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20044SHUILIXUEBAO410559-9350(2004)04-0118-05(310027)(Volterra)VolterraVolterraTV698.1A1(y(t))(x-i(t))()()()∑=++=miiittxty10εββ()2,0~,,,2,1σεNnttL=(1)ti{t}[1]D=3.23.54m=8VolterraVolterraTakenVolterra22003-03-26(1970-)20044SHUILIXUEBAO422.1{xt}mX(t)RmRmF:RmRmX(t+1)=F(X(t))(2)X(t)mX(t)=[x(t),x(t-d),,x(t-(m-1)d)]TX(t+1)(t+1)F)))1((,),(),(()1(ddmtxtxtxftxττ−−−+L(3)f()mf:RmR{xt}f(){xt}{xt})()))1((),(),(()1(tmtxtxtxftxddξττ+−−−=+L(4)(t)2.2Volterraxt=[xt,xt-1,,xt-N+1]T1+=ttxy)Volterra()()()∑∑∑∑∑∑∞=−−∞=∞=∞=∞=−−−∞=++++++=0210000212010121121221,,PmmtmtPmmmmmtmtmtmtxxmmhxxmmhxmhhxLLL(5)),,,(21PPmmmhLpVolterra()∑∑∑−=−=−−−=−++=1010212101012122211,)(NmNmmtmtNmmttxxmmhxmhhx(6)N1N2Takenm2D+1(D)N1N2N1=N2=m2D+1Volterra()jtitmimjmiittxxjihxihhx−−−=−=−=−+∑∑∑+=1010210101,)((7)M=1+m+m(m+1)/220044SHUILIXUEBAO433[3]Xi={x(i),x(i+d),,x(i+(m-1)d)}mn-1Xj={x(j),x(j+d),,x(j+(m-1)d)}(ji)(Xi,Xj)Xii()()()∑=−Θ=njijimXXnC1,2,1ρεε(8)Θ()HeavisidelnCm()lnmmmDlnCm()ln4102m350.6m5m24.6m0.24201#20#4#7#11#13#20#521CG-2A7#7#198861995121911996120027176()()9060301010145.057675.0376075.0300435.0282043.32377255.210221771.2374721.15−−−−+++−+++−=TTThttntyt1100d1dt0.01h=(H-92.0)/100HT1-10110dR=0.9616=2.0533120044SHUILIXUEBAO441()()()()()∑∑==−==−=nininyiyniyyyiyix121/)(,//σσ{y(i)};{x(i)};n[1]3.23.5Volterra8(7)Volterratttttttttttttxxxxxxxxxxxxξ+−++−+++=−−−−−−−+73741321051717.0044709.0030818.0036514.0094241.0104391.0573939.0067936.0R=0.7326=1.411376232Volterra20044SHUILIXUEBAO453Volterra4+VolterraVolterra7#44VolterraVolterra5VolterraVolterra[1]Volterra20044SHUILIXUEBAO46[1].[J].1997(7)22-26.[2].Volterra[J].2000(3)403-408.[3].[Jc.2001(4)486-489.[4]._[J].()200236(5)572-576.ApplicationofVolterrafilterforchaotictimeseriestoanalysisofdammonitoringdataLIFu-qiang(ZhejiangUniversityHangzhou310027,China)AbstractBasedonthereconstructionofstatespaceinchaoticdynamicsystemthesecondorderVolterrafilterisusedtoestablishthemodelfortheresidualerrorseriesofdamdeformationregressionmodel.TheregressionmodelisintegratedwithVolterrafiltertofitthemonitoringdataofdamdeformationandtocarryoutforecasting.Exampleofapplicationshowsthatthismethodeffectivelypromotestheaccuracyofdatafittingandforecasting.Keywordsregressionmodel;chaotictimeseries;residualerror;Voterrafilter;monitoringdata;damdeformation