混沌时间序列的神经网络预测研究

231Vol.23No.120081JournalofNavalAeronauticalandAstronauticalUniversityJan.20082007-07-021978−1940−1673−1522200801-0021−05aabaab264001TP273A[12]“”“”“”[3-7]Takens[8-12][1314]mnBPLorenzMackey-Glass()(())tt=XAX&(1)(1)(())kk+=XGX(2)(1)(2)X()Ag()Gg23·22·{}(),0,1,2,ykk=LTakens[2]21mD≥+D()ykm()[(),(),,((1))]Ykykykykmττ=−−−L(3)τ21mD≥+mmkt∆()kYk()ykt+∆k()ykt+∆kkt+∆Takens:mmFRR→()(())ktFYk+∆=Y(4)()ykt+∆()kYt∆()Fg()ykt+∆BP3BP33BPSBPLevengerg_Marquardt1()(())()max(())min(())kkkykmeanykykykyk−=−(5)2mτ()[(),(),,((1))],1,2,,kykykykmkNττ=−−−=YLL(t),1,2,,ykkN+∆=L3BPm1ΜΜ)(tky∆+)(ky)1(−ky))1((τ−−mky1BP4kY()ykt+∆BP5BPMSEPerr211ˆMSE()()NkykykN==−∑(6)[]2211ˆPerr()()/()NNkkykykyk===−∑∑(7)Lorenz[15]d10()dd(28)dd8d3xyxtyzxytzxyzt⎧=−⎪⎪⎪=−−⎨⎪⎪=−⎪⎩(8)[0.00310.19280.4208]0.01Runge-KuttaLorenz20003000x100020001·23·x2x3m=34τ=Lorenz[x(k+4);x(k),x(k-4),x(k-8)][x(k),x(k-4),x(k-8)]BPx(k+4)BP31010004abBP100BP56812146050010001500200025003000-0.8-0.6-0.4-0.200.20.40.6x2Lorenzx-0.500.51-1-0.500.51-1-0.500.513xLorenz0500100015002000-0.8-0.6-0.4-0.200.20.40.6a0200400600800100012001400160018002000-0.015-0.01-0.00500.0050.010.0150.02b4Lorenz01020304050607080901007891011x10-6MSE010203040506070809010011.21.41.61.8x10-5MSEaMSE01020304050607080901001.61.822.2x10-4Perr010203040506070809010023x10-4PerrbPerr5100Lorenz1001020304050607080901007891011x10-6MSE010203040506070809010011.11.21.31.4x10-5MSEaMSE23·24·01020304050607080901001.61.822.22.4x10-4Perr010203040506070809010022.53x10-4PerrbPerr6100Lorenz8Mackey-Glass[1315]01000.2()d()0.1()d1()xtxtxttxtττ−=−+−(9)017τ≥0τMackey-GlassMackey-Glass[12]100.2(17)(1)0.1()1(17)xnxnxnxn−+=−+−(10)0()|0.1txt≤=2000300010002000Mackey-Galss7Mackey-Galss8050010001500200025003000-0.8-0.6-0.4-0.200.20.40.67Mackey-Glass-0.8-0.6-0.4-0.200.20.40.6-0.8-0.6-0.4-0.200.20.40.6x(k)x(k+17)8Mackey-Glass[x(k+6);x(k),x(k-6),x(k-12),x(k-18)][x(k),x(k-6),x(k-12),x(k-18)]BPx(k+6)BP41010009ab100BP106812145000110500100015002000-0.8-0.6-0.4-0.200.20.40.6a0200400600800100012001400160018002000-0.02-0.015-0.01-0.00500.0050.010.015b9Mackey-Glass1·25·01020304050607080901000.811.21.41.6x10-5MSE010203040506070809010011.21.41.61.8x10-5MSEaMSE01020304050607080901001.522.53x10-4Perr01020304050607080901001.522.53x10-4PerrbPerr10100Mackey-Glass10010203040506070809010000.511.5x10-5MSE01020304050607080901000.511.5x10-5MSEaMSE01020304050607080901000.511.52x10-4Perr01020304050607080901000123x10-4PerrbPerr11100Mackey-Glass12BPLorenzMackey-Galss[1],,.[J].,2007,22(1):177-180.[2]TAKENSF.Detectingstrangeattractorsinturbulence[J].LectureNotesinMathematics,1981,898:366-381.[3]FARMERJD,SIDOROWICHJJ.Predictingchaotictimeseries[J].PhysRevLett,1987,59:845-848.[4]MAGUIRELP,ROCHEB,McginnityTM.Predictingachaotictimeseriesusingafuzzyneuralnetwork[J].InformationSciences,1998,112:125-136.[5]CASDAGLIM.Nonlinearpredictionofchaotictime-series[J].PhysicaD,1989,35:335-356.[6]KUGIUMTZISD,LINGJARDEOC,CHRISTOPHERSENN.RegularizedLocalLinearPredictionofChaoticTimeSeries[J].PhysicaD,1998,112:344-360.[7],,.[J].,2006,21(2):257-259.[8],.[J].,2004,24(6):67-71.[9],,.[J].,1999,33(1):19-21.[10],.[J].,2004,39(3):328-331.[11],.Volterra[J].,2000,49(3):403-408.[12],,.IIR[J].,2001,18(5):751-754,758.32海军航空工程学院学报第23卷·32·MovingObjects[C]//ProceedingofBritishMachineVisionAssociation,2001:705-714.[7]KHOTANZADA,LUJH.ClassificationofInvariantImageRepresentationsUsingaNeuralNetwork[J].IEEETransactionsonAcoustics,SpeechandSignalProcessing,1990,38(6):1028-1038.[8]FLUSSERJ,SUKT.PatternRecognitionbyAffineMomentInvariants[J].PatternRecognition,1993,26(1):167-174[9]张劲锋,蔡伟.基于组合不变矩的空间目标识别[J].控制工程,2006(6):14-17.[10]CHENCC.ImprovedMomentInvariantsforShapeDiscrimination[J].PatternRecognition,1993,26(5):683-686.[11]李迎春,高贺新,高磊.基于仿射不变矩的神经网络目标识别[J].计算机工程,2004,30(2):31-32.[12]曲东才.增强神经网络辨识模型泛化能力的研究[J].海军航空工程学院学报,2007,22(1):109-113.RecognitionofSatelliteTargetsBasedonCombinedInvariantMomentsandArtificialNeuralNetworkZHANGJian1，ZHOUXiao-dong1，ZHANGShi-feng2，GOULei2（1．DepartmentofControlEngineering，NAAU，YantaiShangdong264001，China；2．The92095thUnitofPLA，TaizhouZhejiang318050，China）Abstract:Firstly,thetheoryaboutHu’sinvariantmomentsandaffineinvariantmomentswasintroduced.Then,thefirstfourcomponentsofHu’sinvariantmomentswerecombinedwithaffineinvariantmomentstocreateanewinvariantmoments“combinedinvariantmoments”withoutincreasingthedimensionofthefeaturevectors.Combinedinvariantmomentswereextractedasthefeaturevectorofthesatellitetarget.Finally,withthehelpofclassifier,whichwasbasedontheArtificialNeuralNetwork,thetargetclassificationinthesatelliteimagehasbeenimplementedsuccessfully.Keywords:imagefeatureextraction;combinedinvariantmoments;ArtificialNeuralNetwork(ANN)（上接第25页）[13]王宏伟,马广富.基于模糊模型的混沌时间序列预测[J].物理学报,2004,53(10):3293-3297.[14]刘涵,刘丁,李琦.基于支持向量机的混沌时间序列非线性预测[J].系统工程理论与实践,2005,25(9):94-99.ChaoticTimeSeriesForecastingBasedonNeuralNetworksWANGYong-shenga，FANHong-daa，SHANGChong-weib，LIUZhena（NavalAeronauticalandAstronauticalUniversitya.DepartmentofOrdnanceScienceandTechnology；b.NewEquipmentTrainingCenter，YantaiShangdong264001，China）Abstr