岩质高边坡监测数据的改进变维分形预测模型
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摘要
针对以往预测模型在数据少和噪音干扰下出现预测精度降低的问题,基于分形理论,尝试建立改进的变维分形预测模型,并以小湾工程边坡位移监测数据为例,选取D1、D2曲线作为预测模型的分形参数曲线,计算各曲线的分段分形维数,对位移进行预测,并分别用灰色模型GM(1,1)和BP神经网络进行对比预测.结果证明,这种方法充分利用了分形理论自相似性的特点,抗噪性强,能较好地应用于小数据量监测数据的预测,并且精度较高,有着良好的应用前景.
Aiming at the problem of low precision caused by insufficient data and noise interruption,the paper attempts to set up and improve the forecasting model of variable dimension based on fractal theory.Meanwhile,with the monitoring data of slope displacement from the Xiaowan Project,and Curve D1,D2 as the fractal parameter curves of the forecasting model,it tends to predict the displacement by calculating the sub-fractal dimension,and comparing the forecast result with the gray model GM(1,1) and BP neural network.In this way,it makes good use of the self-similarity of the fractal theory and thus brings about a vast range of prospect for application due to its high precision and noise immunity.
Aiming at the problem of low precision caused by insufficient data and noise interruption,the paper attempts to set up and improve the forecasting model of variable dimension based on fractal theory.Meanwhile,with the monitoring data of slope displacement from the Xiaowan Project,and Curve D1,D2 as the fractal parameter curves of the forecasting model,it tends to predict the displacement by calculating the sub-fractal dimension,and comparing the forecast result with the gray model GM(1,1) and BP neural network.In this way,it makes good use of the self-similarity of the fractal theory and thus brings about a vast range of prospect for application due to its high precision and noise immunity.
引文
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[16]秦鹏.基于非线性理论的高边坡监测数据分析与预测[D].合肥:合肥工业大学,2009.(QI N Peng.Analysis andprediction of high-slope model′s monitoring data based on nonlinear method[D].Hefei:Hefei University of Technology,2009.(in Chinese))
[2]何习平,华锡生,何秀凤.加权多点灰色模型在高边坡变形预测中的应用[J].岩土力学,2007,28(6):1187-1191.(HE Xi-ping,HUA Xi-sheng,HE XI U-feng.Prediction weighted multi-point grey model and its application to high rock slopedeformation forecast[J].Rock and Soil Mechanics,2007,28(6):1187-1191.(in Chinese))
[3]周翠英,陈恒,朱凤贤.边坡演化的非线性时间序列多元混沌判别[J].地球科学:中国地质大学学报,2008,33(3):393-398.(ZHOU Cui-ying,CHEN Heng,ZHU Feng-xian.Multivariable chaotic discrimination for slope evaluationaccording to their nonlinear displacement-time sequence[J].Earth Science-Journal of China University of Geosciences,2008,33(3):393-398.(in Chinese))
[4]林鲁生,刘祖德.人工神经网络在边坡滑移预测中的应用[J].岩土力学,2002,23(4):508-510.(LI N Lu-sheng,LIU Zu-dei.Application of artificial neural network to prediction of sliding slope[J].Rock and Soil Mechanics,2002,23(4),508-510.(in Chinese))
[5]秦鹏,秦植海.基于分形理论的岩质高边坡监测资料分析[J].水利水运工程学报,2008(3):92-97.(QI N Peng,QI N Zhi-hai.Analysis of high rocky slope monitoring data based on fractal theory[J].Hydro-Science and Engineering,2008(3):92-97.(in Chinese))
[6]MANDELBROTB.Les objets fractals:forme,hasard et dimension[M].Paris:Flammarion,1975.
[7]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.(LI Xin-fu,LI Xiao-fan,WU Ye.Application of fractal theory in seismology[J].Progress in Geophysics,2007,4(2):411-417.(inChinese))
[8]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.(LIDa-ye,RUAN Jiong.Applying fractal Hurst exponent to pricing rainbow option[J].Journal of Fudan University(NaturalScience),2007,46(2):156-167.(in English))
[9]宋春林,冯端,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,2007,33(14):174-176.(SONG Chun-lin,FENG Duan,LI U Fu-qiang,et al.Hybrid fractal-wavelet image compression algorithm with variable stepsand thresholds[J].Computer Engineering,2007,33(14):174-176.(in Chinese))
[10]MANDELBROTB.Howlong is the coast of the Britain?Statistical self-similarity and fractional dimension[J].Science,1967,156(375):636-638.
[11]MANDELBROT B,EVERTSZ C J G,JONES P W.Fractals and chaos:the Mandelbrot set and beyond[M].New York:Springer,2004.
[12]MANDELBROT B.Fractal analysis and synthesis of fracture surface roughness and related forms of complexity and disorder[J].International Journal of Fracture,2006,138:13-17.
[13]付昱华.变换形成的分形与海洋环境数据分析预测[J].海洋通报,2000,19(1):79-88.(FU Yu-hua.Transform-formed fractals and analyses and forecast of marine environment data[J].Marine Science Bulleten,2000,19(1):79-88.(in Chinese))
[14]薛天放,杨庆,栾茂田.基于GIS技术的滑坡空间分布的分形特征研究[J].岩土力学,2007,28(2):347-354.(XUE Tian-fang,YANG Qing,LUAN Mao-tian.Research on fractal characters of spatial distribution of landslide based on GIS[J].Rock and Soil Mechanics,2007,28(2):347-354.(in Chinese))
[15]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.(ZOULi-chun,WANG Guo-jin,TANG Xian-liang,et al.Regulation theory and engineering practice on rock high slope[M].Beijing:China WaterPower Press,2006:225-226.(in Chinese))
[16]秦鹏.基于非线性理论的高边坡监测数据分析与预测[D].合肥:合肥工业大学,2009.(QI N Peng.Analysis andprediction of high-slope model′s monitoring data based on nonlinear method[D].Hefei:Hefei University of Technology,2009.(in Chinese))
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