偏最小二乘法在炭黑工艺数据解析中的应用

*(610064)DBPDBPApplicationofPartialLeastSquaresinParameterAnalysisforCarbon-BlackProductionLiJinmingLiMenglong*YinJiajianJiangWei(FacultyofChemistry,SichuanUniversity,Chengdu610064)AbstractIntermsoftheproductionofcarbonblackbymeansofexperienceprincipally,andforpromotingcarbonblackproductiontechnology,partialleastsquares(PLS)isappliedtotheanalysisofthedatafromproductionprocess,andthemathematicsmodelbetweenparametersandtargetsissetup.Aftertheaffectedextentofeachparametertoiodinespecificsurfacearea(ISSA)andDBPabsorptionisparsed,primaryparametersandassistantparametersarefoundout.Basedonthecomputedresults,howtoadjustproductionparametersforimprovingproductqualityofcarbon-blackisdiscussedindetail.Subsequently,theresultsfromPLSareappliedtoguidetheactualproduction,satisfactoryeffectivenessisgained,andtheabilityforproducinghighqualitycarbonblackisimproved.KeywordsPartialleastsquares,Carbon-black,Iodinespecificsurfacearea,DBPabsorption,ParameterAnalysis()()[1]()[1,2]5013DSC29*E-mail:[e-mail]2003-12-302004-03-15[2,3](partialleastsquares,PLS)PLS11.1msmx1x2xmsy1y2ys01(Euclideandistance)FishernnX=[xij](i=1,2,,nj=1,2,,m);Y=[yij](i=1,2,,nj=1,2,,s),X()Y(DBP)PLSYYXXYPLS[4]PLS[3,6]XY(1)XYEPTXTmmmnmn+=×××FQUYTsssnsn+=×××(1)TUPQEF(2)XYetvuhhh+=(2)hehthu(3)XYFTVQYT+=Fmin(3)XY1.2PLS(crossvalidation)PLSK(leave-K-out)(predictionresidualerrorsumofsquaresPRESS)nkkkPRESS[4~8]K1=211)(pijnisjijyy−∑∑==(4)ypynsPLSnPRESSPRESSPRESSPLSMatlab2112(S1)(S2)(S3)7x1x2x3x4x5x6x7y1y2[3]01(Euclideandistance)Fisher[3]FisherFisher1FisherTab.1Fisherweightofeachvariablex1x2x3x4x5x6x7Fishera0.00390.22530.00110.00070.06410.11160.0459Fisherb0.01570.05350.01940.01270.06840.00740.0091Fisherc0.02800.05060.02700.00780.00090.08790.0207a:S1S2Fisherb:S1S3Fisherc:S2S3Fisher17FisherFisherx22x1x77863PLS2YTQXTp⎥⎦⎤⎢⎣⎡−=3628.09319.08828.04697.0TQ⎥⎦⎤⎢⎣⎡−−=2399.01727.00206.03560.08969.01399.03375.02394.01054.08404.03161.00620.05050.01067.0Tp(5)(6)t1=0.1067x10.5050x2+0.0620x3+0.3161x4+0.8404x50.1054x6+0.2394x7(5)t2=0.3375x1+0.1399x2+0.8969x3+0.3560x4+0.0206x5+0.1727x6+0.2399x7(6)Yu1u2u1=0.4697y1+0.8828y2u2=-0.9319y1+0.3628y2(7)⎥⎦⎤⎢⎣⎡=7141.0006244.0Vu1=0.6424t1+eu2=0.7141t2+e(8)YQTy1=0.4697u10.9319u2y2=0.8828u1+0.3628u2(9)(9)y1()u1u2y2()u1u2y1y2u1u2u2(-0.9319)(0.3628)u2(8)u1t1u2t2PLSt1t2u1u2(5)t1x2x5x2x5y1()t2x1x3x4x30.8969x1x3x4y1()x1x2x3x4x5y2()x1x2x3x4x5x2x3x5x6x7y1()y2()x1x2x3x4x5x6x7PLSq1q2p1p2(1)-1-0.500.51-1-0.500.511PLSFig.1TheprojectiondiagramofPLSloadings1y1;2y2;3x1;4x2;5x3;6x4;7x5;8x6;9x7(x5)PLS14(x2)7(x5)PLS15(x3)PLS23(x1)6(x4)PLS23745712y2y13567y1y24y1y2PLSy1y2(x1x7)53PLS522325Tab.2Thetechnicsparameterscorrespondingtofivetargetsamples/(Nm3/h)/(kg/h)/(kg/h)/(kg/h)/(kg/h)//kW11506287034587420.00625824.221505287034807420.00524425.332509280034496310.00822125.543511283034716650.06525726.6053506284034986300.06525126.243Tab.3Thecomparisonbetweenexperimentvalueandenactmentvalue/(g/kg)/(105m3/kg)/%/%111211200.831221252.40211171202.501191222.46321261260.001231211.65431141172.561151160.86531211182.541171170.0032.56%PLS4PLS2.56%[1]..:,2000:122~212.[2]MJanik.FuelandEnergy,2001,42(1):20~24.[3]..:,1991:345~346.[4]ALazraq,RCle´roux.J.Chemometrics,.2001,15:523~536.[5]APhatak,SDJong.J.Chemometrics,1997,11:311~338.[6]XWang,UKruger,Lennox.ControlEngineeringPractice,2003,11(6):613~632.[7]BLi,JMprris,BMartin.Chemom.Intell.Lab.Syst.,2002,64(1):79~89.[8]MCDENHAM.J.Chemometrics.1997,11:39~52.