| 申林方,王志良,常海滨,李邵军.基于概率配点法的岩土材料参数随机场及其响应分析[J].计算力学学报,2015,32(1):64~69 |
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| 基于概率配点法的岩土材料参数随机场及其响应分析 |
| Probabilistic Collocation Method for geotechnical stochastic field and response analysis |
| 投稿时间：2013-11-27 修订日期：2014-01-22 |
| DOI：10.7511/jslx201501011 |
| 中文关键词: 概率配点法 蒙特卡洛 岩土工程 参数 随机场 |
| 英文关键词:Probabilistic Collocation Method Mento Carlo geotechnical parameter stochastic field |
| 基金项目:昆明理工大学人才培养基金(KKSY201306023);国家自然科学基金(51179187)资助项目. |
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| 中文摘要: |
| 概率配点法是进行不确定性问题分析的一种有效方法.通过对输入参数场进行Karhunen-Loeve展开,将其表示为一系列独立随机变量在不同权重下的线性组合,再以与之相同的随机变量组合形成混沌多项式展开对输出随机场进行分解,通过某种算法选取随机变量的值,将其作为插值点的组合(配点),在这些配点上,概率方程演化为一个确定性问题方程.由此,可以直接利用现有软件或者确定性问题计算程序进行求解,生成混沌多项式的系数矩阵后,即可得到该随机问题的各阶统计矩,从而实现参数随机场的不确定性分析.本文将该方法引进岩土工程材料参数随机场,将体积模量视为输入随机场,位移视为输出场,分别进行了弹性及塑性变形计算.结果表明该方法极大地降低了随机问题的求解难度,与MC法(Mento Carlo)相比,减少了运算消耗,提高了计算效率,具有明显的优越性. |
| 英文摘要: |
| Probabilistic Collocation Method (PCM) is an effective way for uncertainty analysis.The input stochastic field is represented by Karhunen-Loeve expansion in terms of a set of independent standard random variables.The output field is approximated using polynomial chaos expansion with the same sets of standard random variables.The value of the sets of standard random variables known as collocation points are determined through certain algorithm.Then let the residual be zero at these given collocation points,therefore the stochastic problem can be simplified to a deterministic problem.And the software for solving deterministic equation could be employed directly.Polynomial expansion coefficients which stand for the statistical property of output can be obtained by solving a set of linear equations.This paper introduces PCM into geotechnical parameter field analysis.The bulk modulus is the input random field,and the displacement is the output random field.Elastic and plastic deformations are investigated under these stochastic field.Results indicate that the PCM greatly reduces the difficulty for solving random problems.Meanwhile,compared with Mento Carlo,PCM is less time-consuming with higher efficiency which exhibits obvious superiority. |
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