Stochastic identification of composite material properties from limited experimental databases, Part II: Uncertainty modelling
Stochastic identification of composite material properties from limited experimental databases, Part II: Uncertainty modelling
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DOI：
10.1016/j.ymssp.2011.09.001
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发表时间：
2012-02
影响因子：
8.4
通讯作者：
L. Mehrez;A. Doostan;D. Moens;D. Vandepitte
中科院分区：
文献类型：
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作者：
L. Mehrez;A. Doostan;D. Moens;D. Vandepitte
本工作的目的是从有限尺寸的宏观尺度实验测量中揭示非均匀复合材料织物的随机宏观材料特性。这项工作是在一个序列的两个文件。在第一篇论文（第一部分）中，由一组确定性反问题得到的观测的异质杨氏模量字段的数据库。在本文中（第二部分），数据同化框架被认为是确定一个随机随机场模型的杨氏模量。这样一个模型的建立，以占偶然的不确定性，有关样本的互变性，以及认识的不确定性，由于现有的数据不足。这种不确定性特征是通过使用称为Karhunen-Loève展开的谱分解过程离散随机场来实现的。这种表示的随机变量展开在埃尔米特多项式混沌（PC）的基础上，其系数本身被认为是随机变量。PC基的高斯变量代表偶然的不确定性，PC系数代表认知的不确定性。采用马尔可夫链蒙特卡罗抽样器进行贝叶斯推断，根据最大后验概率（MAP）估计来估计PC系数。
The objective of this work is to characterise stochastic macroscopic material properties of heterogeneous composite fabrics from limited-size macro-scale experimental measurements. The work is presented in a sequence of two papers. In the first paper (Part I), a database consisting of observations of heterogeneous Young's modulus fields is obtained by a set of deterministic inverse problems. In this paper (Part II), a data assimilation framework is considered to identify a stochastic random field model of the Young's modulus. Such a model is set up to account for both aleatory uncertainties, related to sample inter-variabilities, as well as epistemic uncertainties due to insufficiency of the available data. This uncertainty characterisation is achieved by discretising the random field using a spectral decomposition procedure known as the Karhunen–Loève expansion. Random variables of this representation are expanded in a Hermite Polynomial Chaos (PC) basis whose coefficients themselves are considered as random variables. While the Gaussian variables of the PC basis model the aleatory uncertainty, the PC coefficients represent the epistemic uncertainty. A Bayesian inference scheme with Markov Chain Monte Carlo sampler is implemented to characterise the PC coefficients according to the Maximum A posteriori Probability (MAP) estimator.