14. Multi-setup Problem

This chapter discusses operational modal analysis using data from multiple setups, each covering a possibly different set of measured degrees of freedom. Motivated from practical applications, the focus is on obtaining a ‘global mode shape’ covering a potentially large number of degrees of freedom by incorporating the information from different setups that are measured with a small number of sensors. Least squares methods based only on the ‘local mode shapes’ in different setups are first discussed, which offer a mathematically simple yet reliable solution for modes with high signal-to-noise ratios. Bayesian algorithm is then developed to offer a more robust solution, incorporating all information in different setups and accounting for their data quality. The asymptotic behavior of the MPV for modes with high signal-to-noise ratio is analyzed, which can be mathematically connected with the least squares solution. Analytical formulas are derived for systematically computing the covariance matrix of parameters given the measured data. Field data examples are presented to illustrate the practical aspects of ambient vibration tests with multiple setups and their modal identification.