岩体结构面模拟的统计方法改进研究
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摘要
基于西南某大型在建水电站建基面结构面的精测数据,对结构面模拟的统计方法加以改进,提高了结构面模拟的精度。对结构面数据进行直方图统计时,引入平均积分平方误差以优化带宽,使直方图统计的结果更精确;在蒙特卡洛模拟过程中,使用AD值和P值作为判定标准,定量确定各组数据对假定分布类型的拟合程度;尝试在结构面模拟中使用核密度估计方法,提高模拟精度,并降低工作量;与蒙特卡洛方法模拟结果比较,高斯内核的核密度估计方法得到的结果更精确。
Based on accurate measured data of discontinuities on the foundation surface of a large hydropower station under construction in southwest China,the statistical method of discontinuities simulation is improved,and as a result,the accuracy of discontinuities simulation is also improved. The mean integrated squared error is introduced to optimize bandwidth when making histograms of discontinuities,which make the histograms more accurate. In Monte Carlo simulation process,the AD and P values are used as criteria to quantitatively determine how well each set of data fits the assumed distribution type. The kernel density estimation method is used in the simulation of discontinuities,which can improve simulation accuracy and reduce workload. Compared with the simulation results of Monte Carlo method,the kernel density estimation method using Gaussian kernel is more accurate.
Based on accurate measured data of discontinuities on the foundation surface of a large hydropower station under construction in southwest China,the statistical method of discontinuities simulation is improved,and as a result,the accuracy of discontinuities simulation is also improved. The mean integrated squared error is introduced to optimize bandwidth when making histograms of discontinuities,which make the histograms more accurate. In Monte Carlo simulation process,the AD and P values are used as criteria to quantitatively determine how well each set of data fits the assumed distribution type. The kernel density estimation method is used in the simulation of discontinuities,which can improve simulation accuracy and reduce workload. Compared with the simulation results of Monte Carlo method,the kernel density estimation method using Gaussian kernel is more accurate.
引文
[1]刘佑荣,唐辉明.岩体力学[M].北京:化学工业出版社,2009.
[2]郭亮,李晓昭,周扬一,等.随机与确定耦合的裂隙岩体结构面三维网络模拟[J].岩土力学,2016,37(9):2636-2644.
[3]贾洪彪,马淑芝,唐辉明,等.岩体结构面网络三维模拟的工程应用研究[J].岩石力学与工程学报,2002,21(7):976-979.
[4]杜朋召,刘建,韩志强,等.基于复杂结构精细描述的岩质高边坡稳定性分析[J].岩土力学,2013,34(S1):393-398.
[5]王贵宾,杨春和,包宏涛,等.岩体节理平均迹长估计[J].岩石力学与工程学报,2006,25(12):2589-2589.
[6]伍法权.统计岩体力学原理[M].武汉:中国地质大学出版社,1993.
[7]郭亮,李晓昭,周扬一,等.数字化结构面三维随机网络模拟及其有效性检验[J].岩石力学与工程学报,2015,34(S1):2854-2861.
[8]王述红,张紫杉,王存根,等.岩体结构面产状随机分布空间表征[J].东北大学学报:自然科学版,2017,38(1):121-125.
[9]程爱平,肖术,许梦国,等.基于广义Hoek-Brown准则的节理岩体强度及变形参数随机分析[J].岩土力学,2017,38(1):205-213.
[10]魏翔,杨春和.钻孔岩体裂隙几何参数确定方法及其应用[J].岩石力学与工程学报,2015,34(9):15-15.
[11]ROSENBLATT M.Remarks on some nonparametric estimates of a density function[J].Annals of Mathematical Statistics,1956,27(3):832-837.
[12]SHEATHER S J,JONES M C.A reliable data-based bandwidth selection method for kernel density estimation[J].Journal of the Royal Statistical Society,1991,53(3):683-690.
[13]KROESE D P,BRERETON T,TAIMRE T,et al.Why the Monte Carlo method is so important today[J].Wiley Interdisciplinary Reviews:Computational Statistics,2014,6(6):386-392.
[14]SHIMAZAKI H,SHINOMOTO S.Kernel bandwidth optimization in spike rate estimation[J].Journal of Computational Neuroscience,2010,29(1-2):171-182.
[15]ANDERSON T W,DARLING D A.A test of goodness of fit[J].Journal of the American Statistical Association,1954,268:765-769.
[16]SPENCER C J,YAKYMCHUK C,GHAZNAVI M.Visualizing data distributions with kernel density estimation and reduced chi-squared statistic[J].Geoscience Frontiers,2017,8(6):1247-1252.
[2]郭亮,李晓昭,周扬一,等.随机与确定耦合的裂隙岩体结构面三维网络模拟[J].岩土力学,2016,37(9):2636-2644.
[3]贾洪彪,马淑芝,唐辉明,等.岩体结构面网络三维模拟的工程应用研究[J].岩石力学与工程学报,2002,21(7):976-979.
[4]杜朋召,刘建,韩志强,等.基于复杂结构精细描述的岩质高边坡稳定性分析[J].岩土力学,2013,34(S1):393-398.
[5]王贵宾,杨春和,包宏涛,等.岩体节理平均迹长估计[J].岩石力学与工程学报,2006,25(12):2589-2589.
[6]伍法权.统计岩体力学原理[M].武汉:中国地质大学出版社,1993.
[7]郭亮,李晓昭,周扬一,等.数字化结构面三维随机网络模拟及其有效性检验[J].岩石力学与工程学报,2015,34(S1):2854-2861.
[8]王述红,张紫杉,王存根,等.岩体结构面产状随机分布空间表征[J].东北大学学报:自然科学版,2017,38(1):121-125.
[9]程爱平,肖术,许梦国,等.基于广义Hoek-Brown准则的节理岩体强度及变形参数随机分析[J].岩土力学,2017,38(1):205-213.
[10]魏翔,杨春和.钻孔岩体裂隙几何参数确定方法及其应用[J].岩石力学与工程学报,2015,34(9):15-15.
[11]ROSENBLATT M.Remarks on some nonparametric estimates of a density function[J].Annals of Mathematical Statistics,1956,27(3):832-837.
[12]SHEATHER S J,JONES M C.A reliable data-based bandwidth selection method for kernel density estimation[J].Journal of the Royal Statistical Society,1991,53(3):683-690.
[13]KROESE D P,BRERETON T,TAIMRE T,et al.Why the Monte Carlo method is so important today[J].Wiley Interdisciplinary Reviews:Computational Statistics,2014,6(6):386-392.
[14]SHIMAZAKI H,SHINOMOTO S.Kernel bandwidth optimization in spike rate estimation[J].Journal of Computational Neuroscience,2010,29(1-2):171-182.
[15]ANDERSON T W,DARLING D A.A test of goodness of fit[J].Journal of the American Statistical Association,1954,268:765-769.
[16]SPENCER C J,YAKYMCHUK C,GHAZNAVI M.Visualizing data distributions with kernel density estimation and reduced chi-squared statistic[J].Geoscience Frontiers,2017,8(6):1247-1252.