Research on Application of Sintering Basicity of Based on Various Intelligent Algorithms

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1 ELKOMIKA Indonesan Journal of Elecrcal Engneerng Vol., o., ovember, pp. 778 ~ 777 DOI:.59/elkomnka.v Research on Applcaon of Snerng Bascy of Based on Varous Inellgen Algorhms Song Qang*, Zhang Ha-Feng Mechancal Engneerng Deparmen, Anyang Insue of echnology, Anyang 55, Henan *Correspondng auhor, e-mal: songqang@6.com Absrac Predcon of alkalny n snerng process s dffcul. Wheher he level of he alkalny of snerng process s successful or no s drecly relaed o he qualy of sner. here s no good mehod, predcon of alkalny by hgh compley, he presen nonlnear, srong couplng, hgh me delay, so he recen new echnology, grey leas square suppor vecor machne have been nroduced. In hs paper, he wegh of evaluaon objecves has no gven he correspondng consderaon when solvng he correlaon degree by akng radonal grey relaon analyss and s wh a lo of subjecve facors, easly lead o msakes n decson-makng on program. Wha s more a knd of alkalne grey suppor vecor machne model, enables us o develop new formulaons and algorhms o predc he alkalny. In he model, he daa sequence of flucuaon s composed of grey heory and suppor vecor machne s weakened, can deal wh nonlnear adapve nformaon, combnaon and grey suppor vecor machne hese advanages. he resuls show ha, he bascy of sner, can accuraely predc he small sample and reference nformaon usng he model. he epermenal resuls show ha, he grey suppor vecor machne model s effecve and wh praccal advanages of hgh precson, less samples, and smple calculaon. Keywords: bascy n snerng process, grey relaon analyss, grey leas squares suppor vecor machne, predcon, grey model Copyrgh Insue of Advanced Engneerng and Scence. All rghs reserved.. Inroducon In he modern seel enerprses, he snerng process for blas furnace maerals s one of he mos mporan producon processes. he snerng alkalny has a drec effec on producon and economc benefs of he whole seel enerprse []. herefore, almos every seel facory s equpped wh many nsrumens and auomac conrol sysems n he snerng plan for he producon process conrol. However, he compley of he snerng process makes he process o be dffcully descrbed by a se of mahemacal models. Snce hs process ofen has large me delay and dynamc me varably, s hard o perform conrol asks of he whole snerng process usng convenonal conrol models. Snerng process s a comple physcal-chemsry process, whch relaes o a lo of characerscs ncludng complcaed mechansm, hgh nonlneary, srong couplng, hgh me delay,and ec []. he mahemacal model for whole snerng process canno be esablshed, hus we can only consruc mahemacal model for one of performance ndcaors, and he performance nde of snerng process deermnes he polcy of blendng process. Because of he resrcon of he deecng means, he chemcal eamnaon of sner alkalny generally needs mn. In he whole process, s me somemes can even eceed hour. Obvously, such a long me delay canno mee he needs of acual producvy, and hus, he sner alkalny mus be deeced and a model for predcng he alkalny should be esablshed [].. Grey heory.. Grey GM(,) Model Grey heory s a mehod o sudy he small sample, poor nformaon, uncerany, wh paral nformaon known, par nformaon unknown small sample, poor nformaon uncerany problem as he research objec, he known nformaon hrough daa mnng, o erac valuable nformaon, a correc descrpon of sysem behavor, evoluon and effecve monorng and predcon of he poson nformaon sysem. Sascal predcon mehod has many Receved May 5, ; Revsed June, ; Acceped July,

2 ELKOMIKA ISS: advanages compared wh he radonal mehod, does no need o deermne wheher he forecas varables subjec o normal dsrbuon, don' need large sample sascs, ha s o say he research objec specally for he small sample, poor nformaon uncerany, do no need o change accordng o he change of npu varables forecas model, produced by he grey sequence he grey sysem heory, hnk, alhough he objecve sysem of comple daa represenaon, scaered, bu always has a whole funcon, mus conan he nheren law of some. he key s how o choose he approprae way o ap and use. All he grey sequence can be generaed by a weakenng he randomness, reveal he regulary. A dfferenal equaon s a unfed model, dfferenal equaon model has hgher predcon accuracy. he esablshmen of GM(,) model s bascally a cumulave generaon of he orgnal daa, so ha he generaed sequence has ceran regulary, by esablshng he dfferenal equaon model, oban he fng curve, and hus o predc he unknown pars of he sysem. he GM model s frs of he orgnal daa, a accumulaed, generae -AGO, accumulaed daa hrough daa mnng have ceran regulary, he orgnal daa s no obvous regulary, and s developmen rend s swngng. If he orgnal daa were accumulaed generang, s regulary s obvous Assume ha here s a me response sequence (whch s called orgnal me seres),,,..., n Where ()() sand for he monorng daa an me I,=,,,.,n. () ( n ),,,, R. he forecas value can be derved by he followng hree seps. Buld up he frs-order accumulang generaor operaor (AGO) hs sep s o weaken he ndeermnacy n he orgnal me seres and ge a more regular me seres. Le be he generaed me seres. k,,...,, k k n, k =,,., n () Where s he once Accumulaed Generang Operaon(-AGO) sequence-ago () Consruc frs-order lnear dfferenal equaon, he whenzaon dfferenal equaon can be obaned: d d a u Where, a s a developng coeffcen, whose value reflecs he varaon relaon of daa; and u s grey acon quany, whch s he mos mporan dfference beween grey and common model. Usng he leas squares esmaon, a and u can be obaned: B B a B Y u () Where,.5.5 B.5 n n Research on Applcaon of Snerng Bascy of Based on Varous Inellgen (Song Qang)

3 77 ISS: -6 Y n Accordng o lnear frs-order dfferenal equaon, Equaon (5) can be derved: ˆ u u e ak a a (5) k Inverse he accumulaon generaon () Le ˆ be he fed and forecased seres, k ˆ, ˆ,, ˆ n ˆ, (6) hen, he predced value can be calculaed by Equaon (7), ˆ ( ) ˆ,,, n (), (7) Where, ˆ n, ˆ n ˆ, ˆ,., ˆ n, are he forecas values. () Error eamnaon he relave error can be calculaed by Equaon (8). are fed value of he orgnal seres; and e k k ˆ k k % (8) Where, e s he error percenage... Resdual Forecasng Model o evaluae modelng performance, we should do synhec es of goodness: s C= s (9) Where S () () = n n ) ( ; S = n ( ( ) ) k n k k. Devaon beween orgnal daa and esmang daa: () = {, (),..., ( n)} = { () () () () () () - ˆ, () ˆ (),..., ( n) ˆ ( n) } P=P{ (k ) <.675S } he precson grade of forecasng model can be seen n able. Fnally, applyng he nverse accumulaed generaon operaon (AGO), we hen have predcon values: k ˆ k ˆ k ˆ ELKOMIKA Vol., o., ovember :

4 ELKOMIKA ISS: able. Precson Grade of Forecasng Model Precson grade P C Good.95 p C.5 Qualfed.8 p<.95.5<c.5 Jus.7 p<.8.5<c.65 Unqualfed p<.7.65<c.. Grey Relaon Analyss Grey relaonal s unceran correlaon beween hngs, or unceran correlaon beween he sysem facors, beween he facors o prncpal ac. he fundamenal msson of grey relaonal analyss s geomery approach o he mcro or macro basng on he sequence of behavoral facors, o analyze and deermne he nfluence degree beween each facors or he conrbuon measure of facor o he man behavor, and s fundamenal dea s judge wheher he geomery of he sequence of curves s closely lnked accordng o he level of smlary of, and he closer he curve, he greaer he correlaon of he correspondng sequences, conversely, he smaller[6]. he compuaonal procedure of grey relaonal analyss s epressed below: Assume, hen: s , (),, (), (),, () k () () () () () () () () () () () () () () () () () () () () k =,,,..,9: s =.;s =.75;s =.;s =.9;s =.9;s 5 =.95;s 6 =.6;s 7 =.5;s 8 =.;s 9 =.85; s s k k () k hen we oban: s s =.65; s6 s =.7; ε s s s =.; s s 7 s s s s s =.5; s s =.9; s8 s, =,,..9; =.;, =,,..9; s s =.9; s s 9 =.5; s5 s =.7;, Research on Applcaon of Snerng Bascy of Based on Varous Inellgen (Song Qang)

5 77 ISS: -6 So we wll oban: ε =.79; ε =.857; ε =.98; ε =.86; ε5 =.7; ε6 =.78; ε7 =.777; ε8 =.989; ε9 =.978; hen we may fnd ε8 > ε9 > ε > ε > ε > ε7 > ε > ε5 > ε6, 8 > 9 > > > > 7 > > 5 > 6 By he defnon of he relaonal analyss, he allocaon s sequenced by he relaonal coeffcen. And he sequence of relaonal coeffcen sze s he order of rankng of he nfluence facor. Based on he above resul, s clear ha 8 =.86 s mamum, and represens ha he relaonal degree s bgges beween he frs allocaon cener and he deal allocaon cener. herefore, he frs allocaon cener s he mos opmal choce. 8 s he opmal facors, 9 ranked second, 6 s he wors n all facors. ha s o say, he CaO rao of sner bascy of pulverzed coal rao, bascy on sner nfluence s relavely large, he hckness of he maeral layer and med FeO conen n ore has very lle effec on he bascy of sner, mgh as well pu he wo operang varables from ousde.. Leas-Squares Suppor Vecor Machnes Algorhm Modelng.. Leas-squares Algorhm Suppor Vecor Machne Recenly, leas squares suppor vecor machne (LS-SVM) has been appled o machne learnng doman successfully. I s a promsng echnque owng o s successful applcaon n classfcaon and regresson asks. I s esablshed based on he srucural rsk mnmzaon prncpal raher han he mnmzed emprcal error commonly mplemened n he neural neworks. LS-SVM acheves hgher generalzaon performance han he neural neworks n solvng hese machne learnng problems. Anoher key propery s ha unlke he ranng of neural neworks whch requres nonlnear opmzaon wh he danger of geng suck no local mnma, ranng LS-SVM s equvalen o solvng a se of lnear equaon problem. Consequenly, he soluon of LS-SVM s always unque and globally opmal. In hs sudy, he applcaon of LS-SVM n he predcon of he alkalny n snerng process was dscussed [- ]., y, wh Gvng a ranng se y R R n and y n R R, where s he npu vecor of he frs samples, s he desred oupu value of he frs samples, and s he number of samples, he problem of lnear regresson s o fnd a lnear funcon y(),whch s equvalen o applyng a fed non-lnear mappng of he nal daa o a feaure space.. In feaure space, SVM models ake he form: y ( ) w( ) b () n nh Where, he nonlnear funcon mappng (): R R maps he hgh-dmensonal space no he feaure space; and w s no a pre-specfed dmensonal, possbly nfne dmensonal, b s a real consan. he leas squares approach prescrbes choosng he parameers (w, b) o mnmze he sum of he squared devaons of he daa, and he square loss funcon s descrbed as: mn J( we, ) w w e () Where s he rade-off parameer beween a smooher soluon, and ranng errors. ELKOMIKA Vol., o., ovember :

6 ELKOMIKA ISS: Wh consrans, y ( ) w( ) b+ e, for =,,. Imporan dfferences wh sandard SVM are he equaly consrans and he squared error erm, whch grealy smplfes he problem. Only equaly consrans, and he opmzaon objecve funcon s he error loss, whch wll smplfy he problem solvng. o solve hs opmzaon problem, one defnes he followng Lagrange funcon: (,,, ) (, ) { ( ) L wbe J we w Where, s an Lagrange mulplers. By Karush-Kuhn-ucker (KK) opmal condons, he condons for opmaly are: L w ( ) w L b L e e L w be y () Where, =,,. Afer elmnaon of equaons. e and w, he soluon s gven by he followng se of lnear b ( ) ( ) D α y (5) Where, y y y,,,,,, α [,, D dag,, b guaranee mar φ φ ( ) ( ) D α y. ],. Selec >, and.. Selecon of he Kernel Funcon By he KK-opmal condons, w s obaned, and hus he ranng ses of nonlnear appromaon s obaned oo. y ( ) k (, ) b (6) Where, denoe ranng pon and suppor vecor respecvely,y s he oupu of nework.. and b are he soluons o Equaon. k (, ) ( ) ( ) k,,, (7) k k n nh he Selecon of he kernel funcon (): R R has several possbles. I s arbrary symmerc funcon whch can he Mercer heorem. In hs paper, he radal bass Research on Applcaon of Snerng Bascy of Based on Varous Inellgen (Song Qang)

7 77 ISS: -6 funcon (RBF) s used as he kernel funcon of he LS-SVM, because RBF kernels end o gve good performance under general smoohness assumpons, snce Gaussan RBF (Radal Bass Funcong, RBF) funcon s usually used as a kernel funcon [7], K(, ) ep{ / } (8) Where, s a posve real consan. By Equaon (8) o Equaon, he objec nonlnear model s as follows: (9) y ( ) ep{ / } b he LS-SVM predcon nvolves wo parameers o be opmzed, whch are (he wdh of he Gaussan kernels whch cover he npu space) and s vewed as regularzaon parameers,whch conrols he radeoff beween compley of he machne and he number of non-separable pons [8]. LS-SVM s an effcen verson of hese mproved SVM,Insesd of a quadrac programmng problem n sandard SVM,a se of lnear equaons based on KK opmzaon condon are solved n LS-SVM,whch can reduce he compuaonal compley and me for ranng o a ceran een [9, ].. Grey Leas Squares Suppor Vecor Machnes he objec of boh grey forecas and SVM forecas sudy s small sample predcon. Alhough hey buld on he bass of dfferen heores, here are some smlares beween GM(,) and SVM. grey GM(,l) by denfyng he parameers of he model s acually based on he leas squares lnear regresson, whereas suppor vecor machne s evolved from he lnear opmal surface. Boh models have her own advanages and weaknesses, grey GM(l,l) s a model of he dfferenal equaon, whch srenghens he regulary of raw daa by cumulave generaon; moreover, s he fng of eponenal curve. Based on rsk mnmzaon, here mus be over-f, and suppor vecor machne s a heory based on srucural rsk mnmzaon, whch has very good genaralzaon ably. If he wo combne o enhance he regulary of raw daa by accumulave generaon, and o denfy model parameers, a he same me o adop srucural rsk mnmzaon, whch consoldaes he advanage of he wo models and can oban beer forecas accuracy. Based on he above analyss, a new dea or algorhm s pu forward. A grey suppor vecor machne model s proposed o overcome hese lmaons on he bass of he forecasng models. he flucuaon of daa sequence s weakened by he grey heory and he suppor vecor machne s capable of processng nonlnear adapable nformaon, and he grey suppor vecor machne s a combnaon of hose advanages. Above all, grey heory s used o conduc a cumulave sequence of he raw daa, and he leas squares suppor vecor machne s adoped for he process and predcon. ew algorhm desgn seps as follows: Frsly, he orgnal sequence, (),, ( n),,,, n, and a sequence generaed a cumulave producon, as follows:, (),, ( n),,,, n k ( k) ( ), k,,, n. () Secondly, selec Kernel funcon K(, ); Solvng opmzaon problems Eqn.(8) usng suppor vecor machne mehod. ELKOMIKA Vol., o., ovember :

8 ELKOMIKA ISS: () Buld up regresson funcon y ( ) k (, ) b; (5) Consruc cumulave sequence and ge,where s he predcve value; (6) by he cumulave reducon, by he orgnal daa sequence () forecas model k k k, k n, n,. (7) Fnally, model es. 5. Sner Alkalny Forecass and Smulaon Based on grey Leas Squares Suppor Vecor Machnes 5.. Sysem Inpu Parameers Selecon he grey leas suppor vecor machne s used o predc he alkalny, amng a hs mporan oupu nde. In he whole process, he varables relaed o he alkalny s synheszed and make sure en mporan npu varables as he npu of grey neural nework, such as he layer hckness, he rolley speed, addng waer rae of he frs mure, he mng emperaure, he conen of SO n he mneral, he conen of CaO n he mneral, he conen of FeO n he mneral, addng waer rae of he second mure, he proporon of CaO, and he proporon of coal. 5.. Sample Daa Processng Because all he colleced daa s ofen no n he same order of magnude, he colleced daa are normalzed o [- ]; hs wll mprove he ranng speed of neural nework. We ofen uses he followng formulo o cope wh he nal daa: ' j _ j mn j.8. () j ma _ j mn ' Where j and j were he old and new value of he varable for a samplng pon respecvely, jma and jmn were he mnmum and mamum value of he varable n he orgnal daase. Afer compung usng he neural nework, he annormalzaon processng s done o oban he acual value of he oupu value forecasng. Annormalzaon of he followng formula: j j ma j mn ' j. () j mn In he samplng daase, here were nevably some anomales, and hese daa would gve an mpac on a ceran model, and even lead o msleadng. herefore, he model daa used n ranng samples daase and es samples daase was carefully seleced. error GM(,) model.5. forecas error relave forecas error.5 Orgnal value and forecas value 文中 me seres me seres me seres Fgure. he Predcon of he Alkalny Based on Grey GM(,) Research on Applcaon of Snerng Bascy of Based on Varous Inellgen (Song Qang)

9 776 ISS: -6 he alkalny n snerng process predcon of he alkalny based on grey suppor vecor machne orgnal value forecas value me(un:hours) Fgure. he Predcon of he Alkalny Based on Grey Leas Squares Suppor Vecor Machnes - predcon error of he alkalny based on grey suppor vecor machne absolue error me un:hours Fgure. he Error Curve of he Alkalny Based on Grey Leas Suppor Vecor Machne Fgure llusraes he predcon error and relave predcon error of GM(,) model of he alkalny, Fgure presens he fng curve bases on grey leas squares suppor vecor machne. I can clearly seen ha he predced values are n good agreemen wh he desred ones n he whole ranges of me sep, whle Fgure show predcon error bases on grey leas squares suppor vecor machne. From able, he accuracy of he grey suppor vecor machne reaches.7%, whereas he accuracy of GM(,) approach only s around -.6%. I s no dffcul o see ha he forecas accuracy of grey leas square suppor vecor machne s hgher han ha of a sngle GM(, l) model or he model of SVM, and has beer robusness.herefore, we can conclude ha he grey leas squares suppor vecor machne ehbs ecellen learnng ably wh fewer ranng daa,he generalzaon capably of LS-SVM s grealy mproved. able. he Comparson of he Alkalny Based on Grey GM(,) and Grey Leas Suppor Vecor Machne grey leas suppor vecor GM(,) model umb Orgnal machne er daa Model daa Relave error/% Model daa Relave error/% Average relave error/% ELKOMIKA Vol., o., ovember :

10 ELKOMIKA ISS: Concluson hs paper has proposed a mahemacs model of he alkalny, whch s realzed va grey leas squares suppor vecor machne. hs algorhm combnes he advanages of GM(,) and LS-SVM. he new model fully makes use of he advanages of accumulaon generaon of GM(,) mehod, and weakens he effec of sochasc dsurbng facor n orgnal daa seres, and srenghens he regulary of raw daa, and avods he heorecal defecs esng n he grey forecasng model. Besdes, SVM s ably o handle hgh-dmenson and ncomplee daa allows successful eracon of nformaon even when par of he daa records was mssng or unreasonable owng o he problems of nsrumen malfuncon or manenance, calbraon and clmae nfluences, so LS-SVMs mehod s suable o smulae he alkalny n an effcen and sable way. hese resuls fully demonsrae he predcon accuracy of new model s superor o a sngle model, he heorecal analyss and smulaon resuls are fully presened he valdy of he forecas model. hs shows ha he grey leas squares suppor vecor machne s avalable for he modelng of he alkalny, and can ge beer performance. Alhough he proposed grey LS-SVM-based model may be superor o oher modellng mehods n some aspecs, has some poenal drawbacks such as he underlyng Gaussan assumpons relaed o a leas squares cos funcon. Some researchers have made some effors o overcome hese by applyng an adaped form called weghed LS-SVM. So we wll nend o connue he sudes on he applcaon of he alkalny n snerng process. References [] FA ao-hu, WAG Ha-dong. Mahemacal Model and Arfcal nellgence of snerng process. Cenral Souh Unversy.. [] LIU S-feng, DAG Yao-guo, FAG Zh-geng. Grey Sysems heory and applcaon. Chna scence press.. [] LI Guo-zheng, WAG Meng, ZEG Hua-jun. An Inroducon o suppor Vecor machnes and oher Kernel-based Learnng Mehods. Publshng House of Elecroncs Indusry. 6. [] Evelo H, Yaman A. Conrol of onlnear Sysems Usng Polynomal ARMA Models. AIChE Journal. 99; 9: 6. [5] arendra K S, Parhasarahy K. Idenfcaon and Conrol of Dynamcal Sysems Usng eural eworks. IEEE rans eural eworks. 99; : -7. [6] WAG u-dong, SHAO Hu-he. eural ework Modelng and Sof-Chemcal Measuremen echnology. Auomaon and Insrumenaon. 996; (): 8 (n Chnese). [7] Cores C, Vapnk V. Suppor Vecor Machne. Machne Learnng. 995; : 7. [8] WAG Yong, LIU J-zhen, LIU ang-je e al. Modellng and Applcaon of sof-sensor based on leas squares suppor vecor machnes of oygen-conen n flue gases of plan. Mcro-compuer nformaon. 6; : -5. [9] Kecman V. Learnng and Sof Compung. Cambrdge: he MI Press.. [] CHE ao-fang,gui We-hua,WAG Ya-ln el. Sof-sensng model of sulfur conen n agglomerae based on nellgen negraed sraegy. Conrol heory & Applcaon. ; : 75~8. [] ZHAG ue-gong. On he Sascal Learnng heory and Suppor Vecor Machnes. Auomaon Journal., 6: (n Chnese). [] LI Guo-zheng, WAG Meng, ZEG Hua-jun. Suppor Vecor Machne Inroducon. Bejng: Elecroncs Indusry Publsh Press. (n Chnese). [] Mozer MC, Jordan MI, Pesche, e al. Advances n eural Informaon Processng Sysems. 997; 9(8):. [] ello Crsann, John Shawe-aylor. An Inroducon o Suppor Vecor Machnes and Oher Kernel- Based Learnng Mehod. Bejng: Chna Machne Press. 5. Research on Applcaon of Snerng Bascy of Based on Varous Inellgen (Song Qang)