Operational modal analysis of under-determined system based on Bayesian CP decomposition.

Modal properties such as natural frequencies, modal shapes and damping ratio are useful to understand structural dynamics of mechanical systems. To use the modal properties for structural health monitoring, they need to be estimated under operational conditions. Therefore, operational modal analysis (OMA), extraction of the modal properties without input signals, has been proposed to easily extract the modal properties under operational conditions. Recently, OMA for underdetermined systems, i.e. number of measurements is less than that of active modes, has been paid attention to reduce the number of sensors. This paper proposes the OMA framework for the underdetermined systems based on Bayesian tensor decomposition of second-order statistics data. The proposed method enables us to extract the modal properties from underdetermined systems without tuning the number of active modes because rank of the tensor data corresponding to the number of the active modes is automatically determined via Bayesian inference. To show advantage of the method, the modal properties are extracted from artificial vibration data obtained from a mass-spring system under the operational and the underdetermined conditions.