Identification of the parameters of complex constitutive models: Least squares minimization vs. Bayesian updating

TL;DR

This paper compares least-squares minimization and Bayesian updating for identifying complex material parameters, highlighting the accuracy of Bayesian methods with MCMC despite higher computational costs.

Contribution

It introduces a Bayesian updating approach using MCMC for material parameter identification and discusses efficient likelihood approximation methods.

Findings

Bayesian updating provides a detailed posterior density of parameters.

MCMC methods capture local peaks in parameter space.

Bayesian approach is more computationally intensive than least-squares.

Abstract

In this study the common least-squares minimization approach is compared to the Bayesian updating procedure. In the content of material parameter identification the posterior parameter density function is obtained from its prior and the likelihood function of the measurements. By using Markov Chain Monte Carlo methods, such as the Metropolis-Hastings algorithm \cite{Hastings1970}, the global density function including local peaks can be computed. Thus this procedure enables an accurate evaluation of the global parameter quality. However, the computational effort is remarkable larger compared to the minimization approach. Thus several methodologies for an efficient approximation of the likelihood function are discussed in the present study.