A modal-based Kalman filtering framework for mode extraction and decomposition of damped structures

The mode shape is one of the important modal parameters that enables to visualize the intrinsic behavior of a structure as well as the quantity of interest by extracting or separating modal response from measurements. In this study, a new output-only framework is proposed to extract modes using a modal-based Kalman filter defined in the modal space and identify the mode shape by manipulating the correlation between the separated modes and the measured responses. It is also shown that the proposed framework can be extended to estimate the mode shapes of a non-classically damped structure in state space when the state variable is constructed from the measured responses and applied to the modal-based Kalman filter. The mode shape estimation framework proposed in this study was verified by numerical simulations and full-scale measurements. From the verification examples and their results, it was noted that the proposed modal identification framework is not influenced by the presence of noise, and it can be applied to identify the state-space mode shapes of non-classically damped systems as well as systems with very closely distributed modes such as buildings equipped with tuned mass dampers.