Fisher information-based optimal input locations for modal identification

A method is proposed to determine optimal locations of input forces for experimental modal analysis. The input locations are optimal in a sense that the measured vibration responses, under inputs thus located, contain maximum information about unknown modal parameters of interest. These optimal input locations are obtained by maximizing the trace of the associated Fisher Information Matrix (FIM). Analytical expressions are obtained for the different derivatives involved, by expressing acceleration responses in terms of pseudo-modal responses. A dimensionless scaling is introduced to normalize the effect of different types of modal parameters. An explicit relation is also derived between the FIM and the mode shape components at input locations. It is shown that, in certain experimental scenarios, this relation may be used to directly obtain the optimal input locations from only the mode shapes. An extensive series of numerical simulations, including situations of single/multiple inputs and single/multiple modes of interest, is used to illustrate the proposed approach. It is observed that the modal parameters, identified using any suitable modal identification technique, have the lowest estimation uncertainty when the inputs are optimally located. As an application in damage detection, it is shown that modal parameters estimated from experiments with non-optimally located inputs may lead to incorrect damage localization. The proposed method is also applied to data from experiments performed on a laboratory scale truss model. •FIM-based method proposed to find optimal input locations for identifying modes.•Relations between mode shape components and trace of FIM derived.•Method illustrated using numerical examples and laboratory experiments.•Optimally located inputs lead to minimum uncertainty in identified modal parameters.•Modes identified with non-optimally located inputs give incorrect damage locations.