基于克里金代理模型与子集模拟的边坡高效可靠度分析
投稿时间:2021-04-06  修订日期:2021-07-03  点此下载全文
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作者单位邮编
雷世平 湖南省有色地质勘查局一总队 423099
李京泽 有色金属成矿预测与地质环境监测教育部重点实验室中南大学 410083
刘磊磊 有色金属成矿预测与地质环境监测教育部重点实验室中南大学 410083
李云青 湖南省有色地质勘查局一总队 
基金项目:国家自然科学基金青年项目(No.41902291);湖南省自然科学基金青年项目(No.2020JJ5704)
中文摘要:作为一种高效且准确的代理模型,克里金方法近年来被广泛用于边坡高效可靠度分析。然而,传统方法一般直接将克里金模型与蒙特卡洛模拟耦合进行可靠度分析,导致其在高维小失效概率的边坡可靠度计算中容易出现内存占用过大甚至溢出而无法求解的问题。为此,提出一种基于克里金代理模型的子集模拟方法,以高效解决小概率水平的边坡可靠度分析问题。该方法首先采用一定数量的样本校准克里金模型并进行精度验证,然后基于构建的模型开展子集模拟边坡可靠度计算。最后,采用一个单层黏性土坡与一个工程实例土坡验证所提方法的有效性,并研究回归模型、相关函数模型以及训练样本对该方法精度的影响。结果表明:(1)该方法可以有效计算边坡的失效概率,并且比传统方法更高效;(2)构建克里金模型时,采用10倍随机变量数的训练样本即可得到满足计算精度需求的模型,而额外增加训练样本对计算结果影响较小。
中文关键词:边坡稳定性  可靠度分析  克里金  代理模型  子集模拟
 
Slope reliability analysis using and Kriging-based subset simulation
Abstract:Kriging method, which is an efficient and accurate metamodel, is widely used in slope reliability analysis. However, traditional methods generally directly couple the Kriging model with Monte Carlo simulation method for reliability analysis, which leads to excessive memory usage or even overflow in the high-dimensional slope reliability calculation with small failure probability, and leads to the failure of problem solving. To this end, this paper proposes a subset simulation method based on the Kriging metamodel to efficiently solve the problem of slope reliability analysis with a small probability level. A single-layer cohesive soil slope and a practical soil slope are used to verify the effectiveness of the proposed method, and different regression models and related function models as well as the number of training samples are explored for the accuracy of the method. The results show that: (1) the proposed subset simulation method based on the Kriging metamodel can effectively calculate the failure probability of slopes, and is more efficient than the traditional method; (2) During the construction of the kriging model, the calculation accuracy of the model can be achieved when the number of training samples reaches10 times of the number of random variables. In addition, the number of additional training samples has little effect on the calculation results.
keywords:slope stability  reliability analysis  surrogate model  Kriging  Subset simulation.
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