基于线性滤波法的脉动风速模拟及其MATLAB程序的实现-袁波(1)

23420078StructuralEngineersVo.l23,No.4Aug.2007:2006-12-16MATLAB袁波应惠清徐佳炜(,200092)详细介绍了自回归技术公式,同时采用此技术模拟具有空间相关性的随机风荷载,给出了用自回归技术模拟脉动风荷载的步骤以及具体MATLAB程序,并把所编程序用于江阴长江大桥风荷载模拟,结果表明效果较好自回归,空间相关,脉动风速,MATLAB程序SimulationofTurbulentWindVelocityBasedonLinearFilterMethodandMATLABProgramRealizationYUANBoYINGHuiqingXUJiawei(DepartmentofBuildingEngineering,TongjiUniversity,Shanghai200092,China)AbstractInthispaper,thetechnologyofautogressivemodelisintroduced.Stochasticwindloadingwithtimeandspatialcorrelationisgeneratedbytheautogressivetypesimulationmethod,givingautogressivetypesimulationprocessandMATLABprogram.TurbulentwindvelocityofJiangyingChangjiangBridgeoverYangtseRiverisgeneratedwiththisprogramandtheresultindicatesthattheprogrammeisgood.Keywordsautogressivemode,lspatialcorrelation,turbulentwind,MATLABprogram1,,,,,,,,,,,,CAWS(ConstantAmpfitudeWaveSuperposition)WAWA(WaveswithWeightedAmplitude)[1,3],,,,CAWSWAWA,;Soarl,,,;Iwatani,,,2,,;,;,,[4,5],:{v(t)}=[C]{u(t)}(1),{u(t)};[C],,tz,V(z,t)zv(z)u(z,t){V(z,t)}={v(z)}+[C]{u(z,t)}(2)2.1,:,;,,[4],DavenportDavenport[4]:Sv(n)=4KV210x2n(1+x2)4/3(3)x=1200n/V10;K;V10(10m);n(Hz),,,Davenport2.2,,,,,,z(z1,z2)=exp-|z1-z2|lux(x1,x2)=exp-|x1-x2|lu(4),z(z1,z2);x(x1,x2),Davenport:(n,x1,x2,z1,z2)=exp-nC2x(x1-x2)2+C2z(z1-z2)212(Vz1+Vz2)(5)n,n=/2;Cx,Cz,,Emil,Cz=10,Cx=16[5];x1,x2,z1,z2;Vz1,Vz2,:SViVj(x1,x2,y1,y2,n)=ij(x1,x2,y1,y2,n)SVi(x1,x2,n)SVj(y1,y2,n)(6),;,33.1(WhiteNoiseFiltrationMethod),,,56StructuralEngineersVo.l23,No.4EarthquakeandWindResistanceAM(AutogressiveModel)[615],M[u(x,y,z,t)]=[u1(x,y,z,t),,uM(x,y,z,t)]T:[u(x,y,z,t)]=pk=1[k][u(x,y,z,t-kt)]+[N(t)](7),[u(x,y,z,t-kt)]=[u1(x,y,z,t-kt),,uM(x,y,z,t-kt)]T;[N(t)]=[N1(t),,NM(t)]T,Ni(t)0,,i=1,2,,M;[k]MM;k=1,2,pi(i=1,2,,M)ui(t)ui(t-kt)Riu(x,y,z,kt)=E{ui(x,y,z,t-kt)-E[ui(x,y,z,t-kt)]}{ui(x,y,z,t)-E[ui(x,y,z,t)]}(8)ui(x,y,z,t)ui(x,y,z,t-kt)0,,Riu[x,y,z,kt]=E[ui(x,y,z,t-kt)ui(x,y,z,t)](9)(7)[ui(x,y,z,t-kt)]=[u1(x,y,z,t-kt),,uM(x,y,z,t-kt)],,N(t)0ui(x,y,z,t),Ru(kt),Ru(kt)k:[R]MPM=[R]MPMP[]MPM(10)[R]MPM=[Ru(t),,Ru(pt)]T;[]MPM=[T1,,Tp]T[R]MPMP:[R]MPMP=R11(0)R12(t)R1(p-1)[(p-2)t]R1p[(p-1)t]R21(t)R22(2t)R1(p-1)[(p-1)t]R2p(0)R(p-1)1[(p-2)t]R(p-1)2[(p-1)t]R(p-1)(p-1)[(p-4)t]R(p-1)p[(p-3)t]Rp1[(p-1)t]Rp2(0)Rp(p-1)[(p-3)t]Rpp[(p-2)t][Rik(jt)]=R11(jt)R1M(jt)RM1(jt)RMM(jt);(i,k,j=1,2,,p)[j]=11j1MjM1jMMj,(j=1,2,,p)Ru(jt)-(WienerKhintchine)[Riku(jt)]0Siku(n)cos(2jt)dn(i,k=1,2,,M)(11)[](10),(7)[u(t)]T=[u1(t),,uM(t)],,RNRN=R(0)-pk=1kRu(kt)(12)[RN](Cholesky),[RN]=[L][L]T,[N(t)]=[L][n(t)](13)L=L1100L12L220LM1LM2LMMLij=Rij-i-1k=1LikLjkLjj,Lii=Rii-i-1k=1L2iki,j=1,2,,M[][RN],M(7)tt0,ui(t)=0,:57234u1(jt)uM(jt)=pk=1[k]u1[(j-k)t]uM[(j-k)t]+N1(jt)NM(jt),(jt=0,,T;kj)(14)(14)M0,t0,v(t)=03.2u(t),Nuj(t)Nv(t)vj(t)=Ni=1Cijui(t)(15)(15)Vk(t),,Rvjvk=E[vj(t)vk(t)]=E[Ni=1Cijui(t)Ni=1Cikui(t)](16)u(t)D,[12]:R=CDCT(17),C=[Cij]:C=C110000C12C2200000Cj1Cj2Cjj0Cn1Cn2Cnn-1Cnnui(t),,,DD=2uI(18),Inn(18)(17),R=2uCICT(19)u(t),,uC:Cij=Rij-i-1k=1cikcjkcjjCii=Rii-i-1k=1c2iki,j=1,2,,M(20)4MATLABMATLAB15,1385m,85,16m,10011/m1385/m60/m0.003/(ms-1)40.010/m13.85/Hz0.001/Hz200.00014/s0.1/s0.120006000/s2048,Simiu:S()=200u2*fn(1+50f)5/3(21)f,f=nz/V(z);z;V(z)z;u*,u*=KV(z)/ln(z/z0),,K0.4,z0Matlab,,58StructuralEngineersVo.l23,No.4EarthquakeandWindResistanceFourier(27)1MATLAB5923421324205406607806,,,,,[1]IANNUZZIA,SPINELLIP.ArtificiatWindGenerationandStructuralResponse[J].JournalofStructuralEngineeringASCE,1987,(12):113.[2],.[J].,2000,19(1):5-7.[3].[M].:,1985.[4],,,.[M].:,1993.[5],.[J].,2001,(9):3-11.[6],,.60StructuralEngineersVo.l23,No.4EarthquakeandWindResistance[J].,1996,(5):21-25.[7],.[J].,2005,(2):87-90.[8].[D].:,2001.[9].[D].:,1999.1.[10]DAVENPORWH.ProbabilityandRandomProceases[M].NewYork:McGrawHil.l1990.[11].[D].:,2004.[12]ChenLizhong,ChrisW.Letchford,SimulationofmultivariatestationaryGaussianstochasticprocesses:hybridspectralrepresentationandPODapproach[J].JournalofEngineeringMechanics,2005,131(8):801-808.[13]LizhongChen,ChrisWLetchford.Adeterministicstochastichybridmodelofdownburstsanditsimpactonacantileveredstructure[J].EngineeringStructures,2004,26(5)619-629.[14].[J].,1994,15(1):2.61234