Combining multiple single-reference transmissibility functions in a unique matrix formulation for operational modal analysis

In recent years, the authors have proposed an innovative approach for Operational Modal Analysis based on transmissibility measurements. A method was proposed based on combining 2 single-reference transmissibility functions that were obtained during 2 different loading conditions. However in practice one in general has access to multiple transmissibility functions and perhaps even multiple loading conditions. In this paper a new method is introduced that combines all the measured single-reference transmissibility functions in a unique matrix formulation in order to identify system poles. It will be shown that each element of the pseudo-inverse of this matrix is a rational function with poles equal to the system poles. The proposed method reduces the risk to miss system poles and to identify extra non-physical poles. Therefore the method increases the usability and reliability of transmissibility based operational modal analysis (TOMA). The method will be demonstrated and validated by means of an experiment on a beam excited at multiple inputs for three different loading conditions.