Finite Element Model Updating of Structures in Bayesian Framework and Enhanced Model Reduction Techniques

Abstract

The present research study deals with model updating in the Bayesian frameworks with Metropolis Hastings (MH)-based Markov Chain Monte Carlo (MCMC) and Transitional MCMC (TMCMC) approaches. In the MH-based MCMC based FEMU, the prediction error variance models for non-informative prior estimation are considered for both frequencies and mode shapes following homoscedastic assumption. Further, the Bayesian model updating framework is extended for heteroscedastic model estimations that assign different variances to the modal errors. An eight-story shear building model and an experimental dataset that has been evaluated at the Los Alamos National Laboratory are used to numerically illustrate the proposed homoscedastic and heteroscedastic error models. Further, a two-stage Bayesian model updating framework based on TMCMC algorithm with an iterative model reduction technique is proposed. In the first stage, unknown modal coordinates are identified with an improved iterative model reduction technique which is further integrated into a sub-structuring scheme for applying to large finite element models. Subsequently, a modified TMCMC algorithm is proposed where, an affine-invariance sampling approach is proposed to estimate a multi-dimensional scaling (MDS) factor to account for the eigenfrequencies and mode shapes which are of different nature and dimensions. The effectiveness of the proposed algorithm is demonstrated by considering a simply-supported steel beam, a ten-storied reinforced concrete building model, and the previously used available experimental data set. Finally, an improved Bayesian model updating technique in the TMCMC framework in time domain is investigated wherein a modified iterative model reduction technique is embedded to address the limited availability of measurements. The efficiency of the algorithm is demonstrated considering a multi-storeyed frame and the previously used available experimental data set.