A two-stage fast Bayesian spectral density approach for ambient modal analysis. Part II: Mode shape assembly and case studies

• A Bayesian mode shape assembly method is proposed to assemble the local mode shapes.
• The data qualities of different setups can be accounted for automatically.
• The optimal global mode shapes are obtained by a fast iterative scheme.
• The Hessian matrix is derived analytically to specify the covariance matrix.
• The algorithms are verified using synthetic data and field data successfully.

A two-stage fast Bayesian spectral density approach based on a novel variable separation technique for ambient modal analysis was formulated in the companion paper. In full-scale operational modal tests covering a number of locations, the dofs of interest are usually measured or processed separately in individual setups so that a set of local mode shapes are obtained. The difficulty on how to assemble these local mode shapes to form overall mode shapes is a problem not addressed in the companion paper that needs to be resolved properly. This study presents a theory to assemble the local mode shapes using the Bayesian statistical framework so that the data quality of different clusters can be accounted for automatically. The optimal global mode shape can be obtained by a fast iterative scheme, while the associated uncertainties can be derived analytically. The theory described in Part I and II of this work is applied to modal identification using synthetic data and field data measured from two laboratory models equipped with wireless sensors. Successful validation of the proposed method demonstrates the potential for Bayesian approaches to accommodate multiple uncertainties for ambient modal analysis.