分形学在大坝安全监测资料分析中的应用

20041SHUILIXUEBAO10559-9350(2004)01-0100-05(210098)Hurst105TV698.1AHurst1Hurst{xi},i=1,2,,=tn-t1∑==nitixnx11τ(1)tjA(,tj)∑=−=nitijxxtA1)(),(ττ(2)R()),(min),(max)(1iniinitAtARτττ≤≤≤≤−=(3)2002-09-23(50139030)(1977-)10020041SHUILIXUEBAO1S()2/112)(1)(∑=−=nitixxSτττ(4)HurstR/S=R()/S()R/S=(/2)H(5)HHurst1951HurstH0.5H0.5R/SH200H90%2000H95%FRns0≤⊂=∑∞=∞=110,:inf)(iiiisisUUFUFhδδU(6)UiFUiRn|Ui|Ui)(lim)(0FhFhssδδδ→=(7)RnF0s(F)FsHausdorffHausdorffDD=dimHF=inf{s:hs(F)=0}=sup{s:hs(F)=}(8)D=1D=2D=3DHausdorffDHurstHD=2-H(9)2195819621968197276.3m28(3#30#)105m2.1118218#()10120041SHUILIXUEBAO1118419791976197910519801982218#1983198519862000Hurst2.23418894589526#49D31810220041SHUILIXUEBAO1418526#(1)R/SHurst6H16HH2Hlog(R/S)log1962HH0.56H(2)(9)HausdorffD7DD1D2D105DDDD=1063DD17D10320041SHUILIXUEBAO11HDHHHDD88181826260.8630.9630.8360.9900.6950.9840.6680.9970.9120.9970.6161.0060.9290.9540.9370.8790.9530.9350.0260.0300.0550.0980.0140.0771.0371.1371.0101.1641.0161.3051.0031.3321.0231.0880.9941.3841.0711.0461.0631.1211.0471.0652HDHHHDD818260.9000.9880.8750.9940.8640.9960.9520.9490.9430.0220.0270.0351.0121.1101.0061.1251.0041.1361.0481.0511.057(3)HD38HD10518D18#DD1977D3HustHurstHD1.J.2001(1)1-4.2BassingthwaighteJB,RaymondGM.EvaluatingrescaledrangeanalysisfortimeseriesJ.AnnalsofBiomedicalEngineering,1994,22(4):432-444.3.M.1990.4HurstHE.LongTermStoageinReservoirs:AnExperimentalStudy.Trans.Am.Soc.Civ.Eng.,1951116.5KennethJ.Falconer.M.2001.10420041SHUILIXUEBAO1105ApplicationoffractaltheorytoanalyzedamsafetymonitoringdataLAIDaoping,WUZhongru,ZHOUHong(HohaiUniversity,Nanjing210098,China)AbstractHurst'srescaledrangeanalysisandfractaltheoryfortimeseriesareappliedtostudythedeformationfractalcharacteristicsoftheconcretegravityarchdaminChencunHydroProject.Theeffectof105crevicesondamstructureisevaluatedandthesafetyofthedamisassessed.Itisfoundthattheconcretedammayberegardedasanonlineardynamicsystemandthefractaldimensioncanbeusedtodescribethedynamicvariationcharacteristicsofthewholedamandappliedtodiagnosetheprobableproblemofthedamstructure.Keywordsconcretedam;safety;monitoringdata;fractal;timeseries