微弱信号检测1-4+58-63_pdf_1

1T18101834200164RBFTheDetectiontoWeakSineSignalunderChaosBackgroundBasedonRBFNN20024200342,RBFRBFFKCNRBFRBFRBF3............................................................11.1..........................................11.2................................................31.3..........................................51.4........................................61.5..................................................61.6..........................................................7...................................................82.1..............................................82.2................................................92.3.................................................102.4.........................................................13...............................................143.1.............................................143.2.............................................163.3.........................................................19RBF..............................................204.1RBF..............................204.2RBF..........................................214.3.........................................................26RBF................................285.1RBF..................................285.2.........................................................2945.3.........................................................31RBFLorenz................326.1...................................................326.2...............................................336.3.....................................................346.4.................................................376.5Lorenz...............................386.6Lorenz.............................416.7.........................................................42RBFDuffing...............437.1Duffing..................................................437.2Duffing..............................447.3Duffing............................457.4.........................................................47....................................................488.1.............................................................488.2.............................................................49....................................................................50...............................................................51Abstract51.1[1][2][3]6BurgCaponBurgCapon1973PisarenkoMUSIC12ARMAMAAR(3)PisarenkoMUSIC:[4]7mVVnV10nV-100nVPARC19001nV1-10kHzBoxcar-10dB1.2,[5][6][7][8][9][10]8TakensMPSV[11]Takens[12][13][14][15][16]BPRBFRBF91.340BPBPBPBP101.4RBF1.RBF2.13.dB30−dB50−4.RBF1.5RBFRBFRBFRBFLorenzRBFDuffing111.612[17]2.1E.N.Lorenz,()Li.T.YYorke.J.A3[18]2080TakensPackardFarmerWhitney[19]GrassbergProcaccia,LyapunovKolmogorov901132[20][21][22]2.2Newhouse,Farmer1234123141232.3FFT[23]FFT15FFTFFTD.S.BroomheadG.P.KingPCAPCA[24][25]1Hausdoffx1x2x3DE16DE2D+1,DGP[26]2Lyaponov[27]FRnRnnnxn+1=F(xn)2-2-1nipiniLyapunov()()=∞→0ln1limiinipnpnσ(i=1,2,,n)2-2-2LyapunovLyapunov0Lyapunov0LyapunovLyapunovLyapunovLyapunovLyapunovLyapunovLyapunovLyapunovt0Lyapunov117101λ≈t2-2-3t0Lyapunov132.4183.1N.H.PackardF.Takens()njixfxjii,,2,1,,.Λ==3-1-1()njitxfxjii,,2,1,,,.Λ==3-1-2nxxxΛ,,21nRTakens19FamesP.GrutchfieldJ.DoyneFarmerNormanH.PachardRobertS.Shaw,,()zFdtdz=TakensTakensMnvF,ΜΜF→:RMv→:M12.:+→ΦnvFRM()()()()()()()TnvFzvzvzvz21.,,,ϕϕΛ=Φ3-1-312.:+→ΦnvFRM()zv()Mz∈()MvF.ΦmMM()()()kXkXφ=+1()0X()()(){}Λ2,1,0==kXkXkφ()()()nXfny=f12+mDeTakens12:+→ΦmRMMM→:φ20Takensx(t)t=0,1,2,,Nτy(t1)={x(t1),x(t1-τ),x(t1-2τ),,x[t1-(n-1)τ]}y(t2)={x(t2),x(t2-τ),x(t2-2τ),,x[t2-(n-1)τ]}......y(tN)={x(tN),x(tN-τ),x(tN-2τ),,x[tN-(n-1)τ]}y(ti)nnNnY=[y(t1),y(t2),,y(tN)]3.2Takens{y(n),n=1,,N}DEDE()])1((,),(),([ττ−++=ErDnynynynyΚ3-2-1DEn))(()(nyψnyrr=+τ3-2-221()())](,,2,[τττEDnynyny+++Κ)]))1((,),(),(([ττψ−++=EDnynynyΚ3-2-3y(n+DE)F)))1((,),(),(()(τττ−++=+EEDnynynyFDnyΚ3-2-4FFDE1:{y(n),n=1,2,,N}()()()()∑∑==−−−+=NnNnynyNynyynyNI121][1]][[1ττ3-2-5:()∑==NnnyNy11I222LyapunovD2D2{y(n),n=1,2,,N}ddmX×m=n-d+1)==++×nmmddTmTTdmxxxxxxxxxXXXXΛΛΛΛΛ113221213-2-6dmX×(Xi)i=1,,m()()∑≠−−=jijiXXlHmlC213-2-7||Xi-Xj||XiXj()•HHeaviside()−−=•jijiXXlXXlH,1,03-2-8ClllClD2(d)lnC(l)/llndD2(d)D2(d)ddD2(d)ddD2(d)D2DE2D21233.3Takens24RBF4.1RBFTakensFFF[28]Kolmogorov()YXREnm=→ϕϕ,E[0,1]mEmϕFF[29]S2LRBFI/O25BPBPBPRBFBPRadialBasisFunctionRBF4.2RBFRBFNNJ.MoodyC.Darken80RBFKRBF4-2-1qu...y......K4-2-1RBFyu,q26RBFKKK1RBFRRBFRRτEDR≥4-2-1)]1(),...,1(),([)(−++=Rnynynynyr4-2-23-2-4)])1R(),...,1(),(([)(−++=+nynynyFRny4-2-32RBFi||)(||iicuRq−=4-2-4u----nic----ii=1,2,,m;||||----R()----RBFk∑=ikikqyω4-2-5kiω----kiyq→27TakensDEτ3-2-4RBF12[30]])()[(1∑−−=−iiTiicucuRq4-2-6[]----uic∑−−=−12)()(iiTiicucudiTu∈4-2-7∑i----i∑−1iiT----i=∑iinnnnnnnσσσσσσσσσασσ21321232221131211ΛΜΛΛ4-2-8∑i∑iinjijjijjicuRq])([122∑−==σ4-2-9∑i28])()([2iiTiicucuRqσ−−=4-2-10)21exp()(xxR−=4-2-11u----nj=1~n,ic----iiσ----iijjσ----ij3RBFRBF[31]C-MEANSFKCNC-MEANSRBFFKCNRBF[32]KohonenKohonenKohonenKohonenKohonen[33]FuzzyKohonenClusterNetworkFKCNKohonenFKCNFKCNKohonenC-MEANSFKCNFKCNX