A Deep Learning Model of Radio Wave Propagation for Precision Agriculture and Sensor System in Greenhouses

Ci a ion: Cama-Pin o, D.; Damas, M.; Holgado-Te iza, J.A.; A abal-Campos, F.M.; Ma ínez-Lao, J.A.; Cama-Pin o, A.; Manzano-Aguglia o, F. A Deep Lea ning Model o Radio Wa e P opaga ion o P ecision Ag icul u e and Senso Sys em in G eenhouses. Ag onomy 2023,13, 244. h ps:// doi.o g/10.3390/ag onomy13010244 Academic Edi o : Robe o Ma ani Recei ed: 1 No embe 2022 Re ised: 9 Janua y 2023 Accep ed: 10 Janua y 2023 Published: 13 Janua y 2023 Copy igh : © 2023 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/). ag onomy A icle A Deep Lea ning Model o Radio Wa e P opaga ion o P ecision Ag icul u e and Senso Sys em in G eenhouses Do a Cama-Pin o 1, Miguel Damas 1, Juan An onio Holgado-Te iza 2, F ancisco Manuel A abal-Campos 3,4 , Juan An onio Ma ínez-Lao 3, Alejand o Cama-Pin o 5 and F ancisco Manzano-Aguglia o 3,4,* 1Depa men o Compu e A chi ec u e and Technology, Uni e si y o G anada, 18071 G anada, Spain 2So wa e Enginee ing Depa men , Uni e si y o G anada, 18071 G anada, Spain 3Depa men Enginee ing, Uni e si y o Alme ia, Ca e e a Sac amen o, s/n, La Cañada de San U bano, 04120 Alme ía, Spain 4 CIAIMBITAL Resea ch Cen e , CeiA3, Uni e si y o Alme ía, Ca e e a Sac amen o s/n, 04120 Alme ía, Spain 5Facul y o Enginee ing, Uni e sidad de la Cos a, Calle 58 # 55-66, Ba anquilla 080002, Colombia *Co espondence: [email p o ec ed] Abs ac : The p oduc ion o c ops in g eenhouses will ensu e he demand o ood o he wo ld’s popula ion in he coming decades. P ecision ag icul u e is an impo an ool o his pu pose, sup- po ed among o he hings, by he echnology o wi eless senso ne wo ks (WSN) in he moni o ing o ag onomic pa ame e s. The e o e, p io planning o he deploymen o WSN nodes is ele an because hei co e age dec eases when he adio wa es a e a enua ed by he oliage o he plan a ion. In ha sense, he me hod p oposed in his s udy applies Deep Lea ning o de elop an empi ical model o adio wa e a enua ion when i c osses ege a ion ha includes heigh and dis ance be ween he anscei e s o he WSN nodes. The model quali y is exp essed ia he pa ame e s c oss- alida ion, R2o 0.966, while i s gene alized e o is 0.920 e i ying he eliabili y o he empi ical model. Keywo ds: deep lea ning; neu al ne wo k; p ecision ag icul u e; p opaga ion model; wi eless senso ne wo ks 1. In oduc ion The inc ease in demand o c ops and ood p oduc ion is associa ed wi h he g ow h o he wo ld popula ion, which acco ding o da a om he Food and Ag icul u e O ganiza ion (FAO) o he Uni ed Na ions, is cu en ly 7.7 billion humans, p ojec ed o be 9.4 billion in 2030 and 10.1 billion in 2050, when he wo ld popula ion will need 70% mo e ood, 42% mo e a able land and 120% mo e wa e o ood- ela ed pu poses [ 1 – 4 ]. Since adi ional ou doo ag icul u e does no sa is y ood p oduc ion, coupled wi h he educ ion o limi ed ag icul u al land o ci il wo ks cons uc ion, an op imal solu ion is p o ec ed c ops called g eenhouses ha inc ease he numbe o ha es s. Be e ye , when ans o med o sma g eenhouses using in o ma ion echnology and senso s, can con ibu e o he inc ease o ag icul u al p oduc ion [5]. In ela ion o he echnological ad ances o Indus y 4.0, cloud compu ing and he IoT (In e ne o Things) con ibu e o making adi ional sys ems sma [ 6 – 8 ]. An example o his p ocess is sma a ming (SF) ha imp o es p oduc i i y and educes su plus elemen s used in c ops [9]. On he o he hand, wi hin he IoT concep , he ole o wi eless senso ne wo ks (WSN) is pa amoun [ 10 , 11 ] because se e al IoT applica ions a e based on wi eless da a ansmission allowing senso /ac ua o nodes o communica e wi h each o he h ough a wi eless ne wo k connec ion, e en po en ialized wi hin he mMTC (massi e machine- ype communica ions) scena io o 5G [12–15]. I s senso s eco d a iable da a in c op ields and ans e i wi elessly o he base s a ion o ag icul u al decision-making and moni o ing [ 16 ]. P ope planning o he Ag onomy 2023,13, 244. h ps://doi.o g/10.3390/ag onomy13010244 h ps://www.mdpi.com/jou nal/ag onomy Ag onomy 2023,13, 244 2 o 16 a angemen o he numbe o wi eless nodes wi hin a g eenhouse is a majo challenge. Maximum co e age in wi eless communica ion is a esea ch objec i e o es ablish a model o de e mine he a enua ion cu es o he adio signal when deployed inside he g eenhouse. Se e al empi ical models, such as Weissbee ge ’s o ITU-R’s model o adiowa e a enua ion, ha e signi ican e o a es when compa ed o esul s ob ained in g eenhouse ield es s because hey igno e he an enna heigh a iable in hei equa ions [ 17 , 18 ]. E o s ha e been made o imp o e he p edic ions h ough no el models ha in oduce a iable an enna heigh because oliage in c ops has a di e en densi y a di e en spans. Among hese, we highligh some ha employ linea and polynomial [ 19 – 21 ] eg essions. Howe e , he bes p edic ion was pe o med by egula ized non-linea eg ession in [22]. The e a e se e al easons why deep lea ning models may be use ul, e en in cases whe e he e is a small amoun o da a a ailable. Fi s , deep lea ning models a e pa icula ly well-sui ed o asks ha in ol e lea ning om complex high-dimensional da a. These ypes o asks can be challenging o model using adi ional machine lea ning app oaches, bu deep lea ning models a e able o lea n use ul ea u es and pa e ns di ec ly om he da a. Second, deep lea ning models a e able o lea n hie a chical ep esen a ions o he da a, wi h di e en laye s o he model lea ning o ep esen di e en le els o abs ac ion. This allows he model o lea n complex ela ionships in he da a and make mo e accu a e p edic ions. Thi d, deep lea ning models a e able o handle la ge amoun s o noise and a iabili y in he da a, which can be especially use ul in eal-wo ld applica ions whe e da a is o en messy and incomple e. This esea ch aims o imp o e p edic ion by means o deep lea ning, a sub- ield o machine lea ning, a b anch o a i icial in elligence, o ind a new empi ical model o a enua ion and con as i wi h he p e ious model ( egula ised eg ession) o de e mine whe he i o e s g ea e accu acy in i s p edic ion. Un il now, wi h espec o he li e a u e e iewed, we ound ha his is he i s ime ha , using deep lea ning, an empi ical p opaga ion model has been de eloped o applica ion o any g eenhouse plan a ion. 2. Backg ound Based on he pa adigms o Indus y 4.0 (Fou h Indus ial Re olu ion), he PA (P eci- sion Ag icul u e, Thi d Ag icul u al Re olu ion) e ol ed in o Ag icul u e 4.0 (A4.0) and is also called sma a ming (SF) [ 23 ]. I in eg a es in o ma ion and communica ion ech- nologies (ICT) in o adi ional a ming p ac ices o moni o a wide ange o ag icul u al pa ame e s ha imp o e c op yields [ 24 ]. Bo h e ms (SF and A4.0) ela ed o digi al ag icul u e (DA) a e d i ing change in e olu ion, sus ainabili y, e iciency, p oduc i i y, and ood secu i y. This no el pa adigm is based on echnologies such as IoT, a i icial in elligence, big da a, cloud compu ing, and o he ela ed sma sys ems and de ices o c op and a m managemen [25–27]. Wi hin his echnological scena io, he wi eless senso ne wo ks (WSN) p o ide a local c op moni o ing sys em ha enables app op ia e decisions o be made in a con olled p oduc ion sys em a ec ed by clima e change [ 28 , 29 ]. Th ough wi eless da a ansmission, WSN suppo s he collec ion o in o ma ion in ag icul u e due o hei low cos , minimal powe consump ion, sel -o ganizing capabili y, wide a ea co e age by mul i-hop links, and deploymen in en i onmen s changed by plan g ow h, wi h limi ed powe g id [ 27 ], con ibu ing o imp o ed ag icul u al p oduc i i y in an en i onmen ally sus ainable way [ 30 , 31 ]. The ypes o senso s o ag icul u e a e se acco ding o he cha ac e is ics o each plan a ion [32,33]. The Recei ed Signal S eng h Indica o (RSSI) e eals powe alues in adio wa e p opaga ion. The en i onmen , c op g ow h, and an enna heigh s de e mine RSSI al- ues [ 34 , 35 ]. The models used o p edic he RSSI be ween wo anscei e s a e called p opaga ion models [36]. The F iis model o ee space p opaga ion was used o ob ain he line-o -sigh (LOS) pa h loss incu ed in a ee space en i onmen om a ansmi e o a ecei e , as a ela ion Ag onomy 2023,13, 244 3 o 16 be ween he ecei ed powe o he ansmi ed powe , in e ms o e ec i e a eas o he ecei ing (Rx) and ansmi ing (Tx) an enna h ough ee space [37–44]. In g eenhouses, he e ec s o he ege a ion impac in he adio-wa e p opaga ion, which occu s wi h NLOS (non-line o sigh ). Signals a mic owa e (1–30 GHz) [ 45 ] and millime e (30–300 GHz) equencies [ 14 ] expe ience sca e ing and abso p ion caused by andomly dis ibu ed ege a ion lea es and b anches [ 46 ]. The o al pa h losses a e o mula ed by combining he PL s model losses wi h he PL eg ege a ion losses p edic ed by he di e en ege a ion models [19,47,48]. The second ca ego y, he empi ical model o pa h loss, was chosen o he p esen s udy because o he simplici y wi h which i s equa ions a e o mula ed, no ably hose lis ed in [ 21 , 22 ] based on he EDM (exponen ial decay model). Howe e , i s es ima es ha e a conside able ma gin o e o compa ed o hose aken in ield es s p omp ing us o ocus ou wo k o imp o e hem. Among empi ical models, he au ho s de eloped an empi ical mul i-pa ame ic equa- ion model based on non-linea egula ised eg essions using expe imen al measu emen s o he RSSI signal ob ained om ield es measu emen s o ou g eenhouses. In ha s udy, he e alua ion o he model wi h 5 h deg ee polynomials yielded 0.948 o R 2 , 0.946 in R 2adj (20-pa ame e solu ion), and 0.942 o R 2 , y 0.940 en R 2adj when he equa ion was educed o 15 pa ame e s by applying c oss- alida ion [22]. The a enua ion o he adio wa e inside he g eenhouse depends on he signal e- quency, an enna heigh , and dis ance be ween an ennas, exhibi ing a non-linea i y beha io . The e o e, an in e es ing app oach can also be applied, aking ad an age o machine lea n- ing (ML) [ 49 ] in o de o ind he ela ionship be ween hese non-independen a iables. ML builds a model au oma ically by deducing meaning ul ideas (known as ea u es) om he da ase , wi h ea u e ex ac ion being he mos c i ical s ep in a model gene a ion [ 50 ]. Then he non-linea ea u es o he inpu da a es ablish in e ac ions and ela ionships wi h he ou pu p edic o a iables [ 51 ]. Analogously, humans use a model o he wo ld as a simula o in ou b ain, which is ob ained by lea ning om la ge amoun s o da a collec ed by ou senses in e ac ing wi h he su ounding en i onmen [52]. ML collec s inpu and ou pu da a o subsequen ly p edic u u e alues [ 53 – 55 ]. Fo he implemen a ion o machine lea ning algo i hms ANNs (a i icial neu al ne wo ks) [56–60] . Based on his a chi ec u e, ANNs can be classi ied in o CNNs (con olu ional neu al ne - wo ks) [61–63] and ecu en neu al ne wo ks (RNNs) [62,64]. DL (Deep lea ning) is a o m o sub ield o ML [ 65 , 66 ]. ANNs a e he co e algo i hms o DL. I he dep h o numbe o laye s o he ANN is g ea e han h ee, i will cease o be a simple ANN and become a DL algo i hm [ 67 ], called a deep neu al ne wo k (DLL), allowing i o success ully in e p e mo e complex non-linea inpu s [ 68 – 71 ]. As men ioned be o e, al hough he e has been no esea ch using ML in he es ima ion o adio p opaga ion loss in he p esence o ege a ion, he e a e some wo ks ela ed o adio p opaga ion, such as DNN-based, employing CNN o adio p opaga ion loss es ima ion using spa ial in o ma ion, such as building occupancy maps o inpu da a [ 72 ], pa h loss p edic ion in u al a eas using 3.7 GHz band, combines di e en ML models, o he base lea ning s age uses ANN, DT (decision ees), SVR (suppo ec o eg ession), kNN (k-nea es neighbo s), GLM (gene alized linea model) and a cus om DNN wi h h ee hidden laye s as me a-lea ne [ 73 ]. The pape by Bogdándy e al. [ 74 ] used he log o WiFi RSSI alues as inpu da a o de e mine he indoo posi ioning o nodes wi h an ANN. In addi ion, [ 75 ] used ML o ob ain an ANN-based model ha p edic s adio p opaga ion loss cha ac e is ics inside unnels. 3. Ma e ials and Me hods 3.1. Sou ce o Da a All da a we e collec ed by Cama-Pin o e al. [ 21 , 22 ]. The expe imen was pe o med in g eenhouses loca ed in Alme ía, sou heas e n Spain [ 76 – 79 ]. Vege able and ui p oduc ion is expo ed mainly o he EU [ 80 – 87 ]. RSSI da a a e om ials in ou g eenhouse ields Ag onomy 2023,13, 244 4 o 16 du ing Feb ua y 2020, each wi h a eas o 10,000 m 2 in he Alme ia locali ies o La Cañada, Re ama , El Alquian, Níja , and g eenhouse es da a om La Cañada in 2018. The o al numbe o da a collec ed we e 345. Each expe imen was epea ed 10 imes in 2020 and 60 imes in 2018. The da a used was he a e age o he expe imen s. The ou line o he measu emen sys em ha dwa e con igu a ion is de ailed by he au ho s in [88]. As shown in Figu e 1, du ing he measu emen phase, he an ennas o he T x node and he sink node (R x ) we e placed a he same heigh . The signal a i ed a he ecei e a enua ed a e passing h ough he oma o plan walls (1 m hick) e e y 5 min, epea ing he p ocess 10 imes: (1) Fo he measu emen , bo h he T x node and he sink a e loca ed a equal dis ances om he g ound. E e y 5 min he R x node eco ds he signal om he T x node, which a i es a enua ed. The measu emen is epea ed 10 imes, hen he dis ance be ween he nodes is inc eased by adding one mo e oma o wall and doubling he p e ious p ocedu e. A e he sepa a ion inc eases by adding mo e oma o plan walls, he e comes a poin whe e he e is no communica ion, ending his s age. (2) The T x and R x nodes a e mo ed wo me e s nex o he oma o wall in o he side co ido and s ep 1 is epea ed. (3) S eps 1 and 2 a e ollowed wi h di e en heigh s ( he heigh s in cen ime e s a e 30, 50, 70, 90, 100, 150, and 200). Ag onomy2023,13,xFORPEERREVIEW4o 17   3.Ma e ialsandMe hods 3.1.Sou ceo Da a Allda awe ecollec edbyCama‐Pin oe al.[21,22].Theexpe imen waspe o med ing eenhousesloca edinAlme ía,sou heas e nSpain[76–79].Vege ableand ui p o‐ duc ionisexpo edmainly o heEU[80–87].RSSIda aa e om ialsin ou g eenhouse ieldsdu ingFeb ua y2020,eachwi ha easo 10,000m 2 in heAlme ialocali ieso La Cañada,Re ama ,ElAlquian,Níja ,andg eenhouse es da a omLaCañadain2018. The o alnumbe o da acollec edwe e345.Eachexpe imen was epea ed10 imesin 2020and60 imesin2018.Theda ausedwas hea e ageo  heexpe imen s.Theou line o  hemeasu emen sys emha dwa econ igu a ionisde ailedby heau ho sin[88]. AsshowninFigu e1,du ing hemeasu emen phase, hean ennaso  heT x node and hesinknode(Rx)we eplaceda  hesameheigh .Thesignala i eda  he ecei e  a enua eda e passing h ough he oma oplan walls(1m hick)e e y5min, epea ing hep ocess10 imes: (1) Fo  hemeasu emen ,bo h heT x nodeand hesinka eloca eda equaldis ances om heg ound.E e y5min heRxnode eco ds hesignal om heTxnode,which a i esa enua ed.Themeasu emen is epea ed10 imes, hen hedis ancebe ween henodesisinc easedbyaddingonemo e oma owallanddoubling hep e ious p ocedu e.A e  hesepa a ioninc easesbyaddingmo e oma oplan walls, he e comesapoin whe e he eisnocommunica ion,ending hiss age. (2) TheT x andR x nodesa emo ed wome e snex  o he oma owallin o hesideco ‐ ido ands ep1is epea ed. (3) S eps1and2a e ollowedwi hdi e en heigh s( heheigh sincen ime e sa e30, 50,70,90,100,150,and200).  Figu e1.Loca iono nodesinside heg eenhousedu ing ield es s. Theschema ico  he op iewo  hedeploymen o  heTxandRxnodesinside he g eenhouseisshowninFigu e2. Figu e 1. Loca ion o nodes inside he g eenhouse du ing ield es s. The schema ic o he op iew o he deploymen o he T x and R x nodes inside he g eenhouse is shown in Figu e 2. 3.2. E alua ion o he Model’s Pe o mance The p edic i e pe o mance o he model was assessed using se en (07) c i e ia. The mean squa e e o (MSE), oo mean squa e e o (RMSE), mean absolu e pe cen age e o (MAPE), coe icien o de e mina ion (R 2 ), adjus ed coe icien o de e mina ion (R 2adj ), Akaike in o ma ion c i e ion (AIC), and he Bayesian in o ma ion c i e ion BIC, also called he Schwa z in o ma ion c i e ion—SBC [89–98]. The accu acy o assessmen o model pe o mance can be e i ied by he R 2 , i s a ian , he R 2adj and Q 2 [ 99 – 105 ]. On he o he hand, AIC and SBC a e widely used o model selec ion [106–117]. Ag onomy 2023,13, 244 5 o 16 Ag onomy2023,13,xFORPEERREVIEW5o 17    Figu e2.Top iewo  hedeploymen o  heTxandRxnodesinside heg eenhouse. 3.2.E alua iono  heModel’sPe o mance Thep edic i epe o manceo  hemodelwasassessedusingse en(07)c i e ia.The meansqua ee o (MSE), oo meansqua ee o (RMSE),meanabsolu epe cen agee o  (MAPE),coe icien o de e mina ion(R 2 ),adjus edcoe icien o de e mina ion(R 2 adj), Akaikein o ma ionc i e ion(AIC),and heBayesianin o ma ionc i e ionBIC,also called heSchwa zin o ma ionc i e ion—SBC[89–98]. Theaccu acyo assessmen o modelpe o mancecanbe e i iedby heR 2 ,i s a i‐ an , heR 2adj andQ 2 [99–105].On heo he hand,AICandSBCa ewidelyused o model selec ion[106–117]. 4.ADeepLea ningModelo RadioWa eP opaga ion Ano eldeeplea ningmodelisp oposedin hiswo kbasedonbina y eed o wa d neu alne wo k.I iscomposedo  wolaye s,anencodingandadecodinglaye .Theen‐ codinglaye con e s hedis anceand heheigh a which hea enua ionis obeknown in obina y.Since he angeo da aislimi ed.Thenumbe o bi s ode e mine hein ege  pa and hedecimalpa willbesmall.Thedis ance a ies om1 o35m,and heheigh  a ies om30cm o200cm.Theencodingisdoneusing14bi s o  hedis ance7 o  he in ege pa and heo he 7 o  hedecimalpa .Fo heigh ,weused11bi s,4o  hem o  hein ege pa and he es  o  hedecimalpa ,gi ing wo ealnumbe swi h wodeci‐ malsusing25bi sin o al.Thedecodingcon e s ombina y o ealnumbe wi han accu acyo 3decimalplaces,using17bi s ope o m hiscon e sion o he ealnumbe , soi used7bi s o  hein ege pa and heo he 10 o  hedecimalpa .Theneu alne ‐ wo kiscomposedo 7laye s.The i s and helas a e heinpu andou pu laye s, e‐ spec i ely.The es o  helaye sa ehidden.Figu e3belowshows hes uc u eo  he deepneu alne wo k.Theac i a ion unc ion o  hepe cep onsis hesigmoid unc ion. Theinpu laye has25pe cep onsco esponding o he25inpu bi s,while heou pu  laye has17pe cep onsco esponding o he17ou pu bi s. Figu e 2. Top iew o he deploymen o he Txand Rxnodes inside he g eenhouse. 4. A Deep Lea ning Model o Radio Wa e P opaga ion A no el deep lea ning model is p oposed in his wo k based on bina y eed o wa d neu al ne wo k. I is composed o wo laye s, an encoding and a decoding laye . The encoding laye con e s he dis ance and he heigh a which he a enua ion is o be known in o bina y. Since he ange o da a is limi ed. The numbe o bi s o de e mine he in ege pa and he decimal pa will be small. The dis ance a ies om 1 o 35 m, and he heigh a ies om 30 cm o 200 cm. The encoding is done using 14 bi s o he dis ance 7 o he in ege pa and he o he 7 o he decimal pa . Fo heigh , we used 11 bi s, 4 o hem o he in ege pa and he es o he decimal pa , gi ing wo eal numbe s wi h wo decimals using 25 bi s in o al. The decoding con e s om bina y o eal numbe wi h an accu acy o 3 decimal places, using 17 bi s o pe o m his con e sion o he eal numbe , so i used 7 bi s o he in ege pa and he o he 10 o he decimal pa . The neu al ne wo k is composed o 7 laye s. The i s and he las a e he inpu and ou pu laye s, espec i ely. The es o he laye s a e hidden. Figu e 3below shows he s uc u e o he deep neu al ne wo k. The ac i a ion unc ion o he pe cep ons is he sigmoid unc ion. The inpu laye has 25 pe cep ons co esponding o he 25 inpu bi s, while he ou pu laye has 17 pe cep ons co esponding o he 17 ou pu bi s. Ag onomy 2023, 13, x FOR PEER REVIEW 6 o 17 Figu e 3. Schema ic o he Deep Lea ning Model o he es ima ion o a enua ion om dis ance and heigh . The dis ance and heigh alues compose he ec o X while he es ima ed a enua ion alues 𝑳𝑳𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇(𝒅𝒅,𝒉𝒉) o measu ed dB a e Y. The ep esen a ion o he wo ec o s X and Y is shown in Figu e 4 below, Figu e 4. Rep esen a ion o dis ance and heigh , which is composed he ec o X, while he es i- ma ed a enua ion alues 𝐿𝐿𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓(𝑑𝑑,ℎ) o measu ed dB a e composed o Y. The B alues a e bi s ha can ake he alues ei he 0 o 1. Then, o c ea ing he eal numbe , he dis ance, heigh , and L oliage(d,h) ha e a in ege pa and decimal pa . The pa ame ic adjus men o he deep neu al ne wo k is pe o med by minimizing he ollowing cos unc ion is, 𝐽𝐽(𝜃𝜃)=1 𝑚𝑚���−𝑦𝑦 𝑓𝑓 log �ℎ 𝜃𝜃 (𝑥𝑥 𝑓𝑓 )�−(1−𝑦𝑦 𝑓𝑓 )log �1−ℎ 𝜃𝜃 (𝑥𝑥 𝑓𝑓 )�� 𝐾𝐾 𝑘𝑘=1 𝑚𝑚 𝑓𝑓=1 (1 ) whe e m is he numbe o expe imen pe o med in he g eenhouse, whe e o a dis ance and heigh gi en, we ob ain a signal a enua ion, and K is he o al numbe o bi s in he ou pu laye . The logis ic unc ion is de ined as, ℎ𝜃𝜃=𝑔𝑔(𝜃𝜃𝑇𝑇𝑥𝑥) (2 ) whe e g is he sigmoid unc ion, 𝑔𝑔(𝑧𝑧)=1 1 + 𝑒𝑒−𝑧𝑧 (3 ) To a oid de ia ions and o e i ing o he cos unc ion pa ame e s o Equa ion (1), he egula iza ion unc ion called Tikhono egula iza ion [118,119] is added as ollows, Figu e 3. Schema ic o he Deep Lea ning Model o he es ima ion o a enua ion om dis ance and heigh . Ag onomy 2023,13, 244 6 o 16 The dis ance and heigh alues compose he ec o X while he es ima ed a enua ion alues L oliage(d,h) o measu ed dB a e Y. The ep esen a ion o he wo ec o s X and Y is shown in Figu e 4below, Ag onomy2023,13,xFORPEERREVIEW6o 17     Figu e3.Schema ico  heDeepLea ningModel o  hees ima iono a enua ion omdis anceand heigh . Thedis anceandheigh  aluescompose he ec o Xwhile hees ima eda enua ion alues𝑳𝒇𝒐𝒍𝒊𝒂𝒈𝒆󰇛𝒅,𝒉󰇜o measu eddBa eY.The ep esen a iono  he wo ec o sXand YisshowninFigu e4below,  Figu e4.Rep esen a iono dis anceandheigh ,whichiscomposed he ec o X,while he es ima eda enua ion alues𝐿  󰇛𝑑,ℎ󰇜o measu eddBa ecomposedo Y.TheB aluesa e bi s ha can ake he aluesei he 0o 1.Then, o c ea ing he ealnumbe , hedis ance,heigh , andL oliage (d,h)ha eain ege pa anddecimalpa . Thepa ame icadjus men o  hedeepneu alne wo kispe o medbyminimizing he ollowingcos  unc ionis, 𝐽󰇛𝜃󰇜1 𝑚󰇣𝑦log󰇡ℎ󰇛𝑥󰇜󰇢󰇛1𝑦󰇜log󰇡1ℎ󰇛𝑥󰇜󰇢󰇤     (1) whe emis henumbe o expe imen pe o medin heg eenhouse,whe e o adis ance andheigh gi en,weob ainasignala enua ion,andKis he o alnumbe o bi sin he ou pu laye .Thelogis ic unc ionisde inedas, ℎ𝑔󰇛𝜃𝑥󰇜(2) whe egis hesigmoid unc ion, 𝑔󰇛𝑧󰇜1 1𝑒 (3) Figu e 4. Rep esen a ion o dis ance and heigh , which is composed he ec o X, while he es ima ed a enua ion alues L oliage(d,h) o measu ed dB a e composed o Y. The B alues a e bi s ha can ake he alues ei he 0 o 1. Then, o c ea ing he eal numbe , he dis ance, heigh , and L oliage (d,h) ha e a in ege pa and decimal pa . The pa ame ic adjus men o he deep neu al ne wo k is pe o med by minimizing he ollowing cos unc ion is, J(θ) = 1 m m ∑ i=1 K ∑ k=1h−yiloghθ(xi)−1−yilog1−hθ(xi)i (1) whe e mis he numbe o expe imen pe o med in he g eenhouse, whe e o a dis ance and heigh gi en, we ob ain a signal a enua ion, and Kis he o al numbe o bi s in he ou pu laye . The logis ic unc ion is de ined as, hθ=gθTx(2) whe e gis he sigmoid unc ion, g(z) = 1 1+e−z(3) To a oid de ia ions and o e i ing o he cos unc ion pa ame e s o Equa ion (1), he egula iza ion unc ion called Tikhono egula iza ion [118,119] is added as ollows, J(θ) = 1 m m ∑ i=1 K ∑ k=1h−yiloghθ(xi)−1−yilog1−hθ(xi)i+λ 2m"N−1 ∑ n=1 Jn ∑ j=1 Sn ∑ s=1θ(n) j,s2#(4) The ne wo k pa ame e s a e ep esen ed by θ(i) j,k , whe e Nis he numbe o laye s, Jn is he numbe o o al incoming connec ions a he n- h laye , and Sn is he numbe o o al incoming connec ions a he n- h laye . λ is he egula ising e m and es ablishes he weigh ha he pa ame e s should ha e in he cos unc ion, a oiding o e i ing and a iabili y in he pa ame e ized unc ions. In his op imiza ion p oblem, i is manda o y o de e mine he g adien s in each di ec ion. The g adien s can be calcula ed using he backp opaga ion algo i hm (see Algo i hm 1). Once he g adien s ha e been calcula ed, he Polac–Ribie e me hod [ 120 ] is used o calcula e he conjuga e g adien s o es ima e he sea ch di ec ion. The app oxima ion is pe o med using quad a ic polynomial unc ions. The s opping c i e ion used is he so-called Wol e-Powel condi ions [121,122]. Ag onomy 2023,13, 244 7 o 16 Algo i hm 1 Back acking Algo i hm Applied in he Deep Lea ning 1T aining se nx(1), y(1),x(2), y(2), . . . , x(m), y(m)o 2 Fo he en i e aining package 3I es ablishes ∆(n) ij =0 4 Compu e o wa d p opaga ion 5 Compu e egula ized cos unc ion J(θ) 6Se a(1)=x(i) 7Pe o m o wa d p opaga ion o compu e a(n) o n=2, 3, . . . , N 8Using y(i), compu e δ(N)=a(N)−y(i) 9Compu e δ(N−1),δ(N−2),δ(N−3), . . . , δ(2) 10 ∆(n) ij :=∆(n) ij +an jδ(n+1) i 11 D(l) ij := 1 m∆(n) ij +λθ(n) ij i j6=0 12 D(l) ij := 1 m∆(n) ij i j=0 13 ∂ ∂θ(n) ij J(θ) = D(n) ij The o al numbe o pa ame e s condi ions bo h he aining ime and he densi y o pe cep ons in he neu al ne wo k. A s udy is made o he numbe o pa ame e s o a gi en alue o λ . Figu e 5below ela es he e o in he p edic ion o he a enua ion alue o he numbe o pe cep ons in he ne wo k. Ag onomy2023,13,xFORPEERREVIEW8o 17    Figu e5.RMSEc oss‐ alida ion alues o se ing henumbe o pe cep ons.I isse up o15,575 dis ibu edin7laye s. Theop imalnumbe o pe cep onso  heneu alne wo kis15,575.Following his a chi ec u e, he alueo λisop imizedbychoosing alueso 0.1,0.01,0.001,and0.0001, esul ingin he ollowing(Figu e6).  Figu e6.RMSEc oss‐ alida ion.Theop imal alueo  λ isse nea  o10 −3 . The esul sugges s hebes  alueo λ.The oo meansumsqua ee o (RMSE) e‐ mainscons an whenλisnea  o0.001.Then, heop imal alueisse up o0.001.The alueo λisusedin hebackp opaga ionalgo i hm oa oidbiasando e i ing[118,119]. Figu e7shows heloss unc ion e sus henumbe o epoch.I isnecessa y o 10,000 epoch oob ainalosscos  alueequala0.0332. Figu e 5. RMSE c oss- alida ion alues o se ing he numbe o pe cep ons. I is se up o 15,575 dis ibu ed in 7 laye s. The op imal numbe o pe cep ons o he neu al ne wo k is 15,575. Following his a chi ec u e, he alue o λ is op imized by choosing alues o 0.1, 0.01, 0.001, and 0.0001, esul ing in he ollowing (Figu e 6). The esul sugges s he bes alue o λ . The oo mean sum squa e e o (RMSE) emains cons an when λ is nea o 0.001. Then, he op imal alue is se up o 0.001. The alue o λ is used in he backp opaga ion algo i hm o a oid bias and o e i ing [ 118 , 119 ]. Figu e 7shows he loss unc ion e sus he numbe o epoch. I is necessa y o 10,000 epoch o ob ain a loss cos alue equal a 0.0332. Ag onomy 2023,13, 244 8 o 16 Ag onomy2023,13,xFORPEERREVIEW8o 17    Figu e5.RMSEc oss‐ alida ion alues o se ing henumbe o pe cep ons.I isse up o15,575 dis ibu edin7laye s. Theop imalnumbe o pe cep onso  heneu alne wo kis15,575.Following his a chi ec u e, he alueo λisop imizedbychoosing alueso 0.1,0.01,0.001,and0.0001, esul ingin he ollowing(Figu e6).  Figu e6.RMSEc oss‐ alida ion.Theop imal alueo  λ isse nea  o10 −3 . The esul sugges s hebes  alueo λ.The oo meansumsqua ee o (RMSE) e‐ mainscons an whenλisnea  o0.001.Then, heop imal alueisse up o0.001.The alueo λisusedin hebackp opaga ionalgo i hm oa oidbiasando e i ing[118,119]. Figu e7shows heloss unc ion e sus henumbe o epoch.I isnecessa y o 10,000 epoch oob ainalosscos  alueequala0.0332. Figu e 6. RMSE c oss- alida ion. The op imal alue o λis se nea o 10−3. Ag onomy2023,13,xFORPEERREVIEW9o 17    Figu e7.Loss unc ion e sus henumbe o epoch.Theop imal alueo epochis10,000gi inga losscos  alue0.0332. 5.Resul s Figu e8shows hesolu ionob ained o  hep oposeddeeplea ningmodel.Thisis he3D iewo  heneu alne wo k,ascanbeseeninFigu e3(Figu e8a),whe e he alues akenin heg eenhouseappea asbluedo s.Thex‐axisandy‐axisa edis ance(d)and heigh (h), espec i ely,inme e s.Thez‐axisis alueswhene alua ing hedeepneu al ne wo k𝐿 󰇛𝑑,ℎ󰇜 o  hedis anceandheigh da a.Figu e8bshows he esidual aluesbe weenmeasu edda aand hosecalcula edwi h hedeepneu alne wo k.  Figu e 7. Loss unc ion e sus he numbe o epoch. The op imal alue o epoch is 10,000 gi ing a loss cos alue 0.0332. 5. Resul s Figu e 8shows he solu ion ob ained o he p oposed deep lea ning model. This is he 3D iew o he neu al ne wo k, as can be seen in Figu e 3(Figu e 8a), whe e he alues aken in he g eenhouse appea as blue do s. The x-axis and y-axis a e dis ance (d) and heigh (h), espec i ely, in me e s. The z-axis is alues when e alua ing he deep neu al ne wo k L oliage (d,h) o he dis ance and heigh da a. Figu e 8b shows he esidual alues be ween measu ed da a and hose calcula ed wi h he deep neu al ne wo k. Ag onomy 2023,13, 244 9 o 16 Ag onomy2023,13,xFORPEERREVIEW10o 17   (a)  (b)  Figu e8.(a)Theblackdo s ep esen  he alues akenin ield es s, oge he wi h he𝐿 󰇛𝑑,ℎ󰇜 op imized o  hedeeplea ningmodel.(b)Di e encebe weenmeasu edandp edic edda aa e he Residual alueso 𝐿 󰇛𝑑,ℎ󰇜. Thec oss‐ alida iono pa ame e s e eals hequali yo  henewmodel.R2andQ2, hese alueswe e0.966and0.957.TheRMSECVwas1.98.Thedeepneu alne wo kwas also alida edbype mu a ion es ing. The alues o  hee alua iono  hemul i‐pa ame icop imised unc iona ep e‐ sen edinTable1.The0.966 aluewas headjus edR2. Table1.S a is icalQuali yAssessmen o  hep oposeddeeplea ningmodel. R2R2AdjMSERMSEMAPEAICSBC 𝑳𝒇𝒐𝒍𝒊𝒂𝒈𝒆󰇛𝒅,𝒉󰇜0.9660.9643.391.980.113432221 Figu e 8. ( a ) The black do s ep esen he alues aken in ield es s, oge he wi h he L oliage (d,h) op imized o he deep lea ning model. 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