Bayesian Methods for Updating Dynamic Models

Abstract

Model updating of dynamical systems has been attracting much attention because it has a very wide range of applications in aerospace, civil, and mechanical engineering, etc. Many methods were developed and there has been substantial development in Bayesian methods for this purpose in the recent decade. This article introduces some state-of-the-art work. It consists of two main streams of model updating, namely model updating using response time history and model updating using modal measurements. The former one utilizes directly response time histories for the identification of uncertain parameters. In particular, the Bayesian time-domain approach, Bayesian spectral density approach and Bayesian fast Fourier transform approach will be introduced. The latter stream utilizes modal measurements of a dynamical system. The method introduced here does not require a mode matching process that is common in other existing methods. Afterwards, discussion will be given about the relationship among model complexity, data fitting capability and robustness. An application of a 22-story building will be presented. Its acceleration response time histories were recorded during a severe typhoon and they are utilized to identify the fundamental frequency of the building. Furthermore, three methods are used for analysis on this same set of measurements and comparison will be made.