An online reconstruction method of dynamic loading based on adaptive tracking dual nested Kalman filter

Accurately reconstructing the unknown dynamic loading is crucial for controlling the vibration of mechanical systems. Many methods have been proposed for load identification of time-invariant systems, but in some mechanical systems, their structural parameters exhibit time-varying dynamic characteristics during their operation. Therefore, tracking the time-varying structural parameters to update the transfer function is necessary, which is the most important prerequisite for load reconstruction. However, some existing methods are unstable because of the nonlinear conditions. To overcome this issue, an improved dual-nested Kalman filter framework has been proposed. This method allocates unknown variables to two Kalman filters, allowing them to iterate and loop with each other. As a result, it achieves linear reconstruction of the dynamic loading for a time-varying system. The proposed method has been validated in two numerical examples: one is a spring-mass system with abruptly changing mass parameters, and the other is a milling system with slowly changing mass parameters. The results show that the proposed method can reconstruct loading stably and is not susceptible to noise interference.