Fuzzy controlled wavelet-based edge computing method for energy-harvesting IoT sensors

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. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ 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 .