岩石抗剪强度计算的稳健回归模型及其应用
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摘要
针对岩石抗剪强度确定中图解法和最小二乘法存在的问题:①只适用于实验数据相关性较高的情况,不适用于数据离散并有异常值存在的情况;②在处理由试验法获得的试验数据时,最小二乘法由于采用残差平方和,容易夸大试验数据中异常值的影响,提出了岩石抗剪强度参数的稳健回归分析方法。该方法在实验数据相关性差、数据离散并有异常值存在的情况下,具备削弱数据离散和对异常值进行定位的能力,提高了估计参数的稳健性和可靠性。该方法以残差的绝对值之和代替残差平方和,并通过复形法求得力学参数,避免了异常值的二次项,可有效地减少异常值的影响。通过工程实例表明,在试验数据的相关性较好时,两种方法的计算结果相差不大,但当试验数据的相关性较差,存在异常值时,稳健回归方法的计算结果要优于最小二乘法。
There are two problems in the graphic method and the Least Quares(LS) method in determining the shear strength of rock.(1) The experimental data should be highly correlated,and separate data and anomalous data are not suitable.(2) The effect of anomalous values in test data is markedly shown because of the quadratic sum of residual errors in the least squares method.This paper proposes a shear strength parameter(Robust) regression analysis method.This method can be applied to analyze experimental data with poor correlation,and with anomalous values,and the effects of discrete and abnormal positioning can be weakened to improve the robustness and reliability of estimated parameters.In order to reduce the effect of anomalous values in the test data,the sum of residual absolute value is used instead of the quadratic sum of residual errors in the robust regression method,then the quadratic terms of anomalous value could be avoided,and the effect of anomalous values could be reduced.It is shown that the results of the two methods are the same when the test data is good,but the results of the robust regression method are better than those obtained by the least squares method when there are anomalous values in the test data.
There are two problems in the graphic method and the Least Quares(LS) method in determining the shear strength of rock.(1) The experimental data should be highly correlated,and separate data and anomalous data are not suitable.(2) The effect of anomalous values in test data is markedly shown because of the quadratic sum of residual errors in the least squares method.This paper proposes a shear strength parameter(Robust) regression analysis method.This method can be applied to analyze experimental data with poor correlation,and with anomalous values,and the effects of discrete and abnormal positioning can be weakened to improve the robustness and reliability of estimated parameters.In order to reduce the effect of anomalous values in the test data,the sum of residual absolute value is used instead of the quadratic sum of residual errors in the robust regression method,then the quadratic terms of anomalous value could be avoided,and the effect of anomalous values could be reduced.It is shown that the results of the two methods are the same when the test data is good,but the results of the robust regression method are better than those obtained by the least squares method when there are anomalous values in the test data.
引文
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[3]田斌,戴会超,王世梅.滑带土结构强度特征及其强度参数取值研究[J].岩石力学与工程学报,2004,23(17):2887-2892.Tian Bin,Dai Huichao,Wang Shimei.Chinese Journal of Rock Mechanicsand Engineering,2004,23(17):2887-2892.
[4]廖秋林,杨志法,赏彦军,等.川藏公路102滑坡滑动带力学参数的反分析[J].岩石力学与工程学报,2004,23(24):4119-4123.Liao Qiulin,Yang Zhifa,Shang Yanjun,et al.Chinese Journal of RockMechanics and Engineering,2004,23(24):4119-4123.
[5]Chandler R J.Back analysis techniques for slope stabilization works:Acase record[J].Geotechnique,1977,27(4):479-495.
[6]董陇军,王飞跃.基于未确知测度的边坡地震稳定性综合评价[J].中国地质灾害与防治学报,2007,18(4):74-78.Dong Longjun,Wang Feiyue.The Chinese Journal of Geological Hazardand Control,2007,18(4):74-78.
[7]刘春.黄麦岭磷矿边坡岩体抗剪强度参数的随机-模糊法取值研究[J].岩石力学与工程学报,2005,24(4):653-656.Liu Chun.Chinese Journal of Rock Mechanics and Engineering,2005,24(4):653-656.
[8]董陇军,李夕兵,宫凤强.膨胀土胀缩等级分类的未确知均值聚类方法及应用[J].中南大学学报:自然科学版,2008,39(5):1075-1080.Dong Longjun,Li Xibing,Gong Fengqiang.Journal of Central SouthUniversity:Science and Technology Edition,2008,39(5):1075-1080.
[9]张志刚,王鹏,李安贵,等.随机-模糊线性回归模型的参数估计及应用[J].北京科技大学学报,2004,26(6):326-329.Zhang Zhigang,Wang Peng,Li Angui,et al.Regression parameters esti-mation of random-fuzzy linear regression model and its application[J].Journal of University of Science and Technology Beijing,2004,26(6):326-329.
[10]李胡生,魏国荣.用随机-模糊线性回归方法确定岩石抗剪参数[J].同济大学学报,1993,21(3):421-429.Li Husheng,Wei Guorong.Journal of Tongji University,1993,21(3):421-429.
[11]邵小曼.岩石抗压强度的随机-模糊分析[J].岩石力学与工程学报,2001,20(增):1776-1779.Shao Xiaoman.Journal of Rock Mechanics Engineering,2001,20(suppl):1776-1779.
[12]李华晔,黄志全,刘汉东,等.岩基抗剪参数随机-模糊法和小浪底工程c、φ值计算[J].岩石力学与工程学报,1997,16(2):155-161.Li Huaye,Huang Zhiquan,Liu Handong,et al.Chinese Journal of RockMechanics and Engineering,1997,16(2):155-161.
[13]杨强,陈新,周维垣.抗剪强度指标可靠度分析[J].岩石力学与工程学报,2002,21(6):868-873.Yang Qiang,Chen Xin,Zhou Weiyuan.Chinese Journal of RockMechanics and Engineering,2002,21(6):868-873.
[14]Dong Longjun,Peng Gangjian,Fu Yuhua,et al.Unascertained Mea-surement classifying model of Goal collapse prediction[J].Journal ofCoal Science&Engineering:China,2008,14(2):221-224.
[15]王兴明,董陇军,付玉华.基于未确知均值分类理论的岩爆发生和分级预测方法[J].科技导报,2009,27(18):78-81.Wang Xingming,Dong Longjun,Fu Yuhua.Science&TechnologyReview,2009,27(18):78-81.
[16]Martin R D.Robust statistics with the s-plus robust library and financialapplications[M].New York:Insightful Corp Presentation,2002(1-2):17-18.
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