Herein, we propose a method based on the existing second-order blind identification of underdetermined mixtures technique for identifying the modal characteristics—namely, natural frequencies, damping ratio, and real-valued partial mode shapes of all contributing modes—of structures with a limited number of sensors from recorded free/ambient vibration data. In the second-order blind identification approach, second-order statistics of recorded signals are used to recover modal coordinates and mode shapes. Conventional versions of this approach require the number of sensors to be equal to or greater than the number of active modes. In the present study, we first employ a parallel factor technique to decompose the covariance tensor into rank-one tensors so that the partial mode shapes at the recording locations (sensors) can be estimated. The mode shape matrix identified in this manner is not square, which precludes the use of a simple inversion to extract the modal coordinates. As such, the natural frequencies are identified from the recovered modal coordinates' Autocovariances. The damping ratios are extracted using a least-squares technique from modal free vibrations, as they are not directly recoverable because of the inherent smearing produced by windowing processes. Finally, a Bayesian model updating approach is employed to complete the partial mode shapes—that is, to extract the mode shapes at the DOFs without sensors. We use simulated and physical data for verifying and validating this new identification method, and explore optimal sensor distribution in multistory structures for a given (limited) number of sensors. Copyright © 2012 John Wiley & Sons, Ltd.

Rapid post-earthquake damage diagnosis of bridges can guide decision-making for emergency response management and recovery. This can be facilitated using digital technologies to remove the barriers of manual post-event inspections. Prior mechanics-based Finite Element (FE) models can be used for post-event response simulation using the measured ground motions at nearby stations; however, the damage assessment outcomes would suffer from uncertainties in structural and soil material properties, input excitations, etc. For instrumented bridges, these uncertainties can be reduced by integrating sensory data with prior models through a model updating approach. This study presents a sequential Bayesian model updating technique, through which a linear/nonlinear FE model, including soil-structure interaction effects, and the foundation input motions are jointly identified from measured acceleration responses. The efficacy of the presented model updating technique is first examined through a numerical verification study. Then, seismic data recorded from the San Rogue Canyon Bridge in California are used for a real-world case study. Comparison between the free-field and the foundation input motions reveals valuable information regarding the soil-structure interaction effects at the bridge site. Moreover, the reasonable agreement between the recorded and estimated bridge responses shows the potentials of the presented model updating technique for real-world applications. The described process is a practice of digital twinning and the updated FE model is considered as the digital twin of the bridge and can be used to analyze the bridge and monitor the structural response at element, section, and fiber levels to diagnose the location and severity of any potential damage mechanism.