Ambient modal identification using multi‐rank parallel factor decomposition

Summary In this paper, the problem of underdetermined modal identification where the number of modes to be identified is larger than the available sensor measurements is addressed using parallel factor decomposition and blind source separation. Underdetermined situations not only arise when the number of sensors are limited but also when narrowband excitations are present in the measurements, for example, in pedestrian-induced vibration of footbridges. The basic premise of the proposed algorithm is based on multiple-rank parallel factor decomposition of covariance tensors constituted from vibration response measurements. Unlike conventional parallel factor decomposition using a single rank order, the proposed method utilizes multiple rank order decompositions. A stability chart constructed from identified sources through such multiple rank orders allows for the robust estimation of active modes. The statistical characteristics of the resulting modes are evaluated in order to delineate the sources corresponding to external disturbances versus inherent modes of the system. The proposed framework enables an automated selection of rank order, detection of external harmonics and an estimation of modal parameters that are relatively insensitive to the sensor configuration. The performance of the algorithm is illustrated using both numerical studies and an experimental study using pedestrian-induced vibration measurements of a stress-ribbon bridge located at the Technical University—Berlin, Germany. Copyright © 2014 John Wiley & Sons, Ltd.

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