Water quality prediction based on machine learning and comprehensive weighting methods

Ci a ion: Wang, X.; Li, Y.; Qiao, Q.; Ta a es, A.; Liang, Y. Wa e Quali y P edic ion Based on Machine Lea ning and Comp ehensi e Weigh ing Me hods. En opy 2023,25, 1186. h ps://doi.o g/10.3390/ e25081186 Academic Edi o : Jose San ama ia Recei ed: 30 June 2023 Re ised: 26 July 2023 Accep ed: 2 Augus 2023 Published: 9 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/). en opy A icle Wa e Quali y P edic ion Based on Machine Lea ning and Comp ehensi e Weigh ing Me hods Xianhe Wang 1,2 , Ying Li 1,2, Qian Qiao 1, Ad iano Ta a es 2and Yanchun Liang 3,4,* 1 School o Applied Chemis y and Ma e ials, Zhuhai College o Science and Technology, Zhuhai 519041, China; [email p o ec ed] (X.W.); [email p o ec ed] (Y.L.) 2Depa men o Indus ial Elec onics, School o Enginee ing, Uni e si y o Minho, 4704-553 B aga, Po ugal 3School o Compu e Science, Zhuhai College o Science and Technology, Zhuhai 519041, China 4Key Labo a o y o Symbol Compu a ion and Knowledge Enginee ing o he Minis y o Educa ion, College o Compu e Science and Technology, Jilin Uni e si y, 2699 Qianjin S ee , Changchun 130012, China *Co espondence: [email p o ec ed] Abs ac : In he con ex o escala ing global en i onmen al conce ns, he impo ance o p ese ing wa e esou ces and upholding ecological equilib ium has become inc easingly appa en . As a esul , he moni o ing and p edic ion o wa e quali y ha e eme ged as i al asks in achie ing hese objec i es. Howe e , ensu ing he accu acy and dependabili y o wa e quali y p edic ion has p o en o be a challenging endea o . To add ess his issue, his s udy p oposes a comp ehensi e weigh -based app oach ha combines en opy weigh ing wi h he Pea son co ela ion coe icien o selec c ucial ea u es in wa e quali y p edic ion. This app oach e ec i ely conside s bo h ea u e co ela ion and in o ma ion con en , a oiding excessi e eliance on a single c i e ion o ea u e selec ion. Th ough he u iliza ion o his comp ehensi e app oach, a comp ehensi e e alua ion o he con ibu ion and impo ance o he ea u es was achie ed, he eby minimizing subjec i e bias and unce ain y. By s iking a balance among a ious ac o s, ea u es wi h s onge co ela ion and g ea e in o ma ion con en can be selec ed, leading o imp o ed accu acy and obus ness in he ea u e-selec ion p ocess. Fu he mo e, his s udy explo ed se e al machine lea ning models o wa e quali y p edic ion, including Suppo Vec o Machines (SVMs), Mul ilaye Pe cep on (MLP), Random Fo es (RF), XGBoos , and Long Sho -Te m Memo y (LSTM). SVM exhibi ed commendable pe o mance in p edic ing Dissol ed Oxygen (DO), showcasing excellen gene aliza ion capabili ies and high p edic ion accu acy. MLP demons a ed i s s eng h in nonlinea modeling and pe o med well in p edic ing mul iple wa e quali y pa ame e s. Con e sely, he RF and XGBoos models exhibi ed ela i ely in e io pe o mance in wa e quali y p edic ion. In con as , he LSTM model, a ecu en neu al ne wo k specialized in p ocessing ime se ies da a, demons a ed excep ional abili ies in wa e quali y p edic ion. I e ec i ely cap u ed he dynamic pa e ns p esen in ime se ies da a, o e ing s able and accu a e p edic ions o a ious wa e quali y pa ame e s. Keywo ds: wa e quali y p edic ion; comp ehensi e weigh -based app oach; ea u e selec ion; machine lea ning; LSTM 1. In oduc ion Wi h he inc easing human ac i i ies associa ed wi h indus ializa ion and u baniza- ion de elopmen , he wa e quali y o coas al i e s is acing escala ing and se e e h ea s and deg ada ion [ 1 ]. Coas al i e s play a c i ical ole in connec ing land and ocean, and he wa e quali y di ec ly impac s he well-being and sus ainable de elopmen o coas al ecosys ems. The e o e, i is impe a i e o ecognize and add ess he p essing issue o de e io a ing wa e quali y in coas al i e s [ 2 ]. To p o ec i e wa e quali y, main ain he in eg i y o coas al ecosys ems, and ensu e sus ainable human de elopmen , e ec i e managemen and p o ec ion measu es mus be implemen ed [ 3 ]. Ad anced echnological En opy 2023,25, 1186. h ps://doi.o g/10.3390/e25081186 h ps://www.mdpi.com/jou nal/en opy En opy 2023,25, 1186 2 o 20 means and scien i ic me hods should be employed o s eng hen wa e quali y moni o ing, ea ly wa ning sys ems, and go e nance capabili ies [4]. T adi ional i e wa e quali y moni o ing and wa ning echnology elies on heo e i- cal models ha encompass physical, chemical, and biological p ocesses [5]. These models desc ibe and p edic changes in wa e quali y pa ame e s by es ablishing ma hema ical equa ions. Mechanism models ypically conside ac o s such as wa e low eloci y, low a e, wa e quali y pa ame e s, as well as he anspo and ans o ma ion o pollu an s [ 6 ]. Common mechanism models include hyd odynamic models, wa e quali y models, and ecological models. T adi ional wa e -quali y-moni o ing and ea ly wa ning echnologies based on mechanism models o e ce ain ad an ages [ 7 ]. They a e g ounded in a p o- ound unde s anding o hyd ology, hyd odynamics, wa e quali y, and ecological p ocesses, he eby exhibi ing high in e p e abili y and eliabili y [ 8 ]. These models enable quan i a i e p edic ion and analysis o wa e quali y a ia ions, acili a ing he assessmen o he heal h o he wa e en i onmen and he o mula ion o s a egies o imp o e wa e quali y [ 9 ]. Howe e , adi ional mechanism models also possess ce ain limi a ions. Fi s ly, hey ypi- cally equi e ex ensi e inpu da a and pa ame e s, including low a e, ain all, sedimen cha ac e is ics, e c., which en ail complex da a acquisi ion and p ocessing [ 10 ]. Secondly, es ablishing and calib a ing he model necessi a e deep p o essional knowledge and a subs an ial olume o measu ed da a, demanding high echnical expe ise [ 11 ]. Mo eo e , he ep esen a ion o complex wa e en i onmen s and ecosys ems by mechanism models may in ol e simpli ica ions and idealiza ions ha ail o ully cap u e he complexi y o eal-wo ld si ua ions. In ecen yea s, he e has been ex ensi e esea ch and applica ions o machine-lea ning- based echnology o p edic ing i e wa e quali y [ 12 ]. In he con ex o i e wa e quali y p edic ion, machine lea ning u ilizes a la ge amoun o his o ical wa e quali y da a o cons uc accu a e p edic ion models and enable ea ly wa ning. This echnology o e s se e al ad an ages [ 13 ]. Fi s ly, i acili a es eal- ime and con inuous moni o ing and p edic ion o wa e quali y, enhancing he esponsi eness and e ec i eness o wa e quali y managemen . Secondly, machine lea ning models can au oma ically lea n and adap o he complex ela ionships wi hin wa e quali y da a, esul ing in mo e-accu a e p edic ions [ 14 ]. Addi ionally, hese models can inco po a e o he en i onmen al ac o s and me eo ological da a, he eby imp o ing he accu acy and eliabili y o wa e quali y p edic ion. Howe e , machine lea ning me hods also ace challenges and limi a ions in p edic ing i e wa e quali y. Issues such as da a quali y and missing da a can impac he model’s pe o mance [ 15 ]. Mo eo e , aining and pa ame e selec ion equi e a ce ain le el o p o essional knowledge and expe ience. Addi ionally, he in e p e abili y o he model is ela i ely low, making i di icul o in e p e he p edic ed esul s. The e o e, u he esea ch and imp o emen a e necessa y o enhance he e ec i eness and eliabili y o machine lea ning in i e wa e quali y p edic ion. The en opy weigh ing me hod is an in o ma ion- heo y-based app oach used o e al- ua e he in o ma ion con en and impo ance o ea u es [ 16 ]. By compu ing he en opy alue o ea u es, he pu i y and disc iminabili y o he ea u es can be measu ed [ 17 ]. By combining he Pea son co ela ion coe icien wi h he en opy weigh ing me hod, he co ela ion and in o ma ion con en o he ea u es can be comp ehensi ely conside ed, a oiding o e - eliance on a single c i e ion o ea u e selec ion. This app oach enables a mo e-comp ehensi e e alua ion o he con ibu ion and impo ance o ea u es, educing subjec i i y and unce ain y. By balancing di e en ac o s, ea u es wi h highe co ela ion and g ea e in o ma ion con en can be selec ed, he eby imp o ing he accu acy and s abil- i y o ea u e selec ion. Bo h he Pea son co ela ion coe icien and he en opy weigh ing me hod a e ela i ely simple and in ui i e app oaches, making hem easy o unde s and and in e p e [ 18 ]. By in eg a ing hem in o ea u e selec ion in machine lea ning, ea u e- selec ion esul s wi h highe in e p e abili y and p ac icali y can be ob ained. This enhances he anspa ency and eliabili y o he ea u e-selec ion p ocess, helping decision-make s En opy 2023,25, 1186 3 o 20 unde s and he impo ance and con ibu ion o ea u es while imp o ing he pe o mance and in e p e abili y o he model [19]. The objec i e o his s udy was o u ilize machine lea ning echniques, in conjunc ion wi h he en opy weigh me hod and Pea son co ela ion coe icien me hod as ea u e- selec ion me hods, o achie e high-p ecision p edic ion o majo wa e quali y indica o s, such as Dissol ed Oxygen (DO), Ammonia Ni ogen (NH 3 -N), To al Phospho us (TP), and To al Ni ogen (TN). The models conside ed in his s udy encompass Long Sho -Te m Memo y (LSTM), Suppo Vec o Machine (SVM), Mul ilaye Pe cep on (MLP), Random Fo es (RF), and XGBoos . LSTM, as a a ian o he Recu en Neu al Ne wo k (RNN) sui able o p ocessing ime se ies da a, exhibi ed supe io pe o mance in p edic ing wa e quali y changes. By inpu ing his o ical wa e quali y da a as ime se ies, he LSTM model can be used o e ec i ely cap u e long- e m dependencies and accu a ely o ecas u u e ends in wa e quali y changes. Fu he mo e, o he machine lea ning models o e dis inc ad an ages and applicabili y in wa e quali y p edic ion, enabling he selec ion o app op ia e models based on speci ic equi emen s. 2. Ma e ials and Me hods 2.1. Da a Acquisi ion The da a used o his esea ch we e sou ced om he China En i onmen al Moni o - ing Gene al S a ion, speci ically om he moni o ing poin a Shijiaoju Sec ion in he Pea l Ri e Basin. The da ase comp ises wa e quali y measu emen s collec ed a ou -hou in e als, co e ing he ime pe iod om 8 No embe 2020 o 28 Feb ua y 2023. In o al, he e a e 5058 samples in his da ase , encompassing 9 wa e quali y pa ame e s: Ammonia Ni ogen (NH 3 -N), wa e Tempe a u e (Temp), pH, Dissol ed Oxygen (DO), he pe man- gana e index (KMnO 4 , To al Phospho us (TP), To al Ni ogen (TN), Conduc i i y (Cond), and Tu bidi y (Tu b). 2.2. Da a P ep ocessing Da a p ep ocessing is a i al s ep in machine lea ning, encompassing a ious asks such as handling ou lie s, missing alues, and da a no maliza ion [ 20 ]. Fo his s udy, his o ical moni o ing da a we e collec ed, including wa e quali y indica o s such as em- pe a u e, pH, he po assium pe mangana e index, dissol ed oxygen, ammonia ni ogen, o al phospho us, o al ni ogen, u bidi y, and conduc i i y. Fi s ly, ou lie de ec ion was pe o med on he da a. Ou lie s can a ise due o senso mal unc ions, human e o s, o o he ac o s, esul ing in abno mal da a poin s. S a is ical analysis is commonly employed o ou lie de ec ion, in ol ing calcula ions o he mean and s anda d de ia ion o iden i y alues signi ican ly de ia ing om he mean. I ou lie s a e de ec ed, hey can be ea ed as missing alues o co ec ed based on he speci ic ci cums ances [ 21 ]. Nex , he ocus was placed on add essing missing alues in he da a. Linea in e pola ion was u ilized in his s udy o ill in he missing alues. Linea in e pola ion es ima es he missing alues by conside ing he linea ela ionship be ween known da a poin s. Speci ically, o ime se ies da a, he obse ed alues o he p eceding and succeeding ime poin s a e used o pe o m linea in e pola ion and es ima e he missing alues. Suppose we wan o es ima e he missing alue xbe ween he known da a poin s x1and x2, co esponding o obse ed alues y1 and y2 , espec i ely. The linea in e pola ion o mula o es ima ing he alue y is as ollows: y=y1+(x−x1)y2−y1 x2−x1(1) He e, (x −x1 ) ep esen s he o se o x ela i e o x1 and (( y2−y1 )/( x2−x1 )) ep e- sen s he slope om x1 o x2 . By mul iplying he o se by he slope and adding i o y1 , he missing alue y can be es ima ed [22]. The ad an ages o linea in e pola ion include i s simplici y, ease o use, and he abili y o p oduce easonably accu a e es ima ion esul s in ce ain cases [ 23 ]. Howe e , linea in e pola ion also has limi a ions. Fi s ly, i assumes a linea ela ionship be ween da a En opy 2023,25, 1186 4 o 20 poin s, which may no hold ue in all si ua ions. Secondly, i equi es a high densi y o da a poin s, and spa se o une enly dis ibu ed da a may lead o inaccu a e es ima es. Addi ionally, linea in e pola ion canno cap u e nonlinea ends o special pa e ns in he da a [ 24 ]. The e o e, when applying linea in e pola ion, i is c ucial o assess he cha ac e is ics and alidi y o he da a wi hin he speci ic con ex and conside he sui abili y o al e na i e in e pola ion me hods [25]. Las ly, da a no maliza ion will be pe o med o elimina e dimensional di e ences among di e en wa e quali y indica o s [ 26 ]. The chosen me hod was min–max no mal- iza ion, which linea ly ans o ms he da a o a speci ic ange, ypically [0, 1] o [ −1, 1 ], ensu ing ha ea u e a iables ha e simila scales. Min–max no maliza ion can be calcu- la ed using he ollowing o mula: XN=X−Xmin Xmax −Xmin (2) He e, XN ep esen s he no malized alue, X ep esen s he o iginal alue, Xmin ep esen s he minimum alue and Xmax ep esen s he maximum alue. This o mula maps he o iginal da a o a ange be ween 0 and 1. By ollowing hese da a p ep ocessing s eps, we can ob ain cleaned and p epa ed da a sui able o he subsequen ea u e selec ion, aining, and p edic ion o machine lea ning models. This p ocess will enhance he accu acy and s abili y o he models and p o ide a eliable ounda ion o p edic ing i e wa e quali y. 2.3. Fea u e Va iable Selec ion 2.3.1. En opy Weigh ing Me hod The en opy weigh me hod is a echnique employed o de e mine he weigh s o mul iple indica o s. I u ilizes he concep o en opy o measu e he unce ain y o di e si y o indica o s by compu ing hei in o ma ion en opy [ 27 ]. This me hod inds widesp ead applica ion in mul i-indica o decision-making, e alua ion, and anking, aiding in add ess- ing challenges associa ed wi h ade-o s and op imiza ion among mul iple indica o s [ 28 ]. The s eps in ol ed in calcula ing weigh s using he en opy weigh ing me hod based on in o ma ion en opy a e as ollows: • Calcula e in o ma ion en opy: Compu e he in o ma ion en opy o each indica o . The in o ma ion en opy quan i ies he unce ain y o di e si y o an indica o , wi h highe en opy alues indica ing g ea e di e si y. The calcula ion o mula o he in o ma ion en opy is as ollows: H(X)=−∑(Pi×log2Pi)(3) He e, H(X) ep esen s he in o ma ion en opy o he indica o and Pi ep esen s he no malized alue o he indica o . • Calcula e in o ma ion weigh : De e mine he in o ma ion weigh o each indica o based on i s in o ma ion en opy. The calcula ion o mula o he in o ma ion weigh is as ollows: Wi=(1−H(Xi)) (4) He e, Wi deno es he in o ma ion weigh o indica o Xi and H(Xi) ep esen s he in o ma ion en opy o indica o Xi. The in o ma ion weigh e lec s he le el o in o ma ion con ained wi hin an indica o . A highe in o ma ion weigh signi ies a g ea e impac o he indica o on he decision ou come. Hence, in o ma ion weigh s can be u ilized o assess he signi icance o indica o s and hei con ibu ions o he decision-making p ocess. By calcula ing he in o ma ion en opy and in o ma ion weigh s o each indica o , a weigh ec o can be de i ed o subsequen asks such as mul i-indica o decision-making, e alua ion, o op imiza ion [ 29 ]. Inco po a ing in o ma ion weigh s assis s decision-make s in making in o med ade-o s En opy 2023,25, 1186 5 o 20 and selec ions among indica o s, hus enhancing he accu acy and c edibili y o decisions. Howe e , i is essen ial o ecognize ha in o ma ion weigh s solely conside he di e si y and unce ain y o indica o s, dis ega ding hei in e ela ionships. The e o e, in p ac- ical applica ions, i is c ucial o conside addi ional me hods o domain knowledge o comp ehensi ely assess he indica o s [30]. Acco ding o he analysis p esen ed in Table 1and Figu e 1, se e al a iables s and ou wi h ela i ely highe weigh s. Speci ically, NH 3 -N, DO, KMnO 4 , TP, Cond, and Tu b exhibi highe weigh s compa ed o o he a iables. Among hese, NH 3 -N, Cond, and Tu b eme ge as pa icula ly in luen ial indica o s, indica ing hei signi icance and s onge in luence on he decision ou come. Con e sely, Temp, pH, and TN display ela i ely lowe weigh s, implying hei diminished impo ance and weake impac on he decision ou come. Table 1. Resul s o in o ma ion weigh calcula ion using en opy weigh me hod. Va iables Mean S anda d De ia ion CV Coe icien 1Weigh 2 NH3-N 0.484 0.464 0.958 0.232 Temp 24.504 4.763 0.194 0.047 pH 7.554 0.540 0.072 0.017 DO 7.887 3.642 0.462 0.112 KMnO43.715 1.591 0.428 0.104 TP 0.110 0.047 0.427 0.103 TN 3.274 0.672 0.205 0.050 Cond 1264.521 979.968 0.775 0.188 Tu b 49.761 30.356 0.610 0.148 1CV coe icien = s anda d de ia ion/mean. 2The weigh s a e calcula ed by no malizing he CV coe icien s. Figu e 1. In o ma ion weigh dis ibu ion map (acco ding o Table 1). 2.3.2. Pea son Co ela ion Coe icien Me hod The Pea son co ela ion coe icien is a s a is ical measu e u ilized o e alua e he linea co ela ion be ween wo con inuous a iables [ 31 ]. I p o ides in o ma ion abou he s eng h and di ec ion o he linea ela ionship be ween he a iables, making i a commonly employed me hod o ea u e a iable selec ion and e alua ion [ 32 ]. The coe icien , deno ed as “ ”, anges om − 1 o 1. A alue o = 1 indica es a pe ec posi i e linea ela ionship, while = − 1 indica es a pe ec nega i e linea ela ionship. A alue o En opy 2023,25, 1186 6 o 20 = 0 sugges s no linea ela ionship, indica ing no co ela ion be ween he a iables. The calcula ion o mula is as ollows: R=∑(Xi−Xmean)(Yi−Ymean) NXs dYs d (5) He e, R ep esen s he Pea son co ela ion coe icien , Xi and Yi deno e he alues o he a iables in he obse a ion ma ix, Xmean and Ymean ep esen he means o he a iables, Xs d and Ys d ep esen he s anda d de ia ions o he a iables, and Ndeno es he numbe o obse a ions in he sample. Acco ding o Figu e 2, signi ican co ela ion coe icien s we e obse ed be ween NH 3 - N and pH, DO, KMnO 4 , TP, and TN, indica ing a subs an ial ela ionship. DO exhibi ed signi ican co ela ion coe icien s wi h NH 3 -N, empe a u e, pH, KMnO 4 , TP, conduc i i y, and u bidi y, indica ing signi ican ela ionships. Simila ly, TP showed signi ican co - ela ion coe icien s wi h NH 3 -N, empe a u e, pH, DO, KMnO 4 , TN, conduc i i y, and u bidi y, indica ing signi ican ela ionships. Likewise, TN exhibi ed signi ican co ela- ion coe icien s wi h NH 3 -N, empe a u e, pH, KMnO 4 , TP, conduc i i y, and u bidi y, indica ing signi ican ela ionships. Figu e 2. Visualiza ion o Pea son co ela ion. 2.3.3. Comp ehensi e Weigh Me hod The comp ehensi e weigh me hod is an app oach o selec ing ea u e a iables ha combines he Pea son co ela ion coe icien me hod and he en opy weigh me hod. I aims o e alua e and selec ea u e a iables by calcula ing hei comp ehensi e weigh s, which a e ob ained by mul iplying he Pea son co ela ion coe icien alue o each ea- u e a iable wi h i s co esponding in o ma ion weigh . The o mula o calcula ing he comp ehensi e weigh is as ollows: VCW =VPCC ×VIW (6) He e, VCW ep esen s he comp ehensi e weigh , VPCC ep esen s he Pea son co ela ion coe icien , and VIW ep esen s he in o ma ion weigh . A highe comp ehensi e weigh indica es a g ea e impo ance and ele ance o he ea u e a iable in p edic ing he a ge a iable. The comp ehensi e weigh me hod o e s he ad an age o conside ing bo h linea ela ionships and impo ance ac o s, esul ing in a mo e-comp ehensi e e alua ion and selec ion o ea u e a iables. This, in u n, imp o es he accu acy and s abili y o he ea u e-selec ion p ocess. Based on he comp ehensi e weigh calcula ion esul s p esen ed En opy 2023,25, 1186 7 o 20 in Table 2and Figu e 3, he ollowing inpu a iables we e selec ed o p edic ing he espec i e a ge a iables: • Dissol ed Oxygen (DO) p edic ion: DO, NH 3 -N, Temp, pH, KMnO 4 , TP, Cond, and Tu b; • Ammonia Ni ogen (NH3-N) p edic ion: NH3-N, DO, KMnO4, TP, and TN; • To al Ni ogen (TN) p edic ion: TN, NH3-N, KMnO4, TP, Cond, and Tu b; • To al Phospho us (TP) p edic ion: TP, NH 3 -N, Temp, DO, KMnO 4 , TN, Cond, and Tu b. Figu e 3. The comp ehensi e weigh o inpu a iables unde each ou pu a iable: ( a ) DO and comp ehensi e weigh s o i s co esponding inpu a iables; ( b ) NH 3 -N and comp ehensi e weigh s o i s co esponding inpu a iables; ( c ) TN and comp ehensi e weigh s o i s co esponding inpu a iables; (d) TP and comp ehensi e weigh s o i s co esponding inpu a iables. En opy 2023,25, 1186 8 o 20 Table 2. Summa y o comp ehensi e weigh esul s (The comp ehensi e weigh alues o di e en inpu a iables o p edic ing he a ge a iable). Va iables DO NH3-N TN TP NH3-N 0.091 0.232 0.104 0.142 Temp 0.027 0.001 0.009 0.020 pH 0.014 0.007 0.003 0.007 DO 0.112 0.044 0.006 0.054 KMnO40.053 0.022 0.057 0.015 TP 0.050 0.063 0.048 0.103 TN 0.003 0.022 0.050 0.023 Cond 0.118 0.007 0.079 0.046 Tu b 0.052 0.003 0.022 0.049 These selec ed inpu a iables we e de e mined based on hei espec i e comp e- hensi e weigh s, which conside bo h he Pea son co ela ion coe icien and in o ma ion weigh . By including hese a iables in he p edic ion models, i is expec ed o enhance he accu acy and eliabili y o he p edic ions o Dissol ed Oxygen (DO), Ammonia Ni ogen (NH3-N), To al Ni ogen (TN), and To al Phospho us (TP). 2.4. Models 2.4.1. Suppo Vec o Machine Suppo Vec o Machine (SVM) is a popula supe ised lea ning algo i hm u ilized o classi ica ion and eg ession asks. I s objec i e is o disco e an op imal hype plane ha e ec i ely sepa a es di e en classes o samples while maximizing he ma gin be ween hem, he eby achie ing obus gene aliza ion pe o mance [ 33 ]. SVM achie es his by mapping he samples in o a high-dimensional ea u e space and iden i ying he hype plane ha maximizes he ma gin wi hin his space. This hype plane is de ined as he one wi h he g ea es dis ance o he nea es samples o di e en classes, e e ed o as suppo ec o s, which play a c ucial ole in de e mining he hype plane’s posi ion. SVM demons a es high accu acy and gene aliza ion pe o mance, pa icula ly o small-sized da ase s. I exhibi s obus ness agains noise and ou lie s and is well-sui ed o handling high-dimensional da a. Mo eo e , he decision unc ion o SVM is based on he suppo ec o s, which p o ide aluable insigh s in o he da a dis ibu ion and decision bounda y, hus o e ing in e p e abili y o some ex en . Howe e , SVM also has ce ain limi a ions. I can be compu a ionally slow when applied o la ge-scale da ase s, and i s pe o mance may deg ade on high-dimensional da a o when dealing wi h imbalanced classes. Addi ionally, he selec ion o app op ia e ke nel unc ions and uning o he ela ed pa ame e s a e impo an conside a ions when u ilizing SVM [34]. 2.4.2. Mul ilaye Pe cep on Mul ilaye Pe cep on (MLP) is a neu al ne wo k wi h an inpu laye , mul iple hidden laye s, and an ou pu laye . I uses weigh ed connec ions and nonlinea ac i a ion unc ions o p ocess da a. The ne wo k is ained using he backp opaga ion algo i hm, upda ing weigh s o minimize p edic ion e o s. MLP excels in modeling complex pa e ns and can be adjus ed o i di e en ask complexi ies [ 35 ]. Howe e , aining and p edic ion imes may be longe o la ge-scale o high-dimensional da a. The model’s pe o mance depends on ac o s such as ac i a ion unc ions, he a chi ec u e, and he hype pa ame- e s [ 36 ]. Mul iple me ics should be used o e alua ion, conside ing he model s uc u e, ea u e selec ion, and da a dis ibu ion. Enhancemen s can be made h ough adjus men s, op imiza ion, addi ional ea u es, o al e na i e algo i hms [37]. En opy 2023,25, 1186 9 o 20 2.4.3. Random Fo es Random Fo es is an ensemble lea ning me hod ha cons uc s mul iple weak lea ne s based on decision ees. I combines he p edic ions o indi idual ees h ough o ing o a e aging o make he inal p edic ions. In each node o he decision ee, Random Fo es conside s only a andom subse o ea u es o spli ing. This selec i e ea u e conside a ion educes he co ela ion be ween ees, leading o inc eased model di e - si y. To c ea e di e se decision ees, mul iple aining se s a e gene a ed using boo s ap sampling. This p ocess in ol es andomly selec ing samples wi h eplacemen om he o iginal aining se , enabling he aining o di e en decision ees [ 17 ]. The u iliza ion o boo s ap sampling enhances model di e si y and mi iga es o e i ing. Random Fo es gene a es p edic ions by agg ega ing he collec i e decisions o mul iple decision ees. In classi ica ion asks, he p edic ion is de e mined by he majo i y class ob ained h ough o ing, while in eg ession asks, he a e age p edic ion o he mul iple decision ees is used. Random Fo es models a e highly p o icien in handling high-dimensional and la ge-scale da a, demons a ing hei sui abili y o complex nonlinea ela ionships [ 33 ]. Fu he mo e, hey exhibi obus ness in he p esence o missing alues and ou lie s. 2.4.4. Ex eme G adien Boos ing Ex eme G adien Boos ing (XGBoos ) is an algo i hm de eloped based on he g adien boos ing decision ees app oach. I enhances model accu acy and e iciency by inco po- a ing egula iza ion echniques and pa allel compu ing. XGBoos le e ages he g adien boos ing algo i hm, which i e a i ely ains a sequence o decision ees o p og essi ely enhance he p edic i e model’s pe o mance. Each ee is ained o ec i y he p edic ion e o s made by he p eceding ee, g adually aligning wi h he nega i e g adien o he ob- jec i e unc ion. To add ess he isk o o e i ing, XGBoos employs a ious egula iza ion echniques, including L1 and L2 egula iza ion. Addi ionally, cons ain s on ee dep h and lea weigh s a e applied o manage he model’s complexi y and p e en o e i ing. These measu es collec i ely con ibu e o imp o ing he o e all pe o mance and gene aliza ion capabili y o he XGBoos algo i hm [38]. 2.4.5. Long Sho -Te m Memo y Long Sho -Te m Memo y (LSTM) is a specialized a ian o Recu en Neu al Ne - wo ks (RNNs) ha excels in p ocessing ime se ies da a. Unlike con en ional RNNs, LSTM inco po a es ga ing mechanisms ha e ec i ely cap u e and e ain long- e m dependen- cies [ 39 ]. The co e o an LSTM ne wo k comp ises h ee essen ial ga e uni s: he o ge ga e, he inpu ga e, and he ou pu ga e. These ga e uni s egula e he low and manipula- ion o in o ma ion h ough lea nable weigh s, he eby con olling he inpu , ou pu , and memo y p ocesses. By selec i ely o ge ing, upda ing, and ou pu ing in o ma ion, LSTM enables he model o e ec i ely e ain and u ilize long- e m da a in o ma ion, e ec i ely add essing he challenge o long- e m dependencies encoun e ed in adi ional RNNs. The ga ing mechanisms employed by LSTM also add ess he issues o anishing and exploding g adien s, ensu ing smoo h g adien p opaga ion o e ex ended ime in e als [ 40 ]. LSTM exhibi s e sa ili y in handling di e se inpu and ou pu ypes, including uni a ia e and mul i a ia e ime se ies da a, as well as ex da a. I o e s lexibili y in adjus ing inpu and ou pu dimensions and possesses s ong ep esen a ional capabili ies [ 12 ]. LSTM has achie ed ema kable success in a ious domains such as na u al language p ocessing, speech ecogni ion, machine ansla ion, and ime se ies p edic ion. Consequen ly, LSTM inds widesp ead applica ion in modeling and p edic ion asks ac oss a wide ange o p ac ical p oblems. 2.4.6. G id Sea ch (G idSea chCV) In his s udy, he G id Sea ch echnique (G idSea chCV) was u ilized o ine- une he pa ame e s o he machine lea ning model and iden i y he op imal combina ion o pa ame e s, he eby enhancing he model’s pe o mance and p edic i e capabili y. G id En opy 2023,25, 1186 16 o 20 Table 6. Pe o mance e alua ion o he LSTM model in p edic ing o he wa e quali y a iables. Va iables R2MSE RMSE NSE DO 0.882 3.361 1.827 0.877 NH3-N 0.830 5.614 2.330 0.829 TN 0.745 5.747 2.352 0.745 TP 0.773 5.683 2.332 0.763 Figu e 6. Compa ison o LSTM model’s ac ual and p edic ed alues o o he wa e quali y pa ame e s: ( a ) Compa ison o ue and p edic ed alues o DO; ( b ) Compa ison o ue and p edic ed alues o NH 3 -N; ( c ) Compa ison o ue and p edic ed alues o TN; ( d ) Compa ison o ue and p edic ed alues o TP. Howe e , i is no ewo hy ha Figu e 6c e eals a ela i ely weake p edic i e pe - o mance o he LSTM model o TN con en , pa icula ly in cap u ing ex eme alues accu a ely. This obse a ion can be a ibu ed o se e al con ibu ing ac o s. Fi s ly, he complexi y o he model may no be adequa e o cap u e he in ica e nonlinea ela ion- ships and long- e m dependencies wi hin he da a, pa icula ly when p edic ing ex eme alues. The e o e, i is ecommended o conside u ilizing a mo e-sophis ica ed model s uc u e o enhancing he model’s capaci y o imp o e i s abili y o p edic ex eme alues. Secondly, imp ope ea u e selec ion could be ano he in luen ial ac o . Al hough a com- p ehensi e weigh me hod, along wi h he en opy weigh me hod and Pea son co ela ion coe icien me hod, was employed o ea u e sc eening, he selec ion o indi idual ea u e a iables may ha e been subjec i e. Speci ically, when p edic ing TN con en , he inpu ea- u es o he LSTM model may no e ec i ely cap u e he cha ac e is ics necessa y o handle ex eme in o ma ion. Thi dly, he p esence o noise o ou lie s in he da a can nega i ely impac he accu a e p edic ion o ex eme alues by he model. Las ly, insu icien aining could also con ibu e o he ela i ely weake pe o mance o he LSTM model. To enhance TN con en p edic ion, i is ad isable o inc ease he aining sample size and ex end he aining du a ion o enable he model o ully cap u e ex eme pa e ns. Insu icien aining samples o a ela i ely sho aining pe iod may hinde he model’s abili y o e ec i ely En opy 2023,25, 1186 17 o 20 cap u e ex eme ea u es. To add ess hese po en ial limi a ions, u u e imp o emen s can include inc easing he aining sample size, adjus ing he model s uc u e, op imizing he ea u e selec ion, and conduc ing longe aining sessions o enhance he o e all p edic i e pe o mance o he LSTM model o TN con en . The LSTM model’s p o iciency in cap u ing dynamic ea u es and ends in ime se ies da a signi ican ly con ibu ed o i s accu a e p edic ion o wa e quali y a iables. By le e - aging i s abili y o lea n empo al ela ionships and long- e m dependencies wi hin he sequence da a, he LSTM model excelled in p edic ing u u e alues o wa e quali y a i- ables. Fu he mo e, i s capabili y o handle nonlinea ela ionships and complex empo al pa e ns u he s eng hened i s pe o mance in p edic ing wa e quali y a iables. 4. Conclusions The p ima y objec i e o his s udy was o e alua e he p edic i e capabili ies o a ious machine lea ning models o wa e quali y pa ame e s using he en opy weigh - ing me hod. A comp ehensi e weigh ing me hod was p oposed, which combines he en opy weigh ing me hod wi h he Pea son co ela ion coe icien me hod, o ea u e selec ion in wa e quali y p edic ion. This me hod akes in o accoun bo h he in o ma ion en opy o he inpu ea u es and hei co ela ion wi h he a ge a iable, e ec i ely iden i ying he ea u es possessing a signi ican impac on wa e quali y a iable p edic ion. The me hod o e s aluable insigh s o subsequen wa e quali y p edic ion modeling, including ea u e se selec ion, he educ ion o edundan ea u es, and he op imiza ion o model pe o mance. Mul iple machine lea ning models we e in es iga ed o hei applicabili y in wa- e quali y p edic ion, he Suppo Vec o Machine (SVM), Mul ilaye Pe cep on (MLP), Random Fo es (RF), XGBoos , and LSTM models. These models demons a ed a ying capabili ies in wa e quali y p edic ion. SVM, in pa icula , exhibi ed good gene aliza ion pe o mance and high p edic ion accu acy, speci ically o he p edic ion o Dissol ed Oxygen (DO). The MLP model, known o i s s ong nonlinea modeling capabili y, pe - o med well in p edic ing DO and NH 3 -N, explaining a signi ican p opo ion o he a ge a iable’s a iance and exhibi ing ela i ely small p edic ion e o s. In con as , he RF model, despi e i s abili y o handle high-dimensional da a and complex ela ionships, showed ela i ely poo pe o mance in wa e quali y p edic ion. I displayed lowe R2 alues and highe MSE and RMSE alues, indica ing la ge p edic ion e o s. This could be a ibu ed o he model’s limi a ions in cap u ing complex ela ion- ships and ex eme alues in wa e quali y da a, leading o dec eased p edic ion accu acy. Simila ly, he XGBoos model also exhibi ed ela i ely poo p edic i e pe o mance, wi h lowe R2 alues and highe MSE and RMSE alues, indica ing la ge p edic ion e o s. This migh be due o he model’s limi ed abili y o cap u e complex ela ionship pa e ns and ex eme alues in he wa e quali y da a, esul ing in lowe p edic ion accu acy compa ed o he o he models. The LSTM model demons a ed excellen wa e quali y p edic ion capabili ies. As a ecu en neu al ne wo k model designed o handle sequen ial da a, LSTM possesses s ong memo y and long- e m dependency modeling capabili ies. In wa e quali y p e- dic ion, he LSTM model e ec i ely cap u ed dynamic changes in ime se ies da a and consis en ly deli e ed ou s anding p edic i e pe o mance o a ious wa e quali y pa am- e e s. I s high R2 alues and NSE alues, along wi h low MSE and RMSE alues, indica ed small a e age p edic ion e o s and signi ican imp o emen s o e simple mean alue p edic ion me hods. In summa y, he comp ehensi e weigh ing me hod ha combines he en opy weigh - ing me hod and he Pea son co ela ion coe icien me hod showed e ec i eness in selec ing a ea u e se o wa e quali y p edic ion, enhancing he p edic i e pe o mance o he models. Th ough compa a i e s udies, he LSTM model eme ged as he op-pe o ming model o wa e quali y p edic ion, accu a ely o ecas ing a ia ions in di e en wa e quali y a iables in a s able manne . These esea ch indings p o ide essen ial insigh s o En opy 2023,25, 1186 18 o 20 wa e quali y moni o ing and managemen , assis ing wa e quali y managemen agencies in making in o med decisions and de ising e ec i e managemen s a egies. Howe e , u he esea ch and applica ions a e necessa y o explo e op imized ea u e-selec ion me hods, imp o e machine lea ning models, and enhance he accu acy and eliabili y o wa e quali y p edic ion. Au ho Con ibu ions: Concep ualiza ion, X.W., Y.L. (Yanchun Liang) and A.T.; me hodology, Q.Q.; so wa e, X.W. and Y.L. (Ying Li); alida ion, A.T., X.W. and Y.L. (Yanchun Liang); o mal anal- ysis, X.W. and A.T.; in es iga ion, X.W.; esou ces, Q.Q.; da a cu a ion, X.W. and Y.L. (Ying Li); w i ing—o iginal d a p epa a ion, X.W.; w i ing— e iew and edi ing, Q.Q., A.T. and Y.L. (Yanchun Liang); isualiza ion, X.W.; supe ision, Y.L. (Yanchun Liang); p ojec adminis a ion, Y.L. (Ying Li). All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch was unded in pa by he NSFC G an Numbe 61972174, he Guangdong Uni e si ies’ Inno a ion Team G an Numbe 2021KCXTD015, he Key Disciplines P ojec s G an Numbe 2021ZDJS138, and he Guangdong P o incial Junio Inno a i e Talen s P ojec o O dina y Uni e si ies Numbe 2022KQNCX146. Ins i u ional Re iew Boa d S a emen : No applicable. In o med Consen S a emen : No applicable. Da a A ailabili y S a emen : Da ashallbe p o idedby heco esponding au ho supon special 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. Deng, T.; Chau, K.W.; Duan, H.F. Machine lea ning based ma ine wa e quali y p edic ion o coas al hyd o-en i onmen managemen . J. En i on. Manag. 2021,284, 112051. [C ossRe ] [PubMed] 2. Az ou , M.; Mab ouki, J.; Fa ah, G.; Guezzaz, A.; Aziz, F. 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