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. (
b
) Di e ence be ween measu ed and p edic ed da a a e he
Residual alues o L oliage (d,h).
The c oss- alida ion o pa ame e s e eals he quali y o he new model. R
2
and Q
2
,
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 esen 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.
R2R2Adj MSE RMSE MAPE AIC SBC
L oliage(d,h)0.966 0.964 3.39 1.98 0.113 432 221
Ag onomy 2023,13, 244 16 o 16
104.
Oussama, C.; Abdellah, E.A.; Yousse , E.O.; Mohammed, B.; Abdelk im, O. In silico P edic ion o No el SARS-CoV 3CL p o
Inhibi o s: A Combina ion o 3D-QSAR, Molecula Docking, ADMET P edic ion, and Molecula Dynamics Simula ion. Bioin e ace
Res. Appl. Chem. 2022,12, 5100–5115. [C ossRe ]
105.
G ama ica, P. On he De elopmen and Valida ion o QSAR Models. Me hods Mol. Biol.
2013
,930, 499–526. [C ossRe ] [PubMed]
106.
Gohain, P.B.; Jansson, M. Scale-In a ian and consis en Bayesian in o ma ion c i e ion o o de selec ion in linea eg ession
models. Signal P ocess. 2022,196, 108499. [C ossRe ]
107.
Ban eng, L.; Yang, H.; Chen, Q.; Wang, Z. Resea ch on he sub ac i e clus e ing algo i hm o mobile ad hoc ne wo k based on
he Akaike in o ma ion c i e ion. In . J. Dis ib. Sens. Ne w. 2019,15, 1550147719877612. [C ossRe ]
108.
Banks, H.T.; Joyne , M.L. Adap ion o Akaike in o ma ion c i e ion unde leas squa es amewo ks o compa ison o s ochas ic
models. Q. Appl. Ma h. 2019,77, 831–859. [C ossRe ]
109.
Tozzi, R.; Masci, F.; Pezzopane, M. A s ess es o e alua e he use ulness o Akaike in o ma ion c i e ion in sho - e m ea hquake
p edic ion. Sci. Rep. 2020,10, 21153. [C ossRe ]
110.
Benede , A.L.; B um, W.S.; Hansson, O.; Ka ika i, T.K.; Zimme , E.R.; Ze e be g, H.; Blennow, K.; Ash on, N.J. Alzheime ’s
Disease Neu oimaging Ini ia i e he accu acy and obus ness o plasma bioma ke models o amyloid PET posi i i y. Alzheime ’s
Res. The . 2022,14, 26. [C ossRe ]
111.
Bha acha ya, S.; Biswas, A.; Nandi, S.; Pa a, S.K. Exhaus i e model selec ion in b
→
s
``
decays: Pi ing c oss- alida ion agains
he Akaike in o ma ion c i e ion. Phys. Re . D 2020,101, 055025. [C ossRe ]
112. Pham, H. A New C i e ion o Model Selec ion. Ma hema ics 2019,7, 1215. [C ossRe ]
113.
T an, D.A.; Tsujimu a, M.; Ha, N.T.; Nguyen, V.T.; an Binh, D.; Dang, T.D.; Doan, Q.-V.; Bui, D.T.; Ngoc, T.A.; Phu, L.V.; e al.
E alua ing he p edic i e powe o di e en machine lea ning algo i hms o g oundwa e salini y p edic ion o mul i-laye
coas al aqui e s in he Mekong Del a, Vie nam. Ecol. Indic. 2021,127, 107790. [C ossRe ]
114.
Saez, L.M.A.; Campos, F.M.A.; Callejón-Fe e, J.; Medina, M.D.S.; Fe nández, I. Use o mul i a ia e NMR analysis in he con en
p edic ion o hemicellulose, cellulose and lignin in g eenhouse c op esidues. Phy ochemis y 2019,158, 110–119. [C ossRe ]
115.
Ezuma, M.; Anjinappa, C.K.; Funde bu k, M.; Gu enc, I. Rada C oss Sec ion Based S a is ical Recogni ion o UAVs a Mic owa e
F equencies. IEEE T ans. Ae osp. Elec on. Sys . 2022,58, 27–46. [C ossRe ]
116.
Ikbal, N.A.M.; Halim, S.A.; Ali, N. Es ima ing Weibull Pa ame e s Using Maximum Likelihood Es ima ion and O dina y Leas
Squa es: Simula ion S udy and Applica ion on Me eo ological Da a. Ma h. S a . 2022,10, 269–292. [C ossRe ]
117.
Xu, Q.; Li, R.; Liu, Y.; Luo, C.; Xu, A.; Xue, F.; Xu, Q.; Li, X. Fo ecas ing he Incidence o Mumps in Zibo Ci y Based on a SARIMA
Model. In . J. En i on. Res. Public Heal h 2017,14, 925. [C ossRe ]
118.
Tikhono , A.N. On he solu ion o ill-posed p oblems and he me hod o egula iza ion. In Doklady Akademii Nauk; Russian
Academy o Sciences: Moscow, Russia, 1963; pp. 501–504. [C ossRe ]
119.
Cal e i, D.; Mo igi, S.; Reichel, L.; Sgalla i, F. Tikhono egula iza ion and he L-cu e o la ge disc e e ill-posed p oblems.
J. Compu . Appl. Ma h. 2000,123, 423–446. [C ossRe ]
120.
Rasmussen, C.E.; Williams, C.K.I. Gaussian P ocesses o Machine Lea ning; he MIT P ess: Camb idge, MA, USA, 2006;
ISBN 026218253X.
121. Wol e, P. Con e gence Condi ions o Ascen Me hods. SIAM Re . 1969,11, 226–235. [C ossRe ]
122. Wol e, P. Con e gence Condi ions o Ascen Me hods. II: Some Co ec ions. SIAM Re . 1971,13, 185–188. [C ossRe ]
Disclaime /Publishe ’s No e:
The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .