Cyclical Variational Bayes Monte Carlo for Efficient Multi-Modal Posterior Distributions Evaluation

TL;DR

This paper introduces a novel Cyclical Variational Bayes Monte Carlo method designed to efficiently evaluate complex multi-modal posterior distributions in engineering models, reducing the need for extensive simulations.

Contribution

The paper proposes a new sampling technique combining variational Bayes and Monte Carlo methods to accurately characterize multi-modal posteriors with limited computational resources.

Findings

Effective in capturing multi-modal distributions with fewer simulations

Reduces computational cost compared to traditional sampling methods

Improves accuracy in structural condition monitoring

Abstract

Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity. In statistical model updating, for locally identifiable parameters, it can be anticipated that multi-modal posterior distributions would be found. The full characterization of these multi-modal distributions is important as methodologies for structural condition monitoring in structures are frequently based in the comparison of the damaged and healthy models of the structure. The characterization of posterior multi-modal distributions using state-of-the-art sampling techniques would require a large number of simulations of expensive to run physics-based models. Therefore, when a limited number of simulations can be run, as it often occurs in engineering, the traditional sampling techniques would not be able to capture accurately the multimodal distributions. This could potentially lead to large numerical errors when assessing the performance of an engineering structure under uncertainty.