A VARIABLE SEPARATION TECHNIQUE FOR FAST BAYESIAN OPERATIONAL MODAL ANALYSIS IN THE FREQUENCY DOMAIN

Modal parameters (natural frequencies, damping ratios and mode shapes) have widespread applications in various fields such as structural health monitoring and structural control. Recently, ambient modal analysis using measured response only has aroused increasing interest in real applications in that they can be implemented in a much more efficient manner. In this study, the Bayesian statistical framework which provides a rigorous way for obtaining optimal values as well as their uncertainties is employed for structural operational modal analysis in the frequency domain for the cases of separated modes and closely spaced modes, respectively. To address the computational challenges of conventional Bayesian spectral density approach, a variable separation technique is presented in this study to completely decouple the interaction between spectrum variables (e.g., frequency, damping ratio as well as the amplitude of modal excitation and prediction error) and spatial variables (e.g., mode shape). As a result, the spectrum variables can be identified by using the sum of auto-spectral density in the first stage, while the spatial variables can be estimated by using the cross spectral density matrix in a second stage. The dimension involved in solving the most probable values as well as taking the inversion of the Hessian matrix is reduced significantly after employing the proposed strategy. Also, there is no need to fuse the identified spectrum variables from different setups together since the proposed method is able to incorporate information contained in all measured dofs. The accuracy of the methodology are verified by a numerical example and experimental studies which are conducted by employing a torsional shear building model installed with advanced wireless sensor node platforms.