Markov chain Monte Carlo-based Bayesian model updating of a sailboat-shaped building using a parallel technique

Abstract

In unidentifiable model updating problems, the posterior probability density function (PDF) of uncertain model parameters cannot be well approximated by a multivariate Gaussian distribution. An alternative solution is to estimate the posterior PDF using samples from a multilevel Markov chain Monte Carlo (MCMC) simulation. In general, the accuracy of the approximated posterior PDF highly depends on the number of MCMC samples, which, in turn, depends on the available computational power. For model updating using field test data, a large number of samples are required to ensure the accuracy of the updated results. Inevitably, the computational power needed will be largely increased. To increase the efficiency of the MCMC method, this paper puts forward the parallel MCMC method, which generates several Markov chains (instead of a single chain) using multiple CPUs. As a result, more samples are available for the approximation of the posterior PDF. With the fast development of multicore processors in desktop or even laptop computing, parallel MCMC provides an efficient way to approximate the posterior PDF in model updating accurately, even if the problem is unidentifiable. To demonstrate the algorithm, an ambient vibration test of a 20-story office building was carried out. Owing to the limited number of sensors, the vibration test was divided into multiple setups. This paper not only reports the field test and the operational modal analysis but also the model class selection and the updating of the finite element model of the office building following the parallel MCMC method. The proposed algorithm together with the case studies using field test data presented in this study contributes to the development of structural model updating and structural health monitoring (SHM) on civil engineering structures.