Identification of random material properties as stochastic inversion problem

2026-02-16

AI Summary

This study addresses the challenge of modeling parameter randomness arising from the inherent heterogeneity of construction materials by formulating material property identification as a stochastic inverse problem. Two novel frameworks are proposed: the first integrates Bayesian inference to quantify uncertainty in the statistical moments of prescribed probability distributions, while the second employs a nonlinear probabilistic transformation to directly map the distribution of observational data onto the distribution of stochastic parameters. By synergistically combining Bayesian statistics, stochastic variable modeling, and stochastic inversion algorithms, the proposed approaches effectively capture the intrinsic variability of material parameters. This leads to numerical simulation responses whose distributions align closely with experimental measurements, thereby significantly enhancing the reliability of structural behavior predictions.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Sampling/Simulation-based SearchMachine Learning: Calibration & Uncertainty Quantification

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Models for Web evolutionSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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.

Problem

• stochastic inversion
• material heterogeneity
• random material properties
• Bayesian inference
• probabilistic modeling

Innovation

• stochastic inversion
• Bayesian inference
• random material properties
• nonlinear transformation
• heterogeneous materials