铜锌铝合金“类流态”振荡时间序列的相空间重构
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摘要
为了揭示固体“类流态”的非线性振荡机理,利用普通的光学显微镜、原子力显微镜(AFM)对Cu-Zn-A l合金表面金相组织进行了观察和研究.用计算机编程技术构建了系统的非线性动力模型,重构了系统的相空间.结果表明,系统存在混沌吸引子,最小嵌入维数为5;控制误差在50/0以内,非线性模型可以由原始数据的1 000个点预测100个点,超过100点时误差变大,说明了短期的非线性预报的可行性;R/S方法对时间序列演化特征进行分析,得到拟合线近似为直线,且斜率为0.86,表明“类流态”序列具有明显的Hurst效应,H>1/2,是分式布朗运动,运动具有较强的持续性.
To prove the theory of the non-linear oscillation mechanism about "quasi-fluid", the metallographic structures of Cu-Zn-Al alloy were observed and studied with the optical microscope and the atom force microscope(AFM). The non-linear dynamic model of the system was constructed by the computer programming technology and the phase space of the system was reconstructed. Results showed that there were chaotic attractors in the system and the least embedding dimension was 5 for describing the system, 100 points could be predicted with the non-linear model from the original 1 000 points with errors under 5~0_0. Errors increased when exceeding 100 points, and a short non-linear forecasting was possible. R/S analysis for the time series produced a fitting line whose slope was (0.86), which showed that "quasi-fluid" had an obvious Hurst effect, belonged to fractional Brownian motion because H >1/2, and was strongly durative.
To prove the theory of the non-linear oscillation mechanism about "quasi-fluid", the metallographic structures of Cu-Zn-Al alloy were observed and studied with the optical microscope and the atom force microscope(AFM). The non-linear dynamic model of the system was constructed by the computer programming technology and the phase space of the system was reconstructed. Results showed that there were chaotic attractors in the system and the least embedding dimension was 5 for describing the system, 100 points could be predicted with the non-linear model from the original 1 000 points with errors under 5~0_0. Errors increased when exceeding 100 points, and a short non-linear forecasting was possible. R/S analysis for the time series produced a fitting line whose slope was (0.86), which showed that "quasi-fluid" had an obvious Hurst effect, belonged to fractional Brownian motion because H >1/2, and was strongly durative.
引文
[1]高后秀,杨渝钦,刘文华,等.铜锌铝合金表面非线性振荡花样的研究[J].材料热处理学报,1995,16(4):56—59.Gao Houxiu,Yang Yuq in,L iu W enhua,et al.Study of thenon-linear osc illation pattern on the surface of Cu-Zn-A l al-loy[J].Transactions of Materials and Heat Treatm ent,1995,16(4):56—59(in Ch inese).
[2]高后秀,刘文华,李宝银.Cu-Zn-A l合金表面非线性振荡花样-自组织现象[J].天津大学学报,1997,30(5):567—572.Gao Houxiu,L iuW enhua,L i Baoyin.Study of the non-line-ar osc illation pattern-self-organ ization phenom ena on the sur-face of Cu-Zn-A l alloy[J].Journal of Tianjin University,1997,30(5):567—572(in Ch inese).
[3]Tackard N H,Crutchfield J T.Geom etry from a tim e series[J].Phys Rev Let,1980,45(3):712—716.
[4]曹建福,韩崇昭,方洋旺.非线性系统理论及应用[M].西安:西安交通大学出版社,2001.Cao Jianfu,Han Chongzhao,Fang Yangwang.Theory andApplication of the Non-linear System[M].X i’An:X i’AnJiaotong Un iversity Press,2001(in Ch inese).
[5]徐士良.C语言常用算法程序集[M].北京:清华大学出版社,1995.Xu Sh iliang.Comm on Arithm etics of C Programm es[M].Be ijing:Tsinghua Un iversity Press,1995(in Ch inese).
[6]孙海云,曹庆杰.混沌时间序列建模及预测[J].系统工程理论与实践,2001,21(5):106—109,113.Sun Haiyun,Cao Q ingjie.The Modeling and Forecasting ofChaotic Tim e Series[J].Theory and Application of SystemEngineering,2001,21(5):106—109,113(in Ch inese).
[7]陈,陈凌.分形几何学[M].北京:地震出版社,1998.Chen Yu,Chen L ing.Fractal Geom etry[M].Be ijing:Se is-mological Press,1998(in Ch inese).
[2]高后秀,刘文华,李宝银.Cu-Zn-A l合金表面非线性振荡花样-自组织现象[J].天津大学学报,1997,30(5):567—572.Gao Houxiu,L iuW enhua,L i Baoyin.Study of the non-line-ar osc illation pattern-self-organ ization phenom ena on the sur-face of Cu-Zn-A l alloy[J].Journal of Tianjin University,1997,30(5):567—572(in Ch inese).
[3]Tackard N H,Crutchfield J T.Geom etry from a tim e series[J].Phys Rev Let,1980,45(3):712—716.
[4]曹建福,韩崇昭,方洋旺.非线性系统理论及应用[M].西安:西安交通大学出版社,2001.Cao Jianfu,Han Chongzhao,Fang Yangwang.Theory andApplication of the Non-linear System[M].X i’An:X i’AnJiaotong Un iversity Press,2001(in Ch inese).
[5]徐士良.C语言常用算法程序集[M].北京:清华大学出版社,1995.Xu Sh iliang.Comm on Arithm etics of C Programm es[M].Be ijing:Tsinghua Un iversity Press,1995(in Ch inese).
[6]孙海云,曹庆杰.混沌时间序列建模及预测[J].系统工程理论与实践,2001,21(5):106—109,113.Sun Haiyun,Cao Q ingjie.The Modeling and Forecasting ofChaotic Tim e Series[J].Theory and Application of SystemEngineering,2001,21(5):106—109,113(in Ch inese).
[7]陈,陈凌.分形几何学[M].北京:地震出版社,1998.Chen Yu,Chen L ing.Fractal Geom etry[M].Be ijing:Se is-mological Press,1998(in Ch inese).
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