Identification of Modal and Stiffness Parameters of Time-Varying Train–Bridge Systems from Train-Induced Vibrations Using Autoregressive Modeling and Truncated UKF

Abstract In the identification of railway bridges using train-induced vibrations, moving heavy train mass continuously affects the measured responses, making the modal parameters of the train–bridge system time-varying. A method is developed to identify such time-varying modes, utilizing small overlapping time windows sweeping across the entire response, with the modes identified in each window using autoregressive modeling coupled with the eigensystem realization algorithm. Thereafter, a clustering and outlier analysis is performed for extraction of the meaningful modes. This identified sequence of modal parameters represents the time-varying modes of the train–bridge system as the train passes over the bridge. The identified modes are next used in suitable model-informed constraints, for joint state-parameter estimation from the measured responses, using the truncated unscented Kalman filter (UKF), a constraint-enforcing version of the popular Bayesian estimation algorithm UKF. The methodology is illustrated using numerical examples as well as laboratory-scale experiment with a moving train on a two-span continuous bridge. It is observed that the first few modes are estimated with reasonable accuracy, and also some higher frequency modes can be identified. The mode-based constraints improve the estimation of physical parameters of the train–bridge system, e.g., the bridge stiffness parameters. In the experimental example, it is also seen that the identified parameters can be used for bridge damage detection.