Bayesian model selection for ARX models and its application to structural health monitoring

Abstract

AbstractA Bayesian framework for model order selection of auto‐regressive exogenous (ARX) models is developed and applied to actual earthquake response data obtained by the structural health monitoring system of a high‐rise building. The model orders of ARX models are selected appropriately by the Bayesian framework, and differ significantly from the optimal order estimated by AIC; in fact, in many cases AIC does not even give an optimal order. A method is also proposed for consistently selecting the same ‘genuine’ modes of interest from the whole set of modes corresponding to each of the identified models from a sequence of earthquake records. In the identification analysis based on building response records from 43 earthquakes over 9 years, the modal parameters of the first four modes in each horizontal direction are estimated appropriately in all cases, showing that the developed methods are effective and robust. As the estimates of natural frequency depend significantly on the response amplitude, they are compensated by an empirical correction so that the influence of the response amplitude is removed. The compensated natural frequencies are much more stable over the nine‐year period studied, indicating that the building had no significant change in its global dynamic characteristics during this period. Copyright © 2010 John Wiley & Sons, Ltd.