摘要
提出基于贝叶斯理论的抗剪强度参数最优Copula函数识别方法,首先简要介绍了基于Copula函数的岩土体抗剪强度参数相关结构表征方法,给出常用的识别最优Copula函数的最小平方欧氏距离法和AIC(akaike information criterion)准则。其次,采用蒙特卡洛模拟方法验证了贝叶斯理论识别最优Copula函数的有效性,比较了3种方法的最优Copula函数识别能力,并分析了影响贝叶斯理论识别精度的主要因素。最后,收集了实际工程共23组抗剪强度参数试验数据,研究了贝叶斯理论在抗剪强度参数最优Copula函数识别中的应用。结果表明,贝叶斯理论能够有效地识别表征抗剪强度参数间相关结构的最优Copula函数,且能有效考虑先验信息对识别结果的影响;与传统的最小平方欧氏距离法和AIC准则相比,贝叶斯理论的识别能力和识别精度都更高;抗剪强度参数的样本数目、相关性大小、真实Copula函数类型以及先验信息都对贝叶斯理论的识别精度具有重要的影响。此外,常用的Gaussian Copula函数并不总是表征抗剪强度参数间相关结构的最优Copula函数。
This paper proposes a Bayesian Copula identification method for shear strength parameters of soils and rocks. First, the characterization of dependence structure between shear strength parameters using Copulas is presented. Two commonly-used methods, namely least square method of Euclidean distance and akaike information criterion(AIC), for identifying the best-fit Copula, are given. Then, Monte Carlo simulations are conducted to validate the Bayesian Copula identification method. Moreover, the identification accuracy in the three methods is compared, and the main factors affecting the accuracy in the Bayesian Copula identification are identified. Finally, a total of twenty-three sets of shear strength data are compiled to demonstrate the application of Bayesian theory Copula model identification. The results indicate that with limited project-specific data and prior information, the Bayesian Copula identification method can successfully identify the best-fit Copula from a set of alternative Copulas for shear strength parameters. In comparison with the least square method of Euclidean distance and AIC, the Bayesian Copula identification method produces more accurate results for identifying the best-fit Copula. The sample size, correlation, the type of the true Copula and prior information of shear strength parameters has a significant impact on the accuracy of the Bayesian Copula selection method. Furthermore, the commonly adopted Gaussian copula for characterizing the dependence structure between shear strength parameters does not always provide the best fit to the shear strength data. © 2016, Science Press. All right reserved.
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2016年第S2期578-588,共11页
Rock and Soil Mechanics
基金
国家自然科学基金(No.51225903
No.51329901
No.51509188)
湖北省自然科学基金(No.2014CFA001)~~
关键词
抗剪强度参数
相关性
COPULA函数
贝叶斯理论
模型识别
Correlation methods
Decision theory
Intelligent systems
Least squares approximations
Monte Carlo methods
Parameter estimation
