Abstract: Knowledge on rotor vibration at target positions is essential for evaluating or suppressing rotor vibration. However, limitations such as rotor structure or working environment may impede sensor installation at target positions. In order to reconstruct rotor vibrations at the target position using information collected from other positions, an augmented Kalman filter (AKF) is proposed for joint reconstruction on vibration and unbalanced excitations. Firstly, the influences of unbalance excitation on reconstruction results of classical Luenberger observer are investigated and the potential instability caused by excessive gain is elaborated. Then, a new augmented state variable is designed by expressing the unbalance excitation in the form of unbalance parameters and the discrete state equation of the augmented system is established accordingly. Finally, an AKF is designed to perform real-time estimation of the augmented system states, and the effectiveness of the joint reconstruction strategy is verified through simulation and experiments. The results show that the convergence speed of various observers is faster than dynamic changes of rotor systems, so they can be used for real-time reconstruction of rotor system vibration. Unbalance excitation will affect the reconstruction accuracy, and the accuracy of AKF considering the influence of unbalanced excitation is higher than that of traditional Luenberger observer. By using unbalance parameters instead of unbalanced excitation values as augmented variables, a Kalman filter based on the new augmented variable can achieve real-time reconstruction of rotor vibration over a large speed range.

Key words: augmented Kalman filter, vibration-excitation joint reconstruction, flexible rotor, unbalance, dry friction damper