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

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