基于分形理论的岩质高边坡监测资料分析
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摘要
以小湾水电站高边坡典型位置的位移数据为依据,引入分形理论对监测数据进行分析.通过对数据的Hurst指数和分形维数的讨论,得出岩质高边坡是一种复杂的非线性动态系统,在外界性态和自身结构不发生重大改变的情况下,边坡的Hausdorff维数不随外部环境量和时间跨度的改变而改变,并且测点之间也存在着随深度变化的正相关关系,具有很强的自相似性.分形维数可以从整体上描述边坡系统的动态变化特征以及建立复杂岩质高边坡的时间序列监控体制.
Based on the displacement data of the typical high rocky slope of Xiaowan Hydropower Station,quoting the fractal theory analysis of the data obtained from monitoring is carried out in the paper.Discussions on Hurst exponent and fractal theory of the data show that the high rocky slope is of complicated nonlinear dynamic system,and that Hausdorff dimension of the slope has not changed with external conditions and time span under no great changed conditions of external behavior and self-structure,and there is positive correlation relationships varying with depth between the measuring points and the dimension has strength self-structure.The fractal dimension can describe dynamic changeable feature the slope system and set up time series monitor system of the high rocky slope by discussion on Hurst exponent and fractal dimension.
Based on the displacement data of the typical high rocky slope of Xiaowan Hydropower Station,quoting the fractal theory analysis of the data obtained from monitoring is carried out in the paper.Discussions on Hurst exponent and fractal theory of the data show that the high rocky slope is of complicated nonlinear dynamic system,and that Hausdorff dimension of the slope has not changed with external conditions and time span under no great changed conditions of external behavior and self-structure,and there is positive correlation relationships varying with depth between the measuring points and the dimension has strength self-structure.The fractal dimension can describe dynamic changeable feature the slope system and set up time series monitor system of the high rocky slope by discussion on Hurst exponent and fractal dimension.
引文
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[2]王东升,曹磊.混沌、分形及其应用[M].合肥:中国科学技术出版社,1995:93-99.
[3]Mandelbrot B B.Les objets fractals:fome,hasavd et dimension[M].Flammarion Paris,1975:1-20.
[4]李信富,李小凡,武晔.分形理论在地震学中的应用研究[J].地球物理学进展,2007,4(2):411-417.
[5]厉大业,阮炯.分形Hurst指数在彩虹期权定价中的应用[J].复旦学报:自然科学版,2007,46(2):156-167.
[6]宋春林,冯瑞,刘富强,等.变步长和变阈值的分形小波图像压缩算法[J].计算机工程,2007,14:174-176.
[7]Hurst HE.Long-Term Storage in Reservoirs:An Experimental Study[J].Trans Am Soc Civ Eng,1951,116.
[8]姚勇.熵、分维、李雅普诺夫指数与混沌[J].自然杂志,1987,10(5):359-365.
[9]Bassingthwaighte J B,Raymond G M.Evaluating rescaled range analysis for time series[J].Annals of BiomedicalEngineering,1994,22(4):432-444.
[10]邹丽春,王国进,汤献良,等.复杂高边坡整治理论与工程实践[M].北京:中国水利水电出版社,2006:225-226.
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