Vectorization and distributed parallelization of Bayesian model updating based on a multivariate complex-valued probabilistic model of frequency response functions

Abstract

This study was devoted to investigating stochastic model updating in a Bayesian inference framework based on a frequency response function (FRF) vector without any post-processing such as smoothing and windowing. The statistics of raw FRFs were inferred with a multivariate complex-valued Gaussian ratio distribution. The likelihood function was formulated by embedding the theoretical FRFs that contained the model parameters to be updated in the class of the probability model of the raw FRFs. The Transitional Markov chain Monte Carlo (TMCMC) used to sample the posterior probability density function implies considerable computational toll because of the large batch of repetitive analyses of the forward model and the increasing expense of the likelihood function calculations with large-scale loop operations. The vectorized formula was derived analytically to avoid time-consuming loop operations involved in the likelihood function evaluation. Furthermore, a distributed parallel computing scheme was developed to allow the TMCMC stochastic simulation to run across multiple CPU cores on multiple computers in a network. The case studies demonstrated that the fast-computational scheme could exploit the availability of high-performance computing facilities to drastically reduce the time-to-solution. Finally, parametric analysis was utilized to illustrate the uncertainty propagation properties of the model parameters with the variations of the noise level, sampling time, and frequency bandwidth.