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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.

When the FRF matrix describing the dynamical behavior of a structure is available, the operational loads can be determined by multiplying the pseudo-inverse of the FRF matrix by the operational responses (displacements, velocities or accelerations). In practice, however, the boundary conditions of the structure in operation deviate from the ones in laboratory conditions (due to e.g. aerodynamic loads, fuel consumption, temperature changes). This means that measurements during operation should be taken in order to obtain the correct FRF matrix. Unfortunately, it is not always possible to measure all operational loads acting on the structure (which is needed to calculate the FRFs). In this paper, a method is proposed that enables the on-line determination of operational forces. As input the method uses dynamical response measurements and the measurement of a known force (due to an exogenous excitation input) at one particular location (where it is possible to put an excitation device and a force sensor). A periodic signal is taken as the exogenous excitation. It is assumed that apart from the known force there is also an unknown force (at an unknown location) that is acting on the structure. As a first step in the procedure, the measured responses and the known (i.e. measured) force are compensated in order to eliminate the contribution due to the unknown force. From these compensated measurements the complete FRF matrix is calculated. Then, the forces are calculated from the original (uncompensated) responses and the inverted complete FRF matrix. The method is validated both on a simulation and measurements of a steel beam with an applied unknown impact excitation.