Measurement of moment of inertia based on Hilbert transform

A measurement model based on torsion pendulum was established, in which nonlinear damping and nonlinear restoring force were considered. The calculation method of the moment of inertia was based on Hilbert transform. The motion of torsion pendulum showed the time-frequency characteristics due to the nonlinear factors, which were validated by the experimental data. The analytical signal was formed by Hilbert transform of the angular displacement signal of the test object. The moment of inertia can be computed by the instantaneous undamped natural frequency with Hilbert transform. Prior to the implementation of Hilbert transform, the empirical mode decomposition was used to filter the experimental signal. The moment of inertia of the test object was measured by the torsion pendulum system. The experimental results show that the relative measurement error of the moment of inertia was within 0.7%, which indicated the validity of the measurement method.