  Modal parameters such as natural frequencies, modal shapes, and the damping
ratio are useful to understand structural dynamics of mechanical systems. Modal
parameters need to be estimated under operational conditions for use in
structural health monitoring. Therefore, operational modal analysis (OMA)
without input signals has been proposed to easily extract modal parameters
under operational conditions. Recently, OMA for under-determined systems with
more active modes than measurement outputs has been investigated to reduce the
number of sensors. This study proposes the OMA framework for under-determined
systems based on Bayesian CP (CANDECOMP/PARAFAC) decomposition of second-order
statistical data. The proposed method enables us to extract the modal
parameters from under-determined systems without tuning the number of active
modes, because the rank of the tensor data corresponding to the number of
active modes is automatically determined via Bayesian inference. The
effectiveness of this method is demonstrated using artificial vibration data of
a mass-spring system under operational and under-determined conditions.
