利用马尔科夫链修正的变维分形模型及其应用

2017-01-06 13:41叶伟马福恒周海啸
南水北调与水利科技 2016年6期

叶伟++马福恒++周海啸

摘要:以往的预测模型对数据长度有较强的依赖性,且数据出现较强的非线性时,将增加预测的复杂程度。为使监测数据呈现出一定的线性关系,基于分形理论,将常维分形改进为变维分形,并据此建立相应的数学模型,通过短期监测数据进行预测。考虑到变维分形得到的预测结果不可避免地存在一定的波动误差,对此,利用马尔科夫链(Markov)无后效性的特点对预测结果进行修正,从而提高预测精度。以西溪水库的监测资料数据为样本,建立其马尔科夫链变维分形预测模型,结果显示最大误差修正值可达089%,占原预测误差的679%,表明利用马尔科夫链修正的变维分形模型能有效地减小误差,提高预测精度。

关键词:大坝安全监测;变维分形;马尔科夫链;误差修正

中图分类号:TV698.1文献标志码:A文章编号:

16721683(2016)06011105

Application of modified variable dimension fractal method by Markov chain in dam safety monitoring

YE Wei,MA Fuheng,ZHOU Haixiao

(Dam Safety Management Department,Nanjing Hydraulic Research Institute,Nanjing 210029,China)

Abstract:Previous forecast models have strong dependence on the length of the data,and the data often appears strong nonlinear.Both of these will increase the complexity of the prediction.So in order to make the monitoring data to show a certain linear relationship,this paper changed constant dimension fractal method to variable dimension fractal method to predict shortterm monitoring data based on fractal theory shortterm monitoring data.The corresponding mathematical model was set up.However,inevitably,there were some fluctuation errors in the results predicted by the variable dimension fractal method.This paper used the Markov chain to modify these predicted results based on the characteristic of no aftereffect.The results analyzed by Xixi reservoir monitoring data showed that the revised error could be optimized by 0.89%.Obviously,it could be concluded that the variable dimension fractal method modified by Markov chain could effectively reduce error and improve the precision of prediction.

Key words:dam safety monitoring;variable dimension fractal;Markov chain;error correction

基于实测时间序列的安全监测模型对大坝的安全运行有着重要的意义,现阶段已有多种安全预测模型。刘健等[1]采用遗传神经网络对大坝变形进行预测;宋志宇等[2]采用混沌优化支持向量机对大坝安全进行监控预测;谢荣安等[3]采用灰色理论,建立灰色模型对大坝变形进行预测。但以上的预测模型均需要较长的时间序列数据。

根据分形理论进行预测则可以避免对数据长度的依赖性。常维分形适用于具有线性特征的数据序列,但一方面大坝监测数据常表现出较强的非线性,另一方面随着时间的推移,数据还出现一定的波动性,因此有必要将常维分形改进为变维分形,考虑到马尔科夫链能很好地适应数据波动的特点,同时引入马尔科夫链用以修正分形模型的预测结果。为此,本文建立利用马尔科夫链修正的变维分形大坝安全监测模型,以达到提高预测精度的目的。

5结论

本文通过马尔科夫链修正的分形模型的预测值能较准确地进行大坝安全监测值预测。变维分形模型不需要冗长的时间序列数据,采用短期数据即可实现预测,并且凭借马尔科夫链的无后效性的特点可使大坝安全监测值预测受外界因素影响变小,预测精度较高,两种方法的结合使得预测过程简便可靠,具有实际使用价值。

参考文献(References):

[1][HJ1.7mm]刘健,蔡建军,程森等.基于遗传神经网络的大坝变形预测模型研究[J].山东大学学报:工学版,2006,36(2):62-66.(LIU Jian,CAI Jianjun,CHENG Seng et al.Research on dam displacement forecast model based on genetic algorithm neural network[J].Journal of Shandong University:Engineering Science,2006,36(2):6266.(in Chinese))

[2]宋志宇,李俊杰.基于混沌优化支持向量机的大坝安全监控预测[J].武汉大学学报:工学版,2007,40(1):5357.(SONG Zhiyu,LI Junjie.Research on safety monitoring forecasting model for dam based on chaos optimization support vector machine algorithm[J].Journal of Wuhan University:Engineering Science,2007,40(1):5357.(in Chinese))

[3]谢荣安,张豪,卢辰龙,等.多变量灰色模型在大坝变形监测预报中的应用研究[J].工程勘察,2014,42(11):7477.(XIE Rongan,ZHANG Hao,LU Chenlong et al.Research on the application of multivariable grey model in dam deformation prediction[J].Geotechnical Investigation & Surveying,2014,42(11):7477.(in Chinese))

[4]Mandelbmt.B.B.How long is the coast Britain? Statistical selfsimilarity and fractal dimension[J].Science,1967,156:636638.

[5]金永强.分形学在大坝监测数据处理中的应用[J].合肥工业大学学报:自然科学版,2006,29(11):14301432.(JIN Yongqiang.Application of fractal theory to analysis of the observed data of dams[J].Journal of Hefei University of Technology:Natural Science,2006,29(11):14301432.(in Chinese))

[6]赖道平,吴中如,周红,等.分形学在大坝安全监测资料分析中的应用[J].水利学报,2004(1):100104.(LAI Daoping,WU Zhongru,ZHOU Hong,et al.Application of fractal theory to analyze dam safety monitoring data[J].Journal of Hydraulic Engineering,2004(1):100104.(in Chinese))

[7]邱华旭,黄张裕,郑建雷,等.基于分形原理的时间序列分析及预测研究[J].东南大学学报:自然科学版,2013,(z2):334337.(QIU Huaxu,HUANG Zhangyu,ZHENG Jianlei et al.Time series analysis and prediction based on fractal theory[J].Journal of Southeast University:Natural Science Edition,2013,(z2):334337.(in Chinese))

[8][JP2]宋传旺,王彦磊,于广明,等.分形理论在尾矿坝监测预警中的应用[J].辽宁工程技术大学学报:自然科学版,2013,32(9):11911194.(SONG Chuanwang,WANG Yanlei,YU Guangming et al.Application of fractal theory in monitoring prediction of tailings dam[J].Journal of Liaoning Technical University:Natural Science Edition,2013,32(9):11911194.(in Chinese))

[9]李波,骆进军,远近,等.分形理论在大坝安全监测中的应用[J].三峡大学学报:自然科学版,2009,31(1):3436.(LI Bo,LUO Jinjun,YUAN Jin,et al.Application of fractals theory to dam safety monitoring[J].Journal of China Three Gorges University:Natural Science,2009,31(1):3436.(in Chinese))[ZK)]

[10][ZK(#]王英华,秦鹏,陈斌,等.基于改进变维分形理论的拱坝温度监测数据预测模型[J].长江科学院院报,2009,26(12):3335.(WANG Yinghua,QIN Peng,CHEN Bin,et al.Forecasting model of monitored data of arch dam′s temperature based on improved variable dimension fractal theory[J].Journal of Yangtze River Scientific Research Institute,2009,26(12):3335.(in Chinese))

[11][JP2]宋传旺,王彦磊,于广明,等.分形理论在尾矿坝监测预警中的应用[J].辽宁工程技术大学学报:自然科学版,2013,32(9):11911194.(SONG Chuanwang,WANG Yanlei,YU Gunagming et al.Application of fractal theory in monitoring prediction of tailings dam[J].Journal of Liaoning Technical University:Natural Science Edition,2013,32(9) :11911194.(in Chinese) )

[12]张爱真.Markov链在工程预测中的应用[J].制造业自动化,2011,33(4):106108.(ZHANG Aizhen.Markov chain in engineering application prediction[J].Manufacturing Automation,2011,33(4):106108.(in Chinese) )

[13]邓鑫洋,邓勇,章雅娟,等.一种信度马尔科夫模型及应用[J].自动化学报,2012,38(4):666672.(DENG Xinyang,DENG Yong,ZHANG Yajuan,et al.A belief Markov model and its application[J].Acta Automatica Sinica,2012,38(4):666672.(in Chinese))

[14]张守平,樊科伟.基于自适应 MGM(1,n)马尔科夫链模型的大坝变形预测[J].南水北调与水利科技,2014,(1):145148,153.(ZHANG Shouping,FAN Kewei.Prediction of dam deformation based on selfadaptive MGMmarkov model[J].SouthtoNorth Water Transfers and Water Science & Technology,2014,(1):145148,153.(in Chinese) )

[15]王义民,于兴杰,畅建霞等.基于BP神经网络马尔科夫模型的径流量预测[J].武汉大学学报:工学版,2008,41(5):1417,57.(WANG Yimin,YU Xingjie,CHANG Jianxia et al.Prediction of runoff based on BP neural network and Markov model[J].Engineering Journal of Wuhan University,2008,41(5):1417,57.(in Chinese))

[16]周子东,郑东健,蒋明,等.偏最小二乘马尔科夫模型在大坝位移预测中的应用[J].三峡大学学报:自然科学版,2015,37(3):1518.(ZHOU Zidong,ZHENG Dongjian,JIANG Ming,et al.Application of PLSmarkov model to dam displacement prediction[J].Journal of China Three Gorges University:Natural Sciences,2015,37(3):1518.(in Chinese))

[17]杜传阳,郑东健.基于SVM理论的大坝变形监测模型改进方法研究[J].三峡大学学报:自然科学版,2015,37(2):1014.(DU Chuanyang,ZHENG Dongjian.Improved method of dam deformation monitoring model based on SVM[J].Journal of China Three Gorges University:Natural Sciences,2015,37(2):1014.(in Chinese))

[18][JP2]胡江,苏怀智,马福恒,等.MFDFA在大坝安全监测序列分析和整体性态识别中的应用[J].水利水电科技进展,2014,(3):5055.(HU Jiang,SU Huanzhi,MA Fuheng et al.The application of MFDFA in time series analysis and global state recognition of dam safety monitoring[J].Advances in Science and Technology of Water Resources,2014,(3):5055.(in Chinese))

[19]顾冲时,吴中如.大坝与坝基安全监控理论和方法及其应用[M].南京:河海大学出版社,2006.(GU Chongshi,WU Zhongru.Theory and method of dam and dam foundation safety monitoring and its application[M].Nanjing:Hohai University Press,2006.(in Chinese))

[20]吴中如,等.大坝的安全监控理论和试验技术[M].北京:中国水利水电出版社,2009.(WU Zhongru,et al.Dam safety monitoring theory and test technology[M].Beijing:China Water Power Press,2009.(in Chinese))