Chapter5 Probabilistic Damage Identification of the Dowling Hall Footbridge Using Bayesian FE Model Updating Iman Behmanesh and Babak Moaveni Abstract This paper presents a probabilistic damage identification study on a full-scale structure, the Dowling Hall Footbridge, through Bayesian finite element (FE) model updating. The footbridge is located at Tufts University campus and is equipped with a continuous monitoring system that measures the ambient acceleration response of the bridge. A set of data is recorded once an hour or when triggered by large vibrations. The modal parameters of the footbridge are extracted based on each set of measured ambient vibration data and are used for model updating. In this study, effects of physical damage are simulated by loading a small segment of footbridge’s deck with concrete blocks. The footbridge deck is divided into five segments and the added mass on each segment is considered as an updating parameter. Overall, 72 sets of data are collected during the loading period (i.e., damaged state of the bridge) and different subsets of these data are used to find the location and extent of the damage (added mass). Adaptive Metropolis Hasting algorithm with adaption on the proposal probability density function is successfully used to generate Markov Chains for sampling the posterior probability distributions of the five updating parameters. Effect of the number of data sets used in the identification process is investigated on the posterior probability distributions of the updating parameters. Keywords Bayesian FE model updating • Adaptive metropolises hasting algorithm • Damage identification • Uncertainty analysis • Dowling hall footbridge 5.1 Introduction Although the deterministic FE model updating methods have been used for damage identification of several real-world, largescale structures [1–5], there are few applications of Bayesian FE model updating methods to full-scale complex structures [6–8]. In this paper, the authors investigate the challenges of implementing a Bayesian FE model updating framework for damage identification of a full-scale structure, the Dowling Hall footbridge. Information about deterministic structural identification of this footbridge is available at [9–11]. In this study, damage on the footbridge is simulated by addition of 2.29 metric tons of concrete blocks on a small segment of the bridge deck. The effect of added mass will be similar to a loss of stiffness (commonly used as damage indication) at segments of the bridge. The extracted modal parameters from acceleration time histories of the damaged structure (loaded structure) are used to find the location and extent of damage (added mass) through a Bayesian FE model updating scheme. The footbridge is divided into five segments and the added mass of each segment is considered as a model parameter to be calibrated in the model updating process. Model updating is performed to minimize the misfit between the measured modal parameters and those from the FE model. An adaptive Metropolis-Hasting algorithm [12–15] is used to sample the posterior probability distributions of the updating parameters given the data and model class. Impact of the amount of data used in the updating process is investigated on the accuracy of probabilistic damage identification results. To do this, six different set of damage identification results are obtained based on 1, 2, 5, 10, 36, and all 72 sets of identified modal parameters. This paper is organized in the following order. In Sect. 5.2, the Dowling Hall Footbridge and its continuous monitoring system are introduced. Section 5.3 explains how damage is simulated on the footbridge through addition of mass on a segment I. Behmanesh • B. Moaveni ( ) Department of Civil and Environmental Engineering, Tufts University, Medford, MA, USA e-mail: iman.behmanesh@tufts.edu; babak.moaveni@tufts.edu T. Simmermacher et al. (eds.), Topics in Model Validation and Uncertainty Quantification, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series 41, DOI 10.1007/978-1-4614-6564-5 5, © The Society for Experimental Mechanics, Inc. 2013 43
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