基于贝叶斯理论的土体抗剪强度参数最优二维分布模型识别方法

中国农村水利水电 ›› 2019 ›› (3) : 132-140.

水工建筑

孙骞1，2，冯晓波1，2

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Bayesian Approach to Identifying the Best－fit Bivariate Distribution Model for Shear Strength Parameters

SUN Qian1，2，FENG Xiao-bo1，2

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摘要

提出了基于贝叶斯理论的抗剪强度参数最优二维分布模型的识别方法。首先，介绍了基于Copula函数的岩土体抗剪强度参数二维分布模型的表征方法。其次，采用蒙特卡洛模拟方法验证了贝叶斯理论识别最优二维分布模型的有效性，对比了贝叶斯独立识别、非独立识别、AIC一步识别和AIC两步识别的识别能力，分析了影响贝叶斯理论识别精度的主要因素。最后，搜集了29组实际工程抗剪强度参数试验数据，研究了贝叶斯独立识别和非独立识别在实际工程抗剪强度参数最优二维分布模型识别中的应用。结果表明，贝叶斯理论能够结合先验信息有效地识别表征抗剪强度参数最优的二维分布模型；贝叶斯理论在小样本情况下的识别能力和识别精度与AIC准则相比优势明显；抗剪强度参数的样本数目、参数间相关性、备选二维分布模型集合以及先验信息都显著影响贝叶斯理论的识别精度。

Abstract

This paper proposes a Bayesian bivariate distribution identification method for shear strength parameters of soils and rocks． First，the characterization of bivariate distribution for shear strength parameters using Copulas is presented． Then，Monte Carlo simulations are conducted to validate the Bayesian bivariate distribution identification method． Moreover，the identification accuracy in the four methods is compared，and the main factors affecting the accuracy in the Bayesian bivariate distribution identification are identified． Finally，a total of twenty－nine sets of shear strength data are compiled to demonstrate the application of Bayesian theory bivariate distribution identification． The results indicate that with limited project－specific data and prior information，the Bayesian bivariate distribution identification method can successfully identify the best － fit bivariate distribution from a set of alternative bivariate distributions for shear strength parameters． In comparison with AIC，the Bayesian bivariate distribution identification method produces more accurate results for identifying the best －fit bivariate distribution． The sample size，correlation，the type of the true bivariate distribution and prior information of shear strength parameters has a significant impact on the accuracy of the Bayesian bivariate distribution selection method．

关键词

土体抗剪强度参数 / 二维分布模型 / 贝叶斯方法 / Copula函数

基金

国家自然科学基金项目( 51509188)

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孙骞，冯晓波. 基于贝叶斯理论的土体抗剪强度参数最优二维分布模型识别方法 [J].中国农村水利水电, 2019(3): 132-140

SUN Qian，FENG Xiao-bo. Bayesian Approach to Identifying the Best－fit Bivariate Distribution Model for Shear Strength Parameters[J].China Rural Water and Hydropower, 2019(3): 132-140

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收稿日期	修订日期	出版日期
2018-09-26	2018-10-15	2019-03-15
发布日期
2019-12-11

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