材料表面非线性振荡时间序列的相空间重构
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摘要
在许多固态材料的表面存在着一种天然的非线性振荡花样,这些花样经计算机图像处理在时间和空间上呈现明显的分形特征。利用普通光学显微镜对Cu Zn Al合金表面的金相组织进行观察和分析,用高速摄像机拍摄了典型的振荡现象。借助计算机图像处理技术系统地研究该非线性振荡现象的形貌、结构特征及形成动力学规律,通过计算机编程技术构建系统的非线性动力模型,并重构系统的相空间。用R/S方法对系统时间序列的演化特征进行分析论证,结果表明,这种相空间重构方法具有较好的非线性预报效果。
A kind of natural non-linear oscillation phenomenon on the surface of many solid materials is observed. These non-linear oscillation patterns present evident fractal characters in space and time by computer process. In this paper, we have observed and studied the microstructres of Cu-Zn-Al alloy by the optical microscope, recorded this oscillatory phenomenon by the high-speed video and studied the appearance, characteristic and dynamics law of this nonlinear oscillation phenomenon systematically by the computer picture processing technology. We constructed the non-linear dynamics model of the system by the computer, reconstructed the phase space of the system and made R/S analysis for the time series in order to make nonlinear forecast.
A kind of natural non-linear oscillation phenomenon on the surface of many solid materials is observed. These non-linear oscillation patterns present evident fractal characters in space and time by computer process. In this paper, we have observed and studied the microstructres of Cu-Zn-Al alloy by the optical microscope, recorded this oscillatory phenomenon by the high-speed video and studied the appearance, characteristic and dynamics law of this nonlinear oscillation phenomenon systematically by the computer picture processing technology. We constructed the non-linear dynamics model of the system by the computer, reconstructed the phase space of the system and made R/S analysis for the time series in order to make nonlinear forecast.
引文
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陈颙,陈凌.1998.分形几何学[M].北京:地震出版社.
高后秀,杨渝钦,杨敬武,等.1998.固态合金中的非线性振荡现象观察[J].科学通报,43(15):1667~1671.
高后秀,张贵杰,陈泉水,等.2003.辉长石中的类流态研究[J].中国科学,B辑,33(2):105~110.
彭秋发,王京贵.2003.分形理论与灰色系统理论在南岭地区地质异常圈定和金矿资源预测中的应用[J].华东地质学院学报,26(1):1~4.
孙海云,曹庆杰.2001.混沌时间序列建模及预测[J].系统工程理论与实践.
徐士良.1995.C语言常用算法程序集[M].北京:清华大学出版社.
CasdagliM.1985.Nonlinearpredictionofchaotictimeseries.PhasicaD35~335.
MandelbrotBB.1968.VanNessJW.FractionalBrownianmotionfac tionalnoiseandapplication[J].SIAMReview.
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