推断岩土参数概率分布的二维正态信息扩散法
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摘要
提出推断岩土参数概率分布的二维正态信息扩散法。基于正态信息扩散原理,并考虑二维岩土参数的相关性,建立了二维正态信息扩散法模型的一般表达形式。结合K-S检验法的原理和二维岩土参数的分布特点,提出了一种改进的二维分布K-S检验法和具体的检验步骤。以某水电站工程中的二维抗剪强度参数作为实例,利用二维正态分布和二维正态信息扩散分布对实际数据的分布进行了拟合比较,并利用二维K-S检验方法进行了检验。研究结果表明,二维正态信息扩散分布的检验值要低于二维正态分布的检验值,二维正态信息扩散分布函数更加接近实际数据的分布,表明二维正态信息扩散分布在描述岩土参数概率分布方面更有优势。研究结果也表明,二维正态信息扩散函数的边缘分布同样服从一维正态信息扩散分布,并且其精度同样比一维正态分布高。
A two-dimensional normal information diffusion method was proposed to infer the probability distributions of geotechnical parameters. A general expression of two-dimensional normal information diffusion model was established considering the correlation of two-dimensional geotechnical parameters and the principle of normal information diffusion. The two-dimensional distribution K-S test method was improved and the corresponding specific test procedure was proposed. The two-dimensional shear strength parameters of the geo-materials at a hydropower station project were used as an example,and their distributions were fitted with the two-dimensional normal distribution and two-dimensional normal information diffusion distribution. The proposed two-dimensional distribution K-S test method was used to test the fitting accuracy of the two distributions obtained above. The results show that the testing value of the two-dimensional normal distribution is lower than that of two-dimension normal distribution and that the distribution function of two-dimensional normal information diffusion is closer to the actual distribution of data,showing that the two-dimensional normal information diffusion distribution is better in describing the probability distribution of two-dimensional geotechnical parameters. The edge distribution of the two-dimensional normal information diffusion function obeys the one dimensional normal information diffusion distribution,and the accuracy is also higher than that of the one dimensional normal distribution.
A two-dimensional normal information diffusion method was proposed to infer the probability distributions of geotechnical parameters. A general expression of two-dimensional normal information diffusion model was established considering the correlation of two-dimensional geotechnical parameters and the principle of normal information diffusion. The two-dimensional distribution K-S test method was improved and the corresponding specific test procedure was proposed. The two-dimensional shear strength parameters of the geo-materials at a hydropower station project were used as an example,and their distributions were fitted with the two-dimensional normal distribution and two-dimensional normal information diffusion distribution. The proposed two-dimensional distribution K-S test method was used to test the fitting accuracy of the two distributions obtained above. The results show that the testing value of the two-dimensional normal distribution is lower than that of two-dimension normal distribution and that the distribution function of two-dimensional normal information diffusion is closer to the actual distribution of data,showing that the two-dimensional normal information diffusion distribution is better in describing the probability distribution of two-dimensional geotechnical parameters. The edge distribution of the two-dimensional normal information diffusion function obeys the one dimensional normal information diffusion distribution,and the accuracy is also higher than that of the one dimensional normal distribution.
引文
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[15]黄达,曾彬,顾东明.基于Copula理论的粗粒土渗透破坏临界水力比降估值[J].岩土力学,2015,36(5):1 253-1 260.(HUANGDa,ZENG Bing,GU Dongming.Estimation of critical hydraulic gradient of coarse-grained soils based on Copula theory[J].Rock and Soil Mechanics,2015,36(5):1 253-1 260.(in Chinese))
[16]黄崇福.自然灾害风险评价理论与实践[M].北京:科学出版社,2005:76-89.(HUANG Chongfu.Theory and practice of risk assessment of natural disasters[M].Beijing:Science Press,2005:76-89.(in Chinese))
[17]张韧,徐志升,申双和,等.基于小样本案例的自然灾害风险评估--信息扩散概率模型[J].系统科学与数学,2013,33(4):445-456.(ZHANG Ren,XU Zhisheng,SHEN Shuanghe,et al.An unsymmetrical information diffusion probability model-for risk evaluaiton of natural disaster based on sample cases[J].Journal of Systems Science and Mathematical Science,2013,33(4):445-456.(in Chinese))
[18]李炳华,朱霁平,小出治,等.一种基于小样本数据信息扩散的重大火灾频度估算方法[J].火灾科学,2010,19(2):82-88.(LIU Binghua,ZHU Jiping,XIAO Chuzhi,et al.A method for estimating the frequency of major fire based on the diffusion of small sample data[J].Fire Science,2010,19(2):82-88.(in Chinese))
[19]宫凤强,李夕兵,邓建.小样本岩土参数概率分布的正态信息扩散法推断[J].岩石力学与工程学报,2006,25(12):2 559-2 564.(GONG Fengqiang,LI Xibing,DENG Jian.Probability distribution of small samples of geotechnical parameters using normal information spread method[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2 559-2 564.(in Chinese))
[20]周道成,段忠东,姚迪,等.正态信息扩散法在确定河冰抗压强度概率分布中的应用[J].防灾减灾工程学报,2010,30(4):4 24-4 30.(ZHOU Daocheng,DUAN Zhongdong,YAO Di,et al.Probability distribution of river ice compressive strength using normal information spread method[J].Journal of Disaster Prevention and Mitigation Engineering,2010,30(4):424-430.(in Chinese))
[21]宫凤强,侯尚骞,岩小明.基于正态信息扩散原理的Mohr-Coulomb强度准则参数概率模型推断方法[J].岩石力学与工程学报,2013,32(11):2 225-2 234.(GONG Fengqiang,HOU Shangqian,YAN Xiaoming.Probability model deduction method of Mohr-Coulomb criteria parameters based on normal information diffusion principle[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(11):2 225-2 234.(in Chinese))
[22]宫凤强,黄天朗,李夕兵.岩土参数最优概率分布推断方法及判别准则的研究[J].岩石力学与工程学报,2016,35(12):2 452-2 460.(GONG Fengqiang,HUANG Tianlang,LI Xibing.Research on approximation method and discriminative criterion of the optimal probability distribution of geotechnical parameters[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(12):2 452-2 460.(in Chinese))
[23]朱唤珍,李夕兵,宫凤强.大样本岩土参数概率分布的正态信息扩散推断[J].岩土力学,2015(11):3 275-3 282.(ZHU Huanzhen,LI Xibing,GONG Fengqiang.Assessment of probability distribution of large samples of geotechnical parameters by using normal information spread estimation method[J].Rock and Soil Mechanics,2015(11):3 275-3 282.(in Chinese))
[24]王新洲.基于信息扩散原理的估计理论、方法及其抗差性[J].武汉大学学报:信息科学版,1999,24(3):240-244.(WANG Xinzhou.The theory method and robustess of the paraneter estimation based on the principle of information spread[J].Journal of Wuhan University:Information Science Edition,1999,24(3):240-244.(in Chinese))
[25]赵宇飞,杨钧.岩土强度参数二维正态分布拟合研究[J].华北水利水电大学学报:自然科学版,2006,27(2):79-81.(ZHAO Yufei, YANG Jun.Attribute rough reduction in interval attribute valued decision systems[J].Journal of North China Institute of Water Conservancy and Hydroelectric Pover:Natural Science Edition,2006,27(2):79-81.(in Chinese))
[2]赵宇飞,汪小刚,杨健.基于二维正态分布的岩土参数Bayes方法优化[J].中国水利水电科学研究院学报,2006,4(2):93-96.(ZHAO Yufei,WANG Xiaogang,YANG Jian.Bayes method of optimizing geotechnical parameters based on two-dimension normal distribution[J].Journal of China Institute of Water Resources and Hydropower Research,2006,4(2):93-96.(in Chinese))
[3]兰雁,赵寿刚,沈细中,等.土体强度指标的互相关性对堤防稳定性的影响[J].人民黄河,2007,29(3):12-14.(LAN Yan,ZHAOShougang,SHEN Xizhong,et al.Influence of mutual relativity of intensity index of soil mass to stability of embankments[J].Yellow River,2007,29(3):12-14.(in Chinese))
[4]张蕾,唐小松,李典庆.基于Copula函数的土体抗剪强度参数二维分布模型[J].土木工程与管理学报,2013,30(2):11-17.(ZHANG Lei,TANG Xiaosong,LI Dianqing.Bivariate distribution model of soil shear strength parameter using copula[J].Journal of Civil Engineering and Management,2013,30(2):11-17.(in Chinese))
[5]LOW B K.Reliability analysis of rock slopes involving correlated nonnormals[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(6):922-935.
[6]陈群,唐岷,朱分清.强度参数的不确定性对土石坝坝坡失稳概率的影响[J].岩土工程学报,2008,30(11):1 594-1 599.(CHENQun,TANG Min,ZHU Fenqing.Influence of uncertainty of strength parameters on instability probability of embankment dam slopes[J].Chinese Journal of Geotechnical Engineering,2008,30(11):1 594-1 599.(in Chinese))
[7]ROM M,AVRIEL M.Probabilistic analysis of circular tunnels in homogeneous soil Using response surface methodology[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(9):1 314-1 325.
[8]LI H Z,LOW B K.Reliability analysis of circular tunnel under hydrostatic stress field[J].Computers and Geotechnics,2010,37(1/2):50-58.
[9]CHING J,PHOON K K,HU Y G.Efficient evaluation of reliability for slopes with circular slip surfaces using importance sampling[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(6):768-777.
[10]汪小刚,董育坚.岩基抗剪强度参数[M].北京:中国水利水电出版,2010:382-386.(WANG Xiaogang,DONG Yujian.The shear strength parameters of rock foundation[M].Beijing:China Water Power Press,2010:382-386.(in Chinese))
[11]YUE S.The bivariate lognormal distribution for describing joint statistical properties of a multivariate storm event[J].Environmetrics,2002,13(13):811-819.
[12]李典庆,唐小松,周创兵.基于Copula理论的岩土体参数不确定性表征与可靠度分析[M].北京:科学出版社,2015:6-10.(LIDianqing,TANG Xiaosong,ZHOU Chuangbin.Uncertainty characterization and reliability analysis of geotechnical parameters based on Copula theory[M].Beijing:Science Press,2015:6-10.(in Chinese))
[13]张蕾,唐小松,李典庆.基于Copula函数的土体抗剪强度参数二维分布模型究[J].土木工程与管理学报,2013,30(2):11-17.(ZHANG Lei,TANG Xiaosong,LI Dianqing.Bivariate distribution model of soil shear strength parameter using copula[J].Journal of Civil Engineering and Management,2013,30(2):11-17.(in Chinese))
[14]黄达,曾彬,王庆乐.粗粒土孔隙比及级配参数与渗透系数概率的相关性研究[J].水利学报,2015,46(8):900-907.(HUANGDa,ZENG Bing,WANG Qingle.Study on probabilistic relation between permeability coefficient and void ratio and grain composition of coarse grained soils using Copula theory[J].Journal of Hydraulic Engineering,2015,46(8):900-907.(in Chinese))
[15]黄达,曾彬,顾东明.基于Copula理论的粗粒土渗透破坏临界水力比降估值[J].岩土力学,2015,36(5):1 253-1 260.(HUANGDa,ZENG Bing,GU Dongming.Estimation of critical hydraulic gradient of coarse-grained soils based on Copula theory[J].Rock and Soil Mechanics,2015,36(5):1 253-1 260.(in Chinese))
[16]黄崇福.自然灾害风险评价理论与实践[M].北京:科学出版社,2005:76-89.(HUANG Chongfu.Theory and practice of risk assessment of natural disasters[M].Beijing:Science Press,2005:76-89.(in Chinese))
[17]张韧,徐志升,申双和,等.基于小样本案例的自然灾害风险评估--信息扩散概率模型[J].系统科学与数学,2013,33(4):445-456.(ZHANG Ren,XU Zhisheng,SHEN Shuanghe,et al.An unsymmetrical information diffusion probability model-for risk evaluaiton of natural disaster based on sample cases[J].Journal of Systems Science and Mathematical Science,2013,33(4):445-456.(in Chinese))
[18]李炳华,朱霁平,小出治,等.一种基于小样本数据信息扩散的重大火灾频度估算方法[J].火灾科学,2010,19(2):82-88.(LIU Binghua,ZHU Jiping,XIAO Chuzhi,et al.A method for estimating the frequency of major fire based on the diffusion of small sample data[J].Fire Science,2010,19(2):82-88.(in Chinese))
[19]宫凤强,李夕兵,邓建.小样本岩土参数概率分布的正态信息扩散法推断[J].岩石力学与工程学报,2006,25(12):2 559-2 564.(GONG Fengqiang,LI Xibing,DENG Jian.Probability distribution of small samples of geotechnical parameters using normal information spread method[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2 559-2 564.(in Chinese))
[20]周道成,段忠东,姚迪,等.正态信息扩散法在确定河冰抗压强度概率分布中的应用[J].防灾减灾工程学报,2010,30(4):4 24-4 30.(ZHOU Daocheng,DUAN Zhongdong,YAO Di,et al.Probability distribution of river ice compressive strength using normal information spread method[J].Journal of Disaster Prevention and Mitigation Engineering,2010,30(4):424-430.(in Chinese))
[21]宫凤强,侯尚骞,岩小明.基于正态信息扩散原理的Mohr-Coulomb强度准则参数概率模型推断方法[J].岩石力学与工程学报,2013,32(11):2 225-2 234.(GONG Fengqiang,HOU Shangqian,YAN Xiaoming.Probability model deduction method of Mohr-Coulomb criteria parameters based on normal information diffusion principle[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(11):2 225-2 234.(in Chinese))
[22]宫凤强,黄天朗,李夕兵.岩土参数最优概率分布推断方法及判别准则的研究[J].岩石力学与工程学报,2016,35(12):2 452-2 460.(GONG Fengqiang,HUANG Tianlang,LI Xibing.Research on approximation method and discriminative criterion of the optimal probability distribution of geotechnical parameters[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(12):2 452-2 460.(in Chinese))
[23]朱唤珍,李夕兵,宫凤强.大样本岩土参数概率分布的正态信息扩散推断[J].岩土力学,2015(11):3 275-3 282.(ZHU Huanzhen,LI Xibing,GONG Fengqiang.Assessment of probability distribution of large samples of geotechnical parameters by using normal information spread estimation method[J].Rock and Soil Mechanics,2015(11):3 275-3 282.(in Chinese))
[24]王新洲.基于信息扩散原理的估计理论、方法及其抗差性[J].武汉大学学报:信息科学版,1999,24(3):240-244.(WANG Xinzhou.The theory method and robustess of the paraneter estimation based on the principle of information spread[J].Journal of Wuhan University:Information Science Edition,1999,24(3):240-244.(in Chinese))
[25]赵宇飞,杨钧.岩土强度参数二维正态分布拟合研究[J].华北水利水电大学学报:自然科学版,2006,27(2):79-81.(ZHAO Yufei, YANG Jun.Attribute rough reduction in interval attribute valued decision systems[J].Journal of North China Institute of Water Conservancy and Hydroelectric Pover:Natural Science Edition,2006,27(2):79-81.(in Chinese))