A two-stage Bayesian model updating framework based on an iterative model reduction technique using modal responses

Abstract

A two-stage Bayesian model updating framework based on an affine-invariance sampling in Transitional Markov Chain Monte Carlo (TMCMC) algorithm is proposed. In the first stage, unknown modal coordinates are identified with an improved iterative model reduction technique. Subsequently, a modified TMCMC algorithm is proposed where obtaining the statistical estimators in the usual TMCMC algorithm is not necessary. In detail, an affine-invariance sampling approach is proposed to estimate a multi-dimensional scaling (MDS) factor in the affine-transformed space that accounts for the frequencies and mode shapes which are of different natures and dimensions at the levels of likelihood, prior and posterior distributions. The TMCMC sampling adaptively utilizes the plausibility value from the proposed MDS-based tuning algorithm to improve its transition levels. The proposed algorithm in the affine-invariance sampling space accounting for the observables of different dimensions is expected to facilitate the estimation of the posterior distribution of model parameters. The effectiveness of the proposed algorithm is demonstrated by considering a simply-supported steel beam, a ten-storied reinforced concrete building model and an eight-degree-of-freedom spring–mass model for which experimental data is available. The second example demonstrates the applicability of the approach for updating large finite element models involving substructuring.