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Stochastic identification of composite material properties from limited experimental databases, Part II: Uncertainty modelling

机译：从有限的实验数据库中随机识别复合材料特性，第二部分：不确定性建模

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摘要

The objective of this work is to characterise stochastic macroscopic material properties of heterogeneous composite fabrics from limited-size macro-scale experimental mea surements. 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 insuffi ciency of the available data. This uncertainty characterisation is achieved by discretising the random field using a spectral decomposition procedure known as the Karhunen Loeve 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.
机译：这项工作的目的是通过有限尺寸的宏观实验测量来表征异质复合织物的随机宏观材料特性。这项工作分两篇论文进行介绍。在第一篇论文（第一部分）中，通过一组确定性反问题获得了一个包含异质杨氏模量场观测值的数据库。在本文（第二部分）中，考虑使用数据同化框架来识别杨氏模量的随机随机场模型。建立这种模型的目的是要考虑与样本间变异性相关的偶然不确定性，以及由于可用数据不足而造成的认知不确定性。通过使用称为Karhunen Loeve展开的频谱分解程序离散随机场，可以实现这种不确定性表征。此表示形式的随机变量在Hermite多项式混沌（PC）基础上扩展，其系数本身被视为随机变量。当PC基础的高斯变量模拟偶然不确定性时，PC系数代表认知不确定性。实现了使用马尔可夫链蒙特卡洛采样器的贝叶斯推断方案，以根据最大后验概率（MAP）估计器来表征PC系数。

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