Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent variability of heterogeneous materials, the model parameters describing the material properties are considered as random variables and their identification consists in solving a~stochastic inversion problem. The stochastic inversion is based on searching for probabilistic description of model parameters which provides the distribution of the model response corresponding to the distribution of the observed data. The paper presents two different formulations of the stochastic inversion problem. The first formulation arises from the Bayesian inference of uncertain statistical moments of a prescribed parameters' distribution while the main idea of the second one utilizes nonlinear transformation of random model parameters from distribution of the observed data.

翻译：许多建筑材料的异质性使得结构行为的数值建模变得复杂。材料的随机性可通过每个材料试件材料参数的不同取值来体现。为捕捉异质材料固有的变异性，描述材料特性的模型参数被视为随机变量，其识别过程在于求解一个随机反演问题。随机反演基于寻找模型参数的概率描述，该描述能提供与观测数据分布相对应的模型响应分布。本文提出了随机反演问题的两种不同表述形式。第一种表述源于对预设参数分布不确定统计矩的贝叶斯推断，而第二种表述的核心思想是利用观测数据分布对随机模型参数进行非线性变换。