Non-Intrusive Load Monitoring of Household Devices Using a Hybrid Deep Learning Model through Convex Hull-Based Data Selection

  Ci a ion: Laouali, I.; Ruano, A.; Ruano, M.d.G.; Bennani, S.D.; Fadili, H.E. Non-In usi e Load Moni o ing o Household De ices Using a Hyb id Deep Lea ning Model h ough Con ex Hull-Based Da a Selec ion. Ene gies 2022,15, 1215. h ps://doi.o g/10.3390/en15031215 Academic Edi o : Luis He nández-Callejo Recei ed: 20 Decembe 2021 Accep ed: 1 Feb ua y 2022 Published: 7 Feb ua y 2022 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). ene gies A icle Non-In usi e Load Moni o ing o Household De ices Using a Hyb id Deep Lea ning Model h ough Con ex Hull-Based Da a Selec ion Inoussa Laouali 1,2 , An onio Ruano 1,3,* , Ma ia da G aça Ruano 1,4 , Saad Dosse Bennani 2and Hakim El Fadili 5 1DEEI, Facul y o Science & Technology, Uni e si y o Alga e, 8005-294 Fa o, Po ugal; [email p o ec ed] (I.L.); [email p o ec ed] (M.d.G.R.) 2SIGER, Facul y o Sciences and Technology, Sidi Mohamed Ben Abdellah Uni e si y, Fez P.O. Box 2202, Mo occo; [email p o ec ed] 3IDMEC, Ins i u o Supe io Técnico, Uni e sidade de Lisboa, 1950-044 Lisboa, Po ugal 4CISUC, Uni e si y o Coimb a, 3030-290 Coimb a, Po ugal 5LIPI, Facul y o Sciences and Technology, Sidi Mohamed Ben Abdellah Uni e si y, Bensouda, Fez P.O. Box 5206, Mo occo; [email p o ec ed] *Co espondence: a [email p o ec ed] Abs ac : The a ailabili y o sma me e s and IoT echnology has opened new oppo uni ies, anging om moni o ing elec ical ene gy o ex ac ing a ious ypes o in o ma ion ela ed o household occupancy, and wi h he equency o usage o di e en appliances. Non-in usi e load moni o ing (NILM) allows use s o disagg ega e he usage o each de ice in he house using he o al agg ega ed powe signals collec ed om a sma me e ha is ypically ins alled in he household. I enables he moni o ing o domes ic appliance use wi hou he need o ins all indi idual senso s o each de ice, hus minimizing elec ical sys em complexi ies and associa ed cos s. This pape p oposes an NILM amewo k based on low equency powe da a using a con ex hull da a selec ion app oach and hyb id deep lea ning a chi ec u e. I employs a sliding window o agg ega ed ac i e and eac i e powe s sampled a 1 Hz. A andomized app oxima ion con ex hull da a selec ion app oach pe o ms he selec ion o he mos in o ma i e e ices o he eal con ex hull. The hyb id deep lea ning a chi ec u e is composed o wo models: a classi ica ion model based on a con olu ional neu al ne wo k ained wi h a eg ession model based on a bidi ec ional long- e m memo y neu al ne wo k. The esul s ob ained on he es da ase demons a e he e ec i eness o he p oposed app oach, achie ing F1 alues anging om 0.95 o 0.99 o he ou de ices conside ed and es ima ion accu acy alues be ween 0.88 and 0.98. These esul s compa e a o ably wi h he pe o mance o exis ing app oaches. Keywo ds: non-in usi e load moni o ing; ene gy disagg ega ion; low equency powe da a; con ex hull; bidi ec ional long sho ime memo y; con olu ional neu al ne wo ks 1. In oduc ion The wo ld’s e e -inc easing ene gy consump ion and ongoing dependency on ossil uel-based ene gies ha e c ea ed signi ican en i onmen al conce ns, pa icula ly in e ms o ca bon dioxide (CO 2 ) emissions [ 1 ]. Focusing on he Eu opean coun y hos ing he cu en case-s udy household, Po ugal, g eenhouse gas (GHG) emissions inc eased by 13% om 2014 o 2018 as a esul o inc eased economic ac i i y and a high p opo ion o ossil uels in i s ene gy supply [ 2 ]. In 2019, impo ed ossil uels ep esen ed 76% o Po ugal’s p ima y ene gy (6% coal, 24% na u al gas, and 43% oil) [ 2 ]. Low-ca bon economies ha e eme ged as he ocus o wo ldwide a en ion in o de o minimize ene gy consump ion and g eenhouse gas emissions [ 3 ]. The a ge s se by he EU o 2030 include a minimum 32% sha e o enewable ene gy consump ion in he ene gy mix, a minimum o 32.5% ene gy sa ings, and a 40% educ ion in g eenhouse gas emissions compa ed o 1990 le els [ 4 ]. Po ugal was among he i s coun ies in he wo ld o se ca bon neu ali y goals o he Ene gies 2022,15, 1215. h ps://doi.o g/10.3390/en15031215 h ps://www.mdpi.com/jou nal/ene gies Ene gies 2022,15, 1215 2 o 22 yea 2050 [ 2 ]. The ocus is on minimizing dependency on impo ed ossil uels and e ec i e ene gy demand managemen . A a global pe spec i e, he building sec o accoun s o he la ges wo ldwide elec- ici y consump ion, o oughly 32% o o e all ene gy consump ion, and o 19% o o al ene gy- ela ed g eenhouse gas emissions [ 5 , 6 ]. Residen ial ene gy consump ion accoun ed o 25.71% o he EU’s o al inal ene gy consump ion, making i he second mos ene gy- in ensi e sec o a e anspo [ 7 ]. The e is an u gen need o coun e ac he upwa d end in building ene gy use. The Eu opean Union (EU) is making conside able e o s o p e en global wa ming by enac ing se e al key policies [ 8 ]. The e o e, o mee global and EU ca bon educ ion a ge s, esea ch e o s a e equi ed a he building sec o o lowe i s high con ibu ion o global ene gy consump ion. [9]. Since 2010, he amoun o elec ici y consumed by household de ices has isen by abou 3% pe yea . In 2019, household de ice elec ici y consump ion exceeded 3000 TWh, accoun ing o 15% o wo ldwide inal elec ici y demand [ 10 ]. Ene gy awa eness can help o educe ene gy consump ion in he households [ 11 ]. Hence, occupan beha io s ha e a signi ican ole in inc easing ene gy e iciency. Mo eo e , i end-use s can be no i ied in eal- ime and explici ly abou he consump ion o each appliance in hei home, unnecessa y ene gy usage can be educed [12–14]. The a ailabili y o sma me e s and IoT echnology has opened new oppo uni- ies, anging om moni o ing elec ical ene gy o ex ac ing a ious ypes o in o ma ion ela ed o household occupancy, as well as he equency o usage o di e en appli- ances. De ice moni o ing can be pe o med by ins alling one o a se o senso s in each de ice o in e es [15] , which is known as in usi e load moni o ing (ILM). I allows o accu a e de ec ion o he ope a ing s a e o each appliance [ 16 ]. Howe e , i s deploymen equi es complex ins alla ion and con igu a ion o mul iple senso s, especially when mul i- ple appliances a e in ol ed in he moni o ing scena io [ 14 ]. I also en ails a high cos , and i s in usi e na u e leads o some p i acy conce ns [ 11 ]. All hese disad an ages limi i s p ac ical use. On he o he hand, non-in usi e load moni o ing (NILM) is one o he mos p omising op ions o ene gy disagg ega ion. I allows use s o sepa a e he usage o each de ice in he house by using he o al agg ega ed powe signals collec ed om a sma me e ha is ypically ins alled in a household, while p o ec ing use p i acy [ 11 , 17 ]. The goal o NILM is o es ima e he speci ic consump ion o each appliance in he house based on agg ega ed da a collec ed by a sma me e . Mo eo e , i enables moni o ing domes ic appliance usage wi hou he need o ins all indi idual senso s o each de ice, hus minimizing elec ical sys em complexi ies and associa ed cos s [ 18 ]. Acco ding o [ 19 ], basic appliances, such as a washing machine, e ige a o , and o en, accoun o mo e han 30% o household consump ion. The iden i ica ion o hese ypes o de ices in he agg ega e da a is, howe e , challenging due o hei complex ea u e pa e ns. Fou ypes o de ices a e ca ego ized in he li e a u e [ 14 , 20 ]. The i s ca ego y ( ype I) comp ises wo s a e (ON-OFF) appliances such as oas e s and ligh bulbs. The ini e s a e machines (FSM) o mul i-s a e appliances ca ego ized as ype II de ices include appliances such as washing machines and idges. Type III includes con inuously a iable consume de ices such as powe ools and dimme s. Finally, pe manen consume appliances such as smoke ala ms a e ca ego ized as ype IV. The challenge o NILM algo i hms is he iden i ica ion o all ypes o de ices wi h good pe o mances. Type I de ices a e easie o disagg ega e due o hei basic a chi ec u e. The disagg ega ion o he o he ypes o de ices (Type II o Type IV) is s ill a challenging issue o NILM me hods [11]. The NILM p ocess was desc ibed o he i s ime in [ 21 ]. Ha p oposed ha , based on he en i e agg ega e ene gy usage moni o ed using a senso ins alled on he main powe panel, changes o he de ices could be de ec ed by applying an app op ia e s a is ical es o he collec ed da a. Subsequen ly, he ansi ions we e iden i ied using a con enien ea u es ec o , and inally, he iden i ica ion o each de ice was pe o med using supe ised o Ene gies 2022,15, 1215 3 o 22 unsupe ised app oaches [ 14 ], wi h supe ised echniques being ypically mo e e icien han unsupe ised app oaches [11,22]. The ini ial phase in e e y NILM algo i hm is da a ga he ing. Indeed, he equency wi h which he sma me e collec s da a de e mines he challenges and applica ions ha he NILM algo i hm will encoun e [ 23 ]. Da a may be acqui ed a ei he a high equency sampling a e, in he ange o kHz, o using a low equency (1 Hz o less) sampling a e. Fea u es such as ha monics, ansien s, and V-I ajec o y a e used o de ec he appliance con ibu ion in high equency app oaches [ 24 – 26 ]. On he o he hand, me hods based on low equency sampling a es gene ally employ powe ea u es such as ac i e powe (P), eac i e powe (Q), o appa en powe (S) [ 27 – 30 ]. High equency app oaches ha e he disad an age o making da a ansmission and s o age di icul , as well as being cos ly in e ms o ha dwa e and so wa e complexi y. Low equency echniques, on he con a y, a e he e ec i e choice in NILM applica ions since hey allow he use o comme cial sma me e esou ces wi hou he need o addi ional equipmen [31]. The in e es in NILM esea ch has been di e si ied since i s ea lies days. The o al powe se ies was i s examined o ind powe changes ha e lec de ice swi ching e en s, and hen hese occu ences a ibu ed o speci ic de ices [ 21 , 32 , 33 ]. A la e in e es in NILM esea ch has gi en ise o di e en a ian s o hidden Ma ko models [ 34 – 38 ]. Mo e ecen ly, he huge success o deep lea ning in he ields o ision and na u al language p ocessing has led o a g ea in e es in hese app oaches o NILM, which s a ed wi h he wo ks [ 13 , 39 ]. A comp ehensi e e iew o NILM me hods, including exis ing p oblems, can be ound in [11]. A discussion abou cu en NILM me hods will be de ailed in Sec ion 2. Despi e he nume ous NILM esea ch epo ed in li e a u e, many p oblems pe sis . These challenges include, o ins ance, poo de ec ion pe o mance, pa icula ly o low powe and mul is a e de ices, lesse scalabili y o de ec newly added de ices, and he need o gene a e mo e da ase s [ 14 ]. In o de o ackle hese challenges, deep lea ning algo i hms may be a sui able ool o imp o ing he accu acy and e iciency o ene gy disagg ega ion echniques [ 13 ]. This pape p oposes an NILM amewo k based on low equency powe da a. The amewo k employs a con ex hull da a selec ion me hod and a hyb id deep lea ning a chi ec u e. The main con ibu ions o his esea ch may be summa ized as ollows: • An NILM amewo k based on p i a e house da a ga he ing in a eal-li e si ua ion, using low equency sampling a e o 1 Hz. • A andomized app oxima ion con ex hull da a selec ion app oach using sliding win- dows o ac i e and eac i e powe . I is based on he selec ion o he mos in o ma i e e ices o he eal con ex hull and has he ad an age o educing memo y needs o he lea ning algo i hms. • A hyb id deep lea ning a chi ec u e composed o wo models. A classi ica ion model based on a con olu ional neu al ne wo k ained wi h a eg ession model based on a bidi ec ional long- e m memo y neu al ne wo k. • The esul s ob ained wi h he p oposed NILM amewo k on he es da ase demon- s a e he e ec i eness o he p oposed app oach, as well as achie ing be e esul s han exis ing app oaches. The es o he pape is o ganized as ollows: Sec ion 2p o ides a b ie o e iew o exis ing NILM algo i hms. Sec ion 3desc ibes he p oblem o mula ion, he con ex hull da a selec ion app oach used, he hyb id deep lea ning models, he case s udy employed, and he e alua ion me ics employed. Resul s and discussion a e p esen ed in Sec ion 4. Sec ion 5concludes he pape . 2. Rela ed Wo ks Going back o he genesis o he NILM concep [ 21 ], he au ho s demons a ed ha he appliances exhibi dis inc powe consump ion signa u es. In hei app oach, on/o e en s we e u ilized o iden i y he ope a ing s a e o speci ic de ices in he agg ega e ac i e and eac i e powe s. None heless, he me hod had di icul y iden i ying some ypes o de ices ( ype II, ype III, and ype IV). Following ha , nume ous al e na i e app oaches Ene gies 2022,15, 1215 4 o 22 we e in es iga ed in o de o ackle he NILM p oblem. Hidden Ma ko Models and i s a ian s ha e been widely explo ed ea ly on. Indeed, an addi i e Fac o ial Hidden Ma ko Model o non-in usi e load moni o ing was p oposed in [ 37 ]. The au ho s used an app oach o exploi ing he addi i e s uc u e o he Fac o ial Hidden Ma ko Model (FHMM) o cons uc an es ima e in e ence app oach ha u ilizes an e icien con- ex quad a ic p og amming elaxa ion. The p oposed app oach pe o med well while main aining a easonable compu ing complexi y. The au ho s o [ 40 ] examined se e al Hidden Ma ko Models (HMM). In hei s udy, Condi ional FHMM (CFHMM), Hidden Semi-Ma ko ian Fac o ial Model (HSMM), and he FHSMM/CFHMM combina ion using mul i-dimensional cha ac e is ics we e explo ed. These esea che s used ac ual s eady s a e powe signal in he low equency da a and demons a ed ha unsupe ised me h- ods could be u ilized o iden i y de ices non-in asi ely. The au ho s o [ 36 ] p oposed a ac o ial hidden Ma ko Model o NILM. They concen a ed on de ec ing he bina y and mul is a e ope a ion o de ices using app op ia e ea u e se s. They showed how ea u e conca ena ion can imp o e he accu acy o de ice iden i ica ion. In [ 41 ], p io models o gene ic de ice ypes a e adjus ed o de ice ins ances based only on inge p in s collec ed om he agg ega e load. The adjus ed de ice models a e hen used o p edic he load o each de ice, which is hen emo ed om he o al load. This p ocedu e is epea ed un il all de ices wi h known p io beha io models ha e been disagg ega ed. They showed ha he p oposed app oach pe o ms as well as when using sub-me e ed aining da a. The au ho s o [ 34 ] p esen ed a spa se Vi e bi app oach ha uses a supe -s a e HMM o p ese e load co ela ions and de ec mul i-s a e loads while o e ing compu a ionally e icien in e ence. They e alua ed hei model using a low equency sampling a e and showed ha hei model could un in eal- ime on a low-cos embedded CPU. The au ho s o [ 35 ] de eloped an Addi i e Fac o ial App oxima e Maximum a Pos e io i (AFAMAP) me hod. In hei app oach, ac i e and eac i e powe s a e used a a low equency sampling a e. I en ails modeling he alue o each agg ega ed powe sample as a combina ion o de ice ope a ing s a es and hen ec ea ing he ime se ies o s a e e olu ion o each ini e s a e machine de ice. They demons a ed ha he use o eac i e powe inc eases he pe o mance o he echnique. In [ 42 ], a machine lea ning app oach o on-line non-in usi e load moni- o ing ha combines unsupe ised e en -based p o iling and Ma ko chain de ice load modeling is p esen ed. In hei app oach, he e en -based componen de ec s e en s using con iguous and ansien segmen s and ma ching and e en clus e ing. The speci ic de ice model is c ea ed om a gene ic de ice model using he ea u es ob ained. The de ice model pa ame e s a e hen used o c ea e an addi i e FHMM o online disagg ega ion. They demons a ed ha he sugges ed echnique enables on-line de ec ion while p o iding compa able p edic ion pe o mance o non-online me hods. The complexi y o HMM models and i s a ian s g ow exponen ially as he numbe o a ge appliances g ows. Mo eo e , hei gene aliza ion and scalabili y abili ies a e p oblema ic. Exis ing in e ence me hods o s a e p edic ion a e also ex emely sensi i e o local op ima, hence, limi ing hei applica ion in he eal wo ld [ 15 ]. Consequen ly, deep lea ning and machine lea ning echniques a e sui able al e na i es o add ess he NILM challenges. These include suppo ec o machine [ 43 – 45 ], Decision T ee [ 46 , 47 ], K-nea es neighbo s [ 48 ], K-means clus e ing [ 49 ], and g aph signal p ocessing [ 50 , 51 ] as wo hwhile men ioning app oaches. The au ho s o [ 13 ] in oduced deep lea ning app oach o NILM. In hei pape , h ee deep lea ning models we e explo ed. These include denoising au oencode , long sho - e m memo y combined wi h a con olu ional neu al ne wo k, and a eg ession model ha es ima es he s a ime, end ime, and he a e age powe demand o each de ice. They modeled NILM as a denoising ask, in which he a ge de ice powe load ep esen s he clean signal, and he agg ega e load is he backg ound ‘noise’ gene a ed by he p esence o o he de ices. They showed ha he denoising au oencode ou pe o ms he FHMM and combina o ial op imiza ion s a e o he a echniques. The au ho s o [ 52 ] p esen ed a sequence o poin app oach. They employed a con olu ional neu al ne wo k, wi h he inpu Ene gies 2022,15, 1215 5 o 22 being a window o agg ega e ac i e powe and he ou pu being a single poin o he a ge appliance. They showed using he Re e ence Ene gy Disagg ega ion Da a Se (REDD) [ 53 ] and UK Domes ic Appliance-Le el Elec ici y (DALE) [ 54 ] da ase s ha he sequence- o- poin echnique ou pe o ms he sequence- o-sequence s a e o he a app oaches. In [ 55 ], a deep lea ning based on he con olu ional neu al ne wo k, long- e m sho - e m memo y ne wo k, and andom o es (RF) algo i hm was p esen ed. They in es iga ed he con- cep o label co ela ions and es ed hei model on he Pecan S ee [ 56 ] and REDD [ 49 ] da ase s. A deep lea ning based on bidi ec ional long sho - e m memo y model wi h a con olu ional laye is p oposed in [ 57 ]. The au ho s used a a ie y o elec ical ea u es o gene a e a mul i- ea u e inpu . The model was alida ed using low equency da a om he publicly a ailable da ase s Elec ici y Consump ion & Occupancy (ECO) [ 58 ] and UKDALE [ 54 ]. In he same pape , hey p oposed a pos -p ocessing algo i hm o elimina e supe luous p edic ed sequences. They p o ed ha using he pos -p ocessing echnique, he model pe o ms well. In [ 59 ], an NILM app oach based on he deep con olu ional neu al ne wo k model using da a augmen a ion o p oduce syn he ic da a is p oposed. In hei app oach, he da a augmen a ion me hod in eg a es on and o -du a ions o a a ge appliance om h ee da ase s (ECO, REDD, and UKDALE) using a low equency sampling a e. A uni ied and consis en syn he ic agg ega e and sub-me e p o iles a e hen c ea ed. They showed ha aining he model on he p oduced syn he ic da a enhances i s gene al- izabili y. The au ho s o [ 60 ] p oposed a deep con olu ional neu al ne wo k based on da a augmen a ion o ype II de ices. A pos -p ocessing algo i hm was sugges ed o classi y he ac i a ions es ima ed by he eg ession model. They demons a ed ha using he sugges ed pos -p ocessing echnique g ea ly enhances he model’s pe o mance. The au ho s o [ 61 ] ocused on imp o ing NILM pe o mance ia a ailo ed a en ion mechanism. The ap- p oach is based on deep neu al ne wo k a chi ec u e using he encode -decode amewo k. The p oposed a chi ec u e consis s o a eg ession subne wo k model combined wi h a classi ica ion subne wo k model. They sugges ed he use o con olu ional and ecu en laye s in he eg ession subne wo k o inc ease ea u e ex ac ion and c ea e be e de ice models. They showed ha he p oposed app oach imp o es model pe o mances and gen- e aliza ion abili y. Decision T ee and long sho - e m memo y models a e p oposed in [ 46 ] o pe o m an e en de ec ion app oach using ansien signal. The la e was ex ac ed in low equency using ac i e powe signal. They showed ha including he ansien signal in o he inpu signals imp o es he model’s pe o mance. The au ho s o [ 18 ] p oposed a mul i-label classi ica ion app oach based on a ully con olu ional neu al ne wo k. In hei app oach, he appliance s a es a e classi ied using a ea u es space enhanced by a empo al pooling module. The appliance powe is es ima ed using he cons an a e age alue when he appliance is ac i e. They showed ha he p oposed echnique achie ed good pe o mance in ecognizing he ac i a ion s a us o de ices and es ima ing hei powe consump ions. 3. Ma e ials and Me hods The main objec i e o ene gy disagg ega ion is o b eak down he house’s global agg ega ed da a in o speci ic con ibu ions o each appliance. The pu pose is o ecognize each appliance ope a ing s a e and o es ima e i s ene gy consump ion con ibu ion wi hin he house’s o al consump ion. The p oblem can be s a ed as ollows: gi en a sequence o agg ega ed da a X = {x1,· · · ,xT} , he ask o NILM is o de e mine he con ibu ion o each appliance I, y(i) =ny(i) 1,· · · ,y(i) To , whe e I= {1, . . . ,N} is he index o he appliance ( om a se o Nappliances), and = {1, · · · ,T} is he ime-index o he sequence wi h leng h T. The agg ega ed da a can be exp essed as he sum o he con ibu ion o indi idual appliances plus an unknown pa due o noise, ep esen ed by: X =∑N 1y(i) +∂ (1) whe e ∂ is he noise e m. Ene gies 2022,15, 1215 6 o 22 The con ibu ion o an indi idual appliance y(i) is gi en by: y(i) =ψ(X )(2) whe e ψ is he ope a o ha , when applied o he whole agg ega ed da a, gi es he bes es ima e o he con ibu ion o each indi idual appliance. The ask o ob aining an app oxima ion o he ope a o ψ may be add essed as a su- pe ised lea ning p oblem [ 18 ]. This is he app oach ollowed he e, whe e he a chi ec u e o he p oposed algo i hm includes a con ex hull-based da a selec ion algo i hm called App oxHull, p oposed in [62], and a hyb id deep neu al ne wo k model. The a chi ec u e o he hyb id ne wo k is made up o wo subne wo ks inspi ed in he wo k p oposed in [ 61 , 63 ]. The app oach makes use o an independen classi ica ion subne - wo k ha is ained join ly wi h he ypical eg ession subne wo k. The ne wo k ou pu is gi en by he combina ion o ou pu s o he wo subne wo ks. These lea ning app oaches allow models o gene alize e icien ly o he o iginal ask by sp eading pa ame e s ac oss ela ed asks [ 63 ]. Besides, deep neu al ne wo ks end o de ec i ele an ac i a ions ha a e no ela ed o he a ge de ice ac i a ions [ 57 , 60 ]. The associa ed classi ie enables hese i ele an p edic ions o be elimina ed and conside s only p edic ions in which he de ice is ac i e. 3.1. App oxhull Algo i hm An objec in Euclidean space is con ex i , o each couple o poin s inside he objec , each poin on he s aigh -line segmen joining hem is also inside he objec [ 62 ]. I is assumed ha a se C is con ex i , o each pai (x,y) ∈ C and any k ∈ [0, 1], he poin (1 −k)x+ky is in C. Fu he mo e, i C is a con ex se , o any x 1 ,x 2 , . . . ,x i∈ C and any nonnega i e numbe s { µ1 , µ2 , . . . , µi } ∑i j=1µi= 1, he ec o ∑i j=1µixi is deno ed as a con ex combina ion o x1,x2, . . . , xi. Following he de ini ions abo e, he con ex hull o con ex en elope o he se Ω o poin s in Euclidean space can be Desc ibed ei he in e ms o con ex se s o using con ex combina ions. I can be gi en as he in e sec ion o all con ex se s con aining Ω o as he se o all con ex combina ions o poin s in Ω. App oxHull is a da a selec ion algo i hm based on a andomized app oxima ion con ex hull echnique, capable o handling la ge dimensions o da a in a easonable amoun o ime and memo y [ 62 ]. Indeed, da a used o design a model mus co e he whole inpu ange in which he model will be used o enhance he model’s pe o mance. App oxHull is an inc emen al algo i hm ha s a s wi h an ini ial con ex hull and hen inc emen ally expands he cu en con ex hull by adding new e ices. I assumes a use - de ined h eshold, β , o ob ain a subse o he mos in o ma i e e ices o he eal con ex hull. Figu e 1shows a low cha summa izing he App oxHull algo i hm. Fo mo e de ails, please e e o [62]. I should be no ed ha be o e applying App oxHull, he o iginal da ase is p ep o- cessed. Fo equal columns (iden ical ea u es) and duplica ed ows (equal samples), ows wi h non-nume ical alues and ows wi h missing alues a e excluded o educe he pos- sibili y o App oxHull gene a ing a singula ma ix co esponding o a andom in alid ace . App oxHull ensu es ha all con ex hull poin s om he design da a a e included in he aining se , which is hen augmen ed wi h samples andomly ex ac ed om he design da a o ob ain he use -speci ied numbe o samples o he aining se . The emain- ing design da a a e andomly spli o he es ing and alida ion se s, acco ding o he use speci ica ions. As a esul o his p ocedu e, aining, es ing, and alida ion se s a e gene a ed. Ene gies 2022,15, 1215 7 o 22 Ene gies 2022, 15, 1215 7 o 22 Figu e 1. App oxHull algo i hm lowcha . Adap ed om e e ence [62]. I should be no ed ha be o e applying App oxHull, he o iginal da ase is p ep ocessed. Fo equal columns (iden ical ea u es) and duplica ed ows (equal samples), ows wi h non-nume ical alues and ows wi h missing alues a e excluded o educe he possibili y o App oxHull gene a ing a singula ma ix co esponding o a andom in alid ace . App oxHull ensu es ha all con ex hull poin s om he design da a a e included in he aining se , which is hen augmen ed wi h samples andomly ex ac ed om he design da a o ob ain he use -speci ied numbe o samples o he aining se . The emaining design da a a e andomly spli o he es ing and alida ion se s, acco ding o he use speci ica ions. As a esul o his p ocedu e, aining, es ing, and alida ion se s a e gene a ed. 3.2. Con olu ional Neu al Ne wo k (CNN) In ecen yea s, con olu ional ne wo ks ha e seen a se ies o successes in classi ying la ge-scale images [60]. I s e ec i eness s ems om i s abili y o model nonlinea local dependencies [64,65]. A con olu ional neu al ne wo k a chi ec u e is ypically made up o h ee laye s: con olu ional laye , pooling laye , and ully connec ed laye . The con olu ional laye aims o ex ac ea u es ha ep esen he inpu s. I is made up o many con olu ion ke nels ha a e used o compu e dis inc ea u e maps [66]. Equa ion (3) desc ibes he ea u e maps using se e al dis inc ke nels: 𝑧𝑖,𝑗,𝑘 𝑙 = 𝑊𝑘 𝑙𝑥𝑖,𝑗 𝑙+𝑏𝑘 𝑙 (3) whe e 𝑥𝑖,𝑗 𝑙 deno es he inpu s o he l h laye a loca ion (I, j), 𝑊𝑘 𝑙 and 𝑏𝑘 𝑙 ep esen , espec i ely, he weigh ec o and bias e m o he l h laye and k h il e . Nonlinea i ies a e in oduced in o CNN ia he ac i a ion unc ion, which is use ul o mul i-laye ne wo ks o cap u e nonlinea ea u es. The ac i a ion unc ion is gi en by: 𝜑𝑖,𝑗,𝑘 𝑙 = 𝜑(𝑧𝑖,𝑗,𝑘 𝑙) (4) The ReLu ac i a ion unc ion is used in his wo k [67]. ReLu(𝑥)= max (0,𝑥) (5) Figu e 1. App oxHull algo i hm lowcha . Adap ed om e e ence [62]. 3.2. Con olu ional Neu al Ne wo k (CNN) In ecen yea s, con olu ional ne wo ks ha e seen a se ies o successes in classi ying la ge-scale images [ 60 ]. I s e ec i eness s ems om i s abili y o model nonlinea local dependencies [ 64 , 65 ]. A con olu ional neu al ne wo k a chi ec u e is ypically made up o h ee laye s: con olu ional laye , pooling laye , and ully connec ed laye . The con olu- ional laye aims o ex ac ea u es ha ep esen he inpu s. I is made up o many con o- lu ion ke nels ha a e used o compu e dis inc ea u e maps [ 66 ]. Equa ion (3) desc ibes he ea u e maps using se e al dis inc ke nels: zl i,j,k=Wl kxl i,j+bl k(3) whe e xl i,j deno es he inpu s o he l h laye a loca ion (I,j), Wl k and bl k ep esen , espec- i ely, he weigh ec o and bias e m o he l h laye and k h il e . Nonlinea i ies a e in oduced in o CNN ia he ac i a ion unc ion, which is use ul o mul i-laye ne wo ks o cap u e nonlinea ea u es. The ac i a ion unc ion is gi en by: ϕl i,j,k=ϕzl i,j,k(4) The ReLu ac i a ion unc ion is used in his wo k [67]. ReLu(x)=max (0, x)(5) The pooling laye enables o selec and il e he ea u es ex ac ed by he con olu ional laye . I in ends o achie e shi -in a iance by lowe ing he esolu ion o he ea u e maps. The pooling unc ion o each ea u e map ϕl :,:,kis as ollows: yl i,j,k=poolϕl m,n,k,∀(m,n)∈Rij (6) Ene gies 2022,15, 1215 8 o 22 whe e Rij deno es a local neighbo hood a ound loca ion (I,j). The max-pooling is used in his wo k o pooling ope a ion. I s ou pu wi h s ide land size sis de ined by: y(i) = max x[i×l:i×l+s−1] (7) The ully connec ed laye s seek o conduc high-le el easoning. They connec all neu ons o he p e ious laye o e e y neu on in he cu en laye o p oduce global seman ic in o ma ion. The ou pu is gene a ed by nonlinea ly combining he ea u es ha ha e been selec ed wi h he ully connec ed laye . T aining a CNN in ol es minimizing a sui able loss unc ion. Gi en a se o inpu ou pu {( x(k) , y(k) ), k= [1, . . . , K]} , whe e x(K) deno es he k h inpu da a and y(k) is he ma ching a ge label, assume ha θ ep esen s all he CNN pa ame e s and ois he CNN ou pu . The loss unc ion o CNN may be compu ed as ollows: Γ=1 N∑N n=1`(θ,y(n),o)(8) The bes i ing se o pa ame e s may be ound by minimizing he loss unc ion. Fu he in o ma ion abou CNN models can be ound in [ 66 ]. The ial-and-e o p oce- du e was used o une he CNN hype pa ame e s. The classi ica ion subne wo k CNN a chi ec u e p oposed wi h he bes hype pa ame e s alues is as ollows: •Inpu shape (leng h de ined by he appliance da a). •1D con olu ional laye ( il e s = 32, ke nel size = 3, ac i a ion = ‘ReLu’). •1D con olu ional laye ( il e s = 64, ke nel size = 3, ac i a ion = ‘ReLu’). •1D con olu ional laye ( il e s = 128, ke nel size = 3, ac i a ion = ‘ReLu’). •Maxpool laye . •Fully connec ed dense laye (numbe o uni s = 1024, ac i a ion = ’ReLu’). •Fully connec ed dense laye (numbe o uni s = 1). 3.3. Long Sho -Te m Memo y (LSTM) LSTM has been in oduced by [ 68 ] o add ess bo h long- e m and sho - e m depen- dency issues. I is a deep ecu en neu al ne wo k ha uses a eed- o wa d a ia ion o p ocess sequen ial da a and add ess anishing g adien issues. The LSTM design eplaces he hidden laye o he con en ional neu al ne wo k uni s wi h combined memo y cells. I is made up o h ee ga es: an inpu ga e, a o ge ga e, and an ou pu ga e. The s a e o he memo y cell is e e ed o as a cell s a e. The LSTM ne wo k may add o dele e in o ma ion o he memo y cell s a e ia he inpu ga e, ou pu ga e, and o ge ga e. Each ga e has a speci ic pu pose ha is de e mined by he cu en ex e nal inpu and he p e ious cell’s ou pu . The inpu ga e de e mines how much he block inpu will upda e he cell s a e. The o ge ga e de e mines which in o ma ion om he p io cell s a e should be e ased and which should be s o ed. I enables he cell o memo ize o o ge i s p io s a e, as necessa y. The ou pu ga e de e mines which piece o he cell s a e should be p opaga ed o he ou pu . The block ou pu is hen compu ed by mul iplying he il e ed cu en cell s a e by he ou pu ga e. I can enable o p e en he cell s a e om a ec ing o he neu ons. Figu e 2 p esen s he a chi ec u e o he LSTM cell. The e ms i , , o , h , c deno e, espec i ely, he inpu ga e, o ge ga e, ou pu ga e, he ou pu , and he cell s a e. The symbols σ and anh ep esen he sigmoid ac i a ion unc ion and he anh ac i a ion unc ion, espec i ely. Ene gies 2022,15, 1215 9 o 22 Ene gies 2022, 15, 1215 9 o 22 Figu e 2. LSTM cell a chi ec u e. Adap ed om e e ence [68]. One o he app oaches o imp o e he ecu en neu al ne wo k models is he usage o bidi ec ional laye s [13]. Indeed, one ecu en neu al ne wo k eads he inpu sequence o wa d, while he o he eads i backwa d. To me ge he ou pu om he ne wo k’s o wa d and backwa d sides, an elemen -wise sum is employed. The bidi ec ional LSTM ne wo k p edic s ac ual alue using bo h p io and u u e in o ma ion, and in his way is an ideal model o he NILM p oblem [57]. I is made up o h ee laye s: inpu laye , hidden laye , and ou pu laye . The hidden laye is made up o wo unidi ec ional LSTM laye s ha ha e iden ical a chi ec u e and he same inpu bu p opaga e he da a in he opposi e di ec ion. The ollowing a e he ec o o mulas de ining he o wa d LSTM laye o he p opaga ion p ocess [69]. 𝑓𝑡 = σ (𝑊𝑓.[ℎ𝑡−1,𝑥𝑡]+𝑏𝑓) (9) 𝑖𝑡= σ (𝑊𝑖.[ℎ𝑡−1,𝑥𝑡]+𝑏𝑖) (10) 𝑐𝑡  =𝑡𝑎𝑛ℎ(𝑊𝑐.[ℎ𝑡−1,𝑥𝑡]+𝑏𝑐) (11) 𝑐𝑡= 𝑓𝑡⊙𝑐𝑡−1+𝑖𝑡⊙ 𝑐𝑡  (12) 𝑜𝑡= σ (𝑊𝑜.[ℎ𝑡−1,𝑥𝑡]+𝑏𝑜) (13) ℎ𝑡 = anh (𝑐𝑡) (14) ℎ𝑡=𝑜𝑡⊙ℎ𝑡  (15) whe e ⊙ deno es elemen -by-elemen mul iplica ion. 𝑊𝑓, 𝑊𝑖, 𝑊𝑐, 𝑊𝑜 and 𝑏𝑓, 𝑏𝑖, 𝑏𝑐, 𝑏𝑜 a e he weigh ma ices and bias ec o s o o ge ga e, inpu ga e, cell s a e, and ou pu ga e, espec i ely, in he o wa d LSTM laye . The in o ma ion p opaga ion mechanism in he backwa d LSTM laye is desc ibed as ollows: 𝑓𝑡′ = σ (𝑊𝑓′.[ℎ𝑡+1 ′,𝑥𝑡]+𝑏𝑓 ′) (16) 𝑖𝑡 ′= σ (𝑊𝑖′.[ℎ𝑡+1 ′,𝑥𝑡]+𝑏𝑖′) (17) 𝑐𝑡 ′= anh(𝑊𝐶 ′.[ℎ𝑡+1 ′,𝑥𝑡]+𝑏𝑐 ′) (18) 𝑐𝑡 ′= 𝑓𝑡′⊙𝑐𝑡−1 ′+𝑖𝑡 ′⊙𝑐𝑡 ′ (19) 𝑜𝑡 ′= σ (𝑊𝑜′.[ℎ𝑡+1 ′,𝑥𝑡]+𝑏𝑜 ′) (20) ℎ𝑡 ′ = anh(𝑐𝑡 ′) (21) ℎ𝑡 ′=𝑜𝑡 ′⊙ℎ𝑡 ′  (22) Figu e 2. LSTM cell a chi ec u e. Adap ed om e e ence [68]. One o he app oaches o imp o e he ecu en neu al ne wo k models is he usage o bidi ec ional laye s [ 13 ]. Indeed, one ecu en neu al ne wo k eads he inpu sequence o wa d, while he o he eads i backwa d. To me ge he ou pu om he ne wo k’s o wa d and backwa d sides, an elemen -wise sum is employed. The bidi ec ional LSTM ne wo k p edic s ac ual alue using bo h p io and u u e in o ma ion, and in his way is an ideal model o he NILM p oblem [ 57 ]. I is made up o h ee laye s: inpu laye , hidden laye , and ou pu laye . The hidden laye is made up o wo unidi ec ional LSTM laye s ha ha e iden ical a chi ec u e and he same inpu bu p opaga e he da a in he opposi e di ec ion. The ollowing a e he ec o o mulas de ining he o wa d LSTM laye o he p opaga ion p ocess [69]. =σW .[h −1,x ]+b (9) i =σ(Wi.[h −1,x ]+bi)(10) ˆ c = anh(Wc.[h −1,x ]+bc)(11) c = c −1+i ˆ c (12) o =σ(Wo.[h −1,x ]+bo)(13) ˆ h = anh(c )(14) h =o ˆ h (15) whe e  deno es elemen -by-elemen mul iplica ion. W , Wi , Wc , Wo and b , bi , bc , bo a e he weigh ma ices and bias ec o s o o ge ga e, inpu ga e, cell s a e, and ou pu ga e, espec i ely, in he o wa d LSTM laye . The in o ma ion p opaga ion mechanism in he backwa d LSTM laye is desc ibed as ollows: 0 =σW0 .h0 +1,x +b0 (16) i0 =σW0 i.h0 +1,x +b0 i(17) ˆ c0 = anhW0 C.h0 +1,x +b0 c(18) c0 = 0 c0 −1+i0 ˆ c0 (19) o0 =σW0 o.h0 +1,x +b0 o(20) ˆ h0 = anhc0 (21) h0 =o0 ˆ h0 (22) Ene gies 2022,15, 1215 16 o 22 p esen s he compa ison o he p oposed NILM app oach o s a e o a NILM me hods o washing machine. Ene gies 2022, 15, 1215 16 o 22 Figu e 6. Disagg ega ion ou pu o he washing machine. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Figu e 7. Disagg ega ion ou pu o he idge. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe . Figu e 6. Disagg ega ion ou pu o he washing machine. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Ene gies 2022, 15, 1215 16 o 22 Figu e 6. Disagg ega ion ou pu o he washing machine. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Figu e 7. Disagg ega ion ou pu o he idge. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe . Figu e 7. Disagg ega ion ou pu o he idge. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe . The esul s p esen ed in Tables 8and 9show ha he p oposed app oach is e y e ec i e in iden i ying he s a es o he de ices and in es ima ing he ene gy consumed by each de ice. F idge and washing machine a e e y common mul i-s a e appliances o es ing NILM algo i hms. Fo he washing machine, he p oposed app oach achie es he bes esul s in e ms o p ecision (96%), F1 sco e (96%), mean absolu e e o (1.64 W), and es ima ion accu acy (93%). Howe e , i ob ained a sligh ly wo se ecall (96%) han CNN (98%) p esen ed in [60] and Online-NILM (100%) p oposed in [42]. Fo he idge, he p oposed app oach consis en ly ou pe o ms s a e-o - he-a me h- ods in e ms o ecall (97%), p ecision (92%), F1 sco e (95%), and es ima ion accu acy (88%). Con e sely, i had a sligh ly wo se mean absolu e e o o 12.72 W compa ed o he Online-NILM 4.34 W p esen ed in [ 42 ]. The o e all esul s demons a e ha , when compa ed o s a e-o - he-a algo i hms, he p oposed app oach e ec i ely disagg ega es a ge de ices wi h highe powe es ima ion accu acy and a supe io F1 sco e. Ene gies 2022,15, 1215 17 o 22 Ene gies 2022, 15, 1215 17 o 22 Figu e 8. Disagg ega ion ou pu o he elec ic wa e hea e . Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Figu e 9. Disagg ega ion ou pu o he swimming pool pump. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . As i can be seen in Figu es 6–9, he e is a e y good ag eemen be ween he es ima ed ac i e powe and he g ound u h ac i e o all ou appliances conside ed in he expe imen . The es ima ed powe consump ion signals a e e y close o he g ound u h. I should also be men ioned ha each o hese de ices p esen ed e y sa is ac o y pe o mances. To alida e he ep oducibili y o he expe imen , a i e- old c oss alida ion was used. As in he o iginal expe imen , 80% o he da a was used o aining and 20% o es ing; he design da a was pa i ioned in o i e mu ually exclusi e subse s o equal size, wi h one subse being u ilized o es ing and he emaining ou being used o es ima e he pa ame e s and compu e he model’s accu acy. This p ocess is pe o med k imes by ci cula ly al e na ing he es subse . Table 7 p esen s he esul s o he i e-c oss- alida ion o he washing machine and idge in e m o F1 sco e. Figu e 8. Disagg ega ion ou pu o he elec ic wa e hea e . Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Ene gies 2022, 15, 1215 17 o 22 Figu e 8. Disagg ega ion ou pu o he elec ic wa e hea e . Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Figu e 9. Disagg ega ion ou pu o he swimming pool pump. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . As i can be seen in Figu es 6–9, he e is a e y good ag eemen be ween he es ima ed ac i e powe and he g ound u h ac i e o all ou appliances conside ed in he expe imen . The es ima ed powe consump ion signals a e e y close o he g ound u h. I should also be men ioned ha each o hese de ices p esen ed e y sa is ac o y pe o mances. To alida e he ep oducibili y o he expe imen , a i e- old c oss alida ion was used. As in he o iginal expe imen , 80% o he da a was used o aining and 20% o es ing; he design da a was pa i ioned in o i e mu ually exclusi e subse s o equal size, wi h one subse being u ilized o es ing and he emaining ou being used o es ima e he pa ame e s and compu e he model’s accu acy. This p ocess is pe o med k imes by ci cula ly al e na ing he es subse . Table 7 p esen s he esul s o he i e-c oss- alida ion o he washing machine and idge in e m o F1 sco e. Figu e 9. Disagg ega ion ou pu o he swimming pool pump. Blue, g ound u h ac i e powe ; ed, p edic i e ac i e powe ; yellow, agg ega e ac i e powe . Table 7. F1 sco e using c oss alida ion. Washing Machine 0.963 0.961 0.959 0.958 0.959 F idge 0.944 0.938 0.950 0.934 0.947 Table 8. Compa ison esul s wi h exis ing non-in usi e load moni o ing me hods o washing machine. Me hod Recall P ecision F1 MAE (W) SAE EA Online-NILM [42]10.60 0.70 118.11 - - MFS-LSTM [57] - - 0.76 14.42 0.51 0.74 CNN [83] 0.78 0.20 0.32 18.38 - - LDwA [61] - - 0.69 11.17 - - CNN [60] 0.98 0.87 0.92 - - 0.92 TP-NILM [18] 0.86 0.87 0.86 8.31 0.01 - P oposed 0.96 0.96 0.96 1.64 0.05 0.93 Ene gies 2022,15, 1215 18 o 22 The pe o mances compa ison o he idge o he s a e-o - he-a me hods is p esen ed in Table 9. Table 9. Compa ison esul s wi h exis ing non-in usi e load moni o ing me hods o he idge. Me hod Recall P ecision F1 MAE (W) SAE EA Online-NILM [42] 0.73 0.87 0.79 4.34 - - MFS-LSTM [57] - - 0.87 19.60 0.46 0.76 CNN [83] 0.97 0.80 0.88 7.90 - - LDwA [61] - - 0.86 19.81 - - TP-NILM [18] 0.89 0.85 0.87 17.03 −0.05 - P oposed 0.97 0.92 0.95 12.72 0.09 0.88 5. Conclusions This pape p oposes an NILM amewo k based on low equency powe da a using a con ex hull da a selec ion app oach and a hyb id deep lea ning a chi ec u e. Da a we e collec ed in a p i a e house in Alga e, Po ugal. The inpu o he model is a sliding window o ac i e and eac i e powe alues sampled a 1 Hz. As a p ima y s ep, da a selec ion using a andomized app oxima ion con ex hull is conduc ed. I is based on he selec ion o he mos in o ma i e e ices om he eal con ex hull. Then, a hyb id deep lea ning model is designed by combining wo sub- ne wo k models. I is buil by combining a classi ica ion subne wo k model based on con olu ional neu al ne wo ks wi h a eg ession subne wo k model based on bidi ec ional long sho - e m memo y neu al ne wo ks. The ou pu o he classi ica ion subne wo k is he sequence o s a es o he de ices, whe eas he ou pu o he eg ession subne wo k is he powe sequence o he a ge de ice a each ime ins an . In ac , he eg ession subne wo k ends o p edic i ele an powe s ha do no belong o he a ge de ice. The use o a classi ica ion subne wo k enables he de ec ion o he de ice’s ON/OFF s a e and, he e o e, he elimina ion o any p edic ion ha does no belong o he a ge de ice unde analysis. The model’s ou pu is gene a ed by me ging he esul s o wo subne wo ks. The ob ained esul s demons a ed ha he use o he App oxHull da a selec ion app oach signi ican ly enhances he pe o mance o he designed model pa icula ly o mul i-s a e de ices. Mo eo e , he esul s o he es showed ha he p oposed app oach accu a ely disagg ega es a ge de ices wi h highe powe es ima ion accu acy and a supe io F1 sco e han s a e-o - he-a app oaches. App oxHull da a selec ion may be used o bo h o line aining and online modeling. Fu u e wo k will ocus on he implemen a ion o he p oposed app oach o online non- in usi e load moni o ing applica ion in home ene gy managemen sys ems. Au ho Con ibu ions: Concep ualiza ion, I.L. and A.R.; me hodology, I.L., A.R. and M.d.G.R.; so wa e, I.L. and A.R.; alida ion, I.L., A.R. and M.d.G.R.; o mal analysis, I.L., A.R., M.d.G.R., S.D.B. and H.E.F.; in es iga ion, I.L., A.R., M.d.G.R., S.D.B. and H.E.F.; esou ces, A.R. and M.d.G.R.; da a cu a ion, I.L. and A.R.; w i ing—o iginal d a p epa a ion, I.L., A.R. and M.d.G.R.; w i ing— e iew and edi ing, I.L., A.R., M.d.G.R., S.D.B. and H.E.F.; supe ision, A.R., S.D.B. and H.E.F.; p ojec adminis a ion, A.R. and M.d.G.R.; unding acquisi ion, A.R. and M.d.G.R. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch was unded by P og ama Ope acional Po ugal 2020 and Ope a ional P o- g am CRESC Alga e 2020, g an numbe s 39578/2018 and 72581/2020. An onio Ruano also ac- knowledges he suppo o Fundação pa a a Ciência e Tecnologia, g an UID/EMS/50022/2020, h ough IDMEC unde LAETA. Ins i u ional Re iew Boa d S a emen : No applicable. 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