含相关非正态变量边坡可靠度分析的认知聚类分区方法

Reliability analysis of slope stability involving correlated non-normal variables using knowledge-based clustered partitioning method

提出了分析相关非正态变量可靠度问题一种新的全局优化方法——认知聚类分区方法。首先采用等概率变换原则将非正态变量等效为标准正态变量。然后采用Nataf变换方法成功地解决了输入变量相关时认知聚类分区方法的抽样问题。针对二分认知聚类分区方法和等步长认知聚类分区方法的缺点,提出了变步长认知聚类分区方法,并给出了该方法的计算流程图,编写了基于C语言的计算程序KCPREL。最后,以锦屏一级水电站左岸边坡稳定可靠度问题为例证明了所提方法的有效性。结果表明:提出的认知聚类分区方法能够有效地分析含有相关非正态变量的边坡可靠度问题。认知聚类分区方法能够获得全局最优解,其计算精度和蒙特卡洛模拟方法相当,计算效率远远高于传统的蒙特卡洛模拟方法。变步长认知聚类分区方法能够在计算精度和计算效率之间达到一种最佳平衡状态。研究成果极大地拓展了认知聚类分区方法在边坡可靠度分析中的应用。

A new global optimization reliability method,knowledge-based clustered partitioning method（KCP） for reliability problems involving correlated non-normal random variables,is proposed.Firstly,the isoprobabilistic transformation is adopted to transform the non-normal variables into the standard normal ones.Secondly,the Nataf transformation is used to transform the correlated non-normal random variables into the independent standard normal ones,which facilitate the sampling of the correlated non-normal random variables and reliability computation using the knowledge-based clustered partitioning method.To remove the limitations of the KCP with the binary step length and the KCP with equal step length,the KCP with changing step length is proposed,and the flowchart of reliability analysis using the KCP with changing step length is provided.Furthermore,a C-language based computer program is developed to carry out the reliability computations using the proposed KCP method.Finally,an example of reliability analysis for rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed method.The results indicate that the proposed knowledge-based clustered partitioning method can evaluate the reliability of rock slope stability involving correlated random variables accurately and efficiently.Furthermore,the global optimization solutions can be determined using the proposed KCP method.The proposed KCP method can result in the same accuracy as the traditional Monte Carlo simulations,and its efficiency is significantly higher than that of the traditional Monte Carlo simulations.More importantly,the KCP with changing step length can ensure an optimal balance between the accuracy and the efficiency of reliability computations.