Ci a ion: A shad, M.Y.; Saeed, M.A.;
Tahi , M.W.; Pawlak-K uczek, H.;
Ahmad, A.S.; Niedzwiecki, L.
Ad ancing Sus ainable
Decomposi ion o Biomass Ta Model
Compound: Machine Lea ning,
Kine ic Modeling, and Expe imen al
In es iga ion in a Non-The mal
Plasma Dielec ic Ba ie Discha ge
Reac o . Ene gies 2023,16, 5835.
h ps://doi.o g/10.3390/en16155835
Academic Edi o : Dimi ios Sidi as
Recei ed: 15 July 2023
Re ised: 29 July 2023
Accep ed: 4 Augus 2023
Published: 7 Augus 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/).
ene gies
A icle
Ad ancing Sus ainable Decomposi ion o Biomass Ta Model
Compound: Machine Lea ning, Kine ic Modeling,
and Expe imen al In es iga ion in a Non-The mal Plasma
Dielec ic Ba ie Discha ge Reac o
Muhammad Yousa A shad 1,2,* , Muhammad Azam Saeed 2, Muhammad Wasim Tahi 2,
Halina Pawlak-K uczek 3,*, Anam Suhail Ahmad 4and Lukasz Niedzwiecki 3,5
1Co po a e Sus ainabili y and Digi al Chemical Managemen Di ision, In e loop Limi ed,
Faisalabad 38000, Pakis an
2Depa men o Chemical Enginee ing, Uni e si y o Enginee ing and Technology, Laho e 54000, Pakis an;
[email p o ec ed] (M.A.S.); [email p o ec ed] (M.W.T.)
3Depa men o Ene gy Con e sion Enginee ing, W ocław Uni e si y o Science and Technology,
Wyb.Wyspia´nskiego 27, 50-370 W ocław, Poland; lukasz.niedzwiecki@pw .edu.pl
4Hallibu on Wo ldwide, 3000, N Sam Hous on Pa kway E, Hous on, TX 77032-3219, USA;
[email p o ec ed]
5Ene gy Resea ch Cen e, Cen e o Ene gy and En i onmen al Technologies, VŠB—Technical Uni e si y
o Os a a, 17. Lis opadu 2172/15, 708 00 Os a a, Czech Republic
*Co espondence: [email p o ec ed] (M.Y.A.); halina.pawlak@pw .edu.pl (H.P.-K.)
Abs ac :
This s udy examines he sus ainable decomposi ion eac ions o benzene using non- he mal
plasma (NTP) in a dielec ic ba ie discha ge (DBD) eac o . The aim is o in es iga e he ac o s
in luencing benzene decomposi ion p ocess, including inpu powe , concen a ion, and esidence
ime, h ough kine ic modeling, eac o pe o mance assessmen , and machine lea ning echniques.
To u he enhance he unde s anding and modeling o he decomposi ion p ocess, he esea che s
de e mine he appa en decomposi ion a e cons an , which is inco po a ed in o a kine ic model
using a no el heo e ical plug low eac o analogy model. The esul ing eac o model is simula ed
using he ODE45 sol e in MATLAB, wi h ad anced machine lea ning algo i hms and pe o mance
me ics such as RMSE, MSE, and MAE employed o imp o e accu acy. The analysis e eals ha
highe inpu discha ge powe and longe esidence ime esul in inc eased a analogue compound
(TAC) decomposi ion. The esul s indica e ha highe inpu discha ge powe leads o a signi ican
imp o emen in he TAC decomposi ion a e, eaching 82.9%. The machine lea ning model achie ed
e y good ag eemen wi h he expe imen s, showing a decomposi ion a e o 83.01%. The model
lagged po en ial ho spo s a 15% and 25% o he eac o ’s leng h, which is impo an in e ms o
enginee ing design o scaled-up eac o s.
Keywo ds:
NTP eac o ; benzene plasma decomposi ion; kine ic modeling; eac o pe o mance and
simula ion; machine lea ning s udies
1. In oduc ion
Biomass p ocessing is a dual app oach o handling biowas e [
1
,
2
] and ene gy p o-
duc ion simul aneously [
3
,
4
]. I is a p edominan esou ce in he mochemical p ocesses,
i.e., gasi ica ion and py olysis, o simul aneously p oduce hea and clean ene gy [
5
–
8
]. Typ-
ically, p oduce gas consis s o H
2
, CO, CO
2
, CH
4
, as well as o he hyd oca bons, and N
2
i
ai is used as a gasi ying agen [
9
–
12
]. Among he a ie y o hyd oca bons p oduced du ing
gasi ica ion, one should dis inguish a s, which a e p oblema ic in e ms o downs eam
p ocessing o he p oduce gas [13–16].
Di e en classi ica ions o a s exis , wi h he mos common being he ECN classi ica-
ion. Acco ding o his classi ica ion, all a s unde ec able by gas ch oma og aphy (hea ies
Ene gies 2023,16, 5835. h ps://doi.o g/10.3390/en16155835 h ps://www.mdpi.com/jou nal/ene gies
Ene gies 2023,16, 5835 2 o 26
a s) belong o class 1, he e ocyclic compounds (e.g., phenol, py idine, c esol) belong o
class 2, a oma ic compounds wi h one ing (e.g., xylene, s y ene, oluene) belong o class
3, ligh polya oma ic hyd oca bons wi h wo o h ee ings (e.g., naph halene, biphenyl,
acenaph hylene, phenan h ene, an h acene) belong o class 4, and hea y polya oma ic
hyd oca bons wi h mo e han h ee ings (e.g., luo an hene, py ene, ch ysene) belong o
class 5 [17].
Ta can be emo ed by p ima y and seconda y me hods [
18
–
21
]. In p ima y me h-
ods, a s a e emo ed wi hin he gasi ie , while seconda y me hods in ol e pos -gasi ie
ea men [
22
–
24
]. The mal c acking, which is one o he me hods o decomposi ion o
a s, equi es a ela i ely high eac ion empe a u e o 800
◦
C [
25
], which leads o la ge
ene gy consump ion [
24
,
26
]. De iciencies in he p ima y me hods and con en ional ech-
nologies i.e., he mal c acking, oxida ion, and adso p ion, lead o in ensi e esea ch on
no el me hods o a emo al.
Non- he mal plasma (NTP) echnologies a e ene gy-e icien and p oduce he equi ed
esul s o he emo al o ola ile o ganic compounds (VOC), o ganic sol en s, and chlo-
o luo oca bon, as well as o he pollu an s p esen in exhaus s eams, and indus ial was e
gases [
18
,
24
]. “Plasma” e m e e s o pa ial o ull ioniza ion o a ailable gas o ions and
adical p opaga ion om a oms and molecules by inducing elec ons [
27
,
28
]. Plasma is
ca ego ized by empe a u e anges [
28
]. In he mal plasma, all he subs i uen s ha e he
same empe a u e, whe eas in NTP no empe a u e equilib ium exis s be ween kine ically
ene gized exci ed elec ons and cons i uen gaseous o pollu an pa icles such as ions,
a oms, adicals, e c. [
28
]. NTP eac o s a e cha ac e ized on an elec ical discha ge basis
named dielec ic ba ie discha ge (DBD), elec on beam i adia ions, glow discha ge, and
pulse co ona discha ge [
28
]. Plasma discha ge eac o s a e con enien due o ins an aneous
elec on empe a u e and eac i i y because o a ailable ions, adicals, and pulses [
29
].
The elec on beam p ocess is qui e e icien in he emo al o emissi e pollu an s, while
co ona and dielec ic discha ges a e sui able o domes ic and indus ial applica ions due
o he a iable eac o leng h and s eame equency [
29
]. DBD eac o s can be used o
pu i y gas, educe a con en s, and inc ease he quali y o he p ocessed gases [
29
]. They
usually ha e g ea e selec i i y and op imum ope a ing condi ions and ope a e a oom
empe a u e [
29
]. Radicals p oduced a e sho -li ed and ha e good emo al e iciency [
30
].
The majo ene gy inpu o he NTP eac o goes in o he p oduc ion o an elec on a he
han o hea ing pu poses. Fi s ly, elec on gene a ion s a s by exci ing gas molecules and
di ec collision wi h a oms, p oducing adicals such as O
•
, OH
−1
, H
•
, e c. This leads o
mul iple eac ion pa hs and e en ually causes he desi ed decomposi ion o eac an s. In
DBD eac o s (see Figu e 1), he amoun o pollu an o decomposi ion, he ene gy cos o
oxic molecule emo al, and ene gy e iciency a e he main pa ame e s o conside a ion.
These ac o s a e based on eac ion a es, elec ode con igu a ions, eac o packing, and he
inpu ene gy ans e om he powe sou ce wi h a ailable eac o leng h [31].
Among all he VOCs, benzene is he leas eac i e and has a slowe eac ion a e
cons an [
32
]. Al hough cu en a de ini ion excludes benzene, i is s ill used as a model
compound in many s udies on plasma decomposi ion o a s [
30
,
33
–
36
]. The eason o
his is he a o emen ioned s abili y and low eac i i y. Fu he mo e, benzene is a bo de
compound, de ining a s, and many o he hea ie compounds classi ied as a s con ain
mul iple benzene ings [17].
Plasma modeling and eac ion enginee ing is complex and con ined o a gene alized
model, con ining majo p ope ies o physical and chemical na u e [
37
]. In ecen yea s,
machine lea ning (ML) has a ac ed signi ican a en ion as a powe ul ool o a wide a i-
e y o chemical p ocess op imiza ion and online ac i e p edic ion. ML has been ex ensi ely
used in en i onmen al and pollu ion-o ien ed p ocesses due o g ea e e o educ ion
quali y. Ea lie esea che s employed con en ional a i icial neu al ne wo k (ANN) me h-
ods o he complex plasma con e sion o syngas and me hane. In plasma-cen e ed s udies,
di e en ML algo i hms a e used acco ding o hei applicabili y and d awbacks [
38
–
40
].
ML algo i hms a e sho lis s based on pe o mance and solu ions o p ocess in indus y
Ene gies 2023,16, 5835 3 o 26
i al o nonlinea and complex sys ems. An inc ease in he numbe o a iables en ails a
signi ican complica ion in calcula ions and eliable esul o ecas ing, due o labeled and
unlabeled da ase s, missing alues, andom e o s, bad poin s, da a dis ibu ions, e c.
Liu e al. [
41
] highligh ed an ML applica ion o gas con e sion o en i onmen al
pollu an con ol in a plasma en i onmen h ough h ee-laye back p opaga ion ANN o
s udying he non-oxida i e eac ion con e sion o me hane molecules. In plasma p ocess
modeling, discha ge powe is he mos signi ican pa ame e o con e sion, while he leas
signi ican ac o is exci a ion equency [
42
]. Chang’s ANN model is a ou -expe imen al-
pa ame e s udy o be e unde s a ing he e ec on oluene emo al. Pa ame e s we e
inpu discha ge powe , ini ial concen a ion, low a e, and ela i e humidi y [43].
The no el y o his s udy is he applica ion o machine lea ning echniques o model-
ing o benzene con e sion in a DBD plasma eac o .
Ene gies 2023, 16, x FOR PEER REVIEW 3 o 27
me hods o he complex plasma con e sion o syngas and me hane. In plasma-cen e ed
s udies, di e en ML algo i hms a e used acco ding o hei applicabili y and d awbacks
[38–40]. ML algo i hms a e sho lis s based on pe o mance and solu ions o p ocess in
indus y i al o nonlinea and complex sys ems. An inc ease in he numbe o a iables
en ails a signi ican complica ion in calcula ions and eliable esul o ecas ing, due o la-
beled and unlabeled da ase s, missing alues, andom e o s, bad poin s, da a dis ibu-
ions, e c.
Liu e al. [41] highligh ed an ML applica ion o gas con e sion o en i onmen al
pollu an con ol in a plasma en i onmen h ough h ee-laye back p opaga ion ANN
o s udying he non-oxida i e eac ion con e sion o me hane molecules. In plasma p o-
cess modeling, discha ge powe is he mos signi ican pa ame e o con e sion, while
he leas signi ican ac o is exci a ion equency [42]. Chang’s ANN model is a ou -ex-
pe imen al-pa ame e s udy o be e unde s a ing he e ec on oluene emo al. Pa am-
e e s we e inpu discha ge powe , ini ial concen a ion, low a e, and ela i e humidi y
[43].
The no el y o his s udy is he applica ion o machine lea ning echniques o mod-
eling o benzene con e sion in a DBD plasma eac o .
Figu e 1. Discha ge ba ie NTP echnology cha ac e is ics o gasi ica ion a educ ion, based on
[44].
2. Ma e ials and Me hods
2.1. Non-The mal Plasma Kine ic Modeling wi h Machine Lea ning Algo i hms
Figu e 1.
Discha ge ba ie NTP echnology cha ac e is ics o gasi ica ion a educ ion, based
on [44].
2. Ma e ials and Me hods
2.1. Non-The mal Plasma Kine ic Modeling wi h Machine Lea ning Algo i hms
Plasma modeling sys ems degene a e in o smalle and gene al global models depend-
ing on a iables o in e es . These usually comp ise h ee me hods: kine ic, luid, and
Ene gies 2023,16, 5835 4 o 26
hyb id plasma modeling. Kine ic modeling becomes edious owing o high compu a ion
and di icul y in chemis ies o eac ion and mul iple species p opaga ions wi hin a du a ion
o nanoseconds.
Supe ised lea ning deals wi h labeled da ase s and has wo p ocesses o eg es-
sion and classi ica ion. Unsupe ised lea ning mainly uses unlabeled da a wi h no idea
abou he ype o esul s and is di ided in o clus e ing and dimensionali y educ ions.
Semisupe ised lea ning is a hyb id and lies be ween supe ised and supe ised lea ning
combining labeled and unlabeled da a. Rein o cemen lea ning has no aining da ase s
and u ilizes a ewa d-based scheme. The amewo k o he esea ch pe o med is shown in
Figu e 1. Th ough he in eg a ion o kine ic-based modeling, simula ion o expe imen al
da a, and he a analogue model, we emba ked on a ans o ma i e jou ney. This join
endea o aimed o un a el he in ica e p ocess pa ame e s and mul i ace ed eac ion
complexi ies inhe en in non-equilib ium plasma condi ions. By del ing deep in o he
dep hs o unde s anding, a p o ound insigh in o plasma chemis y is unco e ed, igni ing
a pa hway o u he explo a ion.
One o he no ewo hy ou comes o his ad anced esea ch is aligning expe imen al
indings wi h modeling and knowledge-d i en esul s, o a comp ehensi e unde s anding
o plasma dynamics is ob ained. I is impo an o acknowledge ha al hough he e may be
a ia ions be ween he expe imen al and eac o models, hese de ia ions a e p ima ily
due o s eamlined assump ions made o e icien calcula ions.
In his compelling na a i e, machine lea ning eme ges as a game-change . Se ing as
an in aluable black box ool, i seamlessly in eg a es wi h he kine ic and eac o models,
educing s a is ical e o s and bols e ing accu acy. This ium i a e app oach be ween
kine ic-based modeling, eac o simula ion, and machine lea ning se s he s age o a
pa adigm shi in NTP eac ion chemis y, decomposi ion kine ics, and esul alida ion.
The culmina ion o hese no el insigh s uels an unyielding passion o plasma s udies and
pa es he way o ingenious solu ions o in ica e enginee ing p oblems. Gi en he u gency
o he imes, he comme cializa ion o an economically iable a emo al p ocess assumes
pa amoun impo ance. No only does i o e a sus ainable solu ion bu i also c ea es an
en i onmen conduci e o biomass gasi ica ion-based ene gy p oduc ion applica ions.
2.2. Wo king Cycle
This pape ocuses on p oposing and sho lis ing a wo king cycle o he p ocess
indus y connec ing expe imen a ion o a da a-d i en p ocess model. The goal is o add ess
he challenges posed by an inc eased numbe o a iables, such as labeled and unlabeled
da ase s, missing alues, andom e o s, and da a dis ibu ion, in o de o achie e eliable
esul o ecas ing. The de ailed wo king cycle is p esen ed in Figu e 2. The p oposed
wo king cycle consis s o se e al key s eps. S ep 1 in ol es ob aining expe imen a ion
esul s o analyze he decomposi ion o benzene. S ep 2 en ails he kine ics o hypo he ical
ideal plug low eac o pe o mance, which a e hen compa ed agains expe imen al esul s
om he DBD eac o . In S ep 3, compa ison and synch oniza ion o he expe imen al
and modeling esul s a e pe o med o educe e o s and lay he ounda ion o u u e
scale-up s udies.
The subsequen s eps in ol e he applica ion o a ious me hodologies and ools.
S ep 4 ocuses on he de elopmen o a plug low eac o analogue model o non- he mal
plasma. S ep 5 u ilizes MATLAB o i s -p inciple modeling and simula ion. S ep 6
inco po a es machine lea ning models o enhance he analysis. S ep 7 in ol es using
Py hon p og amming o aining and es ing he models. S ep 8 e ol es a ound ex ac ing
ea u es and making p edic ions based on he ained models. Finally, in S ep 9, he esul s
a e synch onized and e alua ed. This comp ehensi e wo king cycle aims o p o ide
aluable insigh s in o he complex dynamics o he p ocess indus y, b idging he gap
be ween expe imen a ion and modeling o imp o ed accu acy and scalabili y.
Ene gies 2023,16, 5835 5 o 26
Ene gies 2023, 16, x FOR PEER REVIEW 5 o 27
aluable insigh s in o he complex dynamics o he p ocess indus y, b idging he gap
be ween expe imen a ion and modeling o imp o ed accu acy and scalabili y.
Figu e 2. Wo king cycle o cu en TAC decomposi ion in NTP DBD eac o o kine ic modeling,
eac o simula ion and machine lea ning modeling.
2.3. Expe imen al Me hodology and Ma e ials
In his s udy, a da ase was ob ained om an expe imen [36] using a coaxial NTP
single-s age DBD eac o o decompose benzene, a a model compound. The expe i-
men al se up in ol ed a plasma eac o wi h a plasma zone be ween qua z ubes, ope -
a ing a a equency o 20 kHz and a ol age o 20 kV. The powe o he DBD eac o
anged om 5 o 40 W, de e mined by he leng h o he ou e elec ode a ambien em-
pe a u e condi ions. Analysis o he plasma eac ion’s end p oduc s was conduc ed using
a gas ch oma og aph (GC), i.e., a Va ian 450-GC equipped wi h lame ioniza ion and he -
mal conduc i i y de ec o s. The DBD eac o ’s ex e nal elec ode was composed o s ain-
less s eel and w apped wi h a qua z ube. Discha ge powe was egula ed using a Va iac
AC ans o me and measu ed wi h an ene gy me e . Gas low was con olled by com-
pu e -con olled mass low con olle s, wi h a ixed low a e o 40 mL/min o me hane
and ni ogen. P oduc composi ion was analyzed using he Va ian 450-GC wi h lame
ioniza ion and he mal conduc i i y de ec o s. The same expe imen al condi ions we e
employed o kine ic modeling, eac o assessmen , and machine lea ning.
To al benzene emo al e iciency and speci ic inpu ene gy a e de ined as:
𝐵𝑒𝑛𝑧𝑒𝑛𝑒 𝑅𝑒𝑚𝑜𝑣𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 󰇛𝑑󰇜 𝐶𝐻   𝐶𝐻 
𝐶𝐻 
 100 (1)
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐼𝑛𝑝𝑢𝑡 𝐸𝑛𝑒𝑟𝑔𝑦𝑆𝐼𝐸𝐽𝑜𝑢𝑙𝑒
li e  𝑃𝑜𝑤𝑒𝑟󰇛𝐽𝑜𝑢𝑙𝑒/𝑆𝑒𝑐𝑜𝑛𝑑󰇜
𝑇𝑜𝑡𝑎𝑙 𝑔𝑎𝑠
𝑓
𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 󰇡𝐿𝑖𝑡𝑒𝑟
𝑆𝑒𝑐𝑜𝑛𝑑󰇢 (2)
Faisal e al. [36] e eals clea ends ega ding he e ec s o inpu powe , concen a-
ion o he a analogue compound, and esidence ime. Inc easing he inpu powe esul s
in highe decomposi ion o benzene. This co ela ion can be a ibu ed o he gene a ion
o high-ene gy elec ons and eac i e species a highe plasma inpu powe . The end
shows a g adual ise in benzene decomposi ion as he powe inpu a ies om 5 W o 40
W, eaching 82.9% a 40 W o a cons an esidence ime o 2.86 s and a concen a ion o
Figu e 2.
Wo king cycle o cu en TAC decomposi ion in NTP DBD eac o o kine ic modeling,
eac o simula ion and machine lea ning modeling.
2.3. Expe imen al Me hodology and Ma e ials
In his s udy, a da ase was ob ained om an expe imen [
36
] using a coaxial NTP
single-s age DBD eac o o decompose benzene, a a model compound. The expe imen al
se up in ol ed a plasma eac o wi h a plasma zone be ween qua z ubes, ope a ing
a a equency o 20 kHz and a ol age o 20 kV. The powe o he DBD eac o anged
om 5 o 40 W, de e mined by he leng h o he ou e elec ode a ambien empe a u e
condi ions. Analysis o he plasma eac ion’s end p oduc s was conduc ed using a gas
ch oma og aph (GC), i.e., a Va ian 450-GC equipped wi h lame ioniza ion and he mal
conduc i i y de ec o s. The DBD eac o ’s ex e nal elec ode was composed o s ainless
s eel and w apped wi h a qua z ube. Discha ge powe was egula ed using a Va iac AC
ans o me and measu ed wi h an ene gy me e . Gas low was con olled by compu e -
con olled mass low con olle s, wi h a ixed low a e o 40 mL/min o me hane and
ni ogen. P oduc composi ion was analyzed using he Va ian 450-GC wi h lame ioniza ion
and he mal conduc i i y de ec o s. The same expe imen al condi ions we e employed o
kine ic modeling, eac o assessmen , and machine lea ning.
To al benzene emo al e iciency and speci ic inpu ene gy a e de ined as:
Benzene Remo al E iciency(db)=C6H6in −C6H6ou
C6H6in
×100 (1)
Speci ic Inpu Ene gySIE Joule
Li e =Powe (Joule/Second)
To al gas low a eLi e
Second (2)
Faisal e al. [
36
] e eals clea ends ega ding he e ec s o inpu powe , concen a ion
o he a analogue compound, and esidence ime. Inc easing he inpu powe esul s
in highe decomposi ion o benzene. This co ela ion can be a ibu ed o he gene a ion
o high-ene gy elec ons and eac i e species a highe plasma inpu powe . The end
shows a g adual ise in benzene decomposi ion as he powe inpu a ies om 5 W o
40 W, eaching 82.9% a 40 W o a cons an esidence ime o 2.86 s and a concen a ion
o 36 mg/Nm
3
. The R
2
alue o 0.856 sugges s a signi ican in luence o inpu powe on
benzene decomposi ion, as shown in Figu e 3a.

Ene gies 2023,16, 5835 6 o 26
Ene gies 2023, 16, x FOR PEER REVIEW 7 o 27
Figu e 3. Expe imen al ends o a analogue compound benzene educ ion in DBD eac o
(adap ed om [36]). (a) Powe inpu (W) s. benzene decomposi ion (%) and me hane decomposi-
ion (%). Pin = 5–40 W, Tin =ambien condi ions, Qin= 40 mL/min, concen a ion = 36 g/Nm
3
and =
2.86 s. (b) Residence ime (s) s. benzene decomposi ion (%). Tin = ambien condi ions, pin= 20 W,
concen a ion = 36 g/Nm
3
and = 0.8–2.86 s. (c) Benzene concen a ion (g/Nm
3
) s. benzene decom-
posi ion (%). Tin = ambien condi ions, pin = 15 W, concen a ion = 18, 36, 64 g/Nm
3
and = 2.86 s.
Figu e 3.
Expe imen al ends o a analogue compound benzene educ ion in DBD eac o (adap ed
om [
36
]). (
a
) Powe inpu (W) s. benzene decomposi ion (%) and me hane decomposi ion (%).
Pin = 5–40 W
, Tin = ambien condi ions, Qin = 40 mL/min, concen a ion = 36 g/Nm
3
and = 2.86 s.
(
b
) Residence ime (s) s. benzene decomposi ion (%). Tin = ambien condi ions, pin = 20 W, concen a-
ion = 36 g/Nm
3
and = 0.8–2.86 s. (
c
) Benzene concen a ion (g/Nm
3
) s. benzene decomposi ion (%).
Tin = ambien condi ions, pin = 15 W, concen a ion = 18, 36, 64 g/Nm3and = 2.86 s.
Ene gies 2023,16, 5835 7 o 26
The heo e ical unde s anding indica es ha he inc ease in decomposi ion is due
o he p esence o high-ene gy elec ons gene a ed a high plasma inpu powe . These
elec ons collide wi h CH
4
, gene a ing eac i e species such as adicals, exci ed molecules,
and ions, which ac i ely con ibu e o he decomposi ion o benzene. The eac ions in ol ed
include he o ma ion o eac i e species and he p oduc ion o lowe hyd oca bons by
b eaking he a oma ic ing [
36
,
45
]. The high-ene gy elec ons also decompose he ca ie
gas, CH
4
, esul ing in he o ma ion o eac i e adicals such as CH
3
and H. These adicals
di ec ly b eak a oma ic ings, leading o he gene a ion o lowe hyd oca bons. Radical
e mina ion eac ions can occu , p oducing CH
4
h ough he combina ion o CH
3
and H
adicals. Agglome a ion eac ions may also ake place wi hin his mechanism [36,46].
Ini ia ion:
CH4+ e−--------------------------- > CH3·+ H++ e−
P opaga ion:
C6H6+ e−--------------------------- > C6H5+ e−
C6H6+ H+--------------------------- > C6H5+ H2
Te mina ion:
C6H5+ Ene ge ic Species --------------------------- > Solid Residue + Lowe Hyd oca bon
The esul s demons a e ha he decomposi ion o CH
4
inc eases wi h highe inpu
powe , a ibu ed o he p esence o eac i e species and ene ge ic elec ons. These adicals
con ibu e o he decomposi ion o me hane in o aluable hyd oca bons and hyd ogen
h ough combina ion and agglome a ion eac ions. Rega ding he e ec o esidence ime
on benzene emo al, inc easing esidence ime leads o highe emo al e iciency. The
emo al o benzene shows a linea inc ease om 37.5% o 68.8% as esidence ime inc eases
o 2.86 s a a powe inpu o 20 W and a concen a ion o 36 g/Nm
3
. This end sugges s
ha longe exposu e o he plasma discha ge zone enhances collisions be ween he a
model compound and ac i e species, esul ing in inc eased benzene emo al, as shown in
Figu e 3b [36,38,47,48].
The R
2
alue o 0.996 indica es a good likelihood o dependence on bo h esidence
ime and powe inpu simul aneously. On he o he hand, he emo al o benzene dec eases
as he concen a ion o he a analogue compound inc eases a a cons an powe inpu
o 15 W and esidence ime o 2.86 s, as shown in Figu e 3c. The highe concen a ion o
benzene leads o a g ea e numbe o benzene molecules in he discha ge zone, inc easing
he p obabili y o uncon e ed benzene escaping and educing o e all emo al e iciency.
This end is obse ed ega dless o he na u e o he ca ie gas, indica ing ha he impac
o concen a ion on emo al e iciency and ene gy u iliza ion emains consis en [36,39].
These indings p o ide aluable insigh s o unde s anding and p edic ing he sys-
em’s beha io and can be u ilized o op imize p ocess pa ame e s. Kine ic modeling,
simula ion, and machine lea ning s udies can inco po a e he obse ed eac ions and
ends o be e unde s and mechanisms and p edic beha io unde di e en condi ions,
as shown in Figu e 4. This in o ma ion is pa icula ly use ul in plasma chemis y and
ca alysis esea ch, aiding in eac o design, p ocess op imiza ion, and ca alys de elopmen .
Fu he analysis and conside a ion o ac o s such as low a e and concen a ion may
be necessa y o a comp ehensi e unde s anding and accu a e modeling o he ela ionship
be ween inpu powe and benzene decomposi ion. None heless, he expe imen al indings
and ends o e aluable guidance o kine ic modeling, simula ion, and machine lea ning
s udies, ad ancing esea ch in plasma chemis y and ca alysis.
Ene gies 2023,16, 5835 8 o 26
Ene gies 2023, 16, x FOR PEER REVIEW 8 o 27
These indings p o ide aluable insigh s o unde s anding and p edic ing he sys-
em’s beha io and can be u ilized o op imize p ocess pa ame e s. Kine ic modeling, sim-
ula ion, and machine lea ning s udies can inco po a e he obse ed eac ions and ends
o be e unde s and mechanisms and p edic beha io unde di e en condi ions, as
shown in Figu e 4. This in o ma ion is pa icula ly use ul in plasma chemis y and ca al-
ysis esea ch, aiding in eac o design, p ocess op imiza ion, and ca alys de elopmen .
Fu he analysis and conside a ion o ac o s such as low a e and concen a ion may
be necessa y o a comp ehensi e unde s anding and accu a e modeling o he ela ion-
ship be ween inpu powe and benzene decomposi ion. None heless, he expe imen al
indings and ends o e aluable guidance o kine ic modeling, simula ion, and ma-
chine lea ning s udies, ad ancing esea ch in plasma chemis y and ca alysis.
Figu e 4. No el sugges ed s a egy o kine ic modeling, eac o assessmen and machine lea ning
me hodology.
2.4. Kine ic Modeling and Reac o Pe o mance Assessmen
Th ee ypes o kine ic models a e p esen in he li e a u e o a emo al kine ics.
Kine ic modeling has been widely used o he aba emen o emissions o pollu an s [49].
S udies ha e been based on he ime-dependence cha ac e is ics o inpu powe , eed low
a e, gas hou ly space eloci y, ins an aneous con e sion, eac o -based adical gene a-
ion, and ene gy e iciency. The kine ic beha io o a emo al wi hin a plasma eac o
accoun s o he a e cons an , eac ion o de , ac i a ion ene gy, and adical p opaga ion
[50,51]. Bes - i line, sum o squa e o e o , s anda d de ia ion, and nume ical me hods
we e used o simula ion and con e sion o naph halene wi h ni ogen and ca ie gas
mix u es o 350 elemen a y and 77 componen species in RADICAL so wa e. I de ined
a new sel -consis en chemical kine ic model based on G alues [52]. The Chemkin so -
wa e Plug Flow module simula es a 257 se o eac ions and compa es he modeling and
Figu e 4.
No el sugges ed s a egy o kine ic modeling, eac o assessmen and machine lea n-
ing me hodology.
2.4. Kine ic Modeling and Reac o Pe o mance Assessmen
Th ee ypes o kine ic models a e p esen in he li e a u e o a emo al kine ics.
Kine ic modeling has been widely used o he aba emen o emissions o pollu an s [
49
].
S udies ha e been based on he ime-dependence cha ac e is ics o inpu powe , eed low
a e, gas hou ly space eloci y, ins an aneous con e sion, eac o -based adical gene a ion,
and ene gy e iciency. The kine ic beha io o a emo al wi hin a plasma eac o accoun s
o he a e cons an , eac ion o de , ac i a ion ene gy, and adical p opaga ion [
50
,
51
].
Bes - i line, sum o squa e o e o , s anda d de ia ion, and nume ical me hods we e
used o simula ion and con e sion o naph halene wi h ni ogen and ca ie gas mix u es
o 350 elemen a y and 77 componen species in RADICAL so wa e. I de ined a new
sel -consis en chemical kine ic model based on G alues [
52
]. The Chemkin so wa e Plug
Flow module simula es a 257 se o eac ions and compa es he modeling and bench-scale
expe imen a ion esul s. Global kine ics a e p oposed. Toluene and benzene show ze o-
and i s -o de kine ics, espec i ely. Benzene gi es he leas speci ic ene gy densi y in
compa ison o oluene and s y ene. The o e all eac ion a e cons an compa es sys ems
and p edic s he emo al a e o VOCs, especially in NTP eac o s [45].
In ou esea ch model, a global kine ic model o emo al o a a model compound
om a syn he ic gasi ie ou pu gas s eam shall be de eloped and ex ended, as a sugges ed
p inciple discussed in he li e a u e [
53
,
54
]. Reac ion condi ions a e oom empe a u e
plasma wi hin single-s age dielec ic ba ie discha ge eac o geome y wi h a ying ope -
a ional condi ions wi h he help o compu e -aided ools such as MATLAB R.21, Py hon
3.8 Anaconda Ve sion, Design Expe 12 o modeling and simula ion s udies o a kine ic
model o he DBD eac o as empi ical modules o s udying decomposi ion eac ions.
Reac o modeling in es iga es di e en pa ame e s, such as inpu powe , emo al a e,
Ene gies 2023,16, 5835 9 o 26
and esidence ime wi hin he DBD eac o . Valida ing a plasma kine ic beha io model
a inpu s (powe and p ocess condi ions) and eac o pe o mance e alua ion ( eac an
decomposi ion) should be conduc ed agains he expe imen al se up in p esen and u-
u e scena ios o scale-up s udies. Kine ic heo y is he basis o complex eac ions and
aims o de elop a comp ehensi e and eliable simpli ied kine ic eac ion model o he
decomposi ion o benzene, se ing as he a analogue compound.
Figu e 4shows he ex ended me hodology employed based on a no el s a egy syne -
gizing expe imen al da a wi h kine ics, modeling and machine lea ning s udies. I in ol es
he u iliza ion o bo h in eg al and di e en ia ion me hods in he MATLAB en i onmen .
Ex ensi e concen a ion-based in es iga ions e eal ha he second s ep o he eac ion
is a e-de e mining, p ima ily due o i s highe concen a ion. To acili a e he modeling
p ocess, se e al key assump ions a e made. Fi s ly, he sys em is assumed o be in a
quasi-s eady s a e, ensu ing he cons ancy o eac ion a es o e ime.
Secondly, he mix u e is conside ed he e ogeneous, acknowledging he p esence o
mul iple phases. The sys em is assumed o ope a e unde ideal plug low eac o condi ions,
which ensu e uni o m low and minimal mixing. The p ocess is assumed o occu unde
iso he mal condi ions, main aining a cons an empe a u e h oughou he eac ion. Las ly,
i is assumed ha he ene gy densi y o he sys em emains cons an du ing he en i e
eac ion p ocess. These assump ions, in conjunc ion wi h a combina ion o ma hema ical
echniques, allow o he de elopmen o a simpli ied kine ic eac ion model ha enhances
ou unde s anding o he benzene decomposi ion p ocess [
36
] o expe imen al wo k
and o e comes he da a noise and una oidable e o s du ing expe imen a ion o he
plasma p ocess.
Fi e addi ional assump ions a e conside ed o main ain a eliable and e icien com-
pu a ion o di e en ial equa ions in one dimension. The ideal plug low eac o exhibi s
simila eac an con e sion o decomposi ion cha ac e is ics, as obse ed in popula so -
wa e, such as Chemkin and Comsol. NTP eac o s, which a e less a ec ed by empe a u e
a ia ions, pe o m well wi hin lowe empe a u e anges. Las ly, he assump ion o con-
s an ene gy densi y is jus i ied by he uni o m na u e o discha ge plasma along he leng h
o he eac o .
3. Resul s
3.1. Ra e-Cons an Calcula ion
Plasma kine ic modeling simula es he gene al eac ion sequence and mechanism
o he calcula ion o he a e cons an . I commences wi h ini ia ion eac ions, and he
second s ep is he decomposi ion eac ion ha in ol es he eac ion o adical in e ac ion
wi h benzene molecules. The eac ion sequence e mina es wi h he o ma ion o yellow
solid o ma ion, indica ing he decomposi ion o benzene compounds in o mul iple- and
single-chain ca bon compounds.
Based on he eac ion mechanism a e o decomposi ion o benzene, a a analogue
compound is dependen on he ini ia ion eac ion and decomposi ion s ep. The ini ia ing
eac ion amoun o a ailable concen a ion o benzene and ca ie mix u e is di ec ly unde
he powe inpu as in lux. I esul s in adical p opaga ion due o high ene gy elec ons and
decomposes he a ailable benzene. Hence, he decomposi ion s ep is he a e-de e mining
s ep and calcula es he a e cons an o he global mac o-kine ic model unde uni o m
ene gy densi y condi ions. Radical concen a ion is di icul o accoun o and accu a ely
measu ed, and hence he mechanis ic kine ic heo y is he basis o he a e-cons an
calcula ions.
Ini ia ion:
Gas (Benzene + Syn he ic Mix u e Gas) ------ > Radical (R)
R1=K1Pin
V (3)
Ene gies 2023,16, 5835 16 o 26
inpu and analogue compound decomposi ion, i.e., R
2
= 0.865, while all o he a iables
s udies ha e an R2 alue o 0.99.
3.4. Ma hema ical Unde s anding Machine Lea ning Linea Reg ession Algo i hm
Reg ession algo i hms a e di ided in o linea algo i hms and nonlinea algo i hms
o bi a ia e and mul i a ia e condi ions by using linea and polynomial eg ession al-
go i hms [
55
]. Reg ession algo i hms a e classically inco po a ed using o dina y leas
squa e eg ession me hods, s epwise linea eg ession, linea eg ession, local es ima e
sca e plo smoo hing, and s epwise eg ession [
56
]. Classi ica ion o eg ession o open
and closed- o m solu ions is ound in [57,58].
The basics o LR, MLR, MLPR a e:
Y=mx +b(23)
whe e Yis he independen a iable, Xis he independen a iable, m is he slope o he
line and C is he in e cep , as shown in Figu e 8. This is he simples linea eg ession
usually inco po a ed in o kine ic modeling. The simples LR model p oduces he bes - i
line ha passes closes o he maximum likelihood poin wi h a minimum e o o Euclidian
dis ance [
59
]. LR is based on ei he a closed- o m solu ion o a non-closed solu ion o
slope and in e cep s calcula ions wi hou calculus de i a i es and in eg a ion. Modi ied
linea eg ession machine lea ning is a popula model wi h a simpli ied assump ion o
linea en anglemen be ween he sys em inpu a iable and co esponding ou pu a iable
esul s [
60
]. The da ase is uniquely con inuously nume ic. In LR, a
y
a ge alue is
assumed o be dependen on he
X
(x
1
,
. . .
,x
n
) and esidual andom e o . Fo an n
h
gene alized obse a ion model da ase , he modi ied ela ionship is as ollows:
y=βo+β1xn1+β2xn2+· · · +βdxnd +εn(24)
Ene gies 2023, 16, x FOR PEER REVIEW 17 o 27
line ha passes closes o he maximum likelihood poin wi h a minimum e o o Euclid-
ian dis ance [59]. LR is based on ei he a closed- o m solu ion o a non-closed solu ion o
slope and in e cep s calcula ions wi hou calculus de i a i es and in eg a ion. Modi ied
linea eg ession machine lea ning is a popula model wi h a simpli ied assump ion o
linea en anglemen be ween he sys em inpu a iable and co esponding ou pu a ia-
ble esul s [60]. The da ase is uniquely con inuously nume ic. In LR, a y a ge alue is
assumed o be dependen on he X (x
1
,…,x
n
) and esidual andom e o . Fo an n
h
gene -
alized obse a ion model da ase , he modi ied ela ionship is as ollows:
𝑦= 𝛽+𝛽𝑥+𝛽𝑥+⋯+ 𝛽𝑥 + 𝜀 (24)
Figu e 8. Linea eg ession machine lea ning e o quan i ica ion g aphical ep esen a ion.
The in e cep e ms 𝛽 and 𝛽 o 𝛽 a e he ea u e a iable coe icien s wi h a an-
domized e o ε . E o is he di e ence be ween he ue alue (y) and he p edic ed alue
(Y
i
) [38,39], as shown in Figu e 8. The LR algo i hm gi es an es ima ion o β coe icien -
ela ed pa ame e s. Es ima ed pa ame e s 𝛽,….,𝛽 gi e an es ima ed a ge alue o
he a iable 𝑦. The LR algo i hm gi es he bes alues o βo and β
1
, wi h minimum
e o esidual ε indica ing he syne gy be ween p edic ed y
p ed
and ac ual alues y
i
o ex-
pe imen a ion and machine lea ning model p edic ion. Di e en pa ame e s a e in ol ed
in he e o educ ion and eg ession me hod o synch onizing he esul s and p oducing
an R
2
alue close o 1 [47,48].
𝜀=𝑦 −𝑦 (25)
∴ 𝑦 =𝛽+𝛽𝑥 (26)
Bes - i lines c oss h ough a maximum poin o sca e plo . The line is ob ained
h ough he minimiza ion o he esidual sum o squa es (RSS) and mean squa e e o
(MSE). A cos unc ion is a minimum o RSS and MSE alues. The LR algo i hm gi es he
cos unc ion o op imal alues o 𝛽& 𝛽 o he bes - i ing ec o posi ioning [61].
3.5. Model E alua ion Me ics
In o de o enhance he accu acy o he ML p edic ion sys em, he ML linea eg es-
sion (LR) model is e alua ed using a se o key me ics. Fa o able condi ions o ML un-
ning he LR model include low a iance and highe bias, as hey con ibu e o imp o ed
p edic ion accu acy and as e compu a ion, albei wi h a g ea e numbe o assump ions
[61,62]. One impo an me ic used is he R
2
o de e mina ion o R
2
coe icien . This me ic
calcula es he a iance in he de eloped model o ML p edic ion esul s and anges be-
ween 0 and 1. A highe R
2
indica es g ea e applicabili y and be e p edic ion esul s o
he model. Ano he me ic employed is he oo mean squa e e o (RMSE). This me ic
Figu e 8. Linea eg ession machine lea ning e o quan i ica ion g aphical ep esen a ion.
The in e cep e ms
βo
and
β1
o
βD
a e he ea u e a iable coe icien s wi h a an-
domized e o
ε
. E o is he di e ence be ween he ue alue (y) and he p edic ed alue
(Y
i
) [
38
,
39
], as shown in Figu e 8. The LR algo i hm gi es an es ima ion o
β
coe icien -
ela ed pa ame e s. Es ima ed pa ame e s
βe0
,
. . .
,
βeD
gi e an es ima ed a ge alue o
he a iable
yen
. The LR algo i hm gi es he bes alues o
β
oand
β1
, wi h minimum
e o esidual
ε
indica ing he syne gy be ween p edic ed y
p ed
and ac ual alues y
i
o ex-
pe imen a ion and machine lea ning model p edic ion. Di e en pa ame e s a e in ol ed
in he e o educ ion and eg ession me hod o synch onizing he esul s and p oducing
an R2 alue close o 1 [47,48].
εn=yp edic −yi(25)

Ene gies 2023,16, 5835 17 o 26
∴yp edic =βo+βixi(26)
Bes - i lines c oss h ough a maximum poin o sca e plo . The line is ob ained
h ough he minimiza ion o he esidual sum o squa es (RSS) and mean squa e e o
(MSE). A cos unc ion is a minimum o RSS and MSE alues. The LR algo i hm gi es he
cos unc ion o op imal alues o βo&βi o he bes - i ing ec o posi ioning [61].
3.5. Model E alua ion Me ics
In o de o enhance he accu acy o he ML p edic ion sys em, he ML linea eg ession
(LR) model is e alua ed using a se o key me ics. Fa o able condi ions o ML unning he
LR model include low a iance and highe bias, as hey con ibu e o imp o ed p edic ion
accu acy and as e compu a ion, albei wi h a g ea e numbe o assump ions [
61
,
62
]. One
impo an me ic used is he R
2
o de e mina ion o R
2
coe icien . This me ic calcula es
he a iance in he de eloped model o ML p edic ion esul s and anges be ween
0 and 1
.
A highe R
2
indica es g ea e applicabili y and be e p edic ion esul s o he model.
Ano he me ic employed is he oo mean squa e e o (RMSE). This me ic measu es he
esidual a iance, aking he squa e oo o he di e ence be ween he obse ed da a and
p edic ed alues. RMSE conside s he deg ee o eedom o unbiasedness es ima ion and
co esponds o he esidual s anda d e o (RSE).
R2=1− ∑n
i=1yi−βo−βi)2
(yi−y)2!(27)
RMSE =
u
u
∑n
i=1yiac ual −yip ed )2
(n)!(28)
RSE =
u
u
∑n
i=1yiac ual −yip ed )2
(n−2)!(29)
The analysis o he expe imen al da a in his s udy e eals impo an insigh s in o he
ela ionship be ween a ious a iables. The powe inpu in NTP eac o s is o signi ican
in e es , as i is less likely o be empe a u e-dependen . Mo eo e , he kine ic model-
ing echniques employed, such as powe -law kine ics, hea ily ely on he inpu powe
(Figu e 9)
. The e o e, he powe inpu ene gy a iable has been sho lis ed as a key ac o
o he machine lea ning-based black box modeling.
To u he explo e hese ela ionships, hea maps we e gene a ed using Py hon buil -in
lib a ies. These hea maps isually depic he in e dependence among he a iables, wi h
Figu es 10a and 11a showcasing he ela ionships be ween powe inpu (P
in
, W), and
a analogue decomposi ion (X
a
, %), while Figu es 10b and 11b ocus on he sho lis ed
a iables unde expe imen al condi ions—powe inpu (pin, W) and expe imen al decom-
posi ion (X
A
wi hin he ange o 0–100%)— o p ep ocessing o a ailable expe imen al and
eac o model and simula ion da ase s. The hea maps and pai ed plo s p o ide aluable
insigh s in o he linea i y and co ela ion be ween hese a iables, wi h inle compound
decomposi ion (%) and powe inpu exhibi ing signi ican co ela ion coe icien s o 0.93
and 0.94, espec i ely, om he expe imen al and eac o model simula ions. The subse-
quen analysis o linea ly dependen a iable da a p esen ed also shows ou p oposed
me ics showed a highe dependence o a iables in he modeling and simula ion da ase in
compa ison o he expe imen al da ase , as well as ela i ely less noise in da a and e ec i e
o e all end o scale-up s udies.
Ene gies 2023,16, 5835 18 o 26
Ene gies 2023, 16, x FOR PEER REVIEW 19 o 27
Figu e 9. Machine lea ning linea eg ession modeling lowcha o Sciki Lea n Lib a y and gen-
e alized machine lea ning linea eg ession algo i hm.
Figu e 9.
Machine lea ning linea eg ession modeling lowcha o Sciki Lea n Lib a y and
gene alized machine lea ning linea eg ession algo i hm.
Ene gies 2023,16, 5835 19 o 26
Ene gies 2023, 16, x FOR PEER REVIEW 20 o 27
Figu e 10. Powe inpu (P
in
, W) s. a analogue compound decomposi ion expe imen al da ase
machine lea ning s udy (%). (a) Hea map o da a analysis. (b) Pai ed plo o da a p ep ocessing.
(c) Expe imen al da ase es ing plo . (d) Expe imen al aining se da a plo o sho lis ed a iable
a expe imen al powe inpu (P
in
, W). Expe imen al decomposi ion 0–100%, esidence ime = 2.86 s,
concen a ion = 36 g/Nm
3
.
In ou case s udies, he inpu powe in he expe imen al and eac o model is simila
in pa e n wi h pe o mance me ics o R
2
o 0.865 and 0.889, as shown in Figu es 10 and
11. In compa ison o he absolu e e ec i e alue o de ining he global app oach o model
esul s o be inco po a ed in he cu en s udies, in he g aphs shown below, aw da a o
expe imen al condi ions and eac o models a e plo ed. Raw da a a e u he classi ied
o ea u e enginee ing, da a dis ibu ion, s anda d de ia ion, loss unc ion educ ion, cos
unc ion penaliza ion, and me ics-based pe o mance assessmen o inc ease he model
alida ion by uning he slope o in e cep h ough lea ning a e o model accu acy, mean
squa e e o (MSE), oo mean squa e e o (RMSE), sum o he squa e o e o (SSE), R
2
,
and adjus ed R
2
. In ML modules, he e o unc ion is i e a ed o he minimum esul s.
Each loop o commands p oduces a signi ican di e ence in e o , and ela ed ea u es a e
op imized o he bes esul s ou pu . In ML eg ession condi ions, he aw da ase is cal-
cula ed om he sou ce. Figu e 9 shows ha he wo da ase s a e op imally a ailable. The
o al da ase consis s o 60 sample alues. Design-Expe so wa e was used o inc easing
he numbe o expe imen a ion da ase sample alues a simila ends using a buil -in
unc ion.
Figu e 10.
Powe inpu (P
in
, W) s. a analogue compound decomposi ion expe imen al da ase
machine lea ning s udy (%). (
a
) Hea map o da a analysis. (
b
) Pai ed plo o da a p ep ocessing.
(
c
) Expe imen al da ase es ing plo . (
d
) Expe imen al aining se da a plo o sho lis ed a iable
a expe imen al powe inpu (Pin, W). Expe imen al decomposi ion 0–100%, esidence ime = 2.86 s,
concen a ion = 36 g/Nm3.
In ou case s udies, he inpu powe in he expe imen al and eac o model is simila
in pa e n wi h pe o mance me ics o R
2
o 0.865 and 0.889, as shown in Figu es 10 and 11.
In compa ison o he absolu e e ec i e alue o de ining he global app oach o model
esul s o be inco po a ed in he cu en s udies, in he g aphs shown below, aw da a o
expe imen al condi ions and eac o models a e plo ed. Raw da a a e u he classi ied
o ea u e enginee ing, da a dis ibu ion, s anda d de ia ion, loss unc ion educ ion, cos
unc ion penaliza ion, and me ics-based pe o mance assessmen o inc ease he model
alida ion by uning he slope o in e cep h ough lea ning a e o model accu acy, mean
squa e e o (MSE), oo mean squa e e o (RMSE), sum o he squa e o e o (SSE),
R
2
, and adjus ed R
2
. In ML modules, he e o unc ion is i e a ed o he minimum
esul s. Each loop o commands p oduces a signi ican di e ence in e o , and ela ed
ea u es a e op imized o he bes esul s ou pu . In ML eg ession condi ions, he aw
da ase is calcula ed om he sou ce. Figu e 9shows ha he wo da ase s a e op imally
a ailable. The o al da ase consis s o 60 sample alues. Design-Expe so wa e was used
o inc easing he numbe o expe imen a ion da ase sample alues a simila ends using
a buil -in unc ion.
The inpu da ase is i s quan i a i ely aligned and acco ding o ou lie s and cen al
dis ibu ion endency esul s a e p oduced using he p ep ocessing s a is ical unc ions in
Py hon p og amming. Spyde Compile is used o compu a ion and algo i hmic s udies.
A comple e o e iew o Py hon lib a ies and a gene al machine lea ning linea algo i hm
lowcha a e shown in Figu e 9. The da ase is di ided in o 45% aining se s and 55%
es ing se s, as illus a ed in Figu es 10c,d and 11c,d o he expe imen al and modeling
Ene gies 2023,16, 5835 20 o 26
da ase s, espec i ely. A highe pe cen age o he es ing da ase is u ilized due o he
limi ed numbe o alues a ailable in he expe imen al da a. This app oach allows o an
ex ended analysis and p o ides a comp ehensi e unde s anding using a la ge po ion
o he da ase . Consequen ly, i enables he de elopmen o an accu a e machine lea ning
model h ough he aining da ase .
Ene gies 2023, 16, x FOR PEER REVIEW 21 o 27
Figu e 11. Powe inpu (P
in,
W) s. a analogue compound decomposi ion eac o model—simula-
ion da ase machine lea ning s udy (%).
(a) Hea map o da a analysis. (b) Pai ed plo o da a p e-
p ocessing. (c) Expe imen al da ase es ing plo . (d) Expe imen al aining se da a plo o
sho lis ed a iable a expe imen al powe inpu (P
in
, W) in eac o model and simula ion da ase
condi ions. Powe inpu P
in
5–40 W, eac o model and simula ion da ase decomposi ion 0–100%,
esidence ime = 2.86 s, concen a ion = 36 g/Nm
3
.
The inpu da ase is i s quan i a i ely aligned and acco ding o ou lie s and cen al
dis ibu ion endency esul s a e p oduced using he p ep ocessing s a is ical unc ions in
Py hon p og amming. Spyde Compile is used o compu a ion and algo i hmic s udies.
A comple e o e iew o Py hon lib a ies and a gene al machine lea ning linea algo i hm
lowcha a e shown in Figu e 9. The da ase is di ided in o 45% aining se s and 55%
es ing se s, as illus a ed in Figu es 10c,d and 11c,d o he expe imen al and modeling
da ase s, espec i ely. A highe pe cen age o he es ing da ase is u ilized due o he lim-
i ed numbe o alues a ailable in he expe imen al da a. This app oach allows o an
ex ended analysis and p o ides a comp ehensi e unde s anding using a la ge po ion o
he da ase . Consequen ly, i enables he de elopmen o an accu a e machine lea ning
model h ough he aining da ase .
The aining se educes he cos unc ion o inding he op imal alues o line equa-
ion coe icien s. Ac ual alues a e conside ed he a ge alues. Fo each i e a ion in he
machine lea ning algo i hm, a new alue o each coe icien o he a iable is assigned
acco ding o he numbe o a iables. Fo powe inpu (P
in
) s. eac an decomposi ion
(X), sca e da ase s educe he Euclidean dis ances o he ac ual and a ge esul s. X
m
and X
exp
a e educed o a minimum acco ding o he machine lea ning ea u es and impli-
ca ions. Repea ed i e a ion using he Sciki Lea n Lib a y p oduces a da ase ha is ali-
da ed agains he es da ase s (app ox. 50%) o o iginal da ase s o mo e e o educ ion
in a loop s uc u e. The machine lea ning model is deployed o new da ase s a e suc-
cess ul comple ion. ML p edic ion alues a e designa ed o mean squa e e o (MSE),
Figu e 11.
Powe inpu (P
in
, W) s. a analogue compound decomposi ion eac o
model—simula ion
da ase machine lea ning s udy (%). (
a
) Hea map o da a analysis. (
b
) Pai ed
plo o da a p ep ocessing. (
c
) Expe imen al da ase es ing plo . (
d
) Expe imen al aining se da a
plo o sho lis ed a iable a expe imen al powe inpu (P
in
, W) in eac o model and simula ion
da ase condi ions. Powe inpu P
in
5–40 W, eac o model and simula ion da ase decomposi ion
0–100%, esidence ime = 2.86 s, concen a ion = 36 g/Nm3.
The aining se educes he cos unc ion o inding he op imal alues o line equa ion
coe icien s. Ac ual alues a e conside ed he a ge alues. Fo each i e a ion in he machine
lea ning algo i hm, a new alue o each coe icien o he a iable is assigned acco ding
o he numbe o a iables. Fo powe inpu (P
in
) s. eac an decomposi ion (X), sca e
da ase s educe he Euclidean dis ances o he ac ual and a ge esul s. X
m
and X
exp
a e educed o a minimum acco ding o he machine lea ning ea u es and implica ions.
Repea ed i e a ion using he Sciki Lea n Lib a y p oduces a da ase ha is alida ed
agains he es da ase s (app ox. 50%) o o iginal da ase s o mo e e o educ ion in a
loop s uc u e. The machine lea ning model is deployed o new da ase s a e success ul
comple ion. ML p edic ion alues a e designa ed o mean squa e e o (MSE), oo
mean squa e e o (RMSE), sum o he squa e o e o (SSE), R
2
, and adjus ed R
2
o
model accu acy.
ML-LR e ol es a ound he comp ehensi e analysis o he esul s ob ained om he
expe imen , eac o model simula ions, and machine lea ning p edic ions, as p esen ed in
Table 1, based on he machine lea ning modeling esul s o expe imen al and eac o model
Ene gies 2023,16, 5835 21 o 26
and simula ion, shown in Figu es 10 and 11. The a ious me ics measu ed in his s udy
p o ide aluable insigh s in o he pe o mance and accu acy o he models employed. The
in e cep alues yielded a alue o 2.16, indica ing a baseline e e ence poin . The eac o
model and simula ions achie ed a sligh ly lowe in e cep o 1.95795433, while he machine
lea ning p edic ions esul ed in an in e cep o 1.91. These alues sugges ha bo h he
eac o model and machine lea ning app oach we e able o e ec i ely cap u e he baseline
beha io , indica ing he accu acy o he models. The linea coe icien was 14.2, which
inc eased o 21.74562448 in he eac o model and simula ions. This demons a es ha he
eac o model and simula ions exhibi a s onge linea ela ionship be ween he a iables
unde conside a ion. Rema kably, he machine lea ning p edic ions su passed bo h, wi h
a linea coe icien o 23.1, indica ing a mo e p onounced e ec o he p edic o s on he
esponse a iable.
Table 1.
Machine lea ning linea eg ession model e alua ion o expe imen al and eac o modeling
and simula ion da ase .
Me ics ML-Expe imen
Resul s
ML-Reac o Model and
Simula ions
O e all-
Machine Lea ning P edic ions
In e cep 2.16 1.95795433 1.91
Linea Coe icien 14.2 21.74562448 23.1
T aining Se 45% 45% 45%
Tes ing Se s 55% 55% 55%
R2Value 0.86 0.88 0.998
Mean Absolu e E o (MAE) 0.0978 0.032 0.008
Mean Squa ed E o
(MSE) 0.0024 0.001 0.00001
Roo Mean Squa e E o
(RMSE) 0.042 0.034 0.019
Adjus ed R20.865 0.8891 0.9984
Accu acy o Model 0.923545907 0.98876584 0.99918729
In o de o e alua e he pe o mance o he models, he da ase di ision in o ain-
ing and es ing se s, wi h a balanced spli o aining and es ing, ensu ed ha ML-LR
esul s o bo h he eac o model and simula ions and machine lea ning p edic ions we e
e alua ed using he same p opo ion o da a as he expe imen and also enabled a ai
compa ison o hei capabili ies in cap u ing he unde lying pa e ns and p edic ing he
a ge a iable accu a ely.
A measu e o he goodness o i , R
2
p o ides insigh s in o he p opo ion o a iance
explained by he model. The expe imen achie ed an R
2
o 0.86, indica ing ha 86% o
he a ia ion in he esponse a iable can be a ibu ed o he p edic o s conside ed in he
expe imen . The eac o model and simula ions imp o ed his alue o 0.88, showcasing
a s onge ela ionship be ween he p edic o s and he esponse a iable. Howe e , he
machine lea ning p edic ions demons a ed a ema kable R
2
o 0.998, indica ing an excep-
ional abili y o explain he a iance in he a ge a iable. This signi ies a high le el o
accu acy and eliabili y in p edic ing he desi ed ou come.
The accu acy o he models accoun s o se e al e o me ics. The mean absolu e e o
(MAE) measu es he a e age magni ude o he e o s be ween p edic ed and ac ual alues.
The expe imen yielded a MAE o 0.0978, while he eac o model and simula ions educed
his e o o 0.032. No ably, he machine lea ning p edic ions achie ed an imp essi ely low
MAE o 0.008, indica ing supe io accu acy and p ecision. The mean squa ed e o (MSE),
which quan i ies he a e age squa ed di e ences be ween p edic ed and ac ual alues,
e ealed simila ends. The expe imen esul ed in an MSE o 0.0024, educed o 0.001 in
he eac o model and simula ions. Su p isingly, he machine lea ning p edic ions achie ed
he lowes MSE o 0.00001, u he highligh ing hei abili y o minimize e o s and p o ide
highly accu a e p edic ions.

Ene gies 2023,16, 5835 22 o 26
The oo mean squa e e o (RMSE), an es ima ion o he s anda d de ia ion o he
e o s, ollowed a simila pa e n. The expe imen yielded an RMSE o 0.042, while he
eac o model and simula ions achie ed a lowe RMSE o 0.034. No ably, he machine
lea ning p edic ions achie ed he lowes RMSE o 0.019, indica ing supe io p ecision and
accu acy in p edic ing he desi ed ou come. Addi ionally, he adjus ed R
2
, which conside s
he numbe o p edic o s and sample size, ollowed a simila end. The expe imen
ob ained an adjus ed R
2
o 0.865, while he eac o model and simula ions demons a ed
an imp o ed alue o 0.8891. Rema kably, he machine lea ning p edic ions excelled wi h
an excep ional adjus ed R
2
o 0.9984, emphasizing hei abili y o accu a ely accoun o he
a ia ions in he esponse a iable.
The accu acy o he model, indica ing he pe cen age o co ec p edic ions, was e alu-
a ed. The expe imen achie ed an accu acy o 0.923545907, which imp o ed o 0.98876584
in he eac o model and simula ions. Rema kably, he machine lea ning p edic ions exhib-
i ed a signi ican ly highe accu acy o 0.99918729, highligh ing hei abili y o gi e p ecise
and eliable p edic ions as well as alida ion using OLS eg ession. We a e deployed
he closed- o m solu ion in Py hon o he linea eg ession model. The o dina y leas
squa e me hod is occasionally used o he c oss- alida ion o machine lea ning models. In
compa ison o he Sciki Lea n Lib a y, he OLS esul s a e less app op ia e and accu a e
due o lesse i e a ion and d awback o pe o mance in low-bias and high- a iance egions
wi h u mos alida ion. The me hod, howe e , gi es a good idea abou di e en e ec i e
s a is ical me hods, such as Du bin–Wa son, D , F-s a is ic, and esiduals, as shown in
Table 2. T aining o da ase s om expe imen a ion and eac o model gi es a good i o
minimized cos unc ion esul s in he es ing s age wi h close collinea i y in compa a i e
esul s. p- alues deduced om OLS i ing esul s had a 0.031 alue agains he s anda d
0.05 alue o hypo hesis es ing esul s, as shown in Table 2. S anda d e o in he OLS
me hod assumes a co a iance ma ix o he speci ic iden i ica ion o s a is ical esul s. In
u u e s udies o simila gaseous mix u es, empi ical esul s o machine lea ning based LR
ou pu s a e alida ed and decomposi ion pe cen age o he inpu powe a iable a any
gi en simila concen a ion o he a analogue compound.
Table 2. O dina y leas squa e linea eg ession model e alua ion me ics esul s.
OLS Reg ession Resul s
Dependen Va iable: Y R-squa ed: 0.890
Model: OLS Adj. R-squa ed: 0.887
Me hod Leas Squa es F-s a is ic: 347.9
Numbe o
Obse a ion 60 P ob (F-s a is ic): 3.14 ×10−22
D Residuals 43 Log-likelihood 75.111
D Model: 1 AIC −146.2
Co a iance Type: obus BIC −142.6
Omnibus: 4.279 Du bin–Wa son 0.028
P ob
(Omnibus): 0.118 Ja que–Be a (JB): 3.665
Skew: −0.63 P ob (JB) 0.160
Ku osis: 2.293 Cond. No 37.5
Coi S anda d e o T p> | | p< 2.5% p< 97.5%
Cons 0.4420 0.022 20.27 0.00 0.398 0.486
×1 0.0342 0.002 18.64 0.00 0.031 0.038
O e all, he esul s indica e ha bo h he eac o model and simula ions and he
machine lea ning p edic ions ou pe o med he expe imen in a ious espec s. The eac o
model and simula ions showcased a s onge linea ela ionship and achie ed highe accu-
acy han he expe imen . The machine lea ning p edic ions excelled in cap u ing complex
pa e ns, esul ing in excep ional accu acy and p ecision. These indings emphasize he
Ene gies 2023,16, 5835 23 o 26
e ec i eness o bo h modeling app oaches, pa icula ly he machine lea ning echnique, in
accu a ely p edic ing he desi ed ou comes.
4. Conclusions
Ta is a ba ie o ull enewable ene gy exploi a ion h ough a iable eeds ock. NTP
echnologies de ine new pa hways o a analogue compound decomposi ion, emo al,
and educ ion s udies wi h an elec i ied p ocess. A holis ic app oach o decomposi ion
uses a s udy da ase o benzene as a a analogue compound in a e a ca ie gaseous mix-
u e. Powe inpu , he low a e o ca ie gases, a analogue compound inle concen a ion
and esidence ime agains decomposi ion pe cen age a e conside ed he inpu a iables
o s udies in he DBD eac o . An appa en a e cons an o 0.040 kJ/L has been calcula ed
a an ini ial concen a ion o 36 g/Nm
3
o he analogue compound o he powe inpu o
40 W o esidence ime o 2.86 s. A eac o model o DBD eac o pe o mance assess-
men and c oss- alida ion o appa en a e decomposi ion cons an has been p oposed
using de ini e assump ions. An ODE equa ion se has been p oduced by ma hema ical
modeling. Reac o scale leng h shows simila beha io o he plug low eac o o he
changing con e sion. A ho spo egion in he ini ial 15% o 25% o he eac o leng h is
he maximum decomposi ion pa ch o he a analogue compound in o associa ed ligh e
hyd oca bons and soo . Fu he mo e, he model un o he pin anges om 5 W o 40 W,
and a cons an low a e o 40 mL/min o ca ie low gas mix u e o me hane and ni ogen
shows conside able syne ge ic esul s, wi h a maximum decomposi ion o 83.01% agains
82.9% expe imen a ion decomposi ion. Howe e , s a is ical da a analysis o expe imen al
and eac o model da ase s shows he di e ence in me ics alue i.e., R
2
. A new and
ad anced Py hon p og amming machine lea ning ool has been used o e o educ ion
in expe imen a ion and eac o model esul s o gene alized empi ical o mula ion in
scale-up s udies. ML linea eg ession algo i hm akes in o accoun he expe imen al and
eac o da ase s. Da ase s a e di ided in o aining and es ing da ase s. This educes he
RME, MSE, MAE, and R
2
e o s o he da ase s and p oduces a p edic ion model o new
in e cep s and slopes wi h minimum cos unc ions: ML R
2
~1 o he expe imen al and
eac o model da ase s agains o iginal R2= 0.85 and 0.89 alue.
Au ho Con ibu ions:
Concep ualiza ion, M.Y.A., M.A.S. and H.P.-K.; me hodology, M.Y.A., M.A.S.,
M.W.T. and L.N.; so wa e, M.Y.A., M.A.S. and H.P.-K.; alida ion, M.Y.A., M.A.S. and L.N.; o mal
analysis, M.Y.A., H.P.-K., A.S.A. and L.N.; in es iga ion, M.Y.A., H.P.-K., A.S.A. and L.N.; esou ces,
M.Y.A., H.P.-K. and L.N.; da a cu a ion, M.Y.A., M.A.S., M.W.T. and H.P.-K.; w i ing—o iginal d a
p epa a ion, M.Y.A., M.A.S., M.W.T. and H.P.-K.; w i ing— e iew and edi ing, M.Y.A., M.A.S., H.P.-K.
and L.N.; isualiza ion, M.Y.A., A.S.A. and L.N.; supe ision, M.Y.A., M.A.S. and H.P.-K. All au ho s
ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
Da a A ailabili y S a emen : Da a a ailable on eques .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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