Enhanced Bayesian Model Updating with Incomplete Modal Information Using Parallel, Interactive and Adaptive Markov Chains

TL;DR

This paper introduces a novel Bayesian finite element model updating method that employs parallel, interactive, and adaptive Markov chains to efficiently handle incomplete modal data and uncertainties, improving the search for model parameters.

Contribution

It develops a new sampling theory with multiple adaptive Markov chains for Bayesian inference, enhancing computational efficiency and robustness in model updating with incomplete data.

Findings

Effective handling of incomplete modal data.

Improved convergence to multiple local optima.

Validated through systematic case studies.

Abstract

Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to actual measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic finite element model updating using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimization, whereas Bayesian inference is employed to account for the effect of uncertainties. To overcome the computational cost barrier, we adopt Markov chain Monte Carlo (MCMC) to characterize the target function/distribution. Instead of using single Markov chain in conventional Bayesian approach, we develop a new sampling theory with multiple parallel, interactive and adaptive Markov chains and incorporate into Bayesian inference. This can harness the collective power of these Markov chains to realize the concurrent search of multiple local optima. The number of required Markov chains and their respective initial model parameters are automatically determined via Monte Carlo simulation-based sample pre-screening followed by K-means clustering analysis. These enhancements can effectively address the aforementioned challenges in finite element model updating. The validity of this framework is systematically demonstrated through case studies.