Advancing sustainable decomposition of biomass tar model compound: Machine learning, kinetic modeling, and experimental investigation in a non-thermal plasma dielectric barrier discharge reactor

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 . Re e ences 1. Yousa , A.M.; Aqsa, R. 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