In this paper, we present an approximation procedure for identifying lumped mass imbalances at multiple locations without accessing to the shaft 1/rev signal. As a first step, an experimental or analytical procedure is applied to optimize the sensor locations, such that a transmissibility matrix with minor off-diagonal terms can be established. Transfer functions between the mass imbalance correction planes and the vibration sensor locations are established by rotordynamics analytical modeling, finite element methods, or experimental testing through a specially designed unit with access to the 1/rev signal. Then, the synchronous responses of the system are obtained by peak-hold average spectrum or waterfall measurement and post-processing to get the synchronous vibration amplitudes as a function of the running speed. For multiple-plane imbalance detection without access to the rotor 1/rev signal, it is mathematically underdetermined to obtain both the amplitude and the phase of the imbalance. A unique estimation method is developed to extract the lumped mass imbalances from the recorded data. Numerical simulations results are reported in the end.

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