Variations of structural dynamic parameters (e.g., frequencies and damping ratios) can be caused by potential structural damages and environmental effects (e.g., temperature, humidity). It is of critical importance to distinguish them for a reliable vibration-based damage detection. A variational Bayesian mixture of factor analyzers (VB-MFA) is proposed in this paper for the probabilistic modeling of measured natural frequencies. It contains multiple factor analyzers to accommodate the nonlinear effect of environmental factors on the natural frequencies. The variational Bayes with automatic relevance determination prior empowers it to automatically determine the number of analyzers and the dimension of latent factors in each analyzer. In addition, the predictive marginal likelihood of natural frequencies is proposed as a damage index, which naturally considers the uncertainties in latent factors and estimated parameters. The method is verified in two case studies: a laboratory eight-story shear-type building model and the Z24-Bridge, both subjected to temperature variations. It shows that better performance has been achieved comparing to the conventional factor analysis and mixture of factor analyzers. The VB-MFA is capable to model the nonlinear effect of environmental effect on natural frequencies, and improves the accuracy of vibration-based structural damage detection.
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