Bayesian inference calibration of the modulus of elasticity

TL;DR

This paper presents a Bayesian inference approach to calibrate the Young modulus in linear elasticity, combining finite element modeling with quasi-Monte Carlo methods for efficient high-dimensional integration.

Contribution

It introduces a Bayesian framework for Young modulus calibration using Karhunen Loève expansion and advanced numerical integration techniques.

Findings

Accurate inference of Young modulus from stochastic elasticity equations

Efficient high-dimensional integration via quasi-Monte Carlo methods

Integration of Bayesian inference with finite element analysis

Abstract

This work uses the Bayesian inference technique to infer the Young modulus from the stochastic linear elasticity equation. The Young modulus is modeled by a finite Karhunen Lo\'{e}ve expansion, while the solution to the linear elasticity equation is approximated by the finite element method. The high-dimensional integral involving the posterior density and the quantity of interest is approximated by a higher-order quasi-Monte Carlo method.