Polymorphic uncertainty quantification for stability analysis of fluid saturated soil and earth structures
Polymorphic uncertainty quantification for stability analysis of fluid saturated soil and earth structures
复制标题
流体饱和土和土结构稳定性分析的多态不确定性量化
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Ricken
中科院分区：
文献类型：
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作者：
C. Henning;T. Ricken
目前，数值模拟可以描述许多应用领域中的力学问题，例如土力学或固体力学。在物理和计算建模过程中，许多理论模型方法和几何近似是误差的来源。这些不确定性可分为任意不确定性（如模型参数）和认知不确定性（如数值近似）。为了进行风险评估，必须捕获并量化这些不确定性和错误。为此，DFG安装了一个新的优先程序spp1886，该程序侧重于所谓的多态不确定性量化。在我们的子项目中，这是spp1886 （sp12）的一部分，重点是对土结构计算模拟中多态不确定性的量化和评估，特别是对流体饱和土壤。为了描述强耦合固流响应行为，多孔介质理论（TPM）将在有限元法（FEM）的框架内用于初始和边值问题的数值解[2,3]。为了捕捉不同的不确定性对计算结果的影响，分析和随机灵敏度分析两种很有前途的方法将增强确定性结构分析[6-8]。一个简单的固结问题的计算结果对材料参数和初始值的变化具有很高的敏感性。变分和概率敏感性分析可以量化这些敏感性。变分灵敏度被用作优化程序的工具，并捕获不同参数作为连续函数的影响。优点是解空间逼近准确，计算时间短，缺点是解析推导和算法实现困难。在统计学领域的概率敏感性分析中，费用只与问题维度成比例地增加。模型参数定义为提供随机值的概率分布，而不是恒定值。因此，通过几个模拟循环建立了一组解数据。不同的贝叶斯统计方法可以通过少量的模拟获得准确的信息。从长远来看，总体目标是开发更有效的方法和工具来确定土方结构的尺寸。（©2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim）
Nowadays, numerical simulations enable the description of mechanical problems in many application fields, e.g. in soil or solid mechanics. During the process of physical and computational modeling, a lot of theoretical model approaches and geometrical approximations are sources of errors. These can be distinguished into aleatoric (e.g. model parameters) and epistemic (e.g. numerical approximation) uncertainties. In order to get access to a risk assessment, these uncertainties and errors must be captured and quantified. For this aim a new priority program SPP 1886 has been installed by the DFG which focuses on the so called polymorphic uncertainty quantification. In our subproject, which is part of the SPP 1886 (sp12), the focus is driven on quantification and assessment of polymorphic uncertainties in computational simulations of earth structures, especially for fluid‐saturated soils. To describe the strongly coupled solid‐fluid response behavior, the theory of porous media (TPM) will be used and prepared within the framework of the finite element method (FEM) for the numerical solution of initial and boundary value problems [2, 3]. To capture the impacts of different uncertainties on computational results, two promising approaches of analytical and stochastic sensitivity analysis will enhance the deterministic structural analysis [6–8]. A simple consolidation problem already provided a high sensitivity in the computational results towards variation of material parameters and initial values. The variational and probabilistic sensitivity analyses enable to quantify these sensitivities. The variational sensitivities are used as a tool for optimization procedures and capture the impact of different parameters as continuous functions. An advantage is the accurate approximation of the solution space and the efficient computation time, a disadvantage lies in the analytical derivation and algorithmic implementation. In the probabilistic sensitivity analysis from the field of statistics, the expense only increases proportionally to the problems dimension. Instead of a constant value, the model parameters are defined as probability distribution, which provides random values. Thus, a set of solution data is built up by several cycles of the simulation. Different approaches of the Bayes statistics will enable to receive accurate information with just a few simulations. The overall objective is the development of more efficient methods and tools for the sizing of earth structures in the long‐run. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)