Abstract
A Bayesian framework is presented for finite element model-updating using experimental modal data. A novel likelihood formulation is proposed regarding the inclusion of the mode shapes, based on a probabilistic treatment of the MAC value between the model predicted and experimental mode shapes. The framework is demonstrated by performing model-updating for the Metsovo bridge using a reduced high-fidelity finite element model. Experimental modal identification methods are used in order to extract the modal characteristics of the bridge from ambient acceleration time histories obtained from field measurements exploiting a network of reference and roving sensors. The Transitional Markov Chain Monte Carlo algorithm is used to perform the model updating by drawing samples from the posterior distribution of the model parameters. The proposed framework yields reasonable uncertainty bounds for the model parameters, insensitive to the redundant information contained in the measured data due to closely spaced sensors. In contrast, conventional Bayesian formulations which use probabilistic models to characterize the components of the discrepancy vector between the measured and model-predicted mode shapes result in unrealistically thin uncertainty bounds for the model parameters for a large number of sensors.
Highlights
The evaluation of the actual dynamic characteristics of structures, such as modal frequencies, modal damping ratios and mode shapes, through vibration measurements, as well as the development of high-fidelity finite element (FE) models, has been attracting an increasing research effort worldwide
A crucial aspect of the analysis is to examine the effect of the number of mode shape components used in the likelihood function on the model parameter uncertainty and uncertainty in model predictions
A Bayesian framework was presented for FE model updating of structures using experimentally identified modal frequencies and mode shapes
Summary
The evaluation of the actual dynamic characteristics of structures, such as modal frequencies, modal damping ratios and mode shapes, through vibration measurements, as well as the development of high-fidelity finite element (FE) models, has been attracting an increasing research effort worldwide. Instead of following the conventional Bayesian approach of assigning a multivariable Gaussian distribution to the error vector quantifying the discrepancy between the measured and model predicted mode shapes, a truncated Gaussian distribution is proposed for the probabilistic modeling of the scalar MAC value between the model predicted and experimental mode shapes This effectively reduces the number of data points in the likelihood and leads to different uncertainty quantification results compared to the classic vector-based likelihood formulation. The capabilities of the proposed modal-based Bayesian model-updating methodology are demonstrated by calibrating the parameters of a high-fidelity FE model developed for the Metsovo bridge, using modal properties experimentally identified from ambient vibration data.
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