Hierarchical Bayesian calibration and response prediction of a 10-story building model

Abstract

This paper presents Hierarchical Bayesian model updating of a 10-story building model based on the identified modal parameters. The identified modal parameters are numerically simulated using a frame model (exact model) of the considered 10-story building and then polluted with Gaussian white noise. Stiffness parameters of a simplified shear model~- representing modeling errors - are considered as the updating parameters. In the Hierarchical Bayesian framework, the stiffness parameters are assumed to follow a probability distribution (e.g., normal) and the parameters of this distribution are updated as hyperparameters. The error functions are defined as the difference between model-predicted and identified modal parameters of the first few modes and are also assumed to follow a predefined distribution (e.g., normal) with unknown parameters (mean and covariance) which will also be estimated as hyperparameters. The Metropolis-Hastings within Gibbs sampler is employed to estimate the updating parameters and hyperparameters. The uncertainties of structural parameters as well as error functions are propagated in predicting the modal parameters and response time histories of the building. © The Society for Experimental Mechanics, Inc. 2019.