Response-only modal identification of structures using limited sensors

Herein, we propose a method based on the existing second-order blind identification of underdetermined mixtures technique for identifying the modal characteristicsnamely, natural frequencies, damping ratio, and real-valued partial mode shapes of all contributing modesof 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 shapesthat 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 (c) 2012 John Wiley & Sons, Ltd.