基于特定混沌系统微弱谐波信号频率检测的理论分析与仿真
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摘要
为更完整地研究一类特定的Duffing Holmes方程所建立的混沌系统用于确定微弱谐波未知频率 ,论证了方程存在周期解并且该解唯一 ;利用稳定相态周期轨迹特征成功地进行了确定谐波频率的仿真实验 ;从 1Hz至 2 0 0Hz变阻尼比 (α)计算了检测误差 |Δω|;结果表明 ,不同频率带宽、不同频率相应的α值选择需要经过细致仿真实验去加以确定 .
In order to study a kind of chaotic system which is based on the special Duffing-Homes equation, and use it to detect the unknown frequency of weak harmonious signals, we prove the existence of the periodic solution and the exclusivism of the solution, carry out simulation experiments to detect harmonious frequency using the periodic trajectory of a stable phase state.We also compute the detection error |Δ ω |,when the damping ratio ( α ) changes and the frequency changes from 1Hz to 200Hz. The results show that we have to choose the value of α corresponding to the different range of frequency by simulation experiments.
In order to study a kind of chaotic system which is based on the special Duffing-Homes equation, and use it to detect the unknown frequency of weak harmonious signals, we prove the existence of the periodic solution and the exclusivism of the solution, carry out simulation experiments to detect harmonious frequency using the periodic trajectory of a stable phase state.We also compute the detection error |Δ ω |,when the damping ratio ( α ) changes and the frequency changes from 1Hz to 200Hz. The results show that we have to choose the value of α corresponding to the different range of frequency by simulation experiments.
引文
[1]LeungHandLoT 1993IEEEJ .OceanicEngineering18(3)287
[2]ShortKM 1994Int.J .Bifur.Chaos4959
[3]WangGRetal2001Control,SynchronizationandApplicationForChaos(Beijing:PublishingHouseofNationalDefenceIndustry)p190—198(inChinese)[王光瑞等2001混沌的控制、同步与利用(北京:国防工业出版社)第190—198页]
[4]BirxDI 1992IEEEInternationJointConferenceonNeuralNetwords22881
[5]HaykinSandLiXB 1995ProcessingIEEE 8394
[6]LeungHandPhuangX 1996IEEETrans.Sig.Pig.Proc.442456
[7]KennedyMP 2000SignalProcessing801307
[8]GayF 2000Ph.D .MetiersParisFrance36—38
[9]WangFPetal2001ActaPhys.Sin.501019(inChinese)[汪芙平等2001物理学报501019]
[10]ChenSH ,ZhaoLMandLiuJ 2002Chin.Phys.11543
[11]LiZandHanZC 2002Chin.Phys.11666
[12]LiGHetal2002ActaPhys.Sin.51739(inChinese)[李国辉等2002物理学报51739]
[13]TanN ,XuJXandChenYH 2002Chin.Phys.11670
[14]GuanXPetal2002ActaPhys.Sin.51753(inChinese)[关新平等2002物理学报51753]
[15]ZhangSHandShenK 2002Chin.Phys.11894
[16]WangGYetal2002SignalProcessing82103
[17]LiY ,YangBJ,DuLZandYuanY 2003Chin.Phys.12714
[18]LiYandYangBJ 2003ChineseScienceBulletin48508
[19]ZhangZJ 2002Theprocessingandinterpretationmethodfortheanisotropicmediausingmulti componentseismicdata(Harbin:PublishingHouseofHeilongjiangEducation)p15—35(inChinese)[张中杰2002多分量地震资料的各向异性处理和解释方法(哈尔滨:黑龙江教育出版社)第15—35页]
[20]WangGYetal2002SignalProcessing82103
[21]LiYetal2003ActaPhys.Sin.52526(inChinese)[李 月等2003物理学报52526]
[22]LiWetal2001ActaPhys.Sin.501436(inChinese)[李 伟等2001物理学报501436]
[23]LiWetal2001ActaPhys.Sin.501862(inChinese)[李 伟等2001物理学报501862]
[24]SansoneGandContiR 1964NonlinearDifferentialEquations(Florence:Pergamon)[G桑森,R康蒂著,黄启昌等译1983非线性微分方程(北京:科学出版社)第83页]
[2]ShortKM 1994Int.J .Bifur.Chaos4959
[3]WangGRetal2001Control,SynchronizationandApplicationForChaos(Beijing:PublishingHouseofNationalDefenceIndustry)p190—198(inChinese)[王光瑞等2001混沌的控制、同步与利用(北京:国防工业出版社)第190—198页]
[4]BirxDI 1992IEEEInternationJointConferenceonNeuralNetwords22881
[5]HaykinSandLiXB 1995ProcessingIEEE 8394
[6]LeungHandPhuangX 1996IEEETrans.Sig.Pig.Proc.442456
[7]KennedyMP 2000SignalProcessing801307
[8]GayF 2000Ph.D .MetiersParisFrance36—38
[9]WangFPetal2001ActaPhys.Sin.501019(inChinese)[汪芙平等2001物理学报501019]
[10]ChenSH ,ZhaoLMandLiuJ 2002Chin.Phys.11543
[11]LiZandHanZC 2002Chin.Phys.11666
[12]LiGHetal2002ActaPhys.Sin.51739(inChinese)[李国辉等2002物理学报51739]
[13]TanN ,XuJXandChenYH 2002Chin.Phys.11670
[14]GuanXPetal2002ActaPhys.Sin.51753(inChinese)[关新平等2002物理学报51753]
[15]ZhangSHandShenK 2002Chin.Phys.11894
[16]WangGYetal2002SignalProcessing82103
[17]LiY ,YangBJ,DuLZandYuanY 2003Chin.Phys.12714
[18]LiYandYangBJ 2003ChineseScienceBulletin48508
[19]ZhangZJ 2002Theprocessingandinterpretationmethodfortheanisotropicmediausingmulti componentseismicdata(Harbin:PublishingHouseofHeilongjiangEducation)p15—35(inChinese)[张中杰2002多分量地震资料的各向异性处理和解释方法(哈尔滨:黑龙江教育出版社)第15—35页]
[20]WangGYetal2002SignalProcessing82103
[21]LiYetal2003ActaPhys.Sin.52526(inChinese)[李 月等2003物理学报52526]
[22]LiWetal2001ActaPhys.Sin.501436(inChinese)[李 伟等2001物理学报501436]
[23]LiWetal2001ActaPhys.Sin.501862(inChinese)[李 伟等2001物理学报501862]
[24]SansoneGandContiR 1964NonlinearDifferentialEquations(Florence:Pergamon)[G桑森,R康蒂著,黄启昌等译1983非线性微分方程(北京:科学出版社)第83页]
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