acco ding o GoF. The aim o his app oach is o i s ansmi
app oxima e coe icien s wi h high-in o ma ion densi y when
he IoT de ice is low on ene gy; de ailed coe icien s a e hen
la e ansmi ed acco ding o hei in o ma ional alue when
© 2023 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 License.
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18910 IEEE INTERNET OF THINGS JOURNAL, VOL. 10, NO. 21, 1 NOVEMBER 2023
Fig. 1. P inciple o he wa ele -based EC me hod: inpu da a a e comp essed
o wa ele coe icien s which con ain a ious in o ma ion densi ies. The uzzy
con olle d i es a ansmission module which selec s da a acco ding o
speci ic c i e ia o ansmission o he cloud.
he de ice has su icien ene gy o he possibili y a ises o
ob ain a esh supply o ene gy in he nea u u e.
The p oposed app oach in oduces an EC me hod ha p i-
o i izes da a wi h high-in o ma ion densi y o e insigni ican
de ails, hus in oducing in o ma ion la ency. Unlike s a e-o -
he-a me hods, i combines an adap i e comp ession a e wi h
a ollow-up da a upda e when su icien ene gy is ha es ed
by he IoT de ice and hus a emp s o minimize in o ma ion
loss. The applica ion is no domain speci ic since i employs
a disc e e wa ele ans o m (DWT) and does no depend
on supe ised lea ning o loca ion-speci ic pa ame e s. I is
he e o e e sa ile and can be applied in a ious domains.
The p oposed app oach is also sui able o esou ce-limi ed
embedded IoT de ices since he DWT can be e icien ly
p ocessed using ha dwa e ins uc ions execu ed in mode n
mic ocon olle s.
The no el y and he con ibu ion o his a icle is summa-
ized below.
1) This a icle p esen s he design p inciples o a comp es-
sion me hod which pe mi s changes in he comp ession
le el while main aining a de e minis ic ou pu . The
design also allows g adual e inemen o he measu ed
da a in he cloud.
2) This a icle p oposes a da a p io i y engine which
enables he selec ion o app op ia e da a clus e s while
checking he immediacy and impo ance o he da a.
3) This a icle in oduces he concep o a ule-based
con olle sui able o embedded de ices. This con-
olle pe mi s ansmission con ol which suppo s he
dynamic na u e o ha es ed ene gy.
This a icle is o ganized in o se en sec ions. Sec ion Iin o-
duces he mo i a ion, co e objec i es, and no el y o he
p esen s udy. Sec ion II summa izes he s a e-o - he-a ela ed
wo ks. Sec ion III p o ides de ails o he p oposed no el EC
TABLE I
OVERVIEW OF EC METHODS SUITABLE FOR LOW-POWER IOTDEVICES
me hod, da a decomposi ion, da a p io i y engine, uzzy logic
con olle , and da a ansmission module. Sec ion IV desc ibes
he expe imen and i s ha dwa e model, inpu da a, and p e-
dic ed ene gy da a se , along wi h e alua ion c i e ia. Sec ion V
epo s he esul s o he expe imen , discussing bo h he
ime domain and da a a ailabili y. Sec ion VI discusses and
e alua es he esul s wi hin he con ex o he s udy’s no el
con ibu ion. Finally, Sec ion VII concludes his a icle and
ou lines po en ial u u e wo k.
II. RELATED WORKS
Va ious en i onmen al EC algo i hms can be used in combi-
na ion wi h IoT de ices. Based on he speci ic pa ame e s o
in e es , he algo i hms can be classi ied acco ding o lossy
(o lossless) comp ession o da a olume educ ion. O he
pa ame e s, such as compu a ional complexi y and communi-
ca ions in e ace ype, a e also impo an [2]. In p inciple, da a
comp ession me hods can be applied o signi ican ly educe
he ene gy equi emen s o da a ansmission [3]. Table I
summa izes he s a e-o - he-a EC me hods acco ding o con-
en ional ma hema ical app oaches [4], so -compu ing, and
da a educ ion me hods [5].
When da a a e comp essed using he DWT, e y e icien
comp ession can be achie ed i he wa ele ype is app o-
p ia ely selec ed [6],[7]. The shape o he mo he wa ele
KONECNY e al.: FUZZY CONTROLLED WAVELET-BASED EDGE COMPUTING METHOD 18911
should ma ch he shape o he inpu signal as closely as possi-
ble. The algo i hm’s bene i is ha aining on his o ical da a
is no equi ed. To achie e e en mo e e icien comp ession,
his me hod is o en used in conjunc ion wi h o he com-
p ession algo i hms, such as Hu man coding o a disc e e
cosine ans o m [8]. This app oach is no sui able, howe e ,
in deploymen s ha use loa ing poin a iables, which com-
plica e di ec applica ion o IoT senso measu emen s. Ano he
use ul ma hema ically based comp ession me hod is he Walsh
ans o m, which is e y sui able o applica ion o biosignals,
bu i s applicabili y o sma ci ies o en i onmen al da a has
no ye been demons a ed [10].
Many applica ions use so -compu ing me hods o da a
comp ession. A i icial neu al ne wo ks a e ypical so -
compu ing comp ession me hods, bu hei disad an age is he
need o use la ge olumes o speci ic his o ical da a o ain-
ing [11]. Fo example, a neu al ne wo k ained on seismic da a
will unlikely unc ion co ec ly wi h o he ypes o a iable, o
example empe a u e da a [12]. Ano he disad an age is ha
he neu al ne wo k always p oduces lossy comp ession [13] as
a esul o i s cha ac e is ics.
Da a olume educ ion is a me hod o educing he numbe
o da a eco ds o ansmission acco ding o he impo ance
o he in o ma ion con ained wi hin ha da a. This ype o
app oach gene ally is no conside ed a comp ession me hod.
The algo i hms o educing da a olume can be execu ed as
ime-co ela ed p edic i e models o es ima e ends, and when
hese ends di e , he da a a e ansmi ed [14]. Da a olume
educ ion based on a p edic i e model is o en used in conjunc-
ion wi h comp essed sensing [15]. A p edic i e model decides
whe he da a a e ei he sen o elimina ed using a comp ession
me hod based on adap i e piecewise cons an app oxima ion,
symbolic agg ega e app oxima ion, o a ixed code dic iona y
using Hu man encoding [16].
III. METHODS
This sec ion desc ibes he p oposed EC me hod, which
in ol es ou pa s: 1) he da a decomposi ion and composi-
ion p ocedu e; 2) he da a p io i y engine; 3) he uzzy logic
con olle ; and 4) he ansmission module.
A de ailed scheme o he EC is illus a ed in Fig. 2.The e -
ical do ed lines in he scheme sepa a e he IoT de ice, whose
componen s a e depic ed on he le , and he cloud, which is
a he igh . Measu ed da a (32 samples) a e decomposed by
he DWT and s o ed in a memo y able as A3, D3, D2, and
D1 clus e s. This p ocedu e is de ailed in Sec ion III-A.
The p inciple behind he p esen ed me hod is in d i ing da a
ansmission acco ding o he impo ance o he in o ma ion
con ained wi hin he da a. To achie e his, he solu ion uses
he da a p io i y engine desc ibed in Sec ion III-B.The
engine applies a ious le el da a composi ions o de e mine
in o ma ion loss acco ding o GoF, and he GoF alues a e
hen s o ed in a GoF able which co esponds o he A3, D3,
D2, and D1 clus e s.
Since he design solu ion is applied o ene gy ha es ing IoT
senso s, da a ansmission mus be con olled dynamically. The
i mwa e o embedded de ices is commonly implemen ed as
Fig. 2. De ailed block diag am o an EC me hod based on a disc e e wa ele
ans o ma ion d i en by a uzzy logic con olle .
a ini e s a e machine which applies a du y cycle scena io. A
ule based con olle is he e o e a sui able op ion o he an-
si ion unc ion. A uzzy-based solu ion expands he op ions o
he dynamic ene gy managemen s a egy and pe mi s u u e
op imiza ion o uzzy se and ule se ings. These a e use ul
ea u es which a e exploi ed in he uzzy- ule-based solu-
ion de ailed in Sec ion III-C o con ol he da a ansmission
module desc ibed in Sec ion III-D.
A. Da a Decomposi ion
This sec ion desc ibes da a decomposi ion me hod which
applies a DWT o lossy comp ession. The DWT p o ides
de e minis ic decomposi ion and composi ion a a ge le el
which is ully aligned wi h IoT ansmission echnology p in-
ciples. The aim behind using his me hod is o ansmi
app oxima e da a and mino de ails as soon possible acco ding
o he de ice’s a ailable ene gy.
The DWT decomposes acco ding o he ec o
{am,dm,dm−1,...,d1}, o ming a wa ele spec um which
desc ibes he ime- equency localiza ion o he inpu signal.
The ec o coe icien s a e ob ained by applying a con olu ion
o he inpu signal h ough a low-pass il e o app oxima e
coe icien s and a high-pass il e o de ailed coe icien s.
The a o emen ioned decomposi ion can be eapplied o he
app oxima ion coe icien s [17].
The decomposi ion scheme is shown in Fig. 3. Fo his pa -
icula EC me hod implemen a ion, du ing da a comp ession,
he ou pu ec o is o med by app oxima e coe icien s a he
hi d decomposi ion le el and de ailed coe icien s a he hi d,
second, and i s decomposi ion le els. Gene ally, dep h o he
decomposi ion le el can be adjus ed acco ding o he a ge ed
g anula i y o he measu ed da a de ails and op ions a ailable
o he communica ions channel payload. In he p esen ed solu-
ion, he decomposi ion le el is selec ed as a adeo be ween
he minimum ansmission pe iod (quan i y o collec ed da a o
18912 IEEE INTERNET OF THINGS JOURNAL, VOL. 10, NO. 21, 1 NOVEMBER 2023
(a) (b)
Fig. 3. Decomposi ion o he measu ed da a by a DWT. (a) Decomposi ion.
(b) Leng hs.
comp ess) and he comp ession g anula i y (a ailable op ions
o ansmi da a a a ious comp ession le els).
Decomposi ion is dependen on he ype o mo he wa ele
used. Selec ing a mo he wa ele which ma ches he wa e-
o m o an inpu signal as closely as possible can inc ease he
impo ance o he in o ma ion in he app oxima e coe icien s
and dec ease he impo ance in de ailed coe icien s. This
esul s in a be e app oxima ion o he signal when de ailed
coe icien s a e no ansmi ed [18]. The Haa wa ele is used
in he p oposed solu ion since i ep esen s a gene al da a
comp ession app oach.
B. Da a P io i y Engine
The aim o he EC me hod is o g adually e ine he mea-
su ed da a in he cloud. The app oxima ion coe icien s a he
hi d decomposi ion le el a e ansmi ed wi h he highes p i-
o i y, and he econs uc ed da a a e hen g adually e ined by
ansmi ing he de ailed coe icien s. This p ocedu e esul s
in app oxima ed da a being a ailable in he cloud soone han
de ailed da a.
Gene ally, a ull ec o o decomposed coe icien s con ains
he o iginal in o ma ion wi hou any da a loss. I any o he
de ailed coe icien s a e no ansmi ed, hey a e subs i u ed
wi h a ze o du ing econs uc ion, causing da a loss a ha
pa icula le el. The bene i o his app oach is ha de ailed
coe icien s can o be added a any ime o inc ease he da a
p ecision.
The p oposed EC me hod clus e s he measu ed da a wi h
he 32 samples decomposed by he DWT a he hi d le el.
The decomposed clus e s o m a memo y bu e (Fig. 2), and
a GoF able is c ea ed o de e mine which memo y bu e clus-
e is impo an o ansmi . A GoF alue is de ined by he
ollowing:
GoF =1−N
i=1
xi−ˆxi

2
N
i=1|xi−mean(x)|2(1)
whe e GoF is he goodness o i (1 is a bes i ), xis he
o iginal signal, and ˆxis he decomp essed signal.
The GoF able con ains in o ma ion abou he ansmission
impo ance s o ed in he ela ed memo y bu e clus e . The
calcula ion p ocedu e o he GoF able is illus a ed in Fig. 4.
The i s column in he GoF able always con ains nega i e
in ini y, because i an app oxima e coe icien is no ansmi -
ed, he measu ed da a canno be econs uc ed. The second
Fig. 4. Block diag am o GoF able calcula ions.
(a)
(b)
(c)
(d)
Fig. 5. Inpu and ou pu uzzy se s: (a) SoES uzzy inpu , (b) EP uzzy
inpu , (c) app oxima ion coe icien bu e size uzzy inpu , and (d) AP uzzy
ou pu .
column con ains he GoF o he measu ed da a econs uc ed
by DWT composi ion om he app oxima e coe icien s A3
only. The hi d and ou h columns con ains he GoF o
econs uc ed measu ed da a om A3, D3 and A3, D3, D2,
espec i ely. I all coe icien s a e ansmi ed (A3, D3, D2,
and D1), he GoF is always 1.
C. Fuzzy Logic Con olle
The uzzy logic con olle was designed o manage an adap -
able ansmission a e. The con olle selec s whe he da a
ansmission is equi ed and how la ge he payload should be
du ing a single ansmission.
Fig. 5desc ibes h ee inpu se s and one uzzy ou pu se .
All inpu uzzy se s a e ep esen ed by h ee unc ions (low,
KONECNY e al.: FUZZY CONTROLLED WAVELET-BASED EDGE COMPUTING METHOD 18913
Fig. 6. Summa y o uzzy ules applied by he uzzy logic con olle .
mid, and high), wi h a ious shapes designed acco ding o
he se ings c ea ed by an expe . The shape o he S a e-o -
Ene gy-S o age (SoES) uzzy se s ep esen s he p e e ence
o highe SoES alues. The middle uzzy se co esponds o
a 90% cha ge le el, and he high and low- uzzy se s a e dis-
ibu ed ac oss he es o he in e al. These se ings p e e a
conse a i e beha io as he IoT senso accumula es ene gy.
The ene gy p edic ion (EP) uzzy se s use a pa adigm simi-
la o SoES uzzy se s when a p og essi e s a egy is applied.
The middle uzzy se co esponds o 15 % o he maximum
p edic ed ene gy. The aim o he low-EP p e e ence is o
dynamically use ene gy when he EP inpu indica es incom-
ing ene gy in he nea u u e. The inal inpu se ep esen s he
size o he bu e which con ains un ansmi ed A3 coe icien s
and is calcula ed om memo y s a us. This inpu is deno ed
A3BS and ep esen s he A3 coe icien bu e size. The mid-
dle uzzy se is se o 75 %, which esul s in he p e e ence o
use mos o he a ailable memo y.
The uzzy ou pu a ailable payload (AP) ep esen s he max-
imum pe mi ed payload in a single ansmission. The e a e
i e uzzy se s, ep esen ing e y low, low, mid, high, and e y
high- ansmission in ensi y. The low, middle, and high- uzzy
se s a e ex ended by he minimum and maximum ope a-
ional se ings o he LoRaWAN communica ions in e ace
wi h uzzy unc ions ( e y low and e y high). The posi ions
o he ou pu uzzy se s a e de eloped asymme ically when
he low and mid uzzy unc ions a e se in a low in e al o
he AP, esul ing in he p e e ence o ea ly ansmission.
Fig. 6depic s he expe -de ined uzzy logic ules. Se e al
p inciples a e applied o designing ules. The i s p inciple
es ablishes he p e e ence o he SoES. The AP is se o maxi-
mum when he SoES uzzy se is high. The second p inciple is
de e mined by EP, whe e highe ene gy s a es gene ally lead o
a highe AP. The inal p inciple se s he un ansmi ed app ox-
ima e coe icien s ep esen ed by A3BS. When A3BS eaches
highe alues, in o ma ion la ency ca ies a signi ican weigh ,
and he e o e he AP is se o highe alues.
D. Da a T ansmission Module
The ansmission module decides which da a a e ansmi -
ed. The ansmission module’s inpu is he maximum AP
pe mi ed o he cu en pe iod. The AP is ob ained om he
uzzy con olle and may be blocked by a powe down lag
which signals no a ailable ene gy.
Fig. 7. S uc u e o he inpu da a and ha dwa e model wi h da a, model,
and in e ace laye s.
The ansmission module selec s da a clus e s o a o al size
less han o equal o he AP wi h he highes impo ance (i.e.,
da a clus e s wi h he leas GoF a e selec ed). The da a leng h
in he clus e is de ined by wa ele decomposi ion. Me ada a
should also be ansmi ed wi h each clus e . The equi ed
payload o clus e ansmission is calcula ed om
Payload =5+4·Clus e size.(2)
The payload equi ed o a speci ic clus e is calcula ed as
he sum o he me ada a leng h (5 by es) and he clus e size
mul iplied by he size o he loa ing poin da a ype (4 by es).
The ansmission module han calcula es he payload.
The clus e s con ain a imes amp alue and a column iden-
i y. The cloud g adually econs uc s he measu ed da a,
applying e inemen s each ime new da a a e ecei ed om
he IoT senso .
IV. EXPERIMENT
The expe imen al se up uses a ha dwa e model o simula e
an IoT de ice and EP model. The models p esen ed in his sec-
ion we e used as plug-in modules o a simula ion designed o
e alua e wa ele -based EC d i en by a uzzy logic con olle .
The s uc u e o he ha dwa e model and inpu da a (Fig. 7)
con ains h ee laye s. The i s laye p o ides he inpu da a
o calcula ing he quan i ies o ha es ed ene gy and p edic ed
ha es ed ene gy. The inpu da a laye also p o ides measu e-
men da a o he senso s on he IoT de ice. The model laye
con ains h ee blocks, ep esen ing a ha es ing model, an EP

18914 IEEE INTERNET OF THINGS JOURNAL, VOL. 10, NO. 21, 1 NOVEMBER 2023
model, and a consump ion model. The ha es ing model cal-
cula es he ha es ed ene gy acco ding o he inpu condi ions
and ou pu s a quan i y in joules. The EP model p ocesses and
p epa es he ha es ed ene gy da a o use in p edic ing u u e
ha es ed ene gy, and he consump ion model simula es he
beha io o he IoT de ice and o al powe consump ion o i s
componen s, which includes a mic ocon olle , senso s, and
a ansmission module. Finally, he hi d laye p o ides an
in e ace o he beha io simula ed by he EC me hod.
The in e ace laye con ains componen s ha link he ha d-
wa e and EP model o he es o simula ion. The SoES
desc ibes he emaining ene gy as a pe cen age o he max-
imum ene gy s o ed, indica ed as a alue in he ange 0–1.
Ene gy consump ion is calcula ed by he consump ion model
acco ding o he da a designa ed o ansmission. The alue is
no malized o he 0–1 ange and co esponds o 0–240 by es.
A powe down lag signals ansmission ailu e due o a lack
o ene gy. The p edic ed ene gy alue is no malized o he
0–1 ange and indica es he es ima ed a ailable ene gy o he
nex se en days. In his simula ion, 10-min his o ical ai em-
pe a u e measu emen da a p o ided he inpu o a senso ’s
ope a ion.
A. Ha dwa e Model
As men ioned abo e, he ha dwa e model con ains a ha -
es ing model and consump ion model. The ha es ing model
inco po a es a TEG and a DC/DC con e e , and i s inpu is
he di e ence in empe a u e be ween each side o he TEG.
Ano he in eg al pa o he ha es ing model is a supe ca-
paci o wi h a capaci y o 22 J o s o e ene gy o he IoT
de ice. The consump ion model calcula es he IoT de ice’s
powe consump ion. All he ha dwa e model’s pa ame e s a e
measu ed expe imen ally on he assembled ha dwa e se up.
Powe consump ion is measu ed in he ollowing componen s.
1) Mic ocon olle du ing sleep and un modes.
2) De ice senso .
3) Wi eless ansmission module.
The mic ocon olle ’s s andby powe consump ion is
3.63 µW, which ully complies wi h mode n low-powe mic o-
con olle s in sleep o s op mode. The equi ed ene gy o
measu emen and he mic ocon olle in un mode is 9.5 mJ.
The powe consump ion o he ansmission module a ies
acco ding o he size o he ansmi ed payload. The pa am-
e e s o a SemTECH LoRaWAN module we e measu ed o
his pu pose and used o es ablish a linea app oxima ion o
ansmission, de ined by
ET=k·Payload +q(3)
whe e ETis he equi ed ene gy in joules o a payload o
21–240 by es, k=2.4·10−3mJ/B is equi ed ene gy o
ansmi ing one by e ia LoRaWAN, and q=168 ·10−3mJ
is he s a ic powe consump ion in ol ing o e heads, such as
es ablishing a connec ion and acknowledging eceip .
Final consump ion is consis en wi h he s a ic consump-
ion o es ablishing a connec ion. The emaining dynamic
consump ion is dependen on he olume o da a ansmi ed
du ing he ansmission window. Fo pa ame e es ima ion, he
LoRaWAN module was se o a da a a e o 0 and TX-powe 0.
B. Inpu Da a and Es ima ed Ene gy Da a
The inpu da a we e o iginally collec ed a he Chu ano
S a ion, pa o he Czech Hyd o-Me eo ological Ins i u e’s
ex ensi e ne wo k o me eo ological s a ions. Chu ano
S a ion is loca ed a coo dina es 49.0683◦la i ude, 13.615◦
longi ude and 1117.8-m ele a ion.
10-min ai empe a u e da a om 2016–2019 we e used as
measu emen da a o he IoT senso . Fo ene gy ha es ing
pu poses, he simula ed TEG used a soil empe a u e p o ile
wi h 10-min in e als. A de ailed desc ip ion o empe a u e
di e ence es ima ion on he TEG and he o al ene gy ob ained
is gi en in his a icle [19].
The ansmission managemen con olle used weekly EPs
o es ima e he amoun o a ailable ene gy in he nea u u e.
The es ima ed ene gy alue was no malized o he in e al 0–1
and de i ed om ha es ed ene gy calcula ed by he ha es -
ing model. These da a simula ed eal EPs p o ided by local
senso s o om he cloud.
C. E alua ion C i e ia
Se e al assessmen c i e ia we e de ined o e alua ion
pu poses: maximum ou age be ween wo ansmissions, pe -
cen age o ansmi ed da a, penal y, pe cen age ime wi h no
ene gy, and da a a ailabili y pa ame e s.
The maximum ou age be ween wo ansmissions ela es
o he da a a ailabili y equi emen . Because he da a ans-
mission module’s powe consump ion is ela i ely high, da a
ansmission can be delayed and ansmi ed when su icien
ene gy is a ailable. Howe e , his ou age should be b ie since
he cloud s o es no online da a; he i s aim he e o e is o
main ain as b ie as possible ou ages.
The second aim is o ansmi he mos de ailed da a as pos-
sible. Using he ad an ages o wa ele -based comp ession, i is
possible o i s ansmi app oxima e coe icien s while delay-
ing o no ansmi ing de ailed coe icien s, bu he e en ual
a ge is o ansmi all da a as bes as possible. The hi d aim
is o minimize he numbe o powe downs o ailu es due o
lack o ene gy.
To assess da a a ailabili y, a penal y is de ined. The
penal y is he sum o each un ansmi ed block (app oxima e
coe icien s and de ails), weigh ed acco ding o a coe i-
cien and accumula ed in each simula ion s ep. The weigh
coe icien s a e 1, 2, 4, and 16; 1 o D3 de ails (mino de ails)
and 16 o app oxima ion pa ame e s.
V. RESULTS
This sec ion p esen s he esul s o he expe imen and sim-
ula ed uzzy-con olled wa ele -based EC me hod, om wo
pe spec i es. Fi s , he me hod is e alua ed acco ding o a ime
domain analysis o he eliabili y and amoun o ansmi ed
da a and he maximum ansmission delay. A da a a ailabili y
analysis is hen discussed in e ms o he delay pa ame e s o
he app oxima e and de ailed coe icien s.
Fo e alua ion pu poses, wo di e en e e ence con ol
algo i hms we e implemen ed and compa ed o he p oposed
uzzy logic con olle which managed he EC policy.
KONECNY e al.: FUZZY CONTROLLED WAVELET-BASED EDGE COMPUTING METHOD 18915
TABLE II
OVERALL COMPARISON OF RESULTS ACHIEVED BY THE REFERENCE
ALGORITHMS AND FUZZY CONTROL ALGORITHM
1) The i s e e ence algo i hm applied a ixed ansmis-
sion pe iod wi h a maximum ansmission payload. This
solu ion was es ed wi h se en di e en ixed-pe iod
con olle s.
2) The second e e ence was based on he maximum SoES
s a egy, whe e he con olle ansmi ed da a only when
he SoES indica ed a ull cha ge.
A. Time Domain Analysis
This sec ion p esen s a ime domain analysis which com-
pa es he dynamic beha io s o he uzzy con olled EC
me hod o he e e ence solu ions.
Table II compa es he esul s o he e e ence con ol
algo i hms and he uzzy con olle used wi h he EC me hod.
Rega ding he o al ansmi ed da a, only ixed pe iods o
240 and 360 min we e applied he de ailed coe icien . The
e e ence con olle s wi h ixed pe iods g ea e han 360 min
we e unable o ansmi all he da a because o he payload
limi a ion. The ixed algo i hm wi h a pe iod o 1440 min had
he sho es maximum ou age (app oxima ely 10 days).
The maximum SoES s a egy con olle was able o ansmi
all he da a. This algo i hm also achie ed he bes esul s in
he pe cen age o o al up ime and he ime wi h an emp y
SoES wi hou ailu e. I s maximum ou age, howe e , was he
longes o all he con olle s (app oxima ely 26 days).
The uzzy-con olled EC me hod p o ides he bes ade-
o be ween he p esen ed e alua ion c i e ia. The con olle
was able o ansmi all da a, wi h a maximum ou age o
13.49 days; his esul is one o he bes , and e en he bes
among he con olle s able o ansmi comple e da a wi hou
comp ession loss. The up ime a io anked ou h bes , which
is also accep able.
Fig. 8displays he beha io o he uzzy-con olled EC
me hod o e a 60-day in e al. AP indica es he uzzy con-
olle ’s ou pu , ansmi ed e e s o he olume o ansmi ed
by es, SoES ep esen s he amoun o a ailable ene gy, A3BS is
he bu e size s o age o app oxima e coe icien s, EP con ains
no malized da a on p edic ed incoming ene gy, and de ails
bu e size ep esen s he de ailed coe icien s s o age. I is
in e es ing ha when he SoES le el ell, he uzzy con olle
applied a conse a i e s a egy and educed ansmission o
Fig. 8. Fuzzy con olled EC me hod, whe e AP indica es he uzzy con-
olle ’s ou pu , ansmi ed e e s o he olume o ansmi ed by es, SoES
ep esen s he amoun o a ailable ene gy, A3BS is he bu e size s o age o
app oxima e coe icien s, EP e e s o he p edic ed ene gy o se en days,
and de ails bu e size ep esen s he de ailed coe icien s s o age.
p e en de ice ailu e. Howe e , as a esul , de ails bu e s o -
age inc eased. When he SoES le el inc eased again, he uzzy
con olle i s ansmi ed mainly app oxima e coe icien s,
ollowed by de ails.
B. Da a A ailabili y Analysis
This sec ion p esen s an analysis o he da a a ailabili y in
he IoT de ice a pa icula imes. The da a a ailabili y analysis
e alua ed only he h ee he bes pe o ming algo i hms (i.e.,
360 min, maximum SoES s a egy, and he uzzy con olle ).
The aim o his analysis was o de e mine he accu acy o he
o al in o ma ion alue o he ansmi ed da a a a ce ain ime
in he cloud.
Table III summa izes he a e age ansmission delays
o he DWT coe icien s o decomposed measu ed da a. Using
he uzzy con olle , he A3 app oxima e coe icien p oduced
he sho es delay, wi h an a e age o 0.51 days and median o
0.01 days. This is a e y in e es ing esul , because he app ox-
ima e alues a e a ailable in he cloud e y quickly as a esul
o using he DWT comp ession me hod. We can also obse e
ha he mos signi ican de ailed coe icien s we e ansmi -
ed wi h a maximum delay o h ee days. In he case o he
D3 coe icien s, he a e age upload ime was app oxima ely
one week. Fig. 9indica es he a e age ansmission delay
o he DWT-based comp ession coe icien s. The maximum
SoES s a egy ansmi ed only when he SoES indica ed a ull
18916 IEEE INTERNET OF THINGS JOURNAL, VOL. 10, NO. 21, 1 NOVEMBER 2023
TABLE III
AVERAGE TRANSMISSION DELAY FOR SPECIFIC COEFFICIENTS OF
DECOMPOSED MEASURED DATA
Fig. 9. A e age ansmission delay o wa ele -based comp ession
coe icien s.
cha ge, and a his momen , all he DWT coe icien s we e
uploaded simul aneously. This beha io did no achie e he
objec i e o o DWT comp ession, which includes consecu i e
ansmission o app oxima ed and de ailed coe icien s.
As desc ibed in Sec ion III, he con olle examines he
da a se and ansmi s mainly he da a wi h he highes p i-
o i y. App oxima e coe icien s a e p io i ized, and de ailed
coe icien s a e weigh ed acco ding o GoF wi hou any e alua-
ion o hei dep h. The a e age GoF alue o he app oxima e
coe icien s was 0.52; o D3 i was 0.68; and o D2 i was
0.80.
Table IV and Fig. 10 indica e he delay in da a a ailabili y
in he cloud o a ious GoF alues in he bes pe o ming
con olle s. Da a a ailabili y wi h he maximum SoES s a egy
con olle was no dependen on a GoF alue, co esponding
o he esul s p esen ed in he p e ious sec ion. The con olle
wi h a 360-min ixed pe iod p oduced he sho es delay wi h
a GoF o 0.1, bu he delay inc eased wi h highe GoF alues.
The uzzy con olle p oduced he sho es delay o 0.55–1.42
days wi h a GoF in he in e al 0.1–0.5. Mo e p ecise da a
became a ailable in he cloud a e a delay o 2.1–7.35 days.
TABLE IV
AVERAGE DELAY OF TRANSMITTED COMPRESSED DATA
ACCORDING TO GOF
Fig. 10. A e age delay o ansmi ed comp essed da a acco ding o GoF.
VI. DISCUSSION
This sec ion discusses SoA- ela ed s udies and compa es
hei me hods wi h he p oposed EC me hod. The limi a ions
and implica ions o he p oposed solu ion a e also e iewed.
A. Compa ison Wi h SoA App oaches
Table Vsumma izes he key pa ame e s o he ela ed s ud-
ies lis ed in Sec ion II and compa es he ma hema ical, neu al
ne wo k, da a educ ion, and wa ele -based EC me hods. The
EC me hods a e compa ed acco ding o hei capabili ies o
lossless ansmission, ligh weigh implemen a ion, comp es-
sion le el a iabili y, g adual da a e inemen , and sui abili y
o IoT senso s. None o he p esen ed EC me hods a e capa-
ble o ansmi ing app oxima e da a and subsequen ly e ining
he da a a e de ails a e ansmi ed. The me hods based on
neu al ne wo ks exhibi high-compu a ional complexi y and
KONECNY e al.: FUZZY CONTROLLED WAVELET-BASED EDGE COMPUTING METHOD 18917
TABLE V
COMPARISON OF THE FEATURES IN STATE-OF-THE-ART METHODS WITH THE PROPOSED EC METHOD
a e he e o e unsui able o ligh weigh implemen a ion in
low-powe IoT de ices. The da a educ ion echniques o e
lossless comp ession wi h a iable comp ession le els and
ligh weigh implemen a ion, bu hey do no suppo g adual
da a e inemen .
The cu en s udy iden i ied he unc ional pa ame e s o
ene gy consump ion and he ansmission pa ame e s o an
IoT senso powe ed by a TEG. The p oposed app oach
add esses challenges, such as limi ed bandwid h and limi ed
compu a ional esou ces, linked o da a ansmission in IoT
sys ems. A sui able comp ession me hod capable o a ying
he comp ession le el and a uzzy-based con ol algo i hm
enabling ea ly ansmission o app oxima ed da a and subse-
quen enhancemen wi h de ailed da a we e also p esen ed. The
p oposed solu ion ensu es e icien da a ansmission while
obse ing he limi ed esou ces and ene gy cons ain s o he
senso s. By using a a iable comp ession le el and a uzzy
con ol algo i hm, he solu ion op imizes da a ansmission
while main aining an accep able le el o de ail.
The uzzy con olle is well-sui ed o he speci ic equi e-
men s o ene gy ha es ing IoT senso s and he need o
dynamic con ol o ansmission. Fi mwa e implemen a ions
in embedded de ices commonly ollow a ini e s a e machine
app oach and employ du y cycle scena ios. In such cases,
a ule-based con olle is a sui able solu ion, ac ing as a
ansi ion unc ion in he implemen ed ini e s a e machine.
Howe e , by inco po a ing a uzzy-based solu ion, he op ions
o dynamic ene gy managemen s a egies a e expanded and
allow u u e op imiza ion o uzzy se and ule se ings. The
uzzy con olle p o ides a lexible and adap able app oach o
con olling he da a ansmission modules o ene gy ha es -
ing IoT senso s and enables e icien use o a ailable ene gy
esou ces, he eby enhancing o e all sys em pe o mance.
B. Implica ions and Limi a ions
The da a comp ession p ocess is limi ed by i s equi e-
men o a su icien ly long da a inpu da a ec o o achie e
wo hwhile comp ession. Consequen ly, his leads o a delay
in da a ansmission since he measu emen o a da a ec-
o o he same leng h is necessa y. Longe da a ec o s,
howe e , enable deepe decomposi ion and a mo e ex ensi e
comp ession p ocess.
Ano he limi a ion a ises om he impac o he comp es-
sion le el on compu a ional complexi y. As he comp ession
le el inc eases, he me hod becomes mo e compu a ionally
demanding. This should be ac o ed in when implemen ing
comp ession echniques, especially in ligh weigh low-powe
IoT de ices.
The leng h o he inpu da a ec o and he selec ed com-
p ession le el ep esen a comp omise be ween compu a ional
complexi y, he delay caused by measu ing he comple e inpu
da a ec o , and he comp ession a iabili y. Balancing hese
ac o s is c ucial o achie ing an op imal adeo be ween
e iciency and e ec i eness o he comp ession p ocess.
The p oposed solu ion applied comp ession o educe he
olume o ansmi ed da a. Comp ession was lossy o imp o e
da a a ailabili y and dec ease in o ma ion la ency. The esul s
o he expe imen demons a e ha he p oposed EC me hod
and uzzy con olle p io i ized he A3 coe icien s, which
ep esen da a wi h high-in o ma ion densi y.
A signi ican con ibu ion om his s udy is a me hod o
sequen ially e ining da a and educing da a olume du ing
ansmission when an IoT de ice lacks su icien ene gy. In
op imal cases, his app oach leads o a minimum loss o
in o ma ion wi h all de ailed coe icien s being ansmi ed.
The esul s indica e ha he p oposed EC me hod was able o
ansmi a comple e inpu da a se .
The uzzy logic con olle inpu s we e no malized o a ange
o alues, which means ha he uzzy se con igu a ion and
uzzy ules can be applied o o he applica ion a eas wi h di -
e en ene gy inpu s o ha es ing sou ces and exhibi simila
beha io . The DWT comp ession me hod is also comple ely
independen o domain. Al hough di e en measu ed pa am-
e e s can p oduce a iabili y in he GoF alues, his beha io
does no a ec ansmission p io i y.
The DWT comp ession me hod is sui able o execu-
ion in mic ocon olle s, especially digi al signal p oces-
so s which implemen MAC (mul iply–accumula e ope a ion)
ins uc ions. DWTs can also be deployed as mul iplica-
ion a ays. To decompose 32 samples in o he hi d le el,
1344 MAC ins uc ions a e equi ed, bu his numbe can
be educed by using a comp essed spa se ma ix echnique.
This ea u e allows he applica ion o EC me hods in low-
powe IoT de ices cha ac e ized by limi ed compu a ional
powe .