时间序列分析方法预报基坑支撑轴力

20041SHUILIXUEBAO10559-9350(2004)01-0105-051211(1.3100272.310001)AR(n)3%TU431A(AR(n))11.1(Auto-regressiveMmodel)AR(n)(ARMA){xt},t=12Nxt-1xt-1-wxt-2--nxt-n=at-1at-1-2at-2--mat-mxt{xt}ti(i=1,2,,n)j(j=1,2,,m)at{at}(tat)nmARMA(n,m)j=0n(n)∑=−+=ninttititNIDaaxx12),0(~,σϕ(1)2002-09-06(1977-)10520041SHUILIXUEBAO1AR(n)ARMA(n,m)1.2AR(n)(1)t=nn+1Ny=x+a=1,2,,nTy=xn+1,xn+2,,xNTa=an+1,an+2,,anTx=−−−+−nNNNnnnnxxxxxxxxxLLLLLLL212111=(xTx)-1xTy(2){at}a=y-x(3){at}∑∑+==−=−=NntniititaxxnN1212)(1ϕσ(4)1.3AR{xt}(t=1,2,,N)AR(n)(1){xt}{xt}{xt}(2)AR(1)(2)AR(i)AR(i+1)i+1i+10AR(i)AR{xt}(3)at2a(4)AR(i+1)AR(i)AR(i)2nσ21+niσ2aiσ1.4AR(n)AR(n)l∑∑−==−+≤+−=11)1()(ˆ)(ˆlinliiliititnlxilxlxϕϕ(5)x)(ˆlxttl=110620041SHUILIXUEBAO1∑=−=niititxlx1)(ˆϕ(6)22.13.8104m2-2495m52m27.037.43m10.43m45m60m200m8(ACDFHIJL)1(BEGK)12(1)2.24(821918)(9181012)(10121125)(11251215)918122123040d4070d70d(2)(4)9181028401124(KBEG)1811kN88802kNn=52aσ2aσ10720041SHUILIXUEBAO1AR(5)12AR(5)2112AR(1)AR(6)2aσJALICFDHKBEG/kN1072938900010432575000948725100089045560008685437000806353500077125230006403501000283556800161047500153065600126835300AR(1)AR(2)AR(3)AR(4)AR(5)AR(6)1149509686296655902467483574128109020108220723107478973216744631236109669097568904207596868188168100114880115750112960837688761816912013280012108010485086770928012306901918701652601385901193101211402131901590901514801333801155601225801685901486801369701328501163801191201583213626117398868718573734362380039443974357727183034424761235042238518181188031009987498573802766696826212AR(5)iJALICFDHKBEG123450.49200.2695-0.07180.1763-0.02420.7660-0.37210.6024-0.15370.08150.26390.2724-0.02200.22030.01740.32270.47080.04450.1263-0.05340.15380.16840.09500.25920.09940.21520.17830.15200.3880-0.05660.23240.24710.07330.27670.06500.48550.15400.18490.1376-0.07540.57100.2049-0.08990.16680.05710.85290.1898-0.22090.03550.09830.34020.23690.10500.2949-0.07100.57790.21040.10280.0856-0.01512.3AR(5)(6)1=0.3227xtxˆt-1+0.4708xt-2+0.0445xt-3+0.1263xt-4+(-0.0534)xt-55dxt-1=424.05xt-2=447.07xt-3=107.69xt-4=230.23xt-5=497.246d354.64132.6%11.5%I343.1%12.3%1083120041SHUILIXUEBAO1I91840d40dAR2.4EBG5BG6E7LL43355BG16EK1ARMA1097DL120041SHUILIXUEBAO11101.()M.1991.2.J.2000(5)628-629.TimeseriesanalysismethodforpredictingsupportingforcesofexcavationpitXUHaofeng1,2,YINGHongwei1,ZHUXiangrong1(1.GeotechnicalEngineeringInstitute,ZhejiangUniversity,Hangzhou310027,China;2.HangzhouArchitecturalDesignResearchInstituteCorporation,Hangzhou310001,China)AbstractTimeseriesanalysismethodisappliedtoanalyzethemonitoringdataofsupportingforcesofexcavationpit.Theoriginalauto-regressivemodelisutilizedtosearchthemostsuitablemodelbycontinuouslycalculatingtherelevantparameters.Thesuitabilityofthemodelisdeterminedbycheckingtheresidualmeansquaredeviation.Ifthedifferenceofsquaredeviationbetweensuccessivemodelsissmallenough,thelastoneshouldbeidentifiedasthemostsuitablemodel.Onthebasisofthemostsuitablemodelandcorrespondingparametertheformulaforpredictingthesupportingforcesisdeduced.Theapplicationofthismethodshowsthattheaveragedeviationofpredictionislessthan3%,nomatterhowthemonitoringdatavariationis.Itdemonstratesthatthemodelpossessesgoodauto-adaptability.Keywordstimeseriesanalysismethod;excavationpit;supportingforces;prediction