Efficient solution of stochastic systems: Application to the embankment dam problem
Efficient solution of stochastic systems: Application to the embankment dam problem
复制标题
随机系统的有效解决方案：在堤坝问题中的应用
DOI：
10.1016/j.strusafe.2006.07.015
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发表时间：
2007
影响因子：
5.8
通讯作者：
A. Doostan
中科院分区：
文献类型：
--
作者：
R. Ghanem;G. Saad;A. Doostan
基准研究的堤坝问题，采用新开发的多项式混沌表示方法的随机模型降阶。在本问题中，材料的弹性模量和剪切模量被建模为两个随机过程，这两个随机过程是同一过程的显式函数，具有相对较低的相关长度。因此，系统的状态可以被视为定义在高维空间上的函数，与底层过程的波动相关联。在这种情况下，用于指定空间离散化的谱随机有限元方法（SSFEM）在计算上是禁止的。本文采用的方法，使细网格问题的随机特性的基础上的高维多项式混沌解的粗网格分析。通过随机变量的Karhunen-Loeve表示对问题进行相对降维后，得到了粗网格问题的由高斯自变量的高维多项式组成的SSFEM解。然后，获得的解决方案是用来定义一个新的基础，解决细网格问题。本文提出了一些新的算法，估计混沌系数存在复杂的非高斯依赖。数值收敛性研究的结果进行了讨论。
The embankment dam problem of the benchmark study is treated using the newly developed Stochastic Model Reduction for Polynomial Chaos Representations method. The elastic and shear moduli of the material, in the present problem, are modeled as two stochastic processes that are explicit functions of the same process possessing a relatively low correlation length. The state of the system can thus be viewed as a function defined on a high dimensional space, associated with the fluctuations of the underlying process. In such a setting, the spectral stochastic finite element method (SSFEM) for the specified spatial discretization is computationally prohibitive. The approach adopted in this paper enables the stochastic characterization of a fine mesh problem based on the high dimensional polynomial chaos solution of a coarse mesh analysis. After relatively reducing the dimensionality of the problem through a Karhunen–Loeve representation of the stochastic variables, the SSFEM solution consisting of a high dimensional polynomial in Gaussian independent variables is obtained for the coarse mesh problem. Then the attained solution is used to define a new basis for solving the fine mesh problem. The paper presents some new algorithms for the estimation of chaos coefficients in the presence of complex non-Gaussian dependencies. A numerical convergence study is presented together with a discussion of the results.